The number of adults, high school students, and children not yet in high school attended this year are respectively; 70, 100, 120
How to solve a system of simultaneous equations?We are told that a total of 290 people attended the high school play.
If x represents number of adults, y represents number of high school students and z represents number of children, then we have;
x + y + z = 290 ---- (1)
The admission prices were $14 for adults, $7 for high school students, and $3 for children not yet in high school. The ticket sales totaled $2040 . Thus;
14x + 7y + 3z = 2040 ---- (2)
The principal suggested that next year they raise prices to $17 for adults, $8 for high school students, and $4 for children not yet in high school. Total cost of $2470. Thus;
17x + 8y + 4z = 2470 ---- (3)
Solving the three equations simultaneously gives;
x = 70, y = 100, z = 120
Read more about 3 simultaneous equations at; https://brainly.com/question/28048601
#SPJ1
Write -1.111... as a mixed number in simplest form.
Answer:
The answer is -10/9
Step-by-step explanation:
10*x=(-1.111...*10 .) second equation
10x=-11.111....
subtruct second equation from the first equation
10x=10*-11.111.
-
x=-1.1111.
9x=10
x=10/9
What is an equivalent expression for −12(8a − 7b) + 8(4x + 3y)?
−96a + 84b + 32x + 24y
−96a − 84b + 32x − 24y
−96a − 7b + 32x + 3y
−96a + 7b + 32x + 3y
The equivalent expression for −12(8a − 7b) + 8(4x + 3y) is represented as - 96a + 84b + 32x + 24y
How to solve equivalent expression?Two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value(s) for the variable(s).
Therefore, the equivalent expression of −12(8a − 7b) + 8(4x + 3y) can be solved as follows:
−12(8a − 7b) + 8(4x + 3y)
open the bracket
−12(8a − 7b) + 8(4x + 3y)
- 96a + 84b + 32x + 24y
Therefore, the equivalent expression of −12(8a − 7b) + 8(4x + 3y) is - 96a + 84b + 32x + 24y
learn more on equivalent expression here: https://brainly.com/question/10212750
#SPJ1
Sam and his cousin Matt have the same birthday, but Sam is 5 years older than Matt. Let the
variable x represent Sam’s age and y represent Matt’s age. Graph the relationship between
Sam’s age and Matt’s age.
A graph of the relationship between Sam’s age and Matt’s age has been plotted in the graph shown in the image attached below.
What is an equation?An equation can be defined as a mathematical expression which shows that two (2) or more thing are equal.
In order to solve this word problem, we would assign variables to Sam and Matt's age, and then translate the word problem into algebraic equation as follows:
Let the variable x represent Sam’s age.Let the variable y represent Matt’s age.Translating the word problem into an algebraic equation, we have;
x = 5 + y
Re-arranging the algebraic equation, we have;
y = x - 5
Read more on graphs here: brainly.com/question/4546414
#SPJ1
5/6 of number is 30. Find the number.
Answer:
36.
Step-by-step explanation:
I get this answer as I know 30 is divisible by six, so I start to investigate by how much It is divisible by.
30 / 6 = 5
Since I now know that, I can infer that 6x6 is 36.
And since 30 would give you 5/6, I imagine the answer is 36.
Convert 2 grams into milligrams.
*Note: you must use these exact conversion factors to get this question right.
1 pound (lb) = 16 ounces (oz)
1 kilogram (kg) = 1000 grams (g)
1 ton (ton) = 2000 pounds (lb)
1 ounce (oz) = 28.35 grams (g)
1 gram (g) = 1000 milligrams (mg)
1 pound (lb) = 0.454 kilograms (kg)
2 grams = 2000 milligrams
Conversion between different units of measurement of the same quantity is called as conversion of units.
The process of conversion depends on the specific situation and the precision and accuracy of measurement.
Conversions from one unit to another should be exact, without changing the precision of the first. This is sometimes called soft conversion. It does not involve changing of the physical configuration of the unit being calculated.
'g' is the same as grams and similarly 'mg' is the same as milligrams.
Thus, when asked to convert 2 g to mg, as in the given question,
first multiply the value in grams by the conversion factor '1000'.
So, 2 grams = 2 × 1000 = 2000 milligrams.
A gram is larger unit than a milligram.
To know more about conversion of units, refer
https://brainly.com/question/97386
#SPJ13
Two thirds of. The shirts in a tee shirt shop are blue three sevenths are on sale one half are size medium
The fraction of the blue T-shirts that are on sale and are size medium are 1/7.
What is fraction ?A fraction is used to represent the portion/part of the whole thing. It represents the equal parts of the whole. A fraction has two parts, namely numerator and denominator. The number on the top is called the numerator, and the number on the bottom is called the denominator.
