What number makes the equation true? Enter the answer in the box
16= X4

Answer:

x = 3

Step-by-step explanation:

4(x + 3) = 3(3x - 1) ← distribute parenthesis on both sides

4x + 12 = 9x - 3 ( subtract 9x from both sides )

- 5x + 12 = - 3 ( subtract 12 from both sides )

- 5x = - 15 ( divide both sides by - 5 )

x = 3

Answer:

x = 3

Step-by-step explanation:

start off by distributing

4(x +3) turns into 4x + 12

3(3x - 1) turns into 9x - 3

so your equation turns into

3x + 12 = 9x - 3

then you can subtract the x values to move it to the opposite side of the equal sign (=)

3x + 12 = 9x - 3

-3x          -3x

----------------------

12 = 3x - 3

then add the -3

(to find out how to move the values to opposite sides of the equals sign, just isolate the number. whether it is - 3 or just 7x, you keep the sign in front of it. if it is multiplying then divide it to get rid of it. make sure to do it to both sides of the equation.)

12 = 3x - 3

+3         +3

----------------

15 = 3x

divide 3 on both sides

15/ 3 = 3

3x/3 = x

3 = x

the value of x is 3

hope this helps:)

Answer:

14 mm

Step-by-step explanation:

Just as the little side is 1/4 of the larger side , so is the perimeter

1/4 * 56 = 14 mm

The area of the paperboard that remains is 613.92 square inches.

To find the area of the paperboard that remains after a semicircle is cut out, we need to calculate the area of the rectangular paperboard and subtract the area of the semicircle.

The rectangular paperboard has dimensions of 35 inches long and 24 inches wide. Therefore, the area of the rectangular paperboard is:

Area_rectangular = length * width = 35 in * 24 in = 840 in²

Now, let's calculate the area of the semicircle. The semicircle is cut out of the rectangular paperboard, and the diameter of the semicircle is equal to the width of the rectangular paperboard (24 inches).

The formula to calculate the area of a semicircle is:

Area semicircle = (π * r²) / 2

where r is the radius of the semicircle.

Since the diameter of the semicircle is 24 inches, the radius is half of that, which is 12 inches.

Plugging in the values into the formula, we get:

Area_semicircle = (3.14 * 12²) / 2 = (3.14 * 144) / 2 = 226.08 in²

Finally, to find the area of the paperboard that remains, we subtract the area of the semicircle from the area of the rectangular paperboard:

Area remaining = Area rectangular - Area semicircle = 840 in² - 226.08 in² = 613.92 in²

Therefore, the area of the paperboard that remains is 613.92 square inches.

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Answer:

Super Hyper Ultra Ultimate Deluxe Perfect Amazing Shining God 東方不敗 Master Ginga Victory Strong Cute Beautiful Galaxy Baby 無限 無敵 無双 senchou here, thank you for the points :D

Step-by-step explanation:

Answer:

h=0.25t+3

Step-by-step explanation:

y=mx+b

y=0.25x+3

replace y with h and x with t

h=0.25t+3

Answer:

Step-by-step explanation:

3x + 6y = 3

x - y = -7

3x + 6y = 3

-3x - 3y = 21

3y = 24

y = 8

x - 8 = -7

x = 1

(1, 8)

answer is one solution

Answer:

Step-by-step explanation:

150-20/2

Answer:

30 baloons

Step-by-step explanation:

1. Remove the price of the banner from the total amount you can spend.  You should then end up with $90

2.  Divide 90 by 3, because each balloon costs $3.  You should end up with 30.

Answer:

30 balloons

Step-by-step explanation:

Cost of banner = $ 35

Remaining amount after paying for banner = 125 - 35 = $90

Number of balloons = Remaining amount ÷ cost of one balloon

= 90 ÷ 3

 = 30

The diameter of the circle is approximately 60 inches.

To explain further, we can use the formula relating the central angle of a sector to the length of its intercepted arc. The formula states that the length of the intercepted arc (A) is equal to the radius (r) multiplied by the central angle (θ) in radians.

In this case, we are given the central angle (225 degrees) and the length of the intercepted arc (30π inches).

To find the diameter (d) of the circle, we need to find the radius (r) first. Since the length of the intercepted arc is equal to the radius multiplied by the central angle, we can set up the equation 30π = r * (225π/180). Simplifying this equation gives us r = 20 inches.

The diameter of the circle is twice the radius, so the diameter is equal to 2 * 20 inches, which is 40 inches. Therefore, the diameter of the circle is approximately 60 inches.

In summary, by using the formula for the relationship between central angle and intercepted arc length, we can determine the radius of the circle. Doubling the radius gives us the diameter, which is approximately 60 inches.

