Ask question

Ask question

All categories

3 years ago

15

The rectangle below has an area of 70y^8+30y^6.The width of the rectangle is equal to the greatest common monomial factor of 70y

^8 and 30y^6. What is the length and width of the rectangle?

1 answer:

swat323 years ago

8 0

Answer:

Width $10y^6$ units

Length $7y^2+3$ units

Step-by-step explanation:

The rectangle has an area of $70y^8+30y^6.$

The width of the rectangle is equal to the greatest common monomial factor of $70y^8$ and $30y^6.$ Find this monomial factor:

$70y^8=2\cdot 5\cdot 7\cdot y^8\\ \\30y^6=2\cdot 3\cdot 5\cdot y^6\\ \\GCF(70y^8,30y^6)=2\cdot 5\cdot y^6=10y^6$

Hence, the width of the rectangle is $10y^6$ units.

The area of the rectangle can be rewritten as

$10y^6(7y^2+3).$

The area of the rectangle is the product of its width by its length, then the length of the rectangle is $7y^2+3$ units.

You might be interested in

For Triangle PQM, where M is the Right Angle and PQ is the Hypotenuse. You know side PM = 8, side PQ = 17, Side MQ = 15. Find An

Sergeeva-Olga [200]

Answer:

61.9°

Step-by-step explanation:

tan p = opposite/ adjacent

tan p = 15/8

$tan^{-1}$ (15/8)

4 0

3 years ago

The revenue function for a sporting goods company is given by R(x)=x⋅p(x) dollars where x is the number of units sold and p(x)=4

Zina [86]

The maximum revenue generated is $160000.

Given that, the revenue function for a sporting goods company is given by R(x) = x⋅p(x) dollars where x is the number of units sold and p(x) = 400−0.25x is the unit price. And we have to find the maximum revenue. Let's proceed to solve this question.

R(x) = x⋅p(x)

And, p(x) = 400−0.25x

Put the value of p(x) in R(x), we get

R(x) = x(400−0.25x)

R(x) = 400x - 0.25x²

This is the equation for a parabola. The maximum can be found at the vertex of the parabola using the formula:

x = -b/2a from the parabolic equation ax²+bx+c where a = -0.25, b = 400 for this case.

Now, calculating the value of x, we get

x = -(400)/2×-0.25

x = 400/0.5

x = 4000/5

x = 800

The value of x comes out to be 800. Now, we will be calculating the revenue at x = 800 and it will be the maximum one.

R(800) = 400x - 0.25x²

= 400×800 - 0.25(800)²

= 320000 - 160000

= 160000

Therefore, the maximum revenue generated is $160000.

Hence, $160000 is the required answer.

Learn more in depth about revenue function problems at brainly.com/question/25623677

#SPJ1

5 0

1 year ago

What is the perimeter of the triangle shown on the coordinate plane,to the nearest tenth of a unit ?

ollegr [7]

Answer:

25.6 units

Step-by-step explanation:

From the figure we can infer that our triangle has vertices A = (-5, 4), B = (1, 4), and C = (3, -4).

First thing we are doing is find the lengths of AB, BC, and AC using the distance formula:

$d=\sqrt{(x_2-x_1)^{2} +(y_2-y_1)^{2}}$

where

$(x_1,y_1)$ are the coordinates of the first point

$(x_2,y_2)$ are the coordinates of the second point

- For AB:

$d=\sqrt{[1-(-5)]^{2}+(4-4)^2}$

$d=\sqrt{(1+5)^{2}+(0)^2}$

$d=\sqrt{(6)^{2}}$

$d=6$

- For BC:

$d=\sqrt{(3-1)^{2} +(-4-4)^{2}}$

$d=\sqrt{(2)^{2} +(-8)^{2}}$

$d=\sqrt{4+64}$

$d=\sqrt{68}$

$d=8.24$

- For AC:

$d=\sqrt{[3-(-5)]^{2} +(-4-4)^{2}}$

$d=\sqrt{(3+5)^{2} +(-8)^{2}}$

$d=\sqrt{(8)^{2} +64}$

$d=\sqrt{64+64}$

$d=\sqrt{128}$

$d=11.31$

Next, now that we have our lengths, we can add them to find the perimeter of our triangle:

$p=AB+BC+AC$

$p=6+8.24+11.31$

$p=25.55$

$p=25.6$

We can conclude that the perimeter of the triangle shown in the figure is 25.6 units.

6 0

3 years ago

Is (0, 0) a solution to the equation y = x?

Mandarinka [93]

Answer:

yes

Step-by-step explanation:

if both y and x are 0 than it is true that they equal each other since 0=0

8 0

3 years ago

Brian completed 34 free throws and missed 16.

ELEN [110]

46, 16 is a little less than 1/2 of 34, so and 46 is a little less than 1/2 of 100.

4 0

3 years ago

Read 2 more answers