Of all the shirts in the shop , 2/3 of the t-shirts are blue.
Of the blue shirts, 3/7 are on sale.
= 2/3 x 3/7
= 2/7
Out of all the shirts, 2/7 shirts are blue and are on sale.
Of the blue shirts on sale, 1/2 are size medium.
= 2/7 x 1/2
= 1/7
The fraction of the blue T-shirts that are on sale and are size medium are 1/7.
To know more about fractions, visit :-
brainly.com/question/10354322
#SPJ1
Work out the surface area of the solid
cuboid.
7m
6m
3m
The surface area of the solid cuboid 7m 6m and 3m. total surface area of cuboid is 162 [tex]m^{2}[/tex].
What is a cuboid?A cuboid is a six-sided solid known as a hexahedron in the geometry. Quadrilaterals make up its faces. Cuboid implies "like a cube," in the sense that a cuboid can be converted into a cube by varying the length of its edges or the angles between its faces. A cuboid is a convex polyhedron with the same polyhedral graph as a cube in mathematics.
A cube with six square faces, a rectangular prism, rectangular cuboid, or a rectangular box with six rectangle faces are special situations. In both circumstances, the faces of the cube and the rectangular prism come together at a right angle.
total surface area of cuboid
= 2(lb+bl+lh)
=2(7×6+6×3+3×7)
=2(81)
=162 [tex]m^{2}[/tex]
To know more about cuboid visit: https://brainly.com/question/19754639
#SPJ9
is 6 a significantly high number of girls in 8 births? why or why not? use 0.05 as the threshold for a significant event. a. yes, since the appropriate probability is greater than 0.05, it is a significantly high number. b. yes, since the appropriate probability is less than 0.05, it is a significantly high number. c. no, since the appropriate probability is greater than 0.05, it is not a significantly high number. d. no, since the appropriate probability is less than 0.05, it is not a significantly high number.
We can conclude that (A) "Yes since the appropriate probability is greater than 0.05, it is a significantly high numbe"r is the correct reason for the question.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a proposition is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty. The four most popular approaches to probability are classical, empirical, subjective, and axiomatic.So,
Number of Girls x
P(x)
(0)
0.003(1)
0.021(2)
0.118(3)
0.208(4)
0.300(5)
0.208(6)
0.118(7)
0.021(8)
0.003Results from groups of 8 births from 8 different parent sets are shown in the accompanying table.
The proportion of girls among the 8 children is represented by the random variable x. It is a significantly high number because the appropriate probability is higher than 0.05, so yes.Therefore, (A) "yes, since the appropriate probability is greater than 0.05, it is a significantly high number" is the correct reason for the question.
Know more about probability here:
https://brainly.com/question/24756209
#SPJ9
PLEASE HELP
Solve one sixth times quantity x plus 18 end quantity equals negative 5.
x = −48
x = −138
x = 12
x = 18
the answer is x= -48
solve for x by simplifying bith sides of the equation then isolating the variable so the answer is x= -48 your welcome!
Aubrey‘s car used 2 gallons to travel 90 miles how far can she travel on 11 gallons
Answer: 495
Step-by-step explanation:
A veichle uses 150 litres of petrol in 45 minutes. How many litres of petrol will it use in 1 hour 15 minutes?
The amount of petrol consumed in one hour will be 200 liters.
A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.
In 45 minutes, an automobile uses 150 gallons of gasoline.
Consequently, the rate of gasoline consumption in liters per minute will be
= 150 / 45
= 10 / 3 Liters per minute
We are aware that an hour is made up of 60 minutes.
The amount of gasoline that will be used in an hour will then be
= (10 / 3) x 60
= 10 x 20
= 200 liters
Thus, 200 liters of gasoline will be burned in an hour.
To learn more about proportion
https://brainly.com/question/2548537
Answer:
there the vehicle uses 250 litres
Step-by-step explanation:
[tex]150 = 45[/tex]
[tex]x = 75[/tex]
[tex]x = 75 \div 45 \times 150[/tex]
[tex]x = 250litres[/tex]
Ms. May invested $8000 at 7%. How much additional money must she invest at 4% in order that her
total annual income (from interest) may equal 5% of her entire investment?
The additional money Ms. May must invest at rate of 4% to get the 5% interest on entire income is $16,000.
What is meant as the rate of interest?The rate of interest is the amount charged by the lender to the borrower in addition to the principal amount. In aspects of the receiver, an individual who deposits money in any bank or financial institution earns extra money due to the time value of money, which is referred to as interest received by depositor.For the given question,
The money invested by Ms. May at 7% rate of interest is $8,000.