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Answer:

sas

Step-by-step explanation:

Answer:

SAS

Step-by-step explanation:

SAS

Answer: 0.5626

Step-by-step explanation:

just divide 9 by 16

Answer:

the slope is M=-4

Step-by-step explanation:

Answer:

to find slope you need to

Step-by-step explanation:

first the slope formula

\(\frac{y2}{y1}\frac{x2}{x1}\)

then you replace them with the numbers

\(\frac{-10-6}{4-3}\)

solve equasion

\(-10-6=-16\\4-3=1\)

\(\frac{-16}{1}\)

slope=-16

The confidence associated with an interval estimate is called the confidence level.

When making an interval estimate, such as estimating a population parameter based on a sample, it is important to provide an indication of the level of confidence we have in the estimate. The confidence level represents the probability or level of certainty that the true population parameter falls within the calculated interval.

For example, if we calculate a 95% confidence interval for the mean height of a population, it means that we are 95% confident that the true population mean height lies within that interval. This implies that if we were to repeat the sampling and interval estimation process multiple times, approximately 95% of the intervals would contain the true population parameter.

The confidence level is typically expressed as a percentage, such as 90%, 95%, or 99%. A higher confidence level indicates a greater level of certainty in the interval estimate but also results in a wider interval.

In summary, the confidence level associated with an interval estimate represents the level of confidence or probability that the interval contains the true population parameter.

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The correct statement is that Joe performed worse than Eric.

To determine which student performed better, we need to compare their standardized scores. Joe's math score of 160 in class A has a mean (μ) of 150 and a standard deviation (σ) of 20. We calculate the z-score for Joe's score as follows:

z = (160 - 150) / 20 = 0.5

On the other hand, Eric's verbal score in class B is 80, with a mean (μ) of 72 and a standard deviation (σ) of 8. The z-score for Eric's score is calculated as:

z = (80 - 72) / 8 = 1

Comparing the z-scores, we find that Eric has a larger standardized score (z = 1) compared to Joe's score (z = 0.5).

This indicates that Eric's score is relatively higher compared to the mean and standard deviation of his class, suggesting better performance.

Therefore, the correct statement is that Joe performed worse than Eric.

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If f(1)=9, f(n) = -4· f(n-1) then the value of f(4) is f(4) = -576.

In mathematics, a function is a relation between a set of inputs (the domain) and a set of possible outputs (the range), with the property that each input is associated with exactly one output.

We can use the recursive formula provided to find the value of f(4):

f(n) = -4 * f(n - 1)

First, we need to find f(2):

f(2) = -4 * f(1) = -4 * 9 = -36

Next, we need to find f(3):

f(3) = -4 * f(2) = -4 * (-36) = 144

Finally, we can find f(4):

f(4) = -4 * f(3) = -4 * 144 = -576

Therefore, f(4) = -576.

Functions are often represented using function notation, such as f(x) or g(x), where "x" is the input value and the function itself is represented by the symbol on the left-hand side of the equation.

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The change in the area of the surface of the cube when its side length triples from s units to 3s units is 52s³.

To quantify the change in the area of the surface of a cube when its side length triples from s units to 3s units, we can set up an integral.

Let's denote the side length of the cube as "x". The initial side length is "s" and the final side length is "3s". We want to find the change in surface area, which is the difference between the final surface area and the initial surface area.

The surface area of a cube with side length "x" is given by 6x², as each face of the cube has an area of x² and there are 6 faces.

The change in surface area can be calculated as:

ΔA = ∫(6x²) dx,

where the integral is taken from the initial side length "s" to the final side length "3s".

Now let's evaluate the integral:

∫(6x²) dx = 2x³ + C,

where C is the constant of integration.

To find the change in surface area, we substitute the limits of integration:

ΔA = [2x³]s to 3s

= 2(3s)³ - 2s³

= 2(27)s³ - 2s³

= 52s³

Therefore, the change in the area of the surface of the cube when its side length triples from s units to 3s units is 52s³.

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The amount of the annual interest tax shield is  $4,176.13. The correct option is d. $4,176.13.

To calculate the amount of the annual interest tax shield, we can use the formula:

ITRS = (Interest rate x Debt) x Tax Rate

Where:

ITRS = Interest Tax Shield

Debt = Face value of bonds

Interest rate = Coupon rate

Tax rate = Tax rate

First, we need to calculate the semiannual interest rate by dividing the coupon rate by 2:

Semiannual interest rate = Coupon rate / 2

Next, we can calculate the annual interest tax shield:

ITRS = (2 x Semiannual interest rate x Debt) x Tax rate

Plugging in the values:

ITRS = (2 x 2.825% x $215,000) x 0.34

ITRS = $4,176.13

Therefore, the correct option is d. $4,176.13.

