Answer:
y = 12
x = 10/3
Step-by-step explanation:
y = -3.6x + 12
From this equation, which is in slope intercept form (y = mx+b), we already know that b represents the y-intercept, so that means the y-intercept is 12.
To find the x-intercept, we need to make y equal 0 to find x. So:
0 = -3.6x + 12
-3.6x = -12
x = 3.33333 --> 3 1/3
x = 10/3
Answer:
x³ - 10x² + 31x - 30
Step-by-step explanation:
Given
(x - 2)(x - 3)(x - 5) ← expand the second pair of factors using FOIL
= (x - 2)(x² - 8x + 15) ← distribute
= x³ - 8x² + 15x - 2x² + 16x - 30 ← collect like terms
= x³ - 10x² + 31x - 30
Answer:
(1, 5)
Step-by-step explanation:
The solution to the system of equations is the point of intersection of the two lines. From inspection of the graph, the point of intersection is at (1, 5).
<u>Proof</u>
The solution to a system of equations is the point at which the two lines meet.
⇒ g(x) = f(x)
⇒ 3x + 2 = |x - 4| + 2
⇒ 3x = |x - 4|
⇒ 3x = x - 4 and 3x = -(x - 4)
⇒ 3x = x - 4
⇒ 2x = -4
⇒ x = -2
Inputting x = -2 into the 2 equations:
⇒ g(-2) = 3 · -2 + 2 = -4
⇒ f(-2) = |-2 - 4| + 2 = 8
Therefore, as the y-values are different, x = -2 is NOT a solution
⇒ 3x = -(x - 4)
⇒ 3x = 4 - x
⇒ 4x = 4
⇒ x = 1
Inputting x = 1 into the 2 equations:
⇒ g(1) = 3 · 1 + 2 = 5
⇒ f(1) = |1 - 4| + 2 = 5
Therefore, as the y-values are the same, x = 1 IS a solution
and the solution is (1, 5)
Answer:
44
Step-by-step explanation:
if she had 10 left at the end and you add the other half from lunch which is 12, then that gives you 22. Since before lunch she had half (22), all you gotta do is add the other half which is 22. 22+22=44 and that's your answer.
Answer:
w = 12
Step-by-step explanation:
3w = 11 + 25
3w = 36
w = 12
Hope that helps!
