Is it possible to place 158 books on three shelves so that the first shelf has 8 fewer books than the second and 5 more books than the third shelf?


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The pre-image becomes the image in a picture through transformations such as translation, rotation, reflection, or dilation.

The pre-image is the original figure before any transformations. The image is the new figure after a transformation has been applied to the pre-image. In this picture, the pre-image became the image through translation, rotation, reflection, or dilation.

By applying one or more of these transformations to the pre-image, it can become the image in the picture.

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Answer:

The dimensions of the largest possible map that can fit on the page are 10 inches by [tex]6\frac{2}{3}[/tex] inches.

Step-by-step explanation:

You are reducing a map of dimensions 2 ft by 3 ft

Lets change them to inches.

1 foot = 12 inches

So, 2 feet = [tex]2\times12=24[/tex] inches

3 feet = [tex]3\times12=36[/tex] inches

So, dimensions are : 24 inches x 36 inches

[tex]\frac{24}{36}=\frac{2}{3}[/tex]

Since 10 inch will be the longer side, we can find the shorter side by :

[tex]\frac{x}{10}=\frac{2}{3}[/tex]

[tex]3x=20[/tex]

[tex]x=\frac{20}{3}[/tex]

or [tex]x=6\frac{2}{3}[/tex] inches

So, the dimensions of the largest possible map that can fit on the page are 10 inches by [tex]6\frac{2}{3}[/tex] inches.

The dimension of the largest possible map which can fit on the paper can be used is [tex] 6\frac{2}{3} \: inches \: by \: 10 \: inches [/tex]

Converting the map dimension to inches :

2 feets = 2 × 12 = 24 inches

3 feets = 3 × 12 = 36 inches

Scale factor = 24 / 36 = 2/3

Longer side of the paper = 10 inches

Using the scale to obtain the length of the shorter side :

2/3 = x/10

Cross multiply

3x = 2 × 10

3x = 20

x = (20 ÷ 3)

x = 6 2/3 inches

The dimension of the largest possible map would be [tex] 6\frac{2}{3} \: inches \: by \: 10 \: inches [/tex]

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Wolf population and compound interest are exponential functions because both functions are in the form of m x [tex]a^x[/tex] as given below.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

An exponential function is denoted as f(x) = [tex]a^x[/tex]

Where x is a variable and a is a constant.

Now,

Wolf population:

Suppose the wolf population initially is 10.

It grows double every year.

This means,

The population of wolves after 3 years.

x = 3

P = 10 x 2³ = 10 x 2 x 2 x 2 = 80

P = 10 x 2³ is an exponential function.

Now,

Compound interest:

Principal = 10

Rate = 10% per year

Time = 3

Amount = P [tex](1 + r/n)^{nt}[/tex]

A = 10 [tex](1 + 0.1)^3[/tex]

A = 10 x 1.1³

This is an exponential function.

Thus,

Wolf population and compound interest are exponential functions.

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The answer is (A) I find it very easy to see the relationships and why they are all exponential functions.

To see why a wolf population and compound interest both relate to exponential functions, follow these steps:

1. Understand exponential functions: An exponential function has the form [tex]\( f(t) = a \cdot b^t \)[/tex], where a is the initial amount, b is the growth (or decay) factor, and t is time.

2. Wolf population:

  - Suppose a wolf population grows at a constant rate of 5% per year.

  - If the initial population is [tex]\( P_0 \)[/tex], the population after t years is [tex]\( P(t) = P_0 \cdot (1.05)^t \)[/tex], showing exponential growth.

3. Compound interest:

  - For compound interest, if you invest P dollars at an annual interest rate of r, compounded annually, the amount after t years is [tex]\( A(t) = P \cdot (1 + r)^t \)[/tex], which is also an exponential function.

4. Conclusion:

  - Both scenarios involve quantities growing by a constant percentage over time, fitting the exponential model.

Thus, the answer is: A. I find it very easy to see the relationships and why they are all exponential functions.

Complete question:- A wolf population, and compound interest were both used as examples of exponential functions. How easy is it for you to see how these diverse examples relate to exponential functions?

A. I find it very easy to see the relationships and why they are all exponential functions.

B. I have some difficulty seeing the relationships but understand why they are both exponential functions.

C. I don't see the relationships and am not sure why they are both exponential functions.

D. I do not understand what an exponential function is.

Final answer:

To find the fraction of the 2 pizzas left over, calculate the total slices consumed and subtract from the total. Consuela and her friends ate 14 slices out of 16, leaving 2/16 or 1/8 of the 2 pizzas left over.

