The length of a rectangle is
4 meters less than 2 times the width. The perimeter is 22 meters. Find the width.

The scale factor used for the figures are used to find the required dimensions and they are as follows

1.  30 cm

2.  21 cm

3. 49 cm

4. 22 cm

Scale factors are numbers or values used to increase or decrease dimensions

let the scale factor be y

1. The first is a rectangle

3 * y = 18

scale factor, y = 6

Using the scale factor gives

hence 5 * 6 = 30 cm

2. 3 * y = 9

scale factor, y = 3

Using the scale factor gives

7 * 3 = 21 cm

3. 9 * y = 63

scale factor, y = 7

Using the scale factor gives

7 * 7 = 49 cm

4. 8 * y = 16

scale factor, y = 2

Using the scale factor gives

11 * 2 = 22cm

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The unit rate of cups of lemonade per lemon is in the ratio of 6:1.

The unit rate is the ratio of two or more quantities or values that are compared to one another.

Unit rates are also known as the constants of proportionality, constant rate, rate of change, or slope.

The number of lemons required to make 18 cups of lemonade = 3 lemons

Rate of lemonade per lemon = 18/3 = 6/1

Ratio = 6:1 or 1:6

Conversely, the rate of lemon per cup of lemonade = 1/6

Thus, we can conclude that for Zendaya to make 6 cups of lemonade, she requires 1 lemon, or alternatively, the ratio of lemon to a cup of lemonade is 1:6.

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An order-preserving function is one where x < y implies f(x) < f(y). An isomorphism is a one-to-one order-preserving function between two partially ordered sets, while an automorphism is an isomorphism of a set to itself.

In the given excerpt, it explains the concepts of order-preserving functions, isomorphisms, and automorphisms in the context of partially ordered sets.

Order-Preserving Function:

A function f: P -> Q, where P and Q are partially ordered sets, is said to be order-preserving if for any elements x and y in P, if x < y, then f(x) < f(y). In other words, the function preserves the order relation between elements in P when mapped to elements in Q.

Increasing Function:

If P and Q are linearly ordered sets, then an order-preserving function is also referred to as an increasing function. It means that for any elements x and y in P, if x < y, then f(x) < f(y).

Isomorphism:

A one-to-one function f: P -> Q is called an isomorphism of P and Q if it satisfies two conditions:

a. f is order-preserving: For any elements x and y in P, if x < y, then f(x) < f(y).

b. f is onto (surjective): Every element in Q has a pre-image in P.

When an isomorphism exists between (P, <) and (Q, <), it means that the two partially ordered sets have a structure that is preserved under the isomorphism. In other words, they have the same ordering relationships.

Automorphism:

An automorphism of a partially ordered set (P, <) is an isomorphism from P to itself. It means that the function f: P -> P is both order-preserving and bijective (one-to-one and onto). Essentially, an automorphism preserves the structure and order relationships within the same partially ordered set.

These concepts are fundamental in understanding the relationships and mappings between partially ordered sets, particularly in terms of preserving order, finding correspondences, and exploring the symmetry within a set.

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Answer:

The correct graph of the given function is option C. Y.

Step-by-step explanation:

The correct graph is option B (X) because it satisfies all the conditions specified in the function definition.

The first segment of the graph starts at x=-2 and goes to the left, passing through the point (-4,-4) and representing the equation 2x+4. The second segment of the graph starts at x=-2 and goes to the right, passing through the point (2,3) and representing the equation 4+1/2x. The third segment of the graph starts at x=2 and goes to the right, passing through the point (5,0) and representing the equation -x+5.

Option A (W) has a line that passes through the point (2,6), which is not on the graph of the function, and option C (Y) has a line that passes through the point (2,5), which is also not on the graph of the function. Option D (Z) has an open circle at (-2,3), which should be a closed circle according to the function definition, and a closed circle at (2,5), which should be an open circle according to the function definition.

