Hello,
Please, see the attached files.
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2
+ 3x - 4, and the speed of the walkway is W(x) = x
2 - 4x + 7.
20. What is his total speed as he walks along the moving walkway?
21. Carlos turned around because he left his cell phone at a restaurant.
What was his speed as he walked against the moving walkway?
His speed was 2x² + 7x - 11 as he walked against the moving walkway.
Function is a type of relation, or rule, that maps one input to specific single output.
We are given that Carlos is walking on a moving walkway. His speed is given by the function
C(x) = 3x² + 3x - 4,
The speed of the walkway is W(x) = x² - 4x + 7.
The total speed as he walks along the moving walkway is;
x² - 4x + 7+ 3x² + 3x - 4,
= 4x² - x + 3,
Given Carlos turned around because he left his cell phone at a restaurant.
If he walked against the moving walkway
- x² + 4x - 7 + 3x² + 3x - 4,
2x² + 7x - 11
Learn more about function here:
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(a)
4x + 3y = 23
5x + 2y = 20
(b)
4x + 3y = 23 ⇒ -2(4x + 3y = 23) ⇒ -8x - 6y = -46
5x + 2y = 20 ⇒ 3(5x + 2y = 20) ⇒ 15x + 6y = 60
7x = 14
x = 2
5x + 2y = 20
5(2) + 2y = 20
10 + 2y = 20
2y = 10
y = 5
Answer: biscuit = $2, ice cream = $5
Parallel
Perpendicular
They intersect at an angle other than 90 degrees
Answer:
Perpendicular
Step-by-step explanation:
Here, we want to know the relationship between the two lines .
The easiest way to go about this is to get their slopes;
Mathematically, the equation of a straight line can be expressed in the form;
y = mx + c
where m is the slope;
Hence;
2x -5y = 10
Isolating the y part
5y = 2x -10
divide through by 5
y = 2/5x - 2
So the slope here is 2/5
for the second line
10x + 4y = 20
Divide by 2 all through
5x + 2y = 10
Isolate y
2y = 10-5x
Divide by 2 again
y = 5 -5/2x
The slope here is -5/2
What do we notice? we can see that if we multiply the two slopes by each other, we get -1
That is;
2/5 * -5/2 = -1
What this means is that both lines are perpendicular.
This is because the slopes of perpendicular lines, when multiplied by each other = -1
The two given lines, 2x - 5y = 10 and 10x + 4y = 20, intersect at an angle other than 90 degrees. We determined this by finding the slope of each line and seeing that they are neither equal (for parallel lines) nor negative reciprocals (for perpendicular lines).
To determine the relationship between the lines 2x - 5y = 10 and 10x + 4y = 20, we need to analyze their slopes. Both equations can be rewritten in slope-intercept form (y = mx + b) to determine their slopes. The first equation becomes y = (2/5)x - 2, and the second equation becomes y = (-10/4)x + 5.
The slopes of the two lines are m1 = 2/5 and m2 = -10/4. Since the slopes are different, the lines are not parallel. To determine if they are perpendicular, we need to check if their slopes are negative reciprocals.
The product of the slopes is (2/5)(-10/4) = -4/5. Since the product is not -1, the lines are not perpendicular. Therefore, the correct relationship is that the lines intersect at an angle other than 90 degrees.
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