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Answer:

y = \(\sqrt{(k-a)}\)

Step-by-step explanation:

k= y^2 + a

k-a= y^2

y^2 = k-a

y = (k-a)^(1/2)

y = \(\sqrt{(k-a)}\)

Answer:

\(\displaystyle{y=\pm \sqrt{k-a}}\)

Step-by-step explanation:

To make y-term as the subject of formula means to solve for y-term. First, subtract both sides by a-term, this’ll at least isolate y².

\(\displaystyle{k-a=y^2+a-a}\\\\\displaystyle{k-a=y^2}\)

Everything that you do or add to one of both sides, that side will also be done too. (e.g Suppose we have x + 1 = y. If we add 2 to left then 2 should also be added to right too so we’ll have x + 1 + 2 = y + 2)

Then square root both sides to get rid of the exponents of y-term:

\(\displaystyle{\sqrt{k-a}=\sqrt{y^2}}\)

If we substitute y = any numbers, we’ll always get positive result. Therefore, this means that y-term can be any positive or negative values. Hence, write plus-minus to the left side then evaluate the square root of y² to y:

\(\displaystyle{\pm \sqrt{k-a}=y}\)

Therefore, the new equation written in term of y is:

\(\displaystyle{y=\pm \sqrt{k-a}}\)

After finding the value of x, we need to substitute the value of x in either of the two equations to find the value of y. Finally, we get two solutions (10, 98) and (-3, 8).

Given the system of equations:y = x² - 3x - 2 ..............(1)

y = 4x + 28 ..............(2)

We need to solve this system of equations. Equate equation 1 and equation 2 so as to find the value of x.

x² - 3x - 2 = 4x + 28

Simplify and solve for x: x² - 7x - 30 = 0

(x - 10)(x + 3) = 0

x = 10

or x = -3

Substitute the value of x in either of the two equations to find the value of y. If x = 10:

y = x² - 3x - 2

= 10² - 3(10) - 2

= 98

Therefore, the solution is (10, 98). If x = -3:

y = x² - 3x - 2

= (-3)² - 3(-3) - 2

= 8

Therefore, the solution is (-3, 8).

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Answer: 4 since (3x-4)(3x+4) is a difference of squares

Step-by-step explanation:

The probability that a student completely guesses on every question and makes a perfect score of a 100% is 1/64 or approximately 0.0156 or 1.56%.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

The number of possible answer responses for each question is 4, since there are 4 options.

The number of possible answer responses for all 3 questions can be found by multiplying the number of possible answer responses for each question. Therefore, the total number of possible answer responses for the quiz is 4 x 4 x 4 = 64.

If the student completely guesses on every question, there is a 1 in 4 chance (or a 25% chance) of getting each question correct. Since there are 3 questions, the probability of getting all 3 questions correct is (1/4) x (1/4) x (1/4) = 1/64.

Therefore, the probability that a student completely guesses on every question and makes a perfect score of a 100% is 1/64 or approximately 0.0156 or 1.56%.

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Answer:

2x + 2= 18 and 3x + 6= 30

Step-by-step explanation:

Both require addition and subtraction and come out as x=8

The two different equations which give the solution x=8 are 2x + 2= 18 and 3x + 6= 30.

We need to write two different two-step equations whose solutions are x = 8.

Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign. It shows the relationship of equality between the expression written on the left side with the expression written on the right side. In every equation in math, we have, L.H.S = R.H.S (left hand side = right hand side).

Now, the equations which give the solution x=8 are 2x + 2= 18 and 3x + 6= 30.

So, 2x + 2= 18

⇒2x=16

⇒x=8

Now, 3x + 6= 30

⇒3x=24

⇒x=8

Therefore, the two different equations which give the solution x=8 are 2x + 2= 18 and 3x + 6= 30.

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Answer: C

Step-by-step explanation:

Option:-

Ans:-

\( \: \)

hope it helps! :)

Answer:

y=5/2x+5

Step-by-step explanation:

y=mx+b

m=slope=rise/run=5/2

b=y-intercept=5

Answer:

Step-by-step explanation:

Based on the given information in Exhibit Cape May Realty, the question is asking to test the significance of the slope coefficient at a significance level of a = 0.10. The p-value is less than 0.10, which means that the null hypothesis can be rejected. This leads to the conclusion that the population slope coefficient is different from zero. Therefore, option C is the correct answer.

This means that there is a statistically significant relationship between square footage and property rental rate. As the slope coefficient is different from zero, it indicates that there is a positive or negative relationship between the two variables. However, it does not necessarily mean that there is a causal relationship. There could be other factors that influence the rental rate besides square footage.

In summary, the statistical analysis conducted on Exhibit Cape May Realty indicates that there is a significant relationship between square footage and property rental rate. Therefore, the population slope coefficient is different from zero. It is important to note that this only implies a correlation, not necessarily a causal relationship.

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Answer:

24.53

Step-by-step explanation:

9% of 22.50 = 2.03

22.50 + 2.03 = 24.53

Answer:

24.53

Step-by-step explanation: