What percent of 180 is 45

A rectangular prism has a base that is 4 m by 6 m and a height of 10 m. If all dimensions are doubled, what happens to the volum

nirvana33 [79]

When the dimensions of a rectangular prism will be doubled, its volume won't only be doubled but it will be 8 times as much.

The original volume of the rectangular prism is LxWxH.

V= LxWxH
V= (6m) (4m) (10m)
V= 240m³

If we double the dimensions, the volume would be

V= 2L x 2W x 2H
V= 2 x 6m x 2 x 4m x 2 x 10m
V= 2 x 2 x 2 x 6m x 4m x 10m
V= 2³ (6m x 4m x 10m)
V= 2³ x 240m³
V = 8 x 240m³
V= 1920 m³

The new volume now is 1,920 m³, which makes the rectangular prism larger than the original.

3 0

3 years ago

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If r(x)=3x-1 and s(x)=2x+1, which expression is equivalent to (r-s)(6)

daser333 [38]

Answer:

4

Step-by-step explanation:

Step 1: find (r- s) or r(x) - s(x)

r(x) - s(x) = 3x - 1 - (2x + 1)

r(x) - s(x) = 3x - 1 - 2x - 1 (distribute the -1 to 2x and 1)

r(x) - s(x) = x - 2 (combine like terms, 3x + (-2x) = x, -1 + (-1) = -2)

so r(x) - s(x) = x - 2, or (r - s)(x) = x - 2

Step 2: Plug in 6 to 'x' and find (r - s)(x)

(r - s)(6) = 6 - 2 = 4

5 0

2 years ago

Find the area of the shaded segment of the circle.

vredina [299]

Answer:

Around 5.5 square meters

Step-by-step explanation:

You can start by finding the area of the segment. Since the rest of the circle that is not in the segment is 240 degrees, the segment is 120 degrees or a third of the circle. You can therefore find the area of that segment with the formula $\frac{1}{3} \pi r^2 =3\pi$ square meters. Now, you need to find the area of the triangle inside the sector. This is more difficult than last time, because it is not a 90 degree angle. However, you can solve this by dividing this triangle into two 30-60-90 triangles, which you know how to find the ratio of sides for. In a 30-60-90 triangle, the hypotenuse is twice the length of the smallest leg, and the larger leg is $\sqrt{3}$ times larger than the smaller leg. In this case, these dimensions are a base of $\frac{3}{2}$ for the smaller leg and $\frac{3\sqrt{3}}{2}$ for the larger leg, or the base. Using the triangle area formula and multiplying by 2 (because remember, we divided the big triangle in half), you get $\frac{9\sqrt{3}}{4}$ square meters. Subtracting this from the area of the segment, you get about 5.5 square meters. Hope this helps!