The length of a rectangle is increase by 25%. to keep the area of the rectangle the same, by what percent must the width be decreased

The length of XV in triangle VWX is approximately 26 feet.

To find the length of XV, we can use the trigonometric relationship in a right triangle. In triangle VWX, the measure of angle W is 25° and angle X is 90°. We can use the sine function to find the length of XV. The sine of angle W is equal to the length of the side opposite angle W divided by the length of the hypotenuse. So, we have sin(25°) = XV/61. Rearranging the equation, we get XV = 61 * sin(25°). Plugging in the values, we find that XV is approximately 26 feet.

To make the total monthly cost of Silver Gym and Fit Factor equal, Sarah would have to buy 6 personal training sessions in a single month.

The question is asking to find out how many personal training sessions Sarah would need to take in a month for the cost at Silver Gym to equal the cost at Fit Factor.

To solve this, we need to create an equation. Let's represent the number of personal training sessions as x. For Silver Gym, the total cost in a month would be 30 + 45x, and for Fit Factor, it would be 90 + 35x.

Setting these two expressions equal to each other gives us the equation 30 + 45x = 90 + 35x.

Moving the variable terms to one side and the constants to the other side of the equation gives us 10x = 60.

We solve for x by dividing both sides of the equation by 10 to get x = 6.

This means that Sarah would need to take 6 personal training sessions for the total cost at the two gyms to be equal.

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Final answer:

To find the annual inflation rate when prices increase at a monthly rate of 1.1%, you use the formula for compounding interest, resulting in an approximate annual rate of 13.97%.

Explanation:

If prices increase at a monthly rate of 1.1%, to calculate the annual inflation rate, you should consider the compounding effect over the year. The general formula for finding the total percentage increase over multiple periods when compounded at each period is:

(1 + rate)^number of periods - 1.

In this case, the monthly rate is 1.1%, or 0.011 when expressed as a decimal. The number of periods (months) in a year is 12. Plugging these values into the formula gives:

(1 + 0.011)^12 - 1,

which calculates to:

1.011^12 - 1 = 0.1397 or 13.97%.

So, the annual inflation rate when prices increase at a monthly rate of 1.1% is approximately 13.97%.

Using the formula for exponential growth and given an initial population of 4,000 mosquitoes with a 25% monthly growth rate, the mosquito population is expected to grow to approximately 9,766 after 4 months.

The question involves calculating the growth of a mosquito population over a period, specifically after 4 months, given an initial population of 4,000 mosquitoes and a monthly growth rate of 25%. To find the population after 4 months, we use the formula for exponential growth:

P = P0 × (1 + r)n

where P is the population at the end, P0 is the initial population, r is the growth rate (expressed as a decimal), and n is the number of time periods.

Substituting the values, we get:

P = 4000 × (1 + 0.25)4

P = 4000 × (1.25)4

After calculating, we find that P = 9765.63. Thus, the population of mosquitoes after 4 months is expected to be approximately 9,766.

The mosquito population grows from 4,000 to approximately 9,766 over 4 months with a 25% monthly increase.

The initial number of mosquitoes is 4,000, and the population increases at a rate of 25% per month. To find the population after 4 months, we use the formula for compound interest:

P = P0 [tex](1 + r)^{t[/tex]

where:

Given:

Substitute these values into the formula:

P = 4000 × (1 + 0.25)⁴

First, calculate (1 + 0.25):

1 + 0.25 = 1.25

Then, raise this to the power of 4:

(1.25)⁴ = 2.4414

Finally, multiply by the initial population:

P = 4000 × 2.4414 = 9765.6

Thus, the mosquito population after 4 months is approximately 9,766.

Answer:

The answer is B 11/20

Step-by-step explanation:

To transform a decimal to a fraction you must do the following:

1. Multiply by an specific power of 10 until your decimal becomes a whole number. In this case 0.55 we multiply by 10 ^2 or 100 and we obtain 55.

2 Divide the decimal by this same power of 10 so that you do not change the original value. For example

0.55 *(100/100) = 55/100 As you see Im multiplying and dividing by 100 ( thats equivalent to 1 so it doesnt change the original number)

3 Simplify the fraction

To simplify your fraction you must find the Greatest Common Factor of 55 and 100. For doing this, you only perform a prime factorization. Divide 55 and 100 by the smallest common prime factor, besides 1. (For this case is 5) until you arrive to two number without common prime factors.

55/5 = 11

100/5 = 20

As 11 and 20 have no common prime factors it is the most simplified fraction  

To determine the number of dimes Chauncey has, you can use the system of equations stemming from the total number of coins and their total value. Following through with the calculations, it turns out that Chauncey has 32 dimes.

The subject at hand revolves around the concept of linear equations. Given that Chauncey has 42 coins (all dimes and quarters) worth $5.70, you can use a system of equations to figure out the number of each type of coin.

So, Chauncey has 32 dimes.

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Let's analyze each expression:

A. (32ˣ/4) can be rewritten as ((2⁵)ˣ/(2²)) = (2⁵ˣ/2²) = 2⁵ˣ⁻².

This expression is not equivalent to 8ˣ, so it's incorrect.

