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.
In a four-digit number, the first digit cannot be 0, so there are only 4 even numbers available. For the second, third, and fourth digits, there are 5 available numbers. Thus, the number of 4-digit numbers containing only even digits is 4 x 5 x 5 x 5 = 500 numbers.
Answer:
8
Step-by-step explanation:
Answer:
- 15
Step-by-step explanation:
Given f(x) divided by (x + h) then the remainder is the value of f(- h)
Here
f(x) = 3x³ - 5x² - 47x + k ← k is the constant term , then
f(- 3) = 3(- 3)³ - 5(- 3)² - 47(- 3) + k = 0 , that is
3(- 27) - 5(9) + 141 + k = 0
- 81 - 45 + 141 + k = 0
15 + k = 0 ( subtract 15 from both sides )
k = - 15
Answer:
Step-by-step explanation:
