77. 003 x 3.789 ? All steps if you can please
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Answer:
The volume of the dilated prism is .
Step-by-step explanation:
The original prism has base area and a height of
.
The volume of the original prism is .
The prism is dilated by a scale factor of .
To find the volume of the dilated prism, we multiply the volume of the original prism by .
We are asked to find a range for x. Let's start by finding the maximum value. We know, by definition, that a side opposite a larger angle has a longer length. For example, if you think about a right triangle, the hypotenuse (the longest side) is always opposite of the right angle (the largest angle). We are given two side lengths: 23 is opposite of 42 degrees, and 21 is opposite of 3x + 15. Because 42 is opposite the longer side, 42 degrees is a larger angle than 3x + 15. We can set up the inequality and solve for x:
Now, let's look at the minimum value. We know that the angle definitely has to be larger than 0. So, we can set up that inequality and solve for x:
Now, we have our final range: -5 < x < 9