Let 'x' be the money invested at the rate of 4%.
The interest for the total annual income is 5%.
Thus,
7%of 8,000 + 4% of x = 5%(8,000 + x)
8,000×0.07 + 0.04×x = 0.05(8,000 + x)
On solving,
560 + 0.04x = 400 + 0.05x
0.01x = 160
x = 16,000
Thus, the additional money Ms. May must invest at rate of 4% to get the 5% interest on entire income is $16,000.
To know more about the rate of interest, here
https://brainly.com/question/13566135
#SPJ13
A fair die is rolled seven times. What is the probability that it comes up 2 at least once? Write your answer as a fraction or a decimal, rounded to four decimal
places.
The probability of getting 2 at least once is 1/6.
What is probability?Simply put, the probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of events that follow a probability distribution. The probability is calculated by dividing the total number of possible outcomes by the number of possible ways the event could occur.So, the probability of getting a 2 at least once:
The sample space will be (refer to the image attached below).Formula of probability: P = favourable events/total events
At least once, we need to get 2 and a maximum of 7.So, favorable events = 7, and the total number of events will be 6×7 = 42.Now, substitute the values in the formula as follows:
P = 7/42P = 1/6Therefore, the probability of getting 2 at least once is 1/6.
Know more about probability here:
https://brainly.com/question/25870256
#SPJ13
Suppose that diastolic blood pressure readings of adult males have a bell-shaped distribution with a mean of 80 mmhg and a standard deviation of 11 mmhg. using the empirical rule, what percentage of adult males have diastolic blood pressure readings that are greater than 102 mmhg
Answer:
95% of adult males have diastolic blood pressure readings that are at least 102 mmHg
Step-by-step explanation:
The empirical rule states that for a normal distribution, nearly all of the data will fall within three standard deviations of the mean . The empirical rule is further illustrated below
68% of data falls within the first standard deviation from the mean.
95% fall within two standard deviations.
99.7% fall within three standard deviations.
From the information given, the mean is 80 mmHg and the standard deviation is 11 mmHg.
2 standard deviations = 2 × 11= 22
80+ 22= 102 mmHg
Therefore, 95% of adult males have diastolic blood pressure readings that are at least 102 mmHg.
LINK-https://brainly.com/question/15701869
#SPJ4
Find the equation of the line with the given slope and the y-intercept.
slope = 1/5; y-intercept = -5
The equation of the line with the given slope and the y-intercept.
slope = 1/5; y-intercept = -5 is y = 1 / 5 x - 5
How to find the equation of a line?The equation of a line can be described as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore,
slope of the line = 1 / 5
y-intercept = - 5
Hence, the equation of the line can be represented as follows:
y = 1 / 5 x - 5
learn more on equation of a line here: https://brainly.com/question/14978593
#SPJ1
At what rates percent compound interest will Rs2000 amount to Rs 2420 in 2 years.
The interest rates required to get a total amount of $2,420 from compound interest on a principal of $2,000 compounded 1 times per year over 2 years is 10% per year.
What is compound interest?The interest on savings that is calculated on both the initial principal and the interest accrued over time is known as compound interest.
The concept of compound interest, also known as "interest on interest," is thought to have first appeared in Italy in the 17th century. It will accelerate the growth of a sum more quickly than simple interest, which is calculated only on the principal sum.
Money is multiplied more quickly through compounding, and the more times it is compounded, the higher the compound interest will be.
Using the formula A = P(1 + r/n)^nt
Solving for rate r as a decimal
r = n[(A/P)^(1/nt) - 1]
r = 1 × [(2,420/2,000)^{1/(1)(2)} - 1]
r = 0.1
Then convert r to R as a percentage
R = r × 100
R = 0.1 × 100
R = 10%/year
Learn more about compound interest
https://brainly.com/question/12325365
#SPJ9
EASY POINTS WILL GIVE BRAINLIST TO BEST ANSWER
Determine if the sequence is arithmetic. If it is, find the common difference, the 21st term, the explicit rule, the recursive rule, and the three terms in the sequence after the last one given.
-29, -22, -15, 8,…
Answer:
This is not an arithmetic sequence because -15 + 7 = -8, not 8.
During an experiment, the temperature of a liquid, in degrees Celsius, is given by the function t(m) = 0.2m + 6, where m is the number of minutes since the experiment began. Which graph correctly shows this function?
