Answer:
This is the most optimal way to resolve the problem:
Step-by-step explanation:
15/n+2 = 3n/n
15/n+2 = 3
3 (n+2) = 15
n = 5 - 2
n = 3
Mark reads 42 pages of a book every 3/4hour wright a quation that models the relationship between x ,the number of hours Mark reads, and y, the number of pages of the book he reads
Equation is y= 56x that models the relationship between x ,the number of hours Mark reads, and y, the number of pages of the book he reads.
What is rate of change?The term rate of change (ROC) describes the rate at which something changes over time. Thus, it is not the amount of individual changes themselves but rather the acceleration or deceleration of changes (i.e., the rate). Rate of change is a tool used in finance to comprehend price returns and spot trend momentum.
Given Data
The hours are indicated by = x
The calculation for the number of pages is =y
Read 42 pages every [tex]\frac{3}{4}[/tex] hour
You can model the equation as follows:
y = mx +b
Rate of change = [tex]\frac{change in y}{change in x}[/tex]
Rate of change = 42 ÷[tex]\frac{3}{4}[/tex]
Rate of change = 42 ×[tex]\frac{4}{3}[/tex]
Rate of change = 56
Equation y= 56x
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My mom has grounded me and I need a better grade ASAP please help
Answer:
p = 11
Step-by-step explanation:
This Question tests on the concept of Angle Properties.
Given from the diagram above, we can form up a equation:
4p + 7 + 90 + 3p + 6 = 180 (Sum of Angles in a Triangle)
Now we can solve for p from the equation.
[tex]4p + 7 + 90 + 3p + 6 = 180 \\ 7p + 103 = 180 \\ 7p = 180 - 103 \\ 7p = 77 \\ p = \frac{77}{7} = 11[/tex]
a. Find the length of each side of the quadrilateral. What do you notice?
b. Find the slope of each side of the quadrilateral. What do you notice? Are any sides parallel or perpendicular?
c. Find the length of each diagonal (the segment that goes from one vertex to an opposite verter), What do you notice?
d. Find the slope of each diagonal. What do you notice?
(1. List the properties that you find, (Ex. Are all sides congruent? Perpendicular? Etc)
(a) AB, BC, CD, and DA are, respectively, and long.
(b) AB, BC, CD, and DA have slopes of 0, 0, and 2, respectively.
(c) AC and BD have lengths of 8 and 72, respectively.
(d) AC and BD have slopes of 1 and 1, respectively.
What is quadrilateral in math?A quadrilateral is a polygon having four sides, four angles, and four vertices.
There is a quadrilateral called ABCD.
The quadrilateral's vertices are A(3,5), B(7,7), C(5,3), and D. (1,1).
The side AB measures [(3-7)2 + (5-7)2] = 20.
The side BC measures [(7-5)2 + (7-3)2]. =√20 .
The side CD measures [(5-1)2 + (3-1)2] in length. = √20.
The side DA measures [(1-3)2 + (1-5)2] = 20 in length.
The diagonal AC measures [(3-5)2 + (5-3)2] = 8 in length.
The diagonal BD is [(7-1)2 + (7-1)2] in length. =√72 .
The slope of side AB is equal to 1/2 (7-5)/(7-3)
The slope of the side BC is equal to zero (7-3)/(7-3)
The side CD has a slope of (3-1)/(5-1) = 1/2.
DA's side has a slope of (5-1)/(3-1) = 2.
The sides AD and BC are parallel to one another and have the same length.
Equal in length and parallel to one another are sides AB and CD.
Each side is parallel to the side next to it.
As a result, we draw the conclusion that ABCD is a quadrilateral.
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25.42 marked down by 33%
25.42 marked down by 33 % is 17.0314.
This is a question of percentages.
Percentage
A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.
Percentages have no dimension. Hence it is called a dimensionless number.
33 % of 25.42 is given by:-
(33/100)*(25.42) = (33*25.42)/100 = 838.86/100 = 8.3886
25.42 marked down by 33 % = 25.42 - 8.3886 = 17.0314.
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2x-5 > -11 or -10x - 6 ≥ 44
The solution of given inequalities are x > -3 and x ≤ 5.
How do you solve an inequality?When resolving an inequality, you can do one of the following: add the same amount to each side; deduct the same amount from each side; multiply or divide each side by the same positive amount. You must flip the inequality sign if you multiply or divide each side by a negative number.
