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Which algebraic expression represents “Marcus ran four times as far this week”? 4 + n 4n n – 4

disa [49]

Answer:

The Answer would be 4n

Step-by-step explanation:

Since Marcus ran four times as far this week, we need to know how far he ran last week in order to solve this expression. Since we do not know this information it becomes our variable (n). From the statement we can also infer that there is multiplication since he states the word "times". Therefore our Algebraic Expression would be the following.

P = 4n

P being distance ran by Marcus, and n being distance ran last week by Marcus.

I hope this answered your question. If you have any more questions feel free to ask away at Brainly.

5 0

3 years ago

Read 2 more answers

A norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular. Find the dimensions of a norman

Yanka [14]

Answer:

$W\approx 8.72$ and $L\approx 15.57$ .

Step-by-step explanation:

Please find the attachment.

We have been given that a norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular. The total perimeter is 38 feet.

The perimeter of the window will be equal to three sides of rectangle plus half the perimeter of circle. We can represent our given information in an equation as:

$2L+W+\frac{1}{2}(2\pi r)=38$

We can see that diameter of semicircle is W. We know that diameter is twice the radius, so we will get:

$2L+W+\frac{1}{2}(2r\pi)=38$

$2L+W+\frac{\pi}{2}W=38$

Let us find area of window equation as:

$\text{Area}=W\cdot L+\frac{1}{2}(\pi r^2)$

$\text{Area}=W\cdot L+\frac{1}{2}(\pi (\frac{W}{2})^2)$

$\text{Area}=W\cdot L+\frac{\pi}{2}(\frac{W}{2})^2)$

$\text{Area}=W\cdot L+\frac{\pi}{2}(\frac{W^2}{4})$

$\text{Area}=W\cdot L+\frac{\pi}{8}W^2$

Now, we will solve for L is terms W from perimeter equation as:

$L=38-(W+\frac{\pi }{2}W)$

Substitute this value in area equation:

$A=W\cdot (38-W-\frac{\pi }{2}W)+\frac{\pi}{8}W^2$

Since we need the area of window to maximize, so we need to optimize area equation.

$A=W\cdot (38-W-\frac{\pi }{2}W)+\frac{\pi}{8}W^2$

$A=38W-W^2-\frac{\pi }{2}W^2+\frac{\pi}{8}W^2$

Let us find derivative of area equation as:

$A'=38-2W-\frac{2\pi }{2}W+\frac{2\pi}{8}W$

$A'=38-2W-\pi W+\frac{\pi}{4}W$

$A'=38-2W-\frac{4\pi W}{4}+\frac{\pi}{4}W$

$A'=38-2W-\frac{3\pi W}{4}$

To find maxima, we will equate first derivative equal to 0 as:

$38-2W-\frac{3\pi W}{4}=0$

$-2W-\frac{3\pi W}{4}=-38$

$\frac{-8W-3\pi W}{4}=-38$

$\frac{-8W-3\pi W}{4}*4=-38*4$

$-8W-3\pi W=-152$

$8W+3\pi W=152$

$W(8+3\pi)=152$

$W=\frac{152}{8+3\pi}$

$W=8.723210$

$W\approx 8.72$

Upon substituting $W=8.723210$ in equation $L=38-(W+\frac{\pi }{2}W)$ , we will get:

$L=38-(8.723210+\frac{\pi }{2}8.723210)$

$L=38-(8.723210+\frac{8.723210\pi }{2})$

$L=38-(8.723210+\frac{27.40477245}{2})$

$L=38-(8.723210+13.70238622)$

$L=38-(22.42559622)$

$L=15.57440378$

$L\approx 15.57$

Therefore, the dimensions of the window that will maximize the area would be $W\approx 8.72$ and $L\approx 15.57$ .

8 0

3 years ago

What is the difference between domain and range?

alekssr [168]

Domain: all x values between the ends of a line on the x- axis

Range: all y values between the ends of a line on the y-axis

4 0

2 years ago

Given that D(x) = 2x, select all of the following that are true statements

Keith_Richards [23]

Answer:

D(x) is a function

D(x) is a direct variation

D(x) is a rule for the set of points (5.10). (6, 12) and (-2,-4)

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form $y/x=k$ or $y=kx$

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

In this problem

$D(x)=2x$

D(x) is a direct variation (linear function)

The variable x is the independent variable or input value

The variable D(x) is the dependent variable or output value

Verify each statement

case 1) D(x) is a function

The statement is true

see the explanation

case 2) x is the dependent variable

The statement is false

The variable x is the independent variable or input value

case 3) D(x) is a direct variation

The statement is true

see the explanation

case 4) D(x) is a rule for the set of points (5.10). (6, 12) and (-2,-4)

The statement is true

Because

For x=5

substitute in the linear equation

$D(x)=2(5)=10$ ---> is ok

For x=6

substitute in the linear equation

$D(x)=2(6)=12$ ---> is ok

For x=-2

substitute in the linear equation

$D(x)=2(-2)=-4$ ---> is ok

6 0

3 years ago

Wrens first display box is 6 inches long,9 inches wide,and 4 inches high.what is the volume of the display box

Virty [35]

To find the volume, multiply length x width x height.
So you multiply 6 x 9 x 4.

So the volume of the display box is 216 inches cubed.

3 0

3 years ago

Read 2 more answers