Answer:
4
Step-by-step explanation:
Solve for p.
The numerator. difference has to be 4 times the answer of the denomiator.
So we can say
Solve for p
Now plug this in for the other formula.
So
In a rhombus, the sides are 14 inches long. two intersecting sides form a 60 degree angle. what are the exact lengths of the two
1 answer:
You might be interested in
Answer:
The length of the mat is 30 inches.
Step-by-step explanation:
Let H be the hypotenuse of the incline mat, L its length and h its height.
It is given that H = L + 4 and h = L - 14. Now, using Pythagoras' theorem for right-angled triangles, H² = L² + h²
(L + 4)² = L² + (L - 14)²
Expanding, we have
L² + 8L + 16 = L² + L² -28L + 196
collecting all the terms to the right side, we have
L² + L² -28L + 196 - L² - 8L - 16 = 0
L² - 36L + 180 = 0
Using the quadratic formula, L =
L
We use the larger answer L = 30 inches since L = 6 would give h = L -14 = 6 - 14 = -8 .
So, the length of the mat is 30 inches.
Answer:
Step-by-step explanation:
Inches per hour is the rate we are looking for here, which will then be the slope of the linear equation. Slope is the same thing as the rate of change. While this may not seem all that important right now, it's actually a HUGE concept in higher math, especially calculus!
If the pool is filling at a rate of 2 inches per every 4 hours, then by dividing, we get that the rate is 1 inch every 2 hours, which translates to a slope of 1/2. Creating an equation with this slope:
Let's check it. We are told that after 4 hours there are 2 inches of water in the pool. That means if we plug in 4 for t and solve for w, we should get w = 2:
and
w = 2. So we're good!