Your answer is L = 11 cm.
If the volumes of both shapes are the same, then we can set them equal to each other and solve for L to find the answer.
The volume of a rectangular prism is base × height × depth, which comes to 5 × 6 × L = 30L
The volume of the trapezoid prism (the shape on the left) would be the area of the trapezoid on the front, multiplied by the depth. This gives you:
× 6 × 10 = 5.5 × 6 × 10 = 330
So now we get:
330 = 30L
÷ 30
L = 11
I hope this helps!
<h3>Answers:</h3>
- Part A) Solution is (-3,-3)
- Part B) Two solutions are (0,0) and (2,2)
- Part C) Solution is x = -6
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Explanation:
Part A
Ignore the g(x) curve. We're looking for the intersection of the p(x) and f(x) curves. The two cross at (-3,-3) which is the solution to the system of these two equations. This point is on both p(x) and f(x) simultaneously. That means the coordinates of the point satisfy both p(x) and f(x) equations simultaneously.
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Part B
Pick any two points you want from the f(x) curve. You could pick the solution we mentioned, but I'll go for (0,0) and (2,2). When talking about a single curve, it has infinitely many solutions (as long as you pick a point on the curve).
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Part C
Ignore the f(x) curve. The graphs of p(x) and g(x) intersect when x = -6, which is the solution to the equation p(x) = g(x). We're only concerned about the x coordinate of the intersection.
Answer:
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
In the right triangle PQR
The sine of angle R is equal to divide the opposite side to angle R (PQ) by the hypotenuse (PR)
so
substitute the values
Find the measure of angle R
using a calculator
28% of 18.99 is 5.2172
Because 18.99 * 0.28 = 5.2172 which can be rounded to 5.22
So Gio would save about $5.22.
Plug in 3a for x,
2(3a)^2 is 18a^2, then add five
Answer: 18a^2 +5