B. (32/49)ˣ = 8ˣ This expression is equivalent to 8ˣ, so it's correct.

C. 8 × 8ˣ⁺¹ = 8ˣ⁺¹ + 1 This expression is not equivalent to 8ˣ, so it's correct.

D. x⁴ is not equivalent to 8ˣ, so it's correct.

E. (32ˣ/4ˣ) = (32/49)ˣ = 8ˣ This expression is equivalent to 8ˣ, so it's correct.

F. 8 × 8ˣ⁻¹ = 8ˣ⁻¹⁺¹ = 8ˣ This expression is equivalent to 8ˣ, so it's correct.

So, the expressions equivalent to 8x are: B, E, and F.

Let's assess each expression:

A. (32ˣ/4) can be rewritten as ((2⁵)ˣ/(2²)) = (2⁵ˣ/2²) = 2⁵ˣ⁻². This expression is not equivalent to 8ˣ, so it's incorrect.

B. (32/49)ˣ = 8ˣ  This expression is equivalent to 8ˣ, so it's correct.

C. 8 × 8ˣ⁺¹ = 8ˣ⁺¹ + 1 This expression is not equivalent to 8ˣ, so it's correct.

D. x⁴  is not equivalent to 8ˣ, so it's correct.

E. (32ˣ/4ˣ) = (32/49)ˣ = 8ˣ This expression is equivalent to 8ˣ, so it's correct.

F. 8 × 8ˣ⁻¹ = 8ˣ⁻¹⁺¹ = 8ˣ  This expression is equivalent to 8ˣ, so it's correct.

So, the expressions equivalent to 8ˣ are: B, E, and F.

Complete Question:

Which expressions are equivalent to the one below? 8x

A. 32ˣ/4

B. (32/49)ˣ

C. 8 × 8ˣ⁺¹

D. x⁴

E. (32ˣ/4ˣ)

F. 8 × 8ˣ⁻¹

Answer:

C. $150

Step-by-step explanation:

we know that

the area of the room=30*40------> 1200 ft²

1 gallon of paint cover----------------> 200 ft²

x---------------------------> 1200 ft²

x=1200/200------> x=6 gallons

1 gallon cost------------> $25

6 gallons-----------> x

x=6*25-----> x=$150

the answer is

the option C. $150

Final answer:

The center of the circle described by the equation x2 − 4x + y2 + 8y − 29 = 0 is (2, -4), and the radius is 7 units.

Explanation:

The equation of a circle given in the question is x2 − 4x + y2 + 8y − 29 = 0. To find the center and radius of the circle, we will complete the square for both x and y terms.

This involves adding and subtracting the squared half of the coefficients of x and y to complete the square:

(x2 - 4x + 4) - 4 + (y2 + 8y + 16) - 16 = 29 + 4 + 16

(x - 2)2 + (y + 4)2 = 49

This equation is now in standard circle form, which is (x - h)2 + (y - k)2 = r2, where (h, k) is the center and r is the radius.

The center of the circle is therefore at (2, -4) and the radius is √(49) = 7 units.

Answer:

FALSE

Step-by-step explanation:

The correct equation would be y = mx + b

y -->  y coordinate

m --> the slope

x -->  x coordinate

b --> the y-intercept

Answer:

false!

Step-by-step explanation:

Y = mx + b is the generic form of a linear equation written in slope-intercept form.

To find the inverse of a function, follow these steps: replace f(x) with y, interchange x and y, solve for y, and replace y with f-1(x). Applying these steps to the given function f(x) = 3x - 2 results in the inverse function f-1(x) = (x + 2)/3.

To find the inverse of a function, we can follow these steps:

Let's apply these steps to the given function f(x) = 3x - 2:

Therefore, the inverse of the function f(x) = 3x - 2 is f-1(x) = (x + 2)/3.

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The inverse function of [tex]\( f(x) = 3x - 2 \)[/tex] is [tex]\( f^{-1}(x) = \frac{x + 2}{3} \).[/tex]

To find the inverse function [tex]\( f^{-1}(x) \)[/tex] for the given function [tex]\( f(x) = 3x - 2 \)[/tex], follow these steps:

Start with the original function:

  [tex]\[ y = 3x - 2 \][/tex]

Swap y and x to find the inverse:

  [tex]\[ x = 3y - 2 \][/tex]

Solve for y:

  [tex]\[ x + 2 = 3y \][/tex]

  [tex]\[ y = \frac{x + 2}{3} \][/tex]

Rewrite y as [tex]\( f^{-1}(x) \):[/tex]

  [tex]\[ f^{-1}(x) = \frac{x + 2}{3} \][/tex]

So, the inverse function [tex]\( f^{-1}(x) \)[/tex] is:

[tex]\[f^{-1}(x) = \frac{x + 2}{3}\][/tex]

Complete Question:

If [tex]f(x) =3x-2[/tex], find [tex]f^{-1}(x)[/tex]

Answer: A2+B2=C2                                                                                                                                                                                            

             (๑╹ᆺ╹ ) i hope this is right

Answer:

D lie on thesame line as the original

Step-by-step explanation:

I took the test and hurray! It was correct

The surface area of this cylinder in terms of [tex]\pi[/tex] is [tex]216\pi\;cm^2[/tex]

Given the following data:

To calculate the surface area of this cylinder in terms of [tex]\pi[/tex]:

Mathematically, the surface area (SA) of a cylinder is given by this formula:

[tex]S.A = 2\pi rh + 2\pi r^2[/tex]

Where:

Substituting the given parameters into the formula, we have;

[tex]S.A = 2\pi (6)(12) + 2\pi (6)^2\\\\S.A = 144\pi+72\pi\\\\S.A = 216\pi\;cm^2[/tex]

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