Answer:

362%, 3.66, 3 2/3, 36

Step-by-step explanation:

Answer: 362%, 3.66, 3 2/3, 36

I hope this helps!

Answer:

0.29

Step-by-step explanation:

Answer:

it's 0.29 because we move the decimal point 2 spaces to the left

Answer:

well whats the question?

Step-by-step explanation:

Answers:

slope = -5

y intercept = 18

================================================

Work Shown:

Solve for y

10x+2y = 36

2(5x+y) = 36

5x+y = 36/2 .... dividing both sides by 2

5x+y = 18

y = 18-5x .... subtract 5x from both sides

y = -5x+18

The last equation is in slope intercept form y = mx+b.

We have m = -5 as the slope and b = 18 as the y intercept.

The slope -5 can be written as -5/1 to indicate "go down 5, go over to the right 1".

Answer:

  x ≈ 2.09590327429

Step-by-step explanation:

You want the solution to 3^x = 10 using logarithms.

Taking logarithms of both sides of the given equation, we have ...

  x·log(3) = log(10)

Dividing by the coefficient of x gives ...

  x = log(10)/log(3)

  x ≈ 2.09590327429

__

Additional comment

If the logarithm to the base 10 is used, then this becomes ...

  x = 1/log₁₀(3)

The meaning of "log( )" varies with the context. In high-school algebra, it usually means "log₁₀( )". In other contexts, it may mean "ln( )", the natural logarithm.

For the purpose here, it doesn't matter what base the logarithms have, as long as log(10) and log(3) are to the same base.

<95141404393>

The approximate value of x that satisfies the equation 3^x = 10 is approximately 1.46497.

To evaluate the equation 3^x = 10 using logarithms, we can take the logarithm of both sides of the equation. The most commonly used logarithm is the base 10 logarithm, also known as the common logarithm (log).

Taking the log of both sides, we get:

log(3^x) = log(10)

Now, we can apply the logarithmic property that states log(a^b) = b * log(a). Applying this property to the left side of the equation:

x * log(3) = log(10)

Next, we can divide both sides of the equation by log(3) to isolate the variable x:

x = log(10) / log(3)

Using a calculator, we can evaluate the right side of the equation:

x ≈ 1.46497

Therefore, the approximate value of x that satisfies the equation 3^x = 10 is approximately 1.46497.

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Answer:

490

Step-by-step explanation:

Thanks!

Answer: and I oop skssss

Step-by-step explanation:

Explanation:

Let \(f(x) = \sqrt{25x}\) and \(g(x) = \frac{x^2}{25}\). The differential volume dV of the cylindrical shells is given by

\(dV = 2\pi x[f(x) - g(x)]dx\)

Integrating this expression, we get

\(\displaystyle V = 2\pi\int{x[f(x) - g(x)]}dx\)

To determine the limits of integration, we equate the two functions to find their solutions and thus the limits:

\(\sqrt{25x} = \dfrac{x^2}{25}\)

We can clearly see that x = 0 is one of the solutions. For the other solution/limit, let's solve for x by first taking the square of the equation above:

\(25x = \dfrac{x^4}{(25)^2} \Rightarrow \dfrac{x^3}{(25)^3} = 1\)

or

\(x^3 =(25)^3 \Rightarrow x = \pm25\)

Since we are rotating the functions around the y-axis, we are going to use the x = 25 solution as one of the limits. So the expression for the volume of revolution around the y-axis is

\(\displaystyle V = 2\pi\int_0^{25}{x\left(\sqrt{25x} - \frac{x^2}{25}\right)}dx\)

\(\displaystyle\:\:\:\:=10\pi\int_0^{25}{x^{3/2}}dx - \frac{2\pi}{25}\int_0^{25}{x^3}dx\)

\(\:\:\:\:=\left(4\pi x^{5/2} - \dfrac{\pi}{50}x^4\right)_0^{25}\)

