Answer:
b=-7
Step-by-step explanation:
Simplifying
99 = 2(-7b + -3) + 7
Reorder the terms:
99 = 2(-3 + -7b) + 7
99 = (-3 * 2 + -7b * 2) + 7
99 = (-6 + -14b) + 7
Reorder the terms:
99 = -6 + 7 + -14b
Combine like terms: -6 + 7 = 1
99 = 1 + -14b
Solving
99 = 1 + -14b
Solving for variable 'b'.
Move all terms containing b to the left, all other terms to the right.
Add '14b' to each side of the equation.
99 + 14b = 1 + -14b + 14b
Combine like terms: -14b + 14b = 0
99 + 14b = 1 + 0
99 + 14b = 1
Add '-99' to each side of the equation.
99 + -99 + 14b = 1 + -99
Combine like terms: 99 + -99 = 0
0 + 14b = 1 + -99
14b = 1 + -99
Combine like terms: 1 + -99 = -98
14b = -98
Divide each side by '14'.
b = -7
Simplifying
b = -7
Answer:
Step-by-step explanation:
The opposite side (the one not connected to A) = 4
The hypotenuse is 5
The adjacent side needs to be found for the cosine and the tangent.
a^2 + b^2 = c^2
a = opposite side = 4
b = adjacent side = ?
c = hypotenuse = 5
4^2 + x^2 = 5^2
16 + x^2 = 25
x^2 = 25 - 16
x^2 = 9
x = sqrt(9)
x = 3
cos(A) = adjacent / hypotenuse = 3/5
Tan(A) = opposite / adjacent = 4/3
cos(A) + tan(A) = 3/5 + 4/3
cos(A) + tan(A) = 9/15 + 20/15 = 29/15
Answer:
Volume = 144 ft
Step-by-step explanation:
1. Let's write some things down, so we don't forget them!
Length = 12 ft
Height = 2 ft
Width = 6 ft
2. We can probably assume the sandbox is a rectangle. The formula for the volume of a rectangle is Length x Height x Width. So, 12 x 2 x 6 = 144, therefore that's the volume!
The answer to 4x - 5y = 24 is (6, 0).
notice that, if Q is the midpoint of PR, that simply means that PQ = QR = 43.
![\bf \boxed{P}\underset{\leftarrow 9x-31 \to }{\stackrel{\stackrel{\downarrow }{43}}{\rule[0.35em]{10em}{0.25pt}}Q\stackrel{43}{\rule[0.35em]{10em}{0.25pt}}}\boxed{R} \\\\\\ 9x-31=43+43\implies 9x-31=86\implies 9x=117 \\\\\\ x=\cfrac{117}{9}\implies x=13](https://tex.z-dn.net/?f=%5Cbf%20%5Cboxed%7BP%7D%5Cunderset%7B%5Cleftarrow%209x-31%20%5Cto%20%7D%7B%5Cstackrel%7B%5Cstackrel%7B%5Cdownarrow%20%7D%7B43%7D%7D%7B%5Crule%5B0.35em%5D%7B10em%7D%7B0.25pt%7D%7DQ%5Cstackrel%7B43%7D%7B%5Crule%5B0.35em%5D%7B10em%7D%7B0.25pt%7D%7D%7D%5Cboxed%7BR%7D%0A%5C%5C%5C%5C%5C%5C%0A9x-31%3D43%2B43%5Cimplies%209x-31%3D86%5Cimplies%209x%3D117%0A%5C%5C%5C%5C%5C%5C%0Ax%3D%5Ccfrac%7B117%7D%7B9%7D%5Cimplies%20x%3D13)
