Answer: 31y2 + 6
Step-by-step explanation:
61 y2 + 1 y2 = 62 y2
7y + -7y = 0
6+6 =12
62y2 + 12 then divide by 2 and it's 31y2 + 6
In an election, 112 votes were cast and the
winning candidate beat her opponent by a
4:3 ratio. How many more votes did the
winning candidate receive?
8
16
23
28
35
Answer:
16
Step-by-step explanation:
112/7=16, 16x4=64, 16x3=48, 64-48=16
Which of the following is equivalent to 2.76? 2.76%, 27.6%, two and nineteen twenty fifths, or twenty five over nineteen?
The equivalent value to 2.76 is C. two and nineteen twenty-fifths.
What is an equivalent value?An equivalent value is an amount or numerical expression possessing the same value as the other.
Equivalent values are expressed as equations, using the equation symbol (=).
Equations are a class of the properties of mathematical expressions, including numbers and variables.
Two and nineteen twenty-fifths = 2¹⁹/₂₅.
When expressed as a decimal, 2¹⁹/₂₅ = 2.76.
Thus, 2.76%, 27.6%, or twenty-five over nineteen are not equivalent values of 2.76 but 2¹⁹/₂₅.
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А с 5 Find the missing side C 4 9 3 6.4 41
Use the pythagorean theorem to find side C
[tex]\begin{gathered} C=\sqrt[]{5^2+4^2} \\ C=\sqrt[]{25+16} \\ C=\sqrt[]{41} \\ C=6.4 \end{gathered}[/tex]The right answer is 6.4
A Short answer Question
Using multiplication of matrices, it is found that the values of a and b are given as follows:
a = 4.b = 6.How does multiplication of matrices work?To multiply matrices, we multiply the rows of the first matrix by the columns of the second matrix.
Hence, the element of the row 1 and column 1 of the product matrix is given by the multiplication of the row 1 of the first matrix by the column 1 of the second matrix, then:
3(-1) -2(2) + a(3) = 5
-3 - 4 + 3a = 5
3a = 12
a = 4.
The element of the row 2 and column 2 of the product matrix is given by the multiplication of the row 2 of the first matrix by the column 2 of the second matrix, then:
4(3) - 1(b) + 2(-2) = 2
12 - b - 4 = 2
8 - b = 2
b = 8 - 2
b = 6.
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The line y=kx+4 goes through the point (2, -2)
K = -3
Sketch the graph of the line (need answer ASAP!!)
The graph of the linear equation:
y = -3x + 4
Can be seen in the image at the end.
How to sketch the graph of the line?
To draw a line, we just need to find two points that belong to the line, graph them, and then connect them with a line.
Here we know that we have the line:
y = k*x + 4
Where k = -3, then:
y = -3*x + 4
By evaluating this in a value of x, for example, x = 0, we will get:
y = -3*0 + 4 = 4
Then we also have the point (0, 4) (and the given one, (2, -2))
So we can draw these two points and then connect them with a line (just use a ruler and draw a line that passes through both points).
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I can’t find the answer for this question
Answer:
[tex]x = \frac{20}{91}[/tex]
Step-by-step explanation:
Since this is a proportion, first you need to cross multiply.
[tex]\frac{20}{7}[/tex] × [tex]\frac{2}{25}[/tex] = [tex]\frac{40}{175}[/tex]
[tex]\frac{26}{25} x = \frac{40}{175}[/tex]
Now multiply both sides by the reciprocal of 26/25 which is 25/26.
[tex]\frac{25}{26} (\frac{26}{25} )x=\frac{40}{175} (\frac{25}{26} )\\[/tex]
Cancel on the right side, 25 and 175, by 25. Then cancel 40 and 26 by 2.
[tex]x = \frac{20}{7} (\frac{1}{13} )[/tex]
[tex]x = \frac{20}{91}[/tex]
the width of a rectangular field is 3 meters less than its length. Find the length and width is the perimeter is 58meters
Let the Length of the rectangle be l and the width of the rectangle be w
The width of a rectangular field is 3 meters less than its length, this can be represented as
w = l - 3
Given the perimeter = 58meters
Perimeter of the rectangle = 2(l + w)
58 = 2(l + l-3)
58 = 2(2l - 3)
58 = 4l - 6
58 + 6 = 4l
64 = 4l
4l = 64
l = 64/4
l = 16
w = l - 3
w = 16 - 3
w = 13
Hence, the length of the rectangle is 16 meters while the width is 13 meters.
