Answer:
She needs 50 ft² of wood to cover the table
Step-by-step explanation:
You need to know the formula for area of a trapezoid, which is
A = (B1 + B2)h/s (add the bases together, multiply by the height, then divide
by 2)
We are given B1 = 12, B2 = 8, and h = 5, so plug them in and simplify
A = (12 + 8)(5)/2
A = (20)(5)/2
A = 100/2
A = 50 ft²
25 = 5*5 and 9 = 3*3, which we can exploit to write
so that this expression is actually a difference of squares. We can factorize this to get
and given that 
, we divide both sides by this to get
Answer:
4
Step-by-step explanation:
<h3><u>some relevant limit laws</u></h3>
lim C = C where c is a constant.
lim( f(x) + g(x)) =lim f(x) + lim g(x)
lim( f(x)g(x)) =lim f(x) * lim g(x)
lim( cg(x)) =clim g(x)
lim( f(x)/g(x)) =lim f(x) / lim g(x) if lim g(x) is not equal to zero.
lim( f(x))^2 = (lim f(x) )^2
lim square root( f(x)) = square root(lim f(x) )
![\lim_{n \to 3} g(x) = 9\\\\\lim_{n \to 3} f(x) = 6\\\\ \lim_{n \to 3} \sqrt[3]{f(x)g(x) + 10} \\\\ = \lim_{n \to 3} \sqrt[3]{f(x)g(x) + 10}\\\\= \sqrt[3]{lim_{n \to 3}f(x) \times lim_{n \to 3}g(x) + 10}\\\\= \sqrt[3]{6 \times 9 + 10}\\\\= \sqrt[3]{64}](https://tex.z-dn.net/?f=%5Clim_%7Bn%20%5Cto%203%7D%20g%28x%29%20%20%3D%209%5C%5C%5C%5C%5Clim_%7Bn%20%5Cto%203%7D%20f%28x%29%20%20%3D%206%5C%5C%5C%5C%20%5Clim_%7Bn%20%5Cto%203%7D%20%5Csqrt%5B3%5D%7Bf%28x%29g%28x%29%20%2B%2010%7D%20%5C%5C%5C%5C%20%3D%20%5Clim_%7Bn%20%5Cto%203%7D%20%5Csqrt%5B3%5D%7Bf%28x%29g%28x%29%20%2B%2010%7D%5C%5C%5C%5C%3D%20%5Csqrt%5B3%5D%7Blim_%7Bn%20%5Cto%203%7Df%28x%29%20%5Ctimes%20lim_%7Bn%20%5Cto%203%7Dg%28x%29%20%2B%2010%7D%5C%5C%5C%5C%3D%20%5Csqrt%5B3%5D%7B6%20%5Ctimes%209%20%2B%2010%7D%5C%5C%5C%5C%3D%20%5Csqrt%5B3%5D%7B64%7D)
= 4
Problem 7 is choice B, which is the entire number line shaded in but the value -4 has a hole at this location to mean "exclude this point from the solution set". So basically x can be any number but -4.
Problem 8 is choice C. You have a closed circle (or filled in hole) at -1.5 on the number line. Then you shade to the left of the closed circle to indicate the set of values that are smaller than this endpoint. So n can be -1.5 or it can be smaller than -1.5 (something like -2 or -3, etc).
