Answer:
Step-by-step explanation:
we have the expression:
To factor this expression we need to indentify the components that are common in both terms.
At first glance there is nothing in common, but we can notice that 30 and 70 are multiples of 10, that is:
so we can substitute this into the expression:
and now that we have the common term (the number 10) we can factorize it, that is, take out the common term and include a parentheses:
The volume of a square pyramid is (1/3)(area of base)(height of pyramid).
Here the area of the base is (10 ft)^2 = 100 ft^2.
13 ft is the height of one of the triangular sides, but not the height of the pyramid. To find the latter, draw another triangle whose upper vertex is connected to the middle of one of the four equal sides of the base by a diagonal of length 13 ft. That "middle" is 5 units straight down from the upper vertex. Thus, you have a triangle with known hypotenuse (13 ft) and known opposite side 5 feet (half of 10 ft). What is the height of the pyramid?
To find this, use the Pyth. Thm.: (5 ft)^2 + y^2 = (13 ft)^2. y = 12 ft.
Then the vol. of the pyramid is (1/3)(area of base)(height of pyramid) =
(1/3)(100 ft^2)(12 ft) = 400 ft^3 (answer)
Answer:
{x | x ∈ R, x > 3}
Step-by-step explanation:
We are given the following inequality:
x - 5 > -2
In order to find the solution, we have to isolate the x on one side. This can be done by adding 5 to both sides of the inequality as shown below:
x - 5 + 5 > -2 + 5
x > 3
So the solution of the inequality is set of all numbers where x > 3. This is represented by 3rd option.
So, {x | x ∈ R, x > 3} is the answer.
6 because if you multiply 2/3 by 6 it will give 4
Answer:
Length is 15 inches
Width is 8 inches
Step-by-step explanation:
A = L*W
the Width = L-7
120 = L (L-7)
120 = L^2-7L
subtract 120 from each side
0 = L^2 - 7L - 120
(L-15) (L +8 )
so L = 15 inches
and W = 15-7 = 8 inches
check your answer: does 15*8 = 120? yes!
