Answer:
3x - (15 x 3) = 90
or
3x - 45 = 90
Explanation:
there are 3 boxes. We don't know how many are in them yet, so we write this as 3x. However, we know that we give away 15 to 3 different teachers. 15 x 3 = 45
Therefore the first part is 3x - 45
We also know that in the end we have 90 left.
So our final equation is:
3x - 45 = 90
Equation A find “m” and “b”:
“B” is the y-intercept when x = 0. They give this in the table as “-2” so b = -2
Find slope (m) = (-8)-(-2)/(-2)-0 = 3
Equation A is y = 3x - 2 (y = mx + b)
Equation B find “m” and “b”:
Find m = (-9)-(-5)/(-3)-(-1) = 2
To find be, plug in m, x, and y from ANY coordinates in table b into y = mx + b:
-9 = 2(-3) + b
-9 = -6 + b
b = -3
Equation b is y = 2x -3
Use substitution and substitute all of equation “b” for “y” in equation a:
2x - 3 = 3x - 2
Algebra: x = -1
Plug back into equation a:
y = 3(-1) -2
y = -5
x = -1
(-1, -5) final answer (B)
We have a right triangle with
a = one leg = 28
b = other leg = 21
c = hypotenuse = 5x
use the pythagorean theorem (a^2+b^2 = c^2) and solve for x
a^2+b^2 = c^2
28^2+21^2 = (5x)^2
784+441 = 25x^2
1225 = 25x^2
25x^2 = 1225
(25x^2)/25 = 1225/25
x^2 = 49
sqrt(x^2) = sqrt(49)
|x| = 7
x = 7 or x = -7
Since the hypotenuse has length 5x meters, this means
5x = 5*7 = 35
or
5x = 5(-7) = -35
Toss out the negative length as it makes no sense.
The only value of x is x = 7
Therefore the final answer is x = 7
1. The shaded region represents all of the coordinates that make the inequality true
2. B
