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3 years ago

13

A triangular prism is shown below. the base of the prism is a right triangle.

1 answer:

Nimfa-mama [501]3 years ago

6 0

The product is 60.

We start out with the information we have. This forms a right triangle, with one leg being 24, the other leg x, and the hypotenuse 30. Using the Pythagorean theorem we have

x²+24²=30²
x²+576=900

Subtract 576 from both sides:
x²+576-576 = 900-576
x²=324

Take the square root of each side:
√x²=√324
x=18

We know that the formula for the volume of a triangular prism is V=(1/2bh)H, where b is the base of the triangle, h is the height of the triangle, and H is the height of the prism. Substituting our known information we have:

720=(1/2*18*24)y
720=216y

Divide both sides by 216:
720/216 = 216y/216
3 1/3 = y

This means the product of x and y would be:
18(3 1/3)
18(10/3)
180/3
60

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36 divided by 4 show work

8_murik_8 [283]

36÷4. 4 goes into 36, 9 times. Do your check work, which would be 9x4=36√. Hope that helps!

6 0

3 years ago

Read 2 more answers

Tom determines the system of equations below has two solutions, one of which is located at the vertex of the parabola.

Rus_ich [418]

Answer:

b must equal 7 and a second solution to the system must be located at (2, 5).

Step-by-step explanation:

Rearranging the first equation:

y = (x - 3)^2 + 4

From this we see that the vertex is at the point (3,4).

So one solution of equation 2 is (3 ,4).

Substituting in equation 2:

4 = -3 + b

b = 7.

So equation 2 is y = - x + 7.

Now we check if (2, 5) is on this line:

5 = -2 + 7 = 5 , therefore (2, 5) is on this line.

Verifying if (2, 5) is also on y = (x - 3)^2 + 4:

5 = (2 - 3)^2 + 4 = 1 + 4 = 5

- so it is. and a second solution to the system is (2, 5).

5 0

2 years ago

Can someone put a website to help me understand this?

Alenkinab [10]

Answer:

67

Step-by-step explanation:

Since the diagonals in a rectangle are congruent, AC=BD and

7x+18=10x-3

We need to separate x -- to do that, we can first subtract 7x from both sides, resulting in

18=3x-3

Next, add 3 to both sides to get

21=3x

Divide both sides by 3 to get

x=7

Then, we just plug x into 10x-3 to get BD = 7*10-3 = 67

7 0

2 years ago

My math teacher just gave me a super hard question WILL GIVE CROWN!!!!

saveliy_v [14]

This one is super difficult, I see your struggle but the answer is A.

6 0

1 year ago

Read 2 more answers

The region bounded by y=(3x)^(1/2), y=3x-6, y=0

Ganezh [65]

Answer:

4.5 sq. units.

Step-by-step explanation:

The given curve is $y = (3x)^{\frac{1}{2} }$

⇒ $y^{2} = 3x$ ...... (1)

This curve passes through (0,0) point.

Now, the straight line is y = 3x - 6 ....... (2)

Now, solving (1) and (2) we get,

$y^{2} - y - 6 = 0$

⇒ (y - 3)(y + 2) = 0

⇒ y = 3 or y = -2

We will consider y = 3.

Now, y = 3x - 6 has zero at x = 2.

Therefor, the required are = $\int\limits^3_0 {(3x)^{\frac{1}{2} } } \, dx - \int\limits^3_2 {(3x - 6)} \, dx$

= $\sqrt{3} [{\frac{x^{\frac{3}{2} } }{\frac{3}{2} } }]^{3} _{0} - [\frac{3x^{2} }{2} - 6x ]^{3} _{2}$

= $[\frac{\sqrt{3}\times 2 \times 3^{\frac{3}{2} } }{3}] - [13.5 - 18 - 6 + 12]$

= 6 - 1.5

= 4.5 sq. units. (Answer)

7 0

2 years ago