Answer:
You could just replace all the given possible values of k in the inequality and see which ones are solutions, but let's solve this in a more interesting way:
First, remember how the absolute value works:
IxI = x if x ≥ 0
IxI = -x if x ≤ 0
Then if we have something like:
IxI < B
We can rewrite this as
-B < x < B
Now let's answer the question, here we have the inequality:
I-k -2I < 18
Then we can rewrite this as:
-18 < (-k - 2) < 18
Now let's isolate k:
first, we can add 2 in the 3 parts of the inequality:
-18 + 2 < -k - 2 + 2 < 18 + 2
-16 < -k < 20
Now we can multiply all sides by -1, remember that this also changes the direction of the signs, then:
-1*-16 > -1*-k > -1*20
16 > k > -20
Then k can be any value between these two limits.
So the correct options (from the given ones) are:
k = -16
k = -8
k = 0
He could have 30 dimes and 13 quartars
Answer:
y = (x - 4)² - 25
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
To obtain this form use the method of completing the square.
Given
y = (x + 1)(x - 9) ← expand factors using FOIL, thus
y = x² - 8x - 9
To complete the square
add/subtract ( half the coefficient of the x- term )² to x² - 8x
y = x² + 2(- 4)x + 16 - 16 - 9
= (x - 4)² - 25 ← in vertex form
Answer:
Optimal combination of goods can be determined in an economy that produces only two goods, with production of extra units of the two goods at a minimal marginal social cost. The consumption of the additional units of the two goods being produced will be benefitted by the consumers. This is known as marginal social benefit.
Step-by-step explanation:
Marginal social cost is the change in society's total cost brought about by the production of an additional unit of a good or service. It includes both marginal private cost and marginal external cost.
Marginal social benefit is the change in benefits associated with the consumption of an additional unit of a good or service. It is measured by the amount people are willing to pay for the additional unit of a good or service.
Answer:
x=7, y=16
Step-by-step explanation:
2x+5=x+12
2x=x+7
x=7
y-4=x+5
y-4=12
y=16
