Answer:
Step-by-step explanation:
The equation of a straight line can be represented in the slope intercept form as
y = mx + c
Where
m = slope = (change in the value of y on the vertical axis) / (change in the value of x on the horizontal axis)
The equation of the given line is
9x+7y=4
7y = 4 - 9x = -9x + 4
y = -9x/7 + 4/7
Comparing with the slope intercept form, slope = -9/7
If the line passing through the given point is perpendicular to the given line, it means that its slope is the negative reciprocal of the slope of the given line.
Therefore, the slope of the line passing through (7,-4) is 7/9
To determine the intercept, we would substitute m = 7/9, x = 7 and y = - 4 into y = mx + c. It becomes
- 4 = 7/9×7 + c = 49/9 + c
c = - 4 - 49/9
c = - 85/9
The equation becomes
y = 7x/9 - 85/9
Considering the linear function found in part a, we have that:
b) The slope is of AC.
c) The intercept is of AD + B.
<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.
The equation found in part a is:
A(Cx + D) + B.
Placing it in slope-intercept format, we have that it is given by:
ACx + AD + B.
Hence:
b) The slope is of AC, as it is the part that multiplies x.
c) The intercept is of AD + B, as it is the constant term.
More can be learned about linear functions at brainly.com/question/24808124
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Answer: A & B are the same answer --> 96, max
<u>Step-by-step explanation:</u>
Consider m is the degree of the numerator (top) and n is the degree of the denominator (bottom). Then the horizontal asymptote (H.A.) is based on the relationship between m and n:
- If m > n, then there is no H.A.
- If m = n, then y = coefficient of numerator ÷ coefficient of denominator
- If m < n, then y = 0
In the given problem, m = 1 and n = 1 so the H.A. is:
This is the maximum number of moose that the forest can sustain at one time.
Percent discount = (original price - sales price) / original price
1250 - 900 = 350
350/1250 = 0.28
The percent discount is 28%.
Answer:
(x, y) = (-0.6, 0.8) or (1, 4)
Step-by-step explanation:
Use the second equation to substitute for y in the first.
(x -1)² +((2x +2) -2)² = 4
x -2x +1 + 4x² = 4 . . . . . . . eliminate parentheses
5x² -2x -3 = 0 . . . . . . . . . . subtract 4, collect terms
Now we can rearrange the middle term to ease factoring by grouping.
(5x² -5x) +(3x -3) = 0
5x(x -1) +3(x -1) = 0
(5x +3)(x -1) = 0
The values of x that make these factors zero are ...
x = -3/5, x = 1
The corresponding values of y are ...
y = 2(-3/5)+2 = 4/5 . . . . for x = -3/5
y = 2(1) +2 = 4 . . . . . . . . for x = 1
The solutions are: (x, y) = (-3/5, 4/5) or (1, 4).
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A graphing calculator verifies these solutions.