Given inequalities are 2x - 5 > -11 and -10x - 6 ≥ 44.
To solve the first inequality,
2x - 5 > -11
Adding 5 on both sides,
2x - 5 + 5 > -11 + 5
2x > -6
Divide both sides by 2,
x > -3
To solve the second inequality,
-10x - 6 ≥ 44
Adding 6 on both sides,
-10x - 6 + 6 ≥ 44 + 6
-10x ≥ 50
Divide both sides by -10, and change the inequality sign
x ≤ 5
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Factor out the GCF -27z^3-9z^4+18z^6
The simplified expression for -27z^3-9z^4+18z^6, using the greatest common factor, is given as follows:
9z³(-3 - z + 2z³).
How to factor an expression by GCF?To find a symbolic expression by the greatest common factor, we have to:
Find the greatest common factor of the numeric coefficients.Find the greatest common factor of the exponents.Then we multiply these GCFs.
For this problem, the numeric coefficients are given as follows:
27, 9 and 18, hence the GCF is of 9.
The exponents are given as follows:
z³, z^4 and z^6, hence the GCF is of z³, which is the expression with the lowest exponent.
Then the GCF of the expression is given as follows:
9z³.
To simplify the expression, each term of the expression is divided by 9z³, hence the factored expression is:
9z³(-3 - z + 2z³).
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A man's taxable income is $3.060 If tax is paid at 12%. How much is the man's net income
A man's taxable income is $3060 if tax is paid at 12%, then the man's net income is $3477.27
The taxable income = $3060
The tax percentage = 12%
Income tax is the a type of tax impose on income generated by businesses and individuals by the government
Consider the net income as x
Then,
12% of the income = x×(12/100)
Therefore the equation will be
x - x×(12/100) = 3060
x(1-(12/100) = 3060
x(1-0.12) = 3060
0.88x = 3060
x = 3060/0.88
x = $3477.27
Hence, a man's taxable income is $3060 if tax is paid at 12%, then the man's net income is $3477.27
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Elizabeth plans to hand out door prize as the guests arrive. Every 6th guest will receive a mug, and every 14th year guest will receive a t-shirt. How many mugs and t-shirts should Elizabeth order?
BTW 256 ppl are going to the party, I’m not sure if this is relevant to the question or not
Using proportions, it is found that Elizabeth should order 42 mugs and 18 t-shirts.
What is a proportion?A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using the unit rates, then operations such as multiplication or division are used to find the equivalent amounts.
In the context of this problem, we have to consider that:
256 people are going to the party.One in six people will receive a mug.One in 14 people will receive a t-shirt.Hence the number of mugs that she has to order is found as follows:
256/6 = 42 (rounded down, as the remainder means that the last guest to receive a mug is the 252th guest).
The number of t-shirts that she has to order is given as follows:
256/14 = 18 (also rounded down, following the same logic as the number of mugs).
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Identify the x-intercept and y-intercept for the equation 10x+5y=30
Considering the definition of a line, x-intercept and y-intercept, the x-intercept and y-intercept are (3, 0) and (0,6) respectively.
Linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.y-intercept and x-interceptThe point [y-intercept] is where the line crosses the y-axis, and occurs when x = 0.
The point [x-intercept] is that value of x for which the expression is equal to 0 and the line crosses the x-axis.
y-intercept and x-intercept in this caseIn this case, the line is 10x +5y=30. Expressed in the form y = mx + b, you get:
5y= 30 - 10x
y= (-10x + 30)÷5
y= -10/5x + 30/5
y= -2x +6
where:
m= -2b= 6The point [y-intercept] is represented by the value of the y-intercept b. So the point [y-intercept] is (0,6).
Being the point [intersection x] that value of x for which the expression is equal to 0 or y is equal to 0, in this case it is calculated as:
0= -2x + 6
-6= -2x
(-6)÷ (-2)= x
3=x
Finally, the point [x-intercept] is (3,0).
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PLEASE HELP ILL GIVE BRAINLIEST ITS TIMED
The value of x is 18 and the value of ∠A (interior angle) is 73°.
According to the given figure,
We have:
∠A = 6x-35°
∠B = 3x+53°
The two parallel lines have been cut by another line.
(Note that when a line divides two parallel lines then the sum of the interior angles on the same side is 180° and the alternate interior angles are equal to each other.)
