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.
Answer:
a) adjacent angles, complementary angles
b) vertical angles, congruent angles
c) supplementary angles, adjacent angles
d) supplementary angles, adjacent angles
Step-by-step explanation:
Adjacent angles are angles that share a common vertex, ( usually angles that are right next to each other )
Complementary angles are angles that form a 90 degree angle ( right angle )
Supplementary angles are angles that form a straight line
Vertical angles are angles that are vertically aligned with each other ( vertical angles are congruent )
Answer:-5
Step-by-step explanation:
You have your y and k because there + you can - and you get a -5
Answer:
Juan wins the race
Step-by-step explanation:
<em>The complete question is attached.</em>
<em />
Time is on the horizontal axis.
Distance is on the vertical axis.
If you look first at y-axis (vertical), you will see that both lines (curves) go upto a distance of 4 miles. So, the race is of 4 miles. Both of them finish.
Now,
If you look at the corresponding x-axis value of where each curve ends, you will see:
Antonio finishes at 15 mins
Juan finishes at 13 minutes
So we can successfully say that Juan wins the race since he finishes 2 mins faster than Antonio.
Juan wins the race
