The linear functions in this problem are given as follows:
<h3>What is a linear function?</h3>
A linear function is modeled by:
y = mx + b
In which:
- m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
- b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.
For function f(x), when x increases from 2 to 3, f(x) decays from 5 to 1, hence the slope is of -4 and:
f(x) = -4x + b.
When x = 2, f(x) = 5, hence the y-intercept is found as follows:
5 = -4(2) + b
b = 13.
Then:
f(x) = -4x + 13.
For function g(x), when x increases from 4 to 7, g(x) increases from 2 to 8, hence the slope is of:
m = (8 - 2)/(7 - 4) = 6/3 = 2.
Hence:
g(x) = 2x + b.
When x = 4, g(x) = 2, hence the y-intercept is found as follows:
2 = 2(4) + b
2 = 8 + b
b = -6.
Then:
g(x) = 2x - 6.
More can be learned about linear functions at brainly.com/question/24808124
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Answer:
Dana needs 72 feet of ribbon to make all the bows
Step-by-step explanation:
If she needs to make all the bows, she needs a total of:
18 times 4 feet = 18 * 4 = 72 feet of ribbon
6. 6th grade- go to the two columns above $600, which is about 8 students in the first column and 5 students in the 2nd. 8 + 5 = 13, so 13 students in 6th grade earned $600 or more.
7th grade- again, go to the columns above $600, which is about 7 students in the first column and about 3 in the 2nd column. 7 + 3 = 10, so 10 students in 7th grade earned $600 or more.
Do the same thing for #7, just follow the rows exactly as #6.
Answer:
c
Step-by-step explanation:
Given the roots are x = - 1 + 4i and x = - 1 - 4i then the factors are
(x - (- 1 + 4i))(x - (- 1 - 4i))
= (x + 1- 4i )(x + 1 + 4i )
= (x + 1)² - 16i² → [ i² = - 1 ]
Expand and simplify
= x² + 2x + 1 + 16
Hence
x² + 2x + 17 = 0 → c
Answer:
2x^2
Step-by-step explanation:
If you're going to double x^2, you just need to multiply it by 2. You can just put the 2 in front of the x^2 because the order of operations says to do exponents before multiplication.