The graph that correctly represent the experiment that was graphed with the function t(m) = 0.2m + 6 is the first option with points
first point (-30, 0) second point (0, 6)How to match graph to the functiongiven data
t(m) = 0.2m + 6
information deduced from the graph
intercept = 6slope = 0.2examining the graph shows that first graph have the intercept as 6
using the points to calculate slope we have
= (y2 - y1) / (x2 - x1 )
= (6 - 0) / (0 - -30)
= 6 / (0 + 30)
= 6 / 30
= 0.2
Since the points are same with the given information we can conclude that the first option has the graph of the given function
Read more on slope and intercept here: https://brainly.com/question/1884491
#SPJ1
Rosa has $254. She pays $7 for breakfast each day and $13 for lunch each day. If Rosa
does not spend money on anything else or receive any additional money, how many
days can she continue to buy breakfast and lunch?
The number of days that Rosa can continue to buy breakfast and lunch with the money is; 12 days
How to solve algebra Word problems?We are given the following parameters;
Amount held by Rosa = $254
Amount per breakfast = $7
Amount per Lunch = $13
Thus;
Amount spent each day = $7 + $13
Amount spent each day = $20
Now, to find out how many days this money can last her if she doesn't get any more income is;
Number of days = 254/20 = 12 days with $14 left
Read more about Algebra Word Problems at; https://brainly.com/question/13818690
#SPJ1
The following two triangles are similar. Find the missing side length represented by x.
A. 7
B. 5
C. 6
D. 8
The missing side length that is represented by x in the triangles that are similar is: B. 5.
How to Find the Dimensions of Similar Triangles?According to the similarity theorem, the corresponding side lengths of two triangles that are similar have the same ratio and are therefore proportional to each other.
The two triangles are considered similar to each other, this means that their corresponding side lengths would be proportional to each other and would have the following equal ratio:
45/9 = 25/x
Cross multiply
(45)(x) = (9)(25)
45x = 225
Divide both sides by 45
45x/45 = 225/45
x = 5
Learn more about similar triangles on:
https://brainly.com/question/27996834
#SPJ1
NEED NOW OFFERING 100 POINTS!!
Which of the following expressions is equal 5^8/ 5^2 to?
5 · 5 · 5
5 · 5 · 5 · 5
3
The expression 5^8/ 5^2 is equal to 5×5×5×5×5×5. Option C
What is an algebraic expression?An algebraic expression can be defined as a are mathematical expression with a minimum of two terms containing variables, factors, constants and coefficients.
What is an exponential function?An exponential function is simply defined as a function in which its value is a constant that is raised to the power of a variable or number.
It is a relation or expression that takes the form y = aˣ in mathematics, where x is a independent variable.
Given the expression as;
⇒ 5^8 / 5²
⇒ 5^8-2
⇒ 5^6
⇒ 5×5×5×5×5×5
Hence, the value is 5×5×5×5×5×5
Learn more about algebraic expressions here:
https://brainly.com/question/4344214
#SPJ1
The complete question;
Which of the following expressions is equal 5^8/ 5^2 to?
A.5×5×5
B. 1/5×5×5×5
C. 5×5×5×5×5×5
D.3
Players in a racing game earn 3 points for each coin they collect. Each player loses 5 points for each second that he or she finishes after the first-place finisher. The table shows the results of a race.
List the players in order from greatest to least number of points.
If each player loses 5 points for each second that he or she finishes after the first-place finisher. the players in order from greatest to least number of points is: player 4, player 2, player 1, player 4.
Greatest to the least numberPayer 1 :
Player 1 = 3(31) - 5(8)
Player 1 = 93 - 40
Player 1 = 53 points
Player 2 :
Player 2 = 3 (18)
Player 2 = 54 points
Player 3:
Player 3 = 3(24) - 5(3)
Player 3 = 72 - 15
Player 3 = 57 points
Player 4:
Player 4 = 3(27) - 5(6)
Player 4 = 81 -30
Player 4 = 51 points
Now list the players in order from greatest to least number of points.
Player 3 = 57 points
Player 2 = 54 points
Player 1 = 53 points
Player 4 = 51 points
Therefore the player based on ranking is: player 4, player 2, player 1, player 4.
Learn more about Greatest to the least number here: https://brainly.com/question/28394192
#SPJ1
The cost (in dollars) for manufacturing a particular flashdrive is , where x is the number of flashdrives produced. Recall from the previous chapter that the average cost per flashdrive, denoted by , is found by dividing c(x) by x. Find and interpret
The most appropriate choice for cost function and average cost function will be given by -
[tex]\lim_{x \to \infty} \bar{C}(X) = 6[/tex]
The number of flashdrive is very large, the average cost will come down to as low as $6.
What is cost function and average cost function?
Cost function C(x) is a function of x (quantity) which gives the cost of producing x units of the commodity.