\(\:\:\:\:=4\pi(3125) - \pi(7812.5) = 14726.2\)

Answer:

30.5

Step-by-step explanation:

Let ;

Sunny = S ; Medium = M ; Cold = C

_____ S _____ M ___ C

__X : 50 ____ 35 ___ 10

P(X) : 0.2 ____ 0.5 __ 0.3

P(M) = 1 - (0.2 + 0.3)

P(M) = 1 - 0.5 = 0.5

Expected profit per day, E(X)

E(X) = sum of (X * p(x)

E(X) = (50 * 0.2) + (35 * 0.5) + (10 * 0.3)

E(X) = 10 + 17.5 + 3

E(X) = 30.5

The 9/32 of whole pizza Troy had for breakfast. The whole bag of coffee weighs 10/7 pounds

A fraction is defined as a part of a whole quantity.

1. Leftover pizza = 3/8

Pizza used as breakfast = 3/4 of left-over pizza

= 3/4 of 3/8

The of is calculated by the use of multiplication

The fractions are multiplied as follows:

Pizza used as breakfast = 3/4 * 3/8

= 3 * 3 / 4 * 8

= 9/32

2. 3/5 of bag of coffee weighs = 6/7 pounds

1 bag of coffee weighs = 6/7 ÷ 3/5

The fractions are divided as follows:

Thus, = 6/7 * 5/3

= 6 * 5 / 7 * 3

= 30/21

= 10/7 pounds

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Answer:

x = 4

Step-by-step explanation:

if a line is parallel to a side of a triangle and it intersects the other two sides then id divides those sides proportionally.

DE is such a line , then

\(\frac{BD}{AD}\) = \(\frac{BE}{EC}\)  ( substitute values )

\(\frac{x+2}{x}\) = \(\frac{3}{2}\) ( cross- multiply )

3x = 2(x + 2)

3x = 2x + 4 ( subtract 2x from both sides )

x = 4

Given:

Required:

We have to find the arithmetic series.

Explanation:

From the given data if we can find the common difference denoted by d then we can easily find the required arithmetic series.

We use the formula

Now we put the given values in the above equation to find the value of d.

Then the required arithmetic series is

The formula for finding the sum of the arithmetic series is

Then the sum of the above series is

Final answer:

Hence the arithmetic series is

And the sum of the series is

Answer: 6 sq cm

Step-by-step explanation:

Answer:

Perry's claim is correct while Karina is incorrect

Step-by-step explanation:

Question is incomplete (See Attachment)

First, we need to determine the area covered by Karina and Perry

For Karina, there are 9 square boxes each of which has an area of 1 unit sq

So:

\(Karina = 9 * 1\ unit^2\)

\(Karina = 9\ unit^2\)

For Perry:

There are 18 square boxes, each of which has an area of 1 unit sq.

So:

\(Perry = 18 * 1\ unit^2\)

\(Perry = 18\ unit^2\)

Comparing both areas, we can conclude that Perry's claim is correct while Karina is incorrect

Step-by-step explanation:

4/4 of the pie = 8 slices

1/4 of the pie = 8 slices / 4 = 2 slices

Hence Julie ate 2 slices of the pie.

Answer:

2 slices of pie she ate

Step-by-step explanation:

She ate 2/8th of the slice.

Answer: 8k^2 - 19k + 12

Step-by-step explanation: The way we found this answer was by simplifying the expression.

Step 1 : We want to get (x-2) in the numerator so we could cross it out with the x-2 at the bottom to get our simplified expression.

(8k^3-19k^2+2k+10)/(k-2) = (x-2)(8k^2-17k+5)/(x-2)

You would need to factor out the (x-2)

Step 2: When you cross the (x-2) above with the (x-2) below you end up with 8K^2-17k+5 as the answer.

Answer:

\(8k^2-3k-4+\frac{2}{k-2}\)

Step-by-step explanation:

⭐ See the image I attached to my answer to see the working.