Explanation:

Consuela and her friends ordered 2 pizzas, each cut into 8 slices. Consuela saved 2 slices, then shared the rest equally. Each person ate 2 slices.

To find out what fraction of the 2 pizzas is left over, calculate the total slices consumed and subtract from the total.

Answer:

The Answer is 11250 ft~

Step-by-step explanation:

I did the test and got it correct

Answer:

the answer is b 728

Step-by-step explanation:

Answer:

  TRUE

Step-by-step explanation:

When all sides are the same length, at least one pair of sides is the same length.

Answer:

the answer is true

Step-by-step explanation:

answers:

Describe the graph of the function at its roots.

f(x) = (x − 2)3(x + 6)2(x + 12)

At x = 2, the graph crosses the x–axis.

At x = −6, the graph touches the x–axis.

At x = −12, the graph crosses the x–axis.

The required solution of the given function, at x = 2 the graph crosses the x-axis.

Given that,
The graph of the function at its roots. f(x) = (x − 2)³(x + 6)²(x + 12)
To discuss At x = 2, the graph is the x-axis.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

here,
The graph of the given function f(x) = (x − 2)³(x + 6)²(x + 12) is show,
From the graph, it is found that at x = 2, the graph passes through the x-axis.

Thus, the required solution of the given function, at x = 2 the graph crosses the x-axis.

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Answer:

37

Step-by-step explanation:

its 37

The value of a composite function (f•g)(x) at x = 10 is 37 if the function f(x) = x² + 1 and g(x) =x - 4 option (A) 37 is correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

The question is incomplete.

The complete question is:

If f(x) = x² + 1 and g(x) = x - 4, which value is equivalent to (f•g)(10)?

We have a function:

f(x) = x² + 1

g(x) =x - 4

Plug x = 10 in the function g(x)

g(10) = 10- 4

g(10) = 6

Plug the above value in the function f(x)

(f•g)(10) = f(g(10)) = (6)² + 1

(f•g)(10)  = 36 + 1

(f•g)(10)  = 37

Thus, the value of a composite function (f•g)(x) at x = 10 is 37 if the function f(x) = x² + 1 and g(x) =x - 4 option (A) 37 is correct.

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Answer: Non- renewable

The energy is derived from various sources on the basis of origin the energy can be derived from the renewable and non-renewable sources of energy. Renewable sources are those, which are abundantly available in nature and they can be replenished after a single use. For example, sunlight energy, wind energy, tidal energy, geothermal energy. But non- renewable sources are those which are available in limited amount hence, are expensive and cannot be replenished once they are used. For example fossil fuels such as coal, petroleum and natural gas. These are the resources which takes millions of years for their formation. Their genesis takes place inside the earth's geosphere under high heat and pressure conditions and by the action of the soil microbes acting upon the dead remains of plants and animals.

On the basis of the above description, energy resources that exist in limited amounts and, once used, cannot be replaced except over the course of millions of years are called non- renewable resources energy resources

You can buy 32 gumdrops at 8¢ apiece for the same amount of money as buying 8 gumdrops at 2¢ apiece.

To find out how many gumdrops you can buy at 8¢ apiece for the same amount of money as buying 8 gumdrops at 2¢ apiece, you need to compare the prices and calculate the equivalent quantity. Since the prices are different, you can set up a proportion to solve the problem:

2¢ / 8 = 8¢ / x

By cross-multiplying, you get:

2 * x = 8 * 8

Now, solve for x to find the number of gumdrops you can buy at 8¢ apiece:

x = (8 * 8) / 2

x = 32

Therefore, you can buy 32 gumdrops at 8¢ apiece for the same amount of money as buying 8 gumdrops at 2¢ apiece.

To find out how many gumdrops you can buy at 8¢ apiece for the same amount of money you spent on 8 gumdrops at 2¢ apiece, divide the total amount of money by the new price.

To find out how many gumdrops you can buy at 8¢ apiece for the same amount of money you spent on 8 gumdrops at 2¢ apiece, divide the total amount of money by the new price:

Total amount of money = 8 gumdrops x 2¢ apiece = 16¢

Number of gumdrops you can buy at 8¢ apiece = Total amount of money / 8¢

Number of gumdrops you can buy = 16¢ / 8¢ = 2 gumdrops

So, for the same amount of money, you can buy 2 gumdrops at 8¢ apiece.