5y – 3 = 6y + 3
solve y
Answer: y = −6
Step-by-step explanation:
Answer:
5y−3=6y+3
Step 1: Subtract 6y from both sides.
5y−3−6y=6y+3−6y
−y−3=3
Step 2: Add 3 to both sides.
−y−3+3=3+3
−y=6
Step 3: Divide both sides by -1.
−y
−1
=
6
−1
y=−6
Step-by-step explanation:
brainliest please?
-1.4 repeating as a fraction in simplest form
1.4 repeating as a simple fraction is 13/9
Simple fraction is a fraction with whole number as the numerator and denominator. The top term is called numerator and the bottom term is called denominator.
Decimal number is a number that consist of one whole number and a fractional part and those are separated by a decimal point
The repeating decimal = 1.4444
Consider the value x = 1.4444
Then multiply 10 on both side of the equation
We get
10x = 14.444
Subtract x from the 10x
10x-x = 14.444-1.4444
Subtract the like terms in the equation
9x = 13
Move 9 to the right hand side
x = 13/9
Hence, 1.4 repeating as a simple fraction is 13/9
The complete question is
1.4 repeating as a fraction in simplest form
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F (x) = x+1
——
x+8
F-1(-7) =
The value of [tex]f^{-1}(-7)[/tex] is given by -57/8.
Given that:-
f(x) = (x + 1)/(x + 8)
We have to find the value of [tex]f^{-1}(-7)[/tex].
Let f(x) = y
Hence,
[tex]f^{-1}(y) = x[/tex]
Now, we will find the inverse of the given function.
Hence, we can write,
y = (x + 1)/(x + 8)
We can rewrite it as:-
y = (x + 8 - 7)/(x + 8) = (x + 8)/(x + 8) - 7/(x + 8) = 1 - 7/(x + 8).
1 - y = 7/(x + 8)
x + 8 = 7/(1 - y)
x = 7/(1 - y) - 8
x = 7/(1 - y) - 8(1 - y)/(1 - y)
x = (7 - 8(1 - y))/(1 - y)
x = (7 - 8 + 8y)/(1 - y)
[tex]f^{-1}(y) = \frac{(8y - 1)}{( 1 - y)}[/tex]
Replacing y with x in the above equation, we can write,
[tex]f^{-1}(x) = \frac{(8x - 1)}{( 1 - x)}[/tex]
The above equation is the inverse of the function.
Putting x = -7 in the above equation, we get,
[tex]f^{-1}(-7) = \frac{(8(-7) - 1)}{( 1 - (-7))}[/tex]
= (-56 - 1)/ (1 + 7) = - 57/8
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Suppose that $2000 is invested at a rate of 3.4% compounded quarterly. Assuming that no withdrawals are made, find the total amount after 4 years. Do not round any intermediate computations and round your answer to the nearest cent.
Given data:
The amount invested ( principal) is
[tex]P=\text{ \$2,000}[/tex]The interest rate given is
[tex]r=3.4\%[/tex]The number of years is
[tex]t=4\text{ years}[/tex]The number of times compounded is quarterly
A quarterly event happens four times a year, at intervals of three months.
[tex]n=4[/tex]Concept:
The formula to calculate the amount compounded is given below as
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ \text{Where,} \\ A=\text{amount} \\ P=\text{principal} \\ r=\text{rate} \\ n=\text{ number of times compounded} \\ t=\text{ number of years} \end{gathered}[/tex]By substituting the values above in the formula, we will have
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ A=2,000(1+\frac{3.4}{400})^{4\times4} \end{gathered}[/tex]By solving the equation above, we will have
[tex]\begin{gathered} A=2,000(1+\frac{3.4}{400})^{4\times4} \\ A=2,000(1+0.0085)^{16} \\ A=2000(1.0085)^{16} \\ A=2,290.05 \end{gathered}[/tex]Hence,
The final answer = $2,290.05
please can someone help… A cuboid with a volume of 924 cm' has dimensions
4 cm, (x + 1) cm and (x + 11) cm.
Show clearly that x2 + 12x – 220 = 0
By substitute values in formula for volume of cuboid we get;
x² + 12x – 220 = 0
What is mean by Volume?
Volume of cuboid is defined as the amount of space occupied by the sides of cuboid in three-dimensional space.
Given that;
A cuboid with a volume of 924 cm' has dimensions,
4 cm, (x + 1) cm and (x + 11) cm.