So, we will have the following expression:
∠A + ∠B = 180°
(6x-35+3x+53)° = 180°
9x+18 = 180
9x = 180-18
9x = 162
x = 162/9
x = 18
Now, putting the value of x in ∠A,
∠A = 6x-35°
∠A = (6*18-35)°
∠A = (108-35)°
∠A = 73°
Hence, the value of x is 18 and the measurement of ∠A is 73°.
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The figure shows the design of a rectangular windowpane. The four horizontal lines are parallel. The measure of angle 6 is 53 degrees. What is the measure of angle 12? Write and solve an equation to find the answer.
∠6 and ∠12 are supplementary angles. That means, they add up to 180°
[tex]\angle6+\angle12=180\degree[/tex]Substitute ∠6 by 53° to find ∠12.
[tex]53+\angle12=180[/tex]Subtract 53 from both sides to find ∠12.
[tex]\begin{gathered} 53+\angle12-53=180-53 \\ \angle12=127\degree \end{gathered}[/tex]Answer: ∠12 = 127°.
What mental math method will give you the correct answer to 136 + 98?
So basically 130+90=220 and 6+8=14. And 220+14=234.
Jillian and Nikki each filled their cars with gasoline. The graphs below show the amount of gas in each car and the miles driven since filling the tank. A graph titled Jillian's Car has miles driven on the x-axis, and gallons of gas left on the y-axis. A line goes through (0, 22) and (100, 16). A graph titled Nikki's Car has miles driven on the x-axis and gallons of gas left on the y-axis. A line goes through points (0, 20) and (100, 16). Which statement is supported by the graphs? Jillian’s car holds more gasoline and gets better gas mileage. Nikki’s car holds more gasoline and gets better gas mileage. Jillian’s car holds more gasoline, but Nikki’s car gets better gas mileage. Nikki’s car holds more gasoline, but Jillian’s car gets better gas mileage.
The statement that is best supported by the graph is; Jillian's car holds more gasoline, but Nikki's car gets better gas mileage.
How to Interpret Linear Graphs?The total amount of gasoline each car tank can hold is shown on the left of each graph on the y-axis.
Jillian's car holds 22 gallons.
Nikki's car holds 20 gallons.
Jillian's car holds more gasoline.
Now we need to see which car gets better gas mileage. Getting better gas mileage means you can go farther with each gallon of gas.
With Jillian's car, after using 22 gallons of gas, you have gone 350 miles, and the gas tank is empty.
350 miles with 22 gallons is 350/22 = 15.9 miles per gallon.
With Nikki's car, you start with only 20 gallons. By the time you drive 350 miles, you still have some gas left. Not only did you start with less gas, 20 gal vs. 22 gal, but after driving the same distance, 350 miles, there is still some gas left in the tank, 6 gallons.
That means Nikki's car used 20 - 6 = 14 gallons to drive 350 miles. 350/14 = 25 miles per gallon.
The more miles per gallon you get, the better the mileage. Thus;
25 miles per gallon is better mileage than 15.9 miles per gallon.
Nikki's car has a smaller gas tank, but it gets better mileage.
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please answer this question with method
Answer:
see explanation
Step-by-step explanation:
the volume (V) of the container is
V = 10 × 4 × 5 = 200 m³
change the dimensions of the box to m , to be same as container
l = 50 cm = 0.5 m , b = 40 cm = 0.4 m , h = 20 cm = 0.2 m
then
volume of box = 0.5 × 0.4 × 0.2 = 0.04 m³
Number of boxes that can be stored in container is
200 ÷ 0.04 = 5000
thus no more than 5000 boxes can be placed in the container
What is 903 Divided by 72 In Fraction form
Answer: The answer would be 12 39/72
Step-by-step explanation:
903 divided by 72, you'd get 12.5417. You could also express 903/72 as a mixed fraction: 12 39/72.
Enter the correct answer in the box.
