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Alexeev081 [22]

1 year ago

8

You are planning a skating party at a rink that charges a basic fee of $6.00 and $6.50 per person for catered parties. You don’t

want to spend more than $71.00. Write and solve an inequality to find the number of friends you can invite

1 answer:

Alekssandra [29.7K]1 year ago

4 0

Answer:

y = 6.50x + 6 or 71 = 6.50x + 6

10 people are the max you can invite

Step-by-step explanation:

We have the simple equation

y = 6.50x + 6

6.50x because it it per person

6 because it is a flat one time charge

We want the max to be 71 so that will be our y

71 = 6.50x + 6

We are now going to solve for x

65 = 6.5x

x = 10

Hope it helps! (:

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The yard behind the Cindy's house is rectangular in shape and has a perimeter of 72 feet. If the length l of the yard is 18 feet

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Let the width of the yard be w.
Since the length is 18feet longer, l = w + 18

Perimeter for rectangle = 2(l + w)

2(l + w) = 72

2(w+18 + w) = 72    Divide 2 on both sides

   (w + 18 + w) = 36

   2w + 18 = 36

   2w = 36 - 18

2w = 18 Divide 2 on both sides

w = 18/2

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Recall, length l = w + 18, l = 9 + 18 = 27

Hence width, w = 9, length,l = 27

Area of rectangle = l × w = 27 × 9 = 243

Area of rectangular yard = 243 square feet.

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2 years ago

3 lines are shown. A line with points T, R, W intersects with a line with points S, R, V at point R. Another line extends from p

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Answer:

The vertical angles are ∠ WRS and ∠ VRT ⇒ 2nd answer

Step-by-step explanation:

* <em>Lets explain the meaning of the vertical angles</em>

- Vertical angles are the angles opposite to each other when two lines

are intersected

- The vertical angle are equal in measures

- <em>Look to attached figure which represents the lines </em>

∵ Line TW intersects line SV at R

∴ ∠ WRV and ∠ SRT are vertical angle

∴ <u><em>∠ WRS and ∠ VRT</em></u> are vertical angle

∵ RU is between the rays of angle VRW

∴ RU intersects the lines TW and SV at R

∴ No vertical angles between RU and the other two lines because

it intersects them its endpoint R

* <em>Now lets look to the answer to chose the right one</em>

- ∠ WRU and ∠ SRT are not vertical angles

- <em><u>∠ WRS and ∠ VRT are vertical angles </u></em>

- ∠ VRU and ∠ TRS are not vertical angles

- ∠ VRT and ∠ SRT are not vertical angles

4 0

2 years ago

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Find the mass and center of mass of the lamina that occupies the region D and has the given density function rho. D = {(x, y) |

Bas_tet [7]

Answer:

$M=168k$

$(\bar{x},\bar{y})=(5,\frac{85}{28})$

Step-by-step explanation:

Let's begin with the mass definition in terms of density.

$M=\int\int \rho dA$

Now, we know the limits of the integrals of x and y, and also know that ρ = ky², so we will have:

$M=\int^{9}_{1}\int^{4}_{1}ky^{2} dydx$

Let's solve this integral:

$M=k\int^{9}_{1}\frac{y^{3}}{3}|^{4}_{1}dx$

$M=k\int^{9}_{1}\frac{y^{3}}{3}|^{4}_{1}dx$

$M=k\int^{9}_{1}21dx$

$M=21k\int^{9}_{1}dx=21k*x|^{9}_{1}$

So the mass will be:

$M=21k*8=168k$

Now we need to find the x-coordinate of the center of mass.

$\bar{x}=\frac{1}{M}\int\int x*\rho dydx$

$\bar{x}=\frac{1}{M}\int^{9}_{1}\int^{4}_{1}x*ky^{2} dydx$

$\bar{x}=\frac{k}{168k}\int^{9}_{1}\int^{4}_{1}x*y^{2} dydx$

$\bar{x}=\frac{1}{168}\int^{9}_{1}x*\frac{y^{3}}{3}|^{4}_{1}dx$

$\bar{x}=\frac{1}{168}\int^{9}_{1}x*21 dx$

$\bar{x}=\frac{21}{168}\frac{x^{2}}{2}|^{9}_{1}$

$\bar{x}=\frac{21}{168}*40=5$

Now we need to find the y-coordinate of the center of mass.

$\bar{y}=\frac{1}{M}\int\int y*\rho dydx$

$\bar{y}=\frac{1}{M}\int^{9}_{1}\int^{4}_{1}y*ky^{2} dydx$

$\bar{y}=\frac{k}{168k}\int^{9}_{1}\int^{4}_{1}y^{3} dydx$

$\bar{y}=\frac{1}{168}\int^{9}_{1}\frac{y^{4}}{4}|^{4}_{1}dx$

$\bar{y}=\frac{1}{168}\int^{9}_{1}\frac{255}{4}dx$

$\bar{y}=\frac{255}{672}\int^{9}_{1}dx$

$\bar{y}=\frac{255}{672}8=\frac{2040}{672}$

$\bar{y}=\frac{85}{28}$

Therefore the center of mass is:

$(\bar{x},\bar{y})=(5,\frac{85}{28})$

I hope it helps you!

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Ronch [10]

From the table, the speed of Corinne is given by

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From the graph, the speed of Aretha is given by

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2 years ago

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