Since, Volume of cuboid = Length x width x height
After substitute we get;
Volume of cuboid = 4 × (x + 1) × (x + 11)
924 = 4 (x² + 11x + x + 11)
924 = 4 (x² + 12x + 11)
Divide 4 both side;
231 = x² + 12x + 11
x² + 12x + 11 - 231 = 0
x² + 12x - 220 = 0
Thus, By the formula of volume of cuboid we get;
x² + 12x - 220 = 0
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A passenger train traveled 35 miles in 50 minutes. At this rate, how many miles can the train travel in one hour?
Given:
A passenger train traveled 35 miles in 50 minutes.
[tex]\begin{gathered} \text{Number of miles the train travelled in one hour=}\frac{35}{50}\times60 \\ \text{Number of miles the train travelled in one hour=}42\text{ miles} \end{gathered}[/tex]umber of miles that train can travel in one hour is 42 miles.
What is the solution of the linear-quadratic system of equations?
y = r2 +52 _ 3
y = x=2
The value of x is 1 , -5 and y is 3 , -3
What is quadratic equation ?A[tex]x^{2}[/tex] + bx + c = 0 is the form of a quadratic equation, which is an expression in second-degree algebra. Square-sounding "quad" is the root of the term "quadratic," which signifies "quadratic." An "equation of degree 2" is another way to describe a quadratic equation. A quadratic equation is utilized in a wide variety of situations. You may be surprised to learn that a quadratic equation accurately predicts a rocket's trajectory after launch. Additionally, a quadratic equation is useful in many fields, including physics, engineering, astronomy, etc.
Given that : the linear-quadratic system of equations is y = [tex]x^{2}[/tex] +5x - 3 and y -x=2 .
y = [tex]x^{2}[/tex] +5x - 3 .....(i)
y = 2+ x.....(ii)
put the value of y in equation i
2 + x = [tex]x^{2}[/tex] +5x - 3
[tex]x^{2}[/tex] +4x - 5 = 0
[tex]x^{2}[/tex] +(5-1)x - 5 = 0
x(x + 5) -1(x + 5) = 0
(x -1)(x + 5)=0
x=1
x=-5
now put value of x in equation ii
y = 2+ x.....(ii)
y = 3 (when x = 1)
y = -3(when x = -5)
The value of x is 1 , -5 and y is 3 , -3
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cept 3) Which equation represents a pt for line that is parallel to the line y=-4x + 5? 1) y=-4x + 3 cept_ = + 5 5 cept for 3) y = 4x+3 ) 4) y = 4x + 5 2) y=-x+ ) "
y=-4x + 3
EXPLANATION
Given:
y = -4x + 5
To find the equation which represent a line that is parallel to the above, all we need to do is to oserve their slope.
Using a unique properties that states : slope of parallel lines are equal.
Observe that comparing the equation y =-4x + 5 with y=mx + b
slope = m= -4
From the option given, the only equation when compared with y=mx + b that has a slope of -4 is y=-4x + 3.
Therefore, the equation which represent a line that is parallel to y=-4x + 5 is y=-4x + 3
The data represent the results for a test for a certain disease. Assume one individual from the group is randomly selected. Find the probability of getting someone who tested positive, given that he or she did not have the disease.
The individual actually had the disease
No positive 9 negative 133
Yes
Positive 140
Negative 18
The probability is approximately.
The probability of getting someone who tested positive, given that he or she did not have the disease is 0.985
What is probability ?Probability is what has the potential to happen. This area of math examines how random events happen. A value between 0 and 1 is used to express it. In order to anticipate the possibility of events, probability has been introduced to mathematics. The degree of likelihood that something will happen can be used to define probability. This fundamental theory of probability, which is also applied to the probability distribution, can be used to estimate the likelihood of the results of a random experiment. We must first determine the total number of alternatives in order to determine the likelihood that a specific event will occur.
Given that : He or she did not have the disease. The individual actually had the disease No positive 9 , negative 133 Yes Positive 140 ,Negative 18 .
Yes No
Positive : 140 9
negative : 18 133
P = [tex]\frac{Someone get positive }{he not had the disease}[/tex]
= [tex]\frac{140}{142}[/tex]
=0.985
The probability of getting someone who tested positive, given that he or she did not have the disease is 0.985
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29) Tom solved the equation 6x-2(15-2x) = 10 and checked his solution as shown below
6x - 30- 4x = 10
6 (20) - 30-4 (20) = 10
120-30-80 = 10
90-80 = 10
10 = 10
Do you agree or disagree with his check? Explain.
Help me solve the first problem please
Question 14
[tex]\binom{8}{3}=\frac{8!}{5!3!}=56[/tex]
Question 15
[tex]\binom{15}{6}=\frac{15!}{9!6!}=5005[/tex]
I need help with this question
In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between two or more items are frequently represented by the points on a graph.
Explain the graph of the solution?We graph both equations in the same coordinate system in order to visually solve a system of linear equations. The intersection of the two lines is where the system's answer will be found.
Any two ordered pairs can be used to create a solution set on a graph by connecting them with a straight line. Thus, any point along this graphed line would be included in the solution set.
There is only one solution that holds true for both equations if the equations' graphs cross. There are no solutions that hold for both equations if the equations' graphs do not meet (for instance, if they are parallel).
The answer for this graph is -4.
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3. In a video game for
every 5 levels you pass,
you earn 4 points. If you
earned 20 points, how
many levels would you
have passed?
Answer:
If you have earned 20 points, this means you have passed 25 levels.
Step-by-step explanation:
25 = 5 (20/4)
2 tablets 3 times per day 14 day supply 15 tablets needed per bottle. How many bottles are needed
6 bottles are needed.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
given:
2 tablets 3 times per day
so, total tablets = 6 tablets
Total days = 14
so, total tablets in 14 days = 14 x 6 = 96
and, tablets per bottle= 15
Then, the number of bottles required = 96 /15 =6.4
Hence, 6 bottles are needed.
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can someone help me
Write the verbal sentence as an equation or an inequality:
Four is greater than six times a number t.
Answer:
I hope this helps. Four is greater than six times a number t in inequality form is 4 › 6 * t
n-13-25 OR 2 +9n > -43
Need help asap
Answer:
261
Step-by-step explanation:
What is the equation of a line that passes through the points (3, 6) and (8, 4)?
y=5/2x - 3/2
y=5/2x - 27/2
y=-2/5x - 24/5
y=-2/5x + 36/5
Answer: y= -2/5 + 36/5
Step-by-step explanation: when graphed, the slope is negative so it has to be -2/5x, and the y-intercept is positive so it has to be +36/5 (+7.2)
Consider the function
y = 2x.
Complete the table of points for
x = −2, −1, 0, 1, 2.
Find the exact y-values.
The table representing the exact values of y from the function is attached below.
In mathematics, a function from a set X to a set Y assigns each element of X exactly one element of Y. The sets X and Y are referred to as the function's domain and codomain, respectively.
Functions were initially the idealisation of how a changing quantity depends on another quantity, and they can be traced back to the works of Persian mathematicians Al-Biruni and Sharaf al-Din al-Tusi. A planet's position, for instance, depends on time. The idea of a function was developed historically at the end of the 17th century with the infinitesimal calculus function, and until the 19th century, the functions that were taken into consideration were differentiable (that is, they could be divided into two parts).The given function is of the form y = 2x .
Now let us find the respective values of y for the given values of x.
At x = -2
y = 2x = 2 × (-2) = -4
At x = -1
y = 2x = 2 × (-1) = -2
At x = 0
y = 2x = 2 × (0) = 0
At x = 1
y = 2x = 2 × (1) = 2
At x = -2
y = 2x = 2 × (2) = 4
Therefore the table to represent this y-values of the function is [tex]\begin{table}[]\begin{tabular}{lllll} & & & & \\ & & & & \\ & & & & \\ & & & & \end{tabular}\end{table}[/tex][tex]\begin{table}[]\begin{tabular}{ll} & \\ & \\ & \\ & \\ & \end{tabular}\end{table}[/tex]attached below.
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you borrow $200,000.00 that charges you 6.3% interest, compounded monthly. You will make payments monthly in the amount of $1,300.00. How many payments will it take for you to pay off the loan?
The number of payments to pay off the loan of $200,000 at 6.3% interest, compounded monthly is 315 monthly payments.
How is the number of payments computed?Using the compounding format for determining the monthly payments, the number of periods for the periodic payments can be computed.
In this situation, we used the online finance calculator to determine the number of payments.
Compounding accumulates the interest on a loan and adds it to the principal for computing subsequent interest.
At the end of the period, the balance is made up of the principal and compounded interest.
I/Y (Interest per year) = 6.3%
PV (Present Value) = $200,000
PMT (Periodic Payment) = $-1300
FV (Future Value) = $0
Results:
N (# of periods) = 314.854
Sum of all periodic payments = $-409,309.97
Total Interest $209,309.97
Thus, you are likely to make 315 monthly payments to settle the loan.
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5. Betty wants to mail a package. The flat rate for mailing a package is $20, plus $3 per
pound. Write an expression that can be used to determine the total cost of mailing a package
that weighs p pounds.
If Betty spent $56 to mail her package, how many pounds did it weigh?
1. The mathematical expression that can be used to determine the total cost of mailing a package weighing p pounds is f(Tc) = 20 + 3p.
2. Since Betty spent $56 to mail her package, the weight in pounds of the mail must be 12 pounds.
What is a mathematical expression?A mathematical expression is a statement containing numbers, variables, and an arithmetic operation.
Flat (fixed) rate for mailing a package = $20
Variable mailing rate per pound = $3
Expression to model the total cost:
Let Tc = total cost
p = number of pounds
Tc = 20 + 3p
If Betty spent $56 to mail her package, the number of pounds, using the mathematical expression above:
Tc = 20 + 3p
56 = 20 + 3p
56 - 20 = 3p
36 = 3p
p = 12
Check:
Tc = 20 + 3p
56 = 20 + 3 (12)
56 = 20 + 36
56 = 56
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Si la suma de un número y 5 se multiplica por 3, el resultado es igual a 7 veces el número
disminuido en 13. Halla el número.
We construct an equation and calculate that number as 7 .
The equals sign is a symbol used in mathematical formulas to denote the equality of two expressions. The word equation and its cognates can have slightly different meanings in different languages. For instance, in English, an equation is any well-formed formula that consists of two expressions linked by the equals sign, whereas in French, an equation is defined as containing one or more variables.
The equation's solutions are the values of the unknown variables that satisfy the equality, which are often referred to as the variables for which the equation must be solved.
let the number be x .
9 times the number is = 9x
5 times the number added to 3 is
(x + 3) × 5
Now let us set up an equation and find that number :
(x + 3) × 5 = 9x - 13
Simplifying the given equation we get :
5 (x + 3) = 9x - 13
5x + 15 = 9x - 13
5x - 9x = - 13 - 15
- 4x = - 28
x = - 28/-4
x = 7
Hence the required number calculated from the equation is 7 .
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Disclaimer: The complete question is :
If the sum of a number and 3 is multiplied by 5 , the result is equal to 9 times the number decreased by 13. Find the number
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Ms. Lantz recently participated in the Rocket Run 5k. The distribution of finishing time for females is approximately normal with a mean of 57 minutes with a standard deviation of 8 minutes. According to the Houston Chronicle, a healthy female person should be able to run a 5K in less than 50 minutes.
Part B: Ms. Lantz wanted to use her 5K time to qualify for the Houston Marathon. In order to qualify you need to be in the fastest 20% of times. What finishing time would she need in order to qualify for the Houston Marathon?
Answer =___ minutes
**Round to the 4th decimal**
The finishing time would Ms. Lantz need in order to qualify for the Houston Marathon is 50.28 minutes in Rocket Run 5k.
What exactly is the z-score?A Z-Score is just a measurable statistic that represents a score's relationship to the mean across a set of scores.A Z-score can inform a trader why a value is typical for a particular set of data or out of the ordinary.A Z-score of the less than 1.8 indicates that a business is nearing bankruptcy, whereas a score closer to 3 indicates that what a company is in good financial status.The formula for calculating the z-score is;
z = (x - μ)/σ
x = sample size
μ = mean of the sample
σ = standard deviation of the sample
The given values are-
μ = 57 minutes
σ = 8 minutes
Probability = 20% = 0.20
Find the z-score from the negative z table for 0.20
z score = -0.84
Put the values in z formula and find x.
z = (x - μ)/σ
-0.84 = (x - 57)/8
Simplifying;
x = -6.72 + 57
x = 50.28 minutes
Thus, finishing time would Ms. Lantz need in order to qualify for the Houston Marathon is 50.28 minutes Rocket Run 5k.
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Use the information provided to find the vertex form equation of each parabola:-2x^2 + 36x -171
The vertex form of a parabola is expressed as
y = a(x - h)^2 + k
where
a is the leading coefficient
h and k are the horizontal and vertical coordinates of the vertex.
Recall, the general expression for a quadratic equation is
y = ax^2 + bx + c
By comparing with the given equation,
a = - 2, b = 36, c = - 171
The formula for the x coordinate of the vertex is
x = - b/2a
x = - 36/(2 * - 2) = - 36/- 4 = 9
Substituting x = 9 into the equation, we have
y = - 2(9)^2 + 36(9) - 171
y =