Average cost function is the per unit cost of production and can be obtained by dividing the cost function by the quantity of the commodity.
Here,
C(x) = 17000 + 6x
[tex]\bar{C}(x) = \frac{17000 + 6x}{x}\\[/tex]
[tex]= \frac{17000}{x}+ \frac{6x}{x}\\[/tex]
= [tex]\frac{17000}{x}+6[/tex]
[tex]\lim_{x \to \infty} \bar{C}(x)[/tex] = [tex]\lim_{x \to \infty} (\frac{17000}{x} + 6)[/tex]
= 0 + 6
= 6
This means as the number of flashdrive is very large, the average cost will come down to as low as $6
To learn more about Total cost and Average cost, refer to the link:
https://brainly.com/question/25109150
Complete Question
The cost (in dollars) for manufacturing a particular flashdrive is 17000 + 6x , where x is the number of flashdrives produced. Recall from the previous chapter that the average cost per flashdrive, denoted by , is found by dividing c(x) by x. Find and interpret [tex]\lim_{x \to \infty} \bar{C}(X)[/tex]
#SPJ9
In a certain country 23% of the population has a college degree and 7% of those people have an advanced degree (masters of above). If the country has 3,000,000 people than how many people have advanced degree?
Answer: 48300
Step-by-step explanation:
23 % of 3.000.000 is [tex]\frac{3.000.000*23}{100} = 690.000[/tex]
So, 690.000 have college degree.
7 % of 690.000 is [tex]\frac{690.000* 7}{100} = 48.300[/tex]
So, 48.300 people have advanced degree.
hi can someone help me here
Answer:
see explanation
Step-by-step explanation:
[tex]\frac{x+2}{3}[/tex] - [tex]\frac{2x-4}{2}[/tex] = 0
multiply through by 6 ( the LCM of 3 and 2 ) to clear the fractions
2(x + 2) - 3(2x - 4) = 0 ← distribute parenthesis on left side and simplify
2x + 4 - 6x + 12 = 0
- 4x + 16 = 0 ( subtract 16 from both sides )
- 4x = - 16 ( divide both sides by - 4 )
x = 4
------------------------------------------------------------
[tex]\frac{5x}{2}[/tex] + [tex]\frac{x-2}{8}[/tex] = 2 ( multiply through by 8 to clear the fractions )
4(5x) + x - 2 = 16
20x + x - 2 = 16
21x - 2 = 16 ( add 2 to both sides )
21x = 18 ( divide both sides by 21 )
x = [tex]\frac{18}{21}[/tex] = [tex]\frac{6}{7}[/tex]
-----------------------------------------------------------
[tex]\frac{x-5}{4}[/tex] - [tex]\frac{3x-1}{5}[/tex] = - [tex]\frac{3}{2}[/tex]
multiply through by 20 ( the LCM of 4, 5, 2 ) to clear the fractions
5(x - 5) - 4(3x - 1) = - 30 ← distribute parenthesis on left side and simplify
5x - 25 - 12x + 4 = - 30
- 7x - 21 = - 30 ( add 21 to both sides )
- 7x = - 9 ( divide both sides by - 7 )
x = [tex]\frac{9}{7}[/tex]
-------------------------------------------------------------
[tex]\frac{1}{x-1}[/tex] + [tex]\frac{1}{x+1}[/tex] = [tex]\frac{4x+2}{x^2-1}[/tex] ← x² - 1 is a difference of squares , then
[tex]\frac{1}{x-1}[/tex] + [tex]\frac{1}{x+1}[/tex] = [tex]\frac{4x+2}{(x-1)(x+1)}[/tex]
multiply through by (x - 1)(x + 1) to clear the fractions
x + 1 + x - 1 = 4x + 2
2x = 4x + 2 ( subtract 4x from both sides )
- 2x = 2 ( divide both sides by - 2 )
x = - 1
If we substitute this value back into the original equation, we find
[tex]\frac{1}{-1-1}[/tex] + [tex]\frac{1}{-1+1}[/tex] = [tex]\frac{4(-1)+2}{(-1)^2-1}[/tex]
[tex]\frac{1}{-2}[/tex] + [tex]\frac{1}{0}[/tex] = [tex]\frac{-2}{1-1}[/tex]
[tex]\frac{1}{-2}[/tex] + [tex]\frac{1}{0}[/tex] = [tex]\frac{-2}{0}[/tex]
division by zero is undefined
thus x = - 1 is an extraneous solution
the equation has no solution
Answer:
[tex]\textsf{1.} \quad x=4[/tex]
[tex]\textsf{2.} \quad x=\dfrac{6}{7}[/tex]
[tex]\textsf{3.} \quad x=\dfrac{9}{7}[/tex]
[tex]\textsf{4.} \quad \textsf{No solution}[/tex]
Step-by-step explanation:
Question 1Given equation:
[tex]\dfrac{x+2}{3}-\dfrac{2x-4}{2}=0[/tex]
[tex]\textsf{Add \; $\dfrac{2x-4}{2}$ \; to both sides of the equation}:[/tex]
[tex]\implies \dfrac{x+2}{3}-\dfrac{2x-4}{2}+\dfrac{2x-4}{2}=0+\dfrac{2x-4}{2}[/tex]
[tex]\implies \dfrac{x+2}{3}=\dfrac{2x-4}{2}[/tex]
Cross multiply:
[tex]\implies 2(x+2)=3(2x-4)[/tex]
[tex]\implies 2x+4=6x-12[/tex]
Subtract 2x from both sides:
[tex]\implies 2x+4-2x=6x-12-2x[/tex]
[tex]\implies 4=4x-12[/tex]
Add 12 to both sides:
[tex]\implies 4+12=4x-12+12[/tex]
[tex]\implies 16=4x[/tex]
[tex]\implies 4x=16[/tex]
Divide both sides by 4:
[tex]\implies \dfrac{4x}{4}=\dfrac{16}{4}[/tex]
[tex]\implies x=4[/tex]
--------------------------------------------------------------------------
Question 2Given equation:
[tex]\dfrac{5x}{2}+\dfrac{x-2}{8}=2[/tex]
Multiply the numerator and denominator of the first fraction by 4:
[tex]\implies \dfrac{5x \cdot 4}{2\cdot 4}+\dfrac{x-2}{8}=2[/tex]
[tex]\implies \dfrac{20x}{8}+\dfrac{x-2}{8}=2[/tex]
[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{c}+\dfrac{b}{c}=\dfrac{a+b}{c}:[/tex]
[tex]\implies \dfrac{20x+x-2}{8}=2[/tex]
[tex]\implies \dfrac{21x-2}{8}=2[/tex]
Multiply both sides by 8:
[tex]\implies \dfrac{(21x-2) \cdot 8}{8}=2 \cdot 8[/tex]
[tex]\implies 21x-2=16[/tex]
Add 2 to both sides:
[tex]\implies 21x-2+2=16+2[/tex]
[tex]\implies 21x=18[/tex]
Divide both sides by 21:
[tex]\implies \dfrac{21x}{21}=\dfrac{18}{21}[/tex]
[tex]\implies x=\dfrac{18}{21}[/tex]
Reduce the fraction by dividing the numerator and denominator by 3:
[tex]\implies x=\dfrac{18 \div 3}{21 \div 3}[/tex]
[tex]\implies x=\dfrac{6}{7}[/tex]
--------------------------------------------------------------------------
Question 3Given equation:
[tex]\dfrac{x-5}{4}-\dfrac{3x-1}{5}=-\dfrac{3}{2}[/tex]
Multiply the numerator and denominator of the first fraction by 5, and the numerator and denominator of the second fraction by 4:
[tex]\implies \dfrac{(x-5) \cdot 5}{4\cdot 5}-\dfrac{(3x-1)\cdot 4}{5\cdot 4}=-\dfrac{3}{2}[/tex]
[tex]\implies \dfrac{5x-25}{20}-\dfrac{12x-4}{20}=-\dfrac{3}{2}[/tex]
[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{c}-\dfrac{b}{c}=\dfrac{a-b}{c}:[/tex]
[tex]\implies \dfrac{5x-25-(12x-4)}{20}=-\dfrac{3}{2}[/tex]
[tex]\implies \dfrac{5x-25-12x+4}{20}=-\dfrac{3}{2}[/tex]
[tex]\implies \dfrac{-7x-21}{20}=-\dfrac{3}{2}[/tex]
Cross multiply:
[tex]\implies 2(-7x-21)=-3(20)[/tex]
[tex]\implies -14x-42=-60[/tex]
Add 42 to both sides:
[tex]\implies -14x-42+42=-60+42[/tex]
[tex]\implies -14x=-18[/tex]
Divide both sides by -14:
[tex]\implies \dfrac{-14x}{-14}=\dfrac{-18}{-14}[/tex]
[tex]\implies x=\dfrac{18}{14}[/tex]
Reduce the fraction by dividing the numerator and denominator by 2:
[tex]\implies x=\dfrac{18 \div 2}{14 \div 2}[/tex]
[tex]\implies x=\dfrac{9}{7}[/tex]
--------------------------------------------------------------------------
Question 4Given equation:
[tex]\dfrac{1}{x-1}+\dfrac{1}{x+1}=\dfrac{4x+2}{x^2-1}[/tex]
Factor the denominator of the fraction on the right side of the equation:
[tex]\implies \dfrac{1}{x-1}+\dfrac{1}{x+1}=\dfrac{4x+2}{(x+1)(x-1)}[/tex]
Multiply the numerator and denominator of the first fraction by (x+1), and the numerator and denominator of the second fraction by (x-1):
[tex]\implies \dfrac{x+1}{(x+1)(x-1)}+\dfrac{x-1}{(x+1)(x-1)}=\dfrac{4x+2}{(x+1)(x-1)}[/tex]
[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{c}+\dfrac{b}{c}=\dfrac{a+b}{c}:[/tex]
[tex]\implies \dfrac{x+1+x-1}{(x+1)(x-1)}=\dfrac{4x+2}{(x+1)(x-1)}[/tex]
[tex]\implies \dfrac{2x}{(x+1)(x-1)}=\dfrac{4x+2}{(x+1)(x-1)}[/tex]
