Answer:
5 hours
Step-by-step explanation:
31-11 = 20
20/4 = 5
Answer:
O It has the same slope and a different y-intercept.
Step-by-step explanation:
y = mx + b
m = 3/8
b = 12
y = (3/8)x + 12
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Data in the table: slope is the rise (y) over the run (x) between two points (assuming the data represent a linear line).
Change in x and y between two points. I'll choose (-2/3,-3/4) and (1/3,-3/8).
Change in y: (-3/8 - (-3/4)) = (-3/8 - (-6/8)) = 3/8
Change in x: (1/3 - (-2/3)) = (1/3+2/3) = 3/3 = 1
Slope = (Change in y)/(Change in x) = (3/8)/1 = 3/8
The slope of the equation is the same as the data in the table.
Now let's determine if the y-intercept is also the same (12). The equation for the data table is y = (2/3)x + b, and we want to find b. Enter any of the data points for x and y and then solve for b. I'll use (-2/3, -3/4)
y = (3/8)x + b
Use (-2/3, -3/4)
-3/4 =- (3/8)(-2/3) + b
-3/4 = (-6/24) + b
b = -(3/4) + (6/24)
b = -(9/12) + (3/12)
b = -(6/12)
b = -(1/2)
The equation of the line formed by the data table is y = (3/8)x -(1/2)
Therefore, It has the same slope and a different y-intercept.
Answer:
C x=6
Step-by-step explanation:
4x-5=19
+5 on both sides
4x=24
divide both sides by 4
x=6
Step-by-step explanation:
How to simplify
-6x (some sign, it didn't show in the question)30
Divide by -6 on both sides to isolate the variable.
30 divided by -6 is -5, so x=-5.
Answer:
Step-by-step explanation:
We are given the function:
And we want to determine:
Substitute:
![\displaystyle \begin{aligned}g(x + a) - g(x) &=\left[5(x+a)^2 + 2(x+a)\right] -\left[5x^2+2x\right] \end{aligned}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cbegin%7Baligned%7Dg%28x%20%2B%20a%29%20-%20g%28x%29%20%26%3D%5Cleft%5B5%28x%2Ba%29%5E2%20%2B%202%28x%2Ba%29%5Cright%5D%20-%5Cleft%5B5x%5E2%2B2x%5Cright%5D%20%20%20%20%5Cend%7Baligned%7D)
And simplify:
![\displaystyle \begin{aligned}g(x + a) - g(x) &=\left[5(x+a)^2 + 2(x+a)\right] -\left[5x^2+2x\right] \\ \\ &= \left(5(x^2 + 2ax + a^2) + (2x + 2a) \right) + \left(-5x^2 - 2x\right) \\ \\ &= \left((5x^2 + 10ax + 5a^2) + (2x + 2a)\right) + \left(-5x^2 - 2x\right) \\ \\ &= (5x^2-5x^2) + (10ax + 2x - 2x) + (5a^2+2a) \\ \\ &= 10ax + 5a^2 + 2a \end{aligned}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cbegin%7Baligned%7Dg%28x%20%2B%20a%29%20-%20g%28x%29%20%26%3D%5Cleft%5B5%28x%2Ba%29%5E2%20%2B%202%28x%2Ba%29%5Cright%5D%20-%5Cleft%5B5x%5E2%2B2x%5Cright%5D%20%5C%5C%20%20%5C%5C%20%26%3D%20%5Cleft%285%28x%5E2%20%2B%202ax%20%2B%20a%5E2%29%20%2B%20%282x%20%2B%202a%29%20%5Cright%29%20%2B%20%5Cleft%28-5x%5E2%20-%202x%5Cright%29%20%5C%5C%20%5C%5C%20%26%3D%20%5Cleft%28%285x%5E2%20%2B%2010ax%20%2B%205a%5E2%29%20%2B%20%282x%20%2B%202a%29%5Cright%29%20%2B%20%5Cleft%28-5x%5E2%20-%202x%5Cright%29%20%5C%5C%20%5C%5C%20%26%3D%20%285x%5E2-5x%5E2%29%20%2B%20%2810ax%20%2B%202x%20-%202x%29%20%2B%20%285a%5E2%2B2a%29%20%20%20%20%20%5C%5C%20%5C%5C%20%26%3D%2010ax%20%2B%205a%5E2%20%2B%202a%20%5Cend%7Baligned%7D)
In conclusion:
