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3 years ago

The boys wrestling team scored a total of 36 points. Pins are worth 6 points. Major

Mathematics

1 answer:

shtirl [24]3 years ago

5 0

Answer:

6p + 4d = 36

Step-by-step explanation:

If p = number of pins and d = number of major decisions, then the equation is 6p + 4d = 36.

Hope this helps!

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The equation for a circle is (x-2)2+(y+3)2=9, what is the center of the circle?

ki77a [65]

Answer:

(2, -3)

Step-by-step explanation:

Compare the given (x-2)2+(y+3)2=9 to the standard equation

(x - h)^2 + (y - k)^2 = r^2.

It becomes obvious that h = 2, k = -3 and r = 3.

The center of this circle is (h, k): (2, -3).

4 0

3 years ago

Find the volume of the region between the planes x plus y plus 2 z equals 2 and 4 x plus 4 y plus z equals 8 in the first octant

Alex787 [66]

Find the intercepts for both planes.

Plane 1, x + y + 2z = 2:

$y=z=0\implies x=2\implies (2,0,0)$

$x=z=0\implies y=2\implies(0,2,0)$

$x=y=0\implies 2z=2\implies z=1\implies(0,0,1)$

Plane 2, 4x + 4y + z = 8:

$y=z=0\implies4x=8\implies x=2\implies(2,0,0)$

$x=z=0\implies4y=8\impliesy=2\implies(0,2,0)$

$x=y=0\implies z=8\implies(0,0,8)$

Both planes share the same x- and y-intercepts, but the second plane's z-intercept is higher, so Plane 2 acts as the roof of the bounded region.

Meanwhile, in the (x, y)-plane where z = 0, we see the bounded region projects down to the triangle in the first quadrant with legs x = 0, y = 0, and x + y = 2, or y = 2 - x.

So the volume of the region is

$\displaystyle\int_0^2\int_0^{2-x}\int_{\frac{2-x-y}2}^{8-4x-4y}\mathrm dz\,\mathrm dy\,\mathrm dx=\displaystyle\int_0^2\int_0^{2-x}\left(8-4x-4y-\frac{2-x-y}2\right)\,\mathrm dy\,\mathrm dx$

$=\displaystyle\int_0^2\int_0^{2-x}\left(7-\frac72(x+y)\right)\,\mathrm dy\,\mathrm dx=\int_0^2\left(7(2-x)-\frac72x(2-x)-\frac74(2-x)^2\right)\,\mathrm dx$

$=\displaystyle\int_0^2\left(7-7x+\frac74 x^2\right)\,\mathrm dx=\boxed{\frac{14}3}$

3 0

2 years ago

What does the greater than and less than signs look like

sdas [7]

This: >(Greater than) and <(less than)

6 0

3 years ago

Read 2 more answers

A set of cards has 8 red cards, 6 blue cards, and 1 green card. Paula chooses a card without looking. What is the probability th

3241004551 [841]

Answer:

8/15 = 0.53 = 53%

Step-by-step explanation:

The probability is the number of chances divided by the total number of cards. The total number of cards is 8 + 6 +1 = 15. There are 8 red cards and therefore 8 chances to get red.

8 out of 15 cards is 8/15. The probability is 8/15.

5 0

3 years ago

An angle measures 64.8° less than the measure of its complementary angle. What is the measure of each angle?

kirill115 [55]

Answer:

77.4 degrees and 12.6 degrees

Step-by-step explanation:

Let the angles be x and x - 64.8.

Therefore, on the basis of knowledge that complementary angles add up to 90 degrees :

x + x - 64.8 = 90

2x = 154.8

x = 77.4 degrees

x - 64.8 = 77.4 - 64.8 = 12.6 degrees

5 0

2 years ago