Amy jogs 1/3 of a mile in 1/15 of an hour, while john takes 1/30 of an hour to jog 1/5 of a mile. If they continue at this rate,
1 answer:
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Answer: (a) y = -3x + 10
<u>Step-by-step explanation:</u>
The slope of line CD is perpendicular to line OB, which means they have opposite and reciprocal slopes.
Step 1: Find the slope of OB using the formula:
(x₁, y₁) = (0, 0) and (x₂, y₂) = (3, 1)
Step 2: Find the slope of CD (opposite and reciprocal of OB)
Step 3: Input the perpendicular slope and the slope into the Point-Slope formula: y - y₁ = m(x - x₁)
(x₁, y₁) = (3, 1) because it is the point the line will pass through
y - 1 = -3(x - 3)
y - 1 = -3x + 9 <em>distributed -3 into (x - 3)</em>
y = -3x + 10 <em>added 1 to both sides</em>
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The x-intercept of DQ is the same x-intercept as CD. The x-intercept is when y = 0
y = -3x + 10
0 = -3x + 10
-10 = -3x subtracted 10 from both sides
<em>divided both sides by -3</em>
Answer:
a. 2^(x-2) = g^(-1)(x)
b. A, B, D
Step-by-step explanation:
the phrasing attached in the image is flagged as inappropriate, so i will be replacing it with g(x) and its inverse with g^(-1)(x)
1. replace g(x) with y and solve for x
y = log₂(x) + 2
subtract 2 from both sides to isolate the x and its log
y - 2 = log₂(x)
this text is replaced by the second image -- it was marked as inappropriate
thus, 2^(y-2) = x
replace x with g^(-1)(x) and y with x
2^(x-2) = g^(-1)(x)
2. plug this in to points A, B, C, D, E, and F
A: (2,1)
plug 2 in for x
2^(2-2) = 2⁰ = 1 so this works
B: (4, 4)
2^(4-2) = 2²= 4 so this works
C: (9, 3)
2^(9-2) = 2⁷ = 128 ≠ 3 so this doesn't work
(5, 8)
2^(5-2) = 2³ = 8 so this works
E: (3, 5)
2^(3-2) = 2¹ = 2 ≠ 5 so this doesn't work
F: (8, 5)
2^(8-2) = 2⁶ = 64 ≠ 5 so this doesn't work
