Answer:
x = 8, y = 3
Step-by-step explanation:
Equating corresponding x and y coordinates , then
- y = - x + 5 ( multiply through by - 1 )
y = x - 5 → (1)
2x - 5y = 1 → (2)
Substitute y = x - 5 into (2)
2x - 5(x - 5) = 1 ← distribute and simplify left side
2x - 5x + 25 = 1
- 3x + 25 = 1 ( subtract 25 from both sides )
- 3x = - 24 ( divide both sides by - 3 )
x = 8
Substitute x = 8 into (1) for corresponding value of y
y = 8 - 5 = 3
Answer as a fraction: 17/6
Answer in decimal form: 2.8333 (approximate)
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Work Shown:
Let's use the two black points to determine the equation of the red f(x) line.
Use the slope formula to get...
m = slope
m = (y2-y1)/(x2-x1)
m = (4-0.5)/(2-(-1))
m = (4-0.5)/(2+1)
m = 3.5/3
m = 35/30
m = (5*7)/(5*6)
m = 7/6
Now use the point slope form
y - y1 = m(x - x1)
y - 0.5 = (7/6)(x - (-1))
y - 0.5 = (7/6)(x + 1)
y - 0.5 = (7/6)x + 7/6
y = (7/6)x + 7/6 + 0.5
y = (7/6)x + 7/6 + 1/2
y = (7/6)x + 7/6 + 3/6
y = (7/6)x + 10/6
y = (7/6)x + 5/3
So,
f(x) = (7/6)x + 5/3
We'll use this later.
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We ultimately want to compute f(g(0))
Let's find g(0) first.
g(0) = 1 since the point (0,1) is on the g(x) graph
We then go from f(g(0)) to f(1). We replace g(0) with 1 since they are the same value.
We now use the f(x) function we computed earlier
f(x) = (7/6)x + 5/3
f(1) = (7/6)(1) + 5/3
f(1) = 7/6 + 5/3
f(1) = 7/6 + 10/6
f(1) = 17/6
f(1) = 2.8333 (approximate)
This ultimately means,
f(g(0)) = 17/6 as a fraction
f(g(0)) = 2.8333 as a decimal approximation
Given:
May:
hamburger: 3.2 pounds * 4.25 = 13.60
hotdogs: 3 packages * 4 = 12
Total cost: 13.60 + 12 = 25.60
June:
hamburger: 3.2 pounds * 1 1/2 = 4.8 pounds * 4.25 = 20.4
hotdogs: 3 packages * 1/3 = 1 package * 4 = 4
Total cost: 20.4 + 4 = 24.4
25.60 - 24.40 = 1.20
They spent more on May by $1.20. Choice C.
I need to know the sides of the trapezoid in order to find the perimeter
Answer:
x = 5/2
x = 2 1/2
x = 2.5
Step-by-step explanation:
3x - 1 - (x + 3) = 1
3x - 1 - x - 3 = 1
2x - 1 - 3 = 1
2x - 4 = 1
2x = 1 + 4
2x + 5
2x = 5
x = 5/2 → 2 1/2 → 2.5 ( can be written in any of these forms depending on what you need to do)
<em>Hope this helped! :)</em>
