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3 years ago

Find the volume of the triangular prism to the right

Mathematics

1 answer:

tigry1 [53]3 years ago

3 0

Answer:

V = 567 ft³

Step-by-step explanation:

V = Bh

[note: a capital 'B' represents the area of the base]

The right triangle is the triangular prism's base.

Because the triangle's height (9 ft) and it's base are the same value (9 ft), we can solve to find the area.

We can identify the base easily because the base and the top of the prism are exactly the same shape

Area of triangular base:

A = $\frac{bh}{2}$

A = $\frac{1}{2}$ (9 ⋅ 9)

A = $\frac{1}{2}$ (81)

A = 40.5

We have 'B' for the triangular prism's formula, so next we need 'h'. 14 ft is provided as the prism's height, so we just need to multiply 40.5 and 14 for our answer.

Volume of triangular prism:

V = Bh

V = (40.5)(14)

V = 567 ft³

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A straight slide in a playground design makes an isosceles triangle with the

julia-pushkina [17]

Answer:

Option D.

Step-by-step explanation:

First, the you need ti understand that the triangle is an isosceles right angled triangle. In other words, the base and height are equal in length. The third side is the slide. This is the longest side.
Next, we know that the formula for calculating the area of a right angled triangle is given by:

A = 1/2 (base × perpendicular height)

The perpendicular height is equal to the base. Let's say the base is x. It means that the height is also x, since height = base.
Therefore, the formula will be:

A = 1/2 (x.x)

=1/2 (x²)

32 = 1/2 (x²)

Multiplying both sides by 2 gives:

32×2 = x²

64 = x²

8 = x

To find the third side, we use the Pythagoras theorem:

C² = A² + B²

= 8² + 8²

= 128

C = √128

= 8√2

However, the answer will not be exact, so we multiply the length of the base and height by 2. This gives x = 16 (Length of base = length of height)

Repeating the steps above gives C = √ (16)² + (16)²

= √256

This corresponds to option D.

3 0

3 years ago

Solve the quadratic equation for x. What is one of the roots? (x − 5)2 = 9

Sonja [21]

Answer:

x=8, x=2

Step-by-step explanation:

(x-5)^2=9 Solve by completing the square

Find square root of both sides

|x-5|=3

x=8, x=2

7 0

3 years ago

Read 2 more answers

Find the point estimate for the true difference between the given population means. Round your answer to three decimal places.

uranmaximum [27]

Answer:

Point Estimate for different between population means = - 0.99

Step-by-step explanation:

We are given data of two samples and we have to find the best point estimate of the true difference between two population means. Remember that in absence of data about population the best estimator is the sample data. So, we will find the means of both sample data and find the difference of that means. This difference between the means of sample data will be the best point estimate for the true difference between the population means.

Formula to calculate the mean is:

$Mean=\frac{\text{Sum of Values}}{\text{Number of Values}}$