⭐ I recommend you look at the image while following along with the steps to understand the steps.

1. See what multiplies with the first term in the divisor to get the first term in the dividend. Then, put that answer in the quotient space.

2. Under the first term in the dividend, write a - sign and open parentheses. Put the first term inside the parentheses.

3. Multiply what you put in the quotient space from step #1 with the second term in the divisor.

4. Put the product from step #3 inside of the parentheses.

5. Subtract the first two terms in the parentheses from the first two terms in the dividend.

. . . . . . . . . . . . . note: in polynomial division, you will not always subtract two terms. we are subtracting two terms here because there are two terms in the divisor.

6. Write the answer from #5 under the parentheses, and bring down another term from the dividend.

7. See what multiplies with the first term in the dividend to get the answer from #5. Then, put that answer in the quotient space.

8. Under step #6, write a - sign and open parentheses. Put the answer from #5 inside the parentheses.

9. Multiply the answer from #7 with the second term in the divisor.

10. Next to the answer from step #8, write the product of step #9.

11. Subtract the terms from step #10 from step #6.

12. Repeat until you have "brought down" all of the terms from the dividend.

After you are done, your remainder will not be 0. Instead, it will be +2. When you have a remainder that isn't 0, you cannot use the quotient as your answer. Instead, you have to write your answer in this format:

\(q(x)+\frac{r(x)}{d(x)}\), where q(x) is the quotient, r(x) is the remainder, and d(x) is the divisor.

⇒ q(x) = \(8k^2-3k-4\)

⇒ r(x) = +2

⇒ d(x) = k -2

⇒ \(8k^2-3k-4+\frac{2}{k-2}\)

Answer:

Ben stands 4 meter below Surface water

Step-by-step explanation:

In the given situation,

Justin stands 7 meter below Surface water

Ben stands 3 meter above Justin

So,

We can say that Ben stands (7-3) meter below Surface water.

Ben stands 4 meter below Surface water.

Answer:

A)

Function A: Exponential

Function B: Linear

Function C: Exponential

Function D: Exponential

B) Function A

Step-by-step explanation:

Function A: This is exponential because- (1, 3)(2,9)(3,27)

It is not going up by the same number each time. However, it is multiplying by 3 each time which means it is exponential.

Function B: This is linear because- (1, 64)(1, 80)(1, 96)

It is going up by 16 each time, (a constant number) which means it is linear.

Function C: This is exponential because- there is a curve, linear is always a straight line. But, this has a curve which means it is exponential.

Function D: This is exponential because- It is increasing by a percentage and not a constant number. It is increasing by 1% which means it is exponential.

The function that has the greatest growth factor is Function A because, Function A multiplies by 3 each time. Function B is linear, exponential functions always pass linear functions despite how "steep" they are. Eventually, the exponential function will surpass it. Function C is also exponential but is not as "steep" as Function A. Function A multiplies by 3 each time but Function C increases less. Function D is also exponential, and for the same reasons as Function C, Function A has the greatest growth factor.

That both a and b are equally likely, is also not true since the Probability of option b is higher than that of option a.

Option b is more likely to be true. This is because the given information states that the showerhead heights were designed to be 72 inches, which is well above the mean height of 69.5 inches. Therefore, it is reasonable to assume that the majority of the players' heights are below 72 inches. Since the heights of the athletes are normally distributed, the probability of selecting a player at random with a height above 72 inches is relatively low. On the other hand, option a suggests that the mean height of a sample of 20 players is more than 72 inches, which is less likely than option b. Option c, which suggests that both a and b are equally likely, is also not true since the probability of option b is higher than that of option a.

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Answer: Hansel is 32

Step-by-step explanation: 11x3-1=32, 32+11=43

Answer:

63

Step-by-step explanation:

smallest is 38

biggest is 63

the call lasted 16 minutes

Answer: rational numbers

Step-by-step explanation: