Answer:
Step-by-step explanation:
In this problem, we are substituting for x.
Let us take a look at our given answers.
x = -13 and x = -3 would not work because the numbers would not add up to -5. Since we have the positive brackets (or whatever you call them.) surrounding the x variable, that means that all numbers that are plugged into x will be positive.
-13 will be turned into 13,
13 - 8 -5
So that is wrong.
x = 3 and x = 3 would work because plugging it in, all outcomes from the two numbers would be negative.
3 - 8 = -5
- 8 = -5
True.
The third one won't work because of the same reasons as the first one.
Then, the last one would not work well because, there is a solution.
Answer:
y =
Step-by-step explanation:
Given that y varies inversely with x then the equation relating them is
y = ← k is the constant of variation
To find k use the condition y = when x =
, thus
=
= 2k ( divide both sides by 2 )
k =
y = ← equation of variation
When x = , then
y = =
=
well, about A and D, I just plugged the values on the slope formula of
for A the values are 8.01 and 8.0, so indeed those "slopes" are close.
for D the values are -2.25 and 8.0, so no dice on that one.
for B, let's check the y-intercept for g(x), by setting x = 0, we end up g(0) = 0³-4(0)+1, which gives us g(0) = 1.
checking L(x) y-intercept, well, L(x) is in slope-intercept form, thus the +1 sticking out on the far right is the y-intercept, so, dice.
for C, well, the slope if L(x) is 8, since it's in slope-intercept form, the derivative of g(x) is g'(x) = 3x² - 4, and thus g'(0) = -4, so no dice.
for E, do they intercept at (2,1)? well, come on now, L(x) is a tangent line to g(x), so that's a must for a tangent.
for F, we know the slope of the line L(x) is 8, is g'(2) = 8? let's check
recall that g'(x) = 3x² - 4, so g'(2) = 3(2)² - 4, meaning g'(2) = 8, so, dice.