Multiply both sides by (x+1)(x-1):
[tex]\implies \dfrac{2x(x+1)(x-1)}{(x+1)(x-1)}=\dfrac{(4x+2)((x+1)(x-1)}{(x+1)(x-1)}[/tex]
[tex]\implies 2x=4x+2[/tex]
Subtract 4x from both sides:
[tex]\implies 2x-4x=4x+2-4x[/tex]
[tex]\implies -2x=2[/tex]
Divide both sides by -2:
[tex]\implies \dfrac{-2x}{-2}=\dfrac{2}{-2}[/tex]
[tex]\implies x=-1[/tex]
However, if we substitute x = -1 into the original equation we get:
[tex]\implies \dfrac{1}{(-1)-1}+\dfrac{1}{(-1)+1}=\dfrac{4(-1)+2}{(-1)^2-1}[/tex]
[tex]\implies -\dfrac{1}{2}+\dfrac{1}{0}=\dfrac{-2}{0}[/tex]
A number divided by zero is undefined. Therefore, there is no solution for this equation.
I NEED HELP
You recently opened your checking account with ReallyAwesomeBank on August 1 using $200.00.
Complete the checkbook register using the following transactions. Then answer the questions/show your work in the space below the register.
August 1 – Opened the checking account with $200.00
August 2 – Purchased Groceries from Shaw’s for $57.91 plus 3.5% tax. (Check 101)
August 2 – Paid $12 for parking using your debit card.
August 4 – Deposited paycheck from work. (15.50/hr for 30 hours)
August 6 – Paid National Grid $47.50. (Check 102)
August 6 – Bought 3 pairs of pants at $25.98 each with a 15% coupon and 6.5% sales tax from Kohls. (Check 103)
August 7 – Bought a bike for $165.00, helmet for $35.12, and gloves for $10.99 from Bikes-R-Us. Used a 15% off coupon and there was 5% sales tax. (Check 104)
August 11 – Deposited paycheck from work, but took out $100.00 cash (15.50/hr for 25 hours)
August 11 – Opened a savings account with $250 transferred from the checking account.
August 12 – Ate lunch at Red Robin for $24.61 plus 5.5% sales tax. Used your debit card to pay for it.
Number
Date
Transaction Description
Payment Fee, Withdrawal (-)
Deposit, Credit (+)
Balance
Use the space below to explain how you completed the first FOUR transactions.
Use the space below to show your work for how you found the total you spent at Kohl’s on August 6.
Use the space below to show your work for how you found the total you spent at Bikes-R-Us on August 7.
What was your final balance on August 12?
Completing the checkbook register using the transactions done on the checking account at Really Awesome Bank shows that the ending balance was $298.12.
What is a checkbook register?A checkbook register records transactions with a bank for a checking account.
The transactions of a checking account include withdrawals or payments, deposits, and bank charges if any.
Checkbook Register:Check Date Description Payments Deposit, Balance
No. Withdrawal (-) Credit (+)
August 1 Initial deposit $200.00 $200.00
101 August 2 Groceries (Shaw’s) $59.94 140.06
August 2 Parking fee $12 128.06
August 4 Paycheck 465.00 593.06
102 August 6 Electricity $47.50 545.56
103 August 6 Pants $70.56 475.00
104 August 7 Bike, Helmet, Gloves $188.42 286.58
August 11 Paycheck $287.50 574.08
August 11 Savings account $250.00 324.08
August 12 Luch (Red Robin) $25.96 298.12
Transaction Analysis:August 2 – $59.94 ($57.91 x 1.035%)
August 4 – $465 ($15.50 x 30) (15.50/hr for 30 hours)
August 6 – $70.56 (3 x $25.98 x 85% x 1.065)
August 7 – $188.42 ($165 + $35.12 + $10.99 x 85% x 1.05)
August 11 – $287.50 (15.50 x 25 - $100)
August 12 – $25.96 (24.61 x 1.055)
Learn more about a checkbook register at https://brainly.com/question/2886940 and https://brainly.com/question/16850061
#SPJ1
John put 14,000 Euros in an account at a simple interest rate of 1% per year. How much interest will he get after 12 year?
