When shopping for accessories for her action camera, Giana found an advertisement for a replacement battery. The advertisement i
ncludes
the given graph of a function to represent the charge remaining in the battery after streaming x hours of video.
the given graph of a function to represent the charge remaining in the battery after streaming x hours of video.
2 answers:
Answer:
The correct options are;
The equation of the function is 2·y = -25·x + 200
The equation of the function is y = -25/2·x + 100
The x-intercept of the function is (8, 0)
Step-by-step explanation:
From the graph of the function, the y-intercept is observed at (0, 100), the x-intercept occurs at (8, 0)
Therefore, we have the slope, m given by the following relation
Where:
y₁ = 100
x₁ = 0
y₂ = 0
x₂ = 8
Which gives;
The equation in slope can be found as follows
y - 100 = -12.5×(x - 0)
y = -12.5·x + 100 = -25/2·x + 100
Multiplying by 2 gives;
2·y = -25·x + 200
25·x + 2·y = 200
Therefore, the correct options are;
The equation of the function is 2·y = -25·x + 200
The equation of the function is y = -25/2·x + 100
The x-intercept of the function is (8, 0).
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Answer:
Step-by-step explanation:
The standard form of a quadratic is
We will use the x and y values from each of our 3 points to find a, b, and c. Filling in the x and y values from each point:
First point (-5, 0):
and
0 = 25a - 5b + c
Second point (9, 0):
and
0 = 81a + 9b + c
Third point (8, -39):
and
-39 = 64a + 8b + c
Use the elimination method of solving systems on the first 2 equations to eliminate the c. Multiply the first equation by -1 to get:
-25a + 5b - c = 0
81a + 9b + c = 0
When the c's cancel out you're left with
56a + 14b = 0
Now use the second and third equations and elimination to get rid of the c's. Multiply the second equation by -1 to get:
-81a - 9b - c = 0
64a + 8b + c = -39
When the c's cancel out you're left with
-17a - 1b = -39
Between those 2 bolded equations, eliminate the b's. Do this by multiplying the second of the 2 by 14 to get:
56a + 14b = 0
-238a - 14b = -546
When the b's cancel out you're left with
-182a = -546 and
a = 3
Use this value of a to back substitute to find b:
56a + 14b = 0 so 56(3) + 14b = 0 gives you
168 + 14b = 0 and 14b = -168 so
b = -12
Now back sub in a and b to find c:
0 = 25a - 5b + c gives you
0 = 75+ 60 + c so
0 = 135 + c and
c = -135
Put that all together into the standard form equation to get