What are the solutions of this quadratic equation?
x² = 16x - 65
Substitute the values of a and b to complete the solutions.
x = a + bi
x = a - bi
The solutions of the quadratic equation x² = 16x - 65 are:
x = 1/2 + 1/32i
x = 1/2 - 1/32i
What is the solution?We know that a quadratic equation is an equation that is of the sort ax^2 + bx + c = 0. Hence, the equation would be solved and it could have a complex root. By this I mean that the root of the equation could be a complex number as we have in the case of the equation here.
x² = 16x - 65 = 0
x² - 16x + 65 = 0
When we solve by the formula method;
x = -b ±√b^2 - 4ac/2a
x = -(-16) ±√(-16)^2 - 4 (1) (65)/2(16)
x = 16 ±√256 - 260/32
x = 16/32 ±√-4/32
x = 1/2 ± 1/32i
Thus
a = 1/2
b = 1/32
We then obtain;
x = 1/2 + 1/32i
x = 1/2 - 1/32i
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a trough has ends shaped like isosceles triangles, with width 2 m and height 5 m, and the trough is 10 m long. water is being pumped into the trough at a rate of 2 m3/min. at what rate (in m/min) does the height of the water change when the water is 4 m deep?
a trough has ends shaped like isosceles triangles, with width 2 m and height 5 m, and the trough is 10 m long. then the height of the water change when the water is 4 m deep is 1/8 m/min
The depth of the water is 4/5 of the depth of the trough, so the width of the surface will be 4/5 of the width of the trough:
4/5 × 2 m = 8/5 m
Then the surface area of the water is ...
Area = LW = (10 m)(8/5 m) = 16 m²
The rate of change of height multiplied by the area gives the rate of change of volume:
2 m³/min = (16 m²)(h')
h' = (2 m³/min)/(16m²) = 1/8 m/min
Hence , the height of the water change when the water is 4 m deep is 1/8 m/min
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5.45 divided by 65
If rounding show answer.
Step-by-step explanation:
1) 5.45 ÷ 65
2) 109/20 x 1/65=
3) 109/1300 or 0.08384615
can anyone decompose 240 - 135 = 105 ?
need new calculation after decomposing? help
The decomposition of 240 - 135 = 105 will be 15(16 - 9) = 15(7) = 105
What is decomposition?It should be noted that decomposition simply means breaking down of the numbers that are given or illustrated.
It should be noted that the numbers 240 - 135 = 105 all have a common factor of 15. This will be broken down as:
240 - 135 = 105
15(16 - 9)
= 15(7)
= 105
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The graph shows the distance traveled by a bicycle rider.
She moves at a constant speed. Find the slope of the line.
What is the converse of the following conditional statement?
"If a person is a teenager, then the person is 13 years old or older."
Determine the validity of the converse and give a counterexample if the converse is not valid.
If a person is not a teenager, then the person is not 13 years old or older. The converse is invalid; a counterexample is a person who is 12 years old.
If a person is 13 years old or older, then the person is a teenager. The converse is invalid; a counterexample is a person who is 20 years old.
If a person is a teenager, then the person is 13 years old or older. The converse is valid.
If a person is 13 years old or older, then the person is a teenager. The converse is valid.
The converse statement is "If a person is 13 years old or older, then the person is a teenager. The converse is valid" . Option D
What is a converse statement?The converse of a conditional statement is defined as a statement that is formed when the hypothesis and conclusion of a sentence are both reversed or interchanged.
If the conditional statement is expressed as a → b
The converse statement is referred to as b → a
It is important to note that the original statement must be a conditional statement for a converse statement to derived from it.
Given the conditional statement:
"If a person is a teenager, then the person is 13 years old or older."
The converse statement would be written as;
If a person is 13 years old or older, then the person is a teenager.
We can see that the converse statement is valid because anyone that is 13 or older is a teenager
Hence, the converse statement is valid. Option D
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Assume that a new lithium isotope, 8Li, is identified. It is a trace isotope, meaning that it exists in a very tiny quantity. How will this discovery affect the atomic mass of lithium?
Since the isotope has only a very little amount in nature, it does not largely affect the atomic mass of lithium.
What is an isotope?The term isotope has to do with the atoms of the same element that do have the same atomic number but different mass numbers. The implication of this is that isotopes have the same number of protons but do not have the same number of neutrons.
Note that the average atomic mass of an atom is the weighted average of the atomic masses of all the isotopes of the compound. The isotopes that contribute greatly towards the atomic mass are those that have a larger percentage abundance.
Given that the new lithium isotope, 8Li identified is a trace isotope, meaning that it exists in a very tiny quantity, it does not any noticeable effect on the atomic mass of lithium.
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Sue picks a new password for her email that consists of 3 letters, 2 digits, and a special character (! or #). Letters and digits cannot repeat. How many different passwords are possible?
12
2,808,000
2,246,400
3120
There are different 2,808,000 passwords possible which are the correct answer would be option (B)
What is a permutation?A permutation is defined as a mathematical process that determines the number of different arrangements in a set of objects when the order of the sequential arrangements.
Sue picks a new password for her email that consists of 3 letters, 2 digits, and a special character (! or #) which is given in the question.
As per the given condition,
For the first letter, we have 26 options.
For the second letter, we have 25 options, because one letter is already used.
For the third letter, we have 24 options, because 2 letters are already used.
For the first digit, we have 10 options.
For the second digit, we have 9 options, because one is already used.
For the first special character (! or #), we have 2 options.
Then the total number of combinations is:
Combinations = 26×25×24×10×9×2 = 2,808,000
So if we can not repeat digits or letters, we can make 2,808,000 different passwords.
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f(n) = n - 7
f(-9k) =
Answer:
[tex]-9k-7[/tex]
Step-by-step explanation:
Replace n with -9k.
Expand and simplify the expression using properties of operations. 8(3x−7)
The expression 8 ( 3x - 7 ) when expanded gives 24xx - 56.
The cornerstone of mathematics is the theory of operations; we use it to compute and remember fundamental truths. The subsequent three characteristics are applied to addition and multiplication: Commutative Property, Associative Property, and Distributive Property.
The distributive property of binary operations in mathematics generalizes the distributive law, which states that in elementary algebra, equality is always true.
Consider the expression 8( 3x - 7 ),
Let's say y is equal to 8( 3x - 7 ).
By using the distributive property:
y = 8 × 3x - 8 × 7
y = 24x - 56
Therefore,
8( 3x - 7 ) = 24x - 56
Therefore, when the expression 8( 3x - 7 ) is expanded we obtain the expression 24x - 56.
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Find the orthocenter of AABC.
A(3,5), B(6,5), C(5,3)
Answer:
(5, 4)
Step-by-step explanation:
What is Orthocenter?
A point where the altitudes of the triangle meet is known as the point of concurrency or simply the orthocenter of the triangle
2/3 times the quantity n plus 16
(n+16)
O(2n+16)
O(n-16)
O(16-n)
Answer:
24
Step-by-step explanation:
it just is, I don't know how I get this. I just did.
[tex]\frac{2n+48}{3}[/tex]
The length of a violin string varies inversely as the frequency of its vibrations. A violin string 14 inches long vibrates at a frequency of 450 cycles per second. Find the frequency of a 10-inch violin string.
The frequency of the 10 inch violin string will be 630 cycles per second or Hertz if the violin string 14 inches long vibrates at a frequency of 450 cycles per second.
As per the question statement, A violin string 14 inches long vibrates at a frequency of 450 cycles per second and we are supposed to find out the frequency of a 10-inch violin string.
We should be knowing that the length of a violin string varies inversely as the frequency of its vibrations.
f = m/l, where "f" is the frequency and "l" is the length and "m" is the constant number
450 = m / 14
m = 6300
Therefore New frequency = 6300 / 10 = 630 cycles per second
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please help. I will do anything.
Answer:
216 miles
Step-by-step explanation:
so the base fee is 18.99, subtract the total (219.87) by 18.99.
219.87-18.99=200.88
200.88 divided by 0.93 (charge for each mile driven)
200.88/0.93=216
thats a lot of miles.
fill in the blank question. julia wants to purchase a pair of headphones that are on sale for $42.79. the sales tax rate in her county is 6%. calculate the amount of sales tax julia will pay on the purchase. round to the nearest cent if necessary.
julia wants to purchase a pair of headphones that are on sale for $42.79. the sales tax rate in her county is 6%. then Julia have to pay $2.57 as sales tax on purchase of headphones.
Given,
The cost of headphones which Julia wants to purchase on sale = $ 42.79
The sales tax in Julia's country = 6%
We have to calculate the amount of sales tax Julia will pay on the purchase:
That is,
Sales Tax Value = Percentage of sales tax × Price of headphones
Sales Tax Value = (6 / 100) × 42.79
Sales Tax Value = 0.06 × 42.79
Sales Tax Value = 2.5674
Sales Tax Value ≈ 2.57
Therefore, Julia have to pay $2.57 as sales tax on purchase of headphones.
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