The correct answer is C because when using distributive property it simplifies back to 5b+30
Math. When no number occurs more than once in a data set, there is no mode. If each of two numbers occurs twice, we say the set is bimodal.
a). No. Variation in 'y' has no effect on 'x'.
b). No. Variation in 'x' has exactly the opposite effect on 'y'.
c). Yes. Variation in 'x' causes 'y' to vary 6 times as much in the same direction.
d). No. Doubling 'x' does not double 'y'.
The answer is 8 ft.
The base area of rectangular prism is: A = l * w = 56 ft²
<span>The length of the base is longer than the width: l > w
The volume of the prism is: V = l * w * h = 840 ft</span>³
<span>The sum of the length and width of the base is equal to the height of the pyramid: l + w = h
So:
</span>l * w = 56
l * w * h = 840
___
56 * h = 840
h = 840 / 56
h = 15 ft
Now, we know that
l + w = 15 ⇒ w = 15 - l
l * w = 56
___
l * (15 - l) = 56
15l - l² = 56
0 = l² - 15l + 56
Or: l² - 15l + 56 = 0
Let's solve the quadratic function:
l = (-b +/-√(b² - 4ac)/(2a)
= (15 +/-√(-15)² - 4 * 1 * 56))/(2*1)
= (15 +/- √(225 - 224))/2
= (15 +/- √1)/2
= (15 +/-1)/2
l = (15+1)/2 = 16/2 = 8
or
l = (15-1)/2 = 14/2 = 7
If l = 8, then w = 15 - 8 = 7. So, l > w
If l = 7, then w = 15 - 7 = 8. So, l < w
Therefore, l = 8 ft.
