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4 years ago

Solve the system of equations and choose the correct ordered pair.

Mathematics

1 answer:

frez [133]4 years ago

3 0

What I would do:

5x + 10y = 35

Divide everything by 5.

x + 2y = 7

x = 7 - 2y

Now plug "x" into either one of the equations.

2(7-2y) + 5y = 15

14 - 4y + 5y = 15

14 + y = 15

y = 1

Now, solve for x by plugging in y into either one of the equations.

2x + 5y = 15

2x + 5 =15

2x = 10

x = 5

So x is 5 and y is 1.

Check by plugging in the values into the other equation.

5x + 10y = 35

5(5) + 10(1) = 35

25 + 10 = 35

35 = 35

The values are correct so, the answer for this problem is B (5, 1).

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From 10 pm to 6 am the temperature decreases an average of of a degree per hour how long in hours and minutes does it take to de

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4 years ago

A farmer wants to build a rectangular pen and then divide it with two interior fences. The total area inside of the pen will be

irina [24]

Answer:

Dimensions of the pen:

x = 11 ft

y = 6 ft

Step-by-step explanation:

Let call "x" and "y" dimensions of the rectangular pen and x > y, so the interior fences will be equal to y.

The exterior length is 2*x + 2*y and its cost is (2*x + 2*y ) *20.40

The interior fences are 2*y and its cost is 2*y* 17

Total cost C = (2*x + 2*y ) *20.40 + 2*y* 17 (1)

Now area inside the pen is 66 ft² and it is equal to:

A = x*y ⇒ 66 = x*y ⇒ y = 66/x

Plugging that value in equation (1) will give C as a function of x

C(x) = [ 2*x + 2* (66/x) ]* 20.40 + 2* (66/x) * 17

C(x) = ( 2*x + 132/x ) 20.40 + 2244/x

C(x) = 40,80*x + 2692.8/x + 2244/x

C(x) = 40.80*x + 4936,8/x

Taking derivatives on both sides of the equation we get

C´(x) = 40.80 - 4936,8/x²

C´(x) = 0 ⇒ 40.80 - 4936,8/x² = 0 ⇒ 40.80 *x² = 4936,8

x² = 4936,8 / 40.80 ⇒ x² = 121 ⇒ x √121

x = 11 ft

And y = 66/x ⇒ y = 66/11 ⇒ y = 6 ft

3 0

4 years ago

1.5x1.5 with a base of 2

nordsb [41]

Answer:

If you mean 1.5 * 1.5^2 then the answers 3.375

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. x

miskamm [114]

Answer:

$\frac{784}{15} \pi$

Step-by-step explanation:

According to the given situation, the calculation of volume of the solid is shown below:-

Here we will consider the curves that is

$x = 7y^2, x = 7$

Now, rotating the line for the line x which is equals to 7

$7y^2 = 7\\\\y^2 = 1\\\\ y = \pm1$

So, the inner radio is

7 - 7 = 0

and the outer radius is

$7y^2 - 7\\\\ = 7(y^2 - 1)$

Now, the area of cross section is

$A(y) = \pi(7(y^2 - 1))^2\\\\ = 49\pi(y^4 - 2y^2 + 1)$

The volume is

$V = \int\limits^1_{-1} A(y)dy$

now we will put the values into the above formula

$= \int\limits^1_{-1} 49\pi(y^4 - 2y^2 + 1)dy\\\\ = 49\pi(\frac{y^5}{5} - \frac{2y^3}{3} + y)^{-1}\\\\ = 49\pi(\frac{1}{5} - \frac{2}{3} + 1 + \frac{1}{5} - \frac{2}{3} + 1)\\\\ = 49\pi(2 + \frac{2}{5} - \frac{4}{3} )\\\\ = 49\pi(\frac{30+6-20}{15} )\\\\ = \frac{49\pi}{15} (16)$

After solving the above equation we will get

$= \frac{784}{15} \pi$

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