<span>Simplifying
0x + 7 + 5x = 2x + 30 + 40
Anything times zero is zero.
0x + 7 + 5x = 2x + 30 + 40
Combine like terms: 0 + 7 = 7
7 + 5x = 2x + 30 + 40
Reorder the terms:
7 + 5x = 30 + 40 + 2x
Combine like terms: 30 + 40 = 70
7 + 5x = 70 + 2x
Solving
7 + 5x = 70 + 2x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-2x' to each side of the equation.
7 + 5x + -2x = 70 + 2x + -2x
Combine like terms: 5x + -2x = 3x
7 + 3x = 70 + 2x + -2x
Combine like terms: 2x + -2x = 0
7 + 3x = 70 + 0
7 + 3x = 70
Add '-7' to each side of the equation.
7 + -7 + 3x = 70 + -7
Combine like terms: 7 + -7 = 0
0 + 3x = 70 + -7
3x = 70 + -7
Combine like terms: 70 + -7 = 63
3x = 63
Divide each side by '3'.
x = 21
Simplifying
x = 21</span>
Answer:
3
Step-by-step explanation:
Answer:
-2
Step-by-step explanation:
In a linear regression model we have the equation 
that relates 
and 
, where 
is the estimator of the slope and 
is the estimator of the Y-intercept. The coefficients and can be estimated with the equations:
. Thus,
1.
8 > 1 so: a(x) = -4x + 7
a(8) = - 4(8) + 7 = - 32 + 7 = - 25
2.
-6 ≤ 1 ≤ 1 so: a(x) = 2x - x²
a(1) = 2(1) - (1)² = 2 - 1 = 1
3.
-7 ≤ -6 so: a(x) = |x - 8|
a(-7) = |-7 - 8| = |-15| = 15
4.
-6 ≤ -3 ≤ 1 so: a(x) = 2x - x²
a(-3) = 2(-3) - (-3)² = -6 - 9 = - 15
5.
-6 ≤ -¹/₂ ≤ 1 so: a(x) = 2x - x²
a(-¹/₂) = 2(-¹/₂) - (-¹/₂)² = - 1 - ¹/₄ = - 1¹/₄
6.
⁹/₄ > 1 so: a(x) = -4x + 7
a(⁹/₄) = - 4(⁹/₄) + 7 = - 9 + 7 = - 2
