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A square hot tub will be placed in the center of an enclosed area near the pool. Each side of the hot tub measures 6 feet. It will be surrounded by x feet of deck on each side. The enclosed space is also square and has an area of 169 square feet. Find the width o the deck space around the hot tub, x.

Part 1
Write an equation for the area of the enclosed space in the form y=(side length)^2. Hint: Don't forget to add x to each side of the hot tub.

Part 2
Substitute the area of the enclosed space for y in your equation.

Part 3 Solve your equation from part 2 for x.

Part 4
What is the width of the deck around the hot tub.

When the function f(x)=25[tex]x^2[/tex]−2 is vertically stretched by a factor of 2 to create the function g(x), the resulting equation is g(x) = 50[tex]x^2[/tex]−4.

The equation of g(x) can be found by vertically stretching f(x) by a factor of 2. Since f(x) = 25[tex]x^2[/tex] - 2, we can multiply the function by 2 to get g(x) the equation:

The function g(x) is described as a vertical stretch of the function f(x) by a factor of 2. If f(x)=25[tex]x^2[/tex]−2, a vertical stretch implies that we multiply all y-coordinates by the given factor, which is 2 in this case. Therefore, g(x) will be 2*f(x).

This gives us:

g(x) = 2*(25[tex]x^2[/tex] −2)

Expand this:

g(x) = 50[tex]x^2[/tex]−4

So, the equation of g(x) after the vertical stretch of f(x) by a factor of 2 is g(x) = 50[tex]x^2[/tex] −4.

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The equation of g(x), which is a vertical stretch of f(x) = 25x² - 2 by a factor of 2, is g(x) = 50x² - 4.

To solve this, we need to apply a vertical stretch to the function f(x).

A vertical stretch by a factor of 2 means multiplying the entire function f(x) by 2.

Given :

f(x) = 25x² - 2

we multiply it by 2:

g(x) = 2 * (25x² - 2)

g(x) = 50x² - 4

So, the equation of g(x) is g(x) = 50x² - 4.

The equivalent expressions are [tex]-6+8d-2c[/tex] and [tex]-2c+8d-6[/tex]. So, the correct options are B and C.

Given:

The given expression is:

[tex]-\dfrac{2}{5}(15-20d+5c)[/tex]

To find:

The equivalent expressions.

Explanation:

We have,

[tex]-\dfrac{2}{5}(15-20d+5c)[/tex]

Using the distributive property, we get

[tex]=-\dfrac{2}{5}(15)-\dfrac{2}{5}(-20d)-\dfrac{2}{5}(5c)[/tex]

[tex]=-6+8d-2c[/tex]

It can be rewritten as:

[tex]=-2c+8d-6[/tex]

The equivalent expressions are [tex]-6+8d-2c[/tex] and [tex]-2c+8d-6[/tex]. Therefore, the correct options are B and C.

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Upon applying the distributive property, the given expression, –25(15 – 20d + 5c), simplifies to –375 + 500d – 125c. None of the options provided match this expression, making the correct answer 'None of the above'.

The student is asked to find an expression equivalent to –25(15 – 20d + 5c). To do this, we will apply the distributive property to multiply –25 by each term inside the brackets. This gives us:

Combining these we get the expression –375 + 500d – 125c. When we look at the options provided, none are equivalent to the expression we derived. Therefore, the correct answer is:

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Zoe's Fish tank holds 27 L of water, so this is the capacity of the tank. On the other hand, Zoe uses a 3L container in order to fill the tank, so the question is  how many times does she have to fill the three litter container in order to fill the fish tank? Let's solve this as follows:

First time:

She pours 3L

Second time:

She pours another 3L, but she previously poured 3L, so she has poured 6L

Third time:

She pours another 3L, but she previously poured 6L, so she has poured 9L

Fourth time:

She pours another 3L, but she previously poured 9L, so she has poured 12L

Fifth time:

She pours another 3L, but she previously poured 12L, so she has poured 15L

Sixth time:

She pours another 3L, but she previously poured 15L, so she has poured 18L

Seventh time:

She pours another 3L, but she previously poured 18L, so she has poured 21L

Eighth time:

She pours another 3L, but she previously poured 21L, so she has poured 24L

Ninth time:

She pours another 3L, but she previously poured 24L, so she has poured 27L

According to this, she needs to pours the 3L container nine times in order to fill the fish tank. This can also be solved dividing 27L/3L= 9

The answer is not A because T would be flipped,  the answer is not D because T can not be reflected in that area without translations, and the answer is not B because T cannot (once again) be reflected in such locations without translations, Therefore, that leaves us with our best bet being the answer C.

Answer:

3

Step-by-step explanation:

Answer:

the median is the number in the middle the mean is the sum of all numbers and divided

Step-by-step explanation:

mean 1,2,3,4,5,6

1+2+3+4+5+6=21

21/6= 3.5 <- mean

Median 1,2,3,4,5,6

2,3,4,5

3,4

median 3.5

Answer:

147

Step-by-step explanation:

Answer:

So the Variable D has to be less than 120, which means the problem has to state that a certain number cannot be bigger than 120.

Step-by-step explanation:

Final answer:

Sarah will take approximately 0.6 minutes or 34 seconds to inflate a spherical balloon with a radius of 3 inches at a rate of 200 cubic inches per minute, after calculating the volume of the balloon and dividing by the rate.

Explanation:

How long will it take Sarah to inflate a spherical balloon with a radius of 3 inches at a rate of 200 cubic inches per minute?

To solve this problem, we first need to calculate the volume of the spherical balloon using the formula for the volume of a sphere, which is [tex]V = \(\frac{4}{3}\)\pi r^3[/tex], where r is the radius of the sphere. In this case, the radius is 3 inches. Plugging the values into the formula, we get:

[tex]V = \(\frac{4}{3}\)\pi (3)^3 = \(\frac{4}{3}\)\pi (27) = 36\pi cubic inches[/tex]

Now, given that Sarah can inflate the balloon at a rate of 200 cubic inches per minute, we can calculate the time it takes to inflate the balloon by dividing the total volume by the rate:

[tex]Time = \(\frac{Volume}{Rate}\) = \(\frac{36\pi}{200}\) minutes[/tex]

Using the approximation \(\pi = 3.14\), this results in:

[tex]Time = \(\frac{36 \times 3.14}{200}\) = \(\frac{113.04}{200}\) ≈ 0.565 minutes[/tex] or about 33.9 seconds, rounded to the nearest tenth.

Therefore, it will take Sarah approximately 0.6 minutes or 34 seconds to inflate the balloon.

288 would be your Answer hope this helps