Answer:
Ashley can travel 10 miles with $10.
Step-by-step explanation:
This problem can be modeled with a linear equation:
where y is the total cost and x is the number of miles.
Given a y of 10, you can plug that in and solve for x:
Ashley can travel 9 miles with $10. You can check that either by solving the equation in the other direction, or doing it logically like this:
If she can travel 9 miles at $0.75 per mile, that's $6.75.
$6.75 + the flat rate of $3.25 is $10, so it works.
45÷60 = .75
100-75 = 25
Answer is 25% off:)
It’s 5 and 1/5 because 5.2 equals 5 and 2/10, then simplify the 2/10 to 1/5. The answer is 5 and 1/5
If you distribute -4 through (5k-7), it equals -20k + 28. Then put on the other -2k on that side of the equals sign and you should have -22k + 28 = -2(9k+5) Then you need to distribute -2 through (9k+5) which equals -18k - 10. You then should have -22k+28=-18k-10. Add 22k to both sides to cancel it out, then you should have 28=4k-10. Add 10 to both sides to get the 4k by itself, which will be 38=4k, then divide both sides by 4 to get k by itself. 38/4 = 19/2. k = 19/2
Answer:
c) 3 units
d) g(x) - f(x) = x² + 2x
e) (-∞, -2] ∪ [0, ∞)
Step-by-step explanation:
<h3><u>Part (c)</u></h3>
To calculate the length of FC, first find the coordinates of point C.
The y-value of point C is zero since this is where the function f(x) intercepts the x-axis. Therefore, set f(x) to zero and solve for x:
As point C has a <u>positive</u> x-value, C = (1, 0).
To find point F, substitute the x-value of point C into g(x):
⇒ F = (1, 3).
Length FC is the <u>difference</u> in the y-value of points C and F:
<h3><u>Part (d)</u></h3>
Given functions:
Therefore:
<h3><u>Part (e)</u></h3>
The values of x for which g(x) ≥ f(x) are where the line of g(x) is above the curve of f(x):
Point A is the <u>y-intercept</u> of both functions, therefore the x-value of point A is 0.
To find the x-value of point E, equate the two functions and solve for x:
As the x-value of point E is negative ⇒ x = -2.
Therefore, the values of x for which g(x) ≥ f(x) are:
- <u>Solution</u>: x ≤ -2 or x ≥ 0
- <u>Interval notation</u>: (-∞, -2] ∪ [0, ∞)