The amount of interest John will get after 12 years given his savings and interest rate is 1,680 Euros
How to find simple interest?Simple interest is a type of interest rate paid only on principal. It is called by multiplying principal by interest rate by time.
Principal, P = 14,000 EurosRate, r = 1% = 0.01Time, t = 12 yearsSimple interest = principal × rate × time
= 14,000 × 0.01 × 12
= 1,680 Euros
In conclusion, given John's savings and interest rate, he'll earn 1,680 Euros as interest after 12 years.
Read more on simple interest:
https://brainly.com/question/20690803
#SPJ1
The cube of the sum of a number and 3
The expression for the cube of the sum of a number and 3 is (x+3)³
What are algebraic expressions?Algebraic expressions are simply defined as arithmetic expressions made up of variables, terms, coefficients, factors and constants
They may also be known to consist of certain mathematical operations, such as;
ParenthesesAdditionSubtractionDivisionBracketMultiplication, etcBased on the information given, we have;
cube of the sum of a number and 3
Let the number be x
We have the expression to be;
x + 3
Find the cube
(x+3)³
Hence, the expression is (x+3)³
Learn more about algebraic expressions here:
https://brainly.com/question/4344214
#SPJ1
The complete question is;
Write the expression for The cube of the sum of a number and 3
What are the domain and range of f(x) = 4x – 8?
domain: {x | x is a real number}; range: {y | y > –8}
domain: {x | x is a real number}; range: {y | y > 8}
domain: {x | x > 4}; range: {y | y > –8}
domain: {x | x > –4}; range: {y | y > 8}
The domain and range of this linear function f(x) = 4x – 8 is: A. domain: {x | x is a real number}; range: {y | y > –8}.
What is a linear function?A linear function can be defined as a type of function whose equation is graphically represented by a straight line on the cartesian coordinate. This ultimately implies that, a linear function is typically used for uniquely mapping an input variable to an output variable.
What is a domain?A domain can be defined as the set of all real numbers for which a particular function is defined. This ultimately implies that, a domain refers to the set of all possible input numerical values (numbers) to a function and the domain of a graph comprises all the input numerical values which are shown on the x-axis.
In conclusion, the domain of this linear function consist of all real numbers while the range comprises the set of all real numbers on the y-axis that are greater than negative eight (-8).
Read more on domain here: https://brainly.com/question/8838568
#SPJ1
Answer:
its a
Step-by-step explanation:
Hudson owns a food truck that sells tacos and burritos. He only has enough supplies
to make 100 tacos or burritos. He sells each taco for $3 and each burrito for $7.
Hudson must sell at least $420 worth of tacos and burritos each day. If a represents
the number of tacos sold and y represents the number of burritos sold, write and
solve a system of inequalities graphically and determine one possible solution.
One possibility for resolving the inequality is (20, 60) in which x represents the number of tacos sold, and y the number of burritos sold
How are inequalities graphed?When graphing inequalities, the dependent variable, or y, is placed on the left side of the equation, while the other variables are placed on the right side.
The parameters are as follows:
Hudson has enough ingredients to make 90 tacos.
Each taco costs $3 to purchase.
Each burrito costs $7 to purchase.
Hudson must sell $420 worth of tacos and burritos per day.
x = number of tacos sold
y = the number of burritos sold
We need to graphically represent and solve the system of inequalities, and to identify one possible solution
The inequalities in the system are as follows:
x + y ≤ 90
3·x + 7·y ≥ 420
We have the following graphs to plot the above inequalities:
y ≤ 90 - x
y ≥ 420/7 - 3·x/7
y ≥ 60 - 3·x/7
The vertices of the feasible region's triangle are as follows from the inequality graph:
(0, 90), (0, 60), and the third vertex is found as follows for accuracy;
90 - x = 60 - 3·x/7
x = 52.5
y = 90 - x
∴ y = 37.5 at the vertex
The third vertex is (52.5, 37.5)
Therefore, the feasible region's vertices are (0, 90), (0, 60), and (52.5, 37.5), and one possible solution within the feasible region is (20, 60)
Learn more about graphing inequalities here.
https://brainly.com/question/11234618
#SPJ9