Answer:
9 hours
Step-by-step explanation:
Set up the equations: x is the amount of hours Amber worked and y is the hours Jake worked
8x + 8y = 120
y = 3 + x
Substitute the second equation into the first
8x + 8(3+x) = 120
Distribute
8x + 24 + 8x = 120
Combine like-terms
16x + 24 = 120
Subtract 24 on both sides
16x = 96
Divide 16 on both sides
x = 6 (hours Amber worked)
Plug in this x-value into on of the two equations. I will use the second
y = 3 + 6
y = 9
Find the total cost of producing 5 widgets. Widget Wonders produces widgets. They have found that the cost, c(x), of making x widgets is a quadratic function in terms of x. The company also discovered that it costs $15.50 to produce 3 widgets, $23.50 to produce 7 widgets, and $56 to produce 12 widgets.
OK...so we have
a(7)^2 + b(7) + c = 23.50 → 49a + 7b + c = 23.50 (1)
a(3)^2 + b(3) + c = 15.50 → 9a + 3b + c = 15.50 subtracting the second equation from the first, we have
40a + 4b = 8 → 10a + b = 2 (2)
Also
a(12)^2 + b(12) + c = 56 → 144a + 12b + c = 56 and subtracting (1) from this gives us
95a + 5b = 32.50
And using(2) we have
95a + 5b = 32.50 (3)
10a + b = 2.00 multiplying the second equation by -5 and adding this to (3) ,we have
45a = 22.50 divide both sides by 45 and a = 1/2 and using (2) to find b, we have
10(1/2) + b = 2
5 + b = 2 b = -3
And we can use 9a + 3b + c = 15.50 to find "c"
9(1/2) + 3(-3) + c = 15.50
9/2 - 9 + c = 15.50
-4.5 + c = 15.50
c = 20
So our function is
c(x) = (1/2)x^2 - (3)x + 20
And the cost to produce 5 widgets is = $17.50
Hello :
<span>f(x) = 6 – 5x and g(x) = 4x – 1
f(x)-g(x) = 6-5x-(4x-1) = 6-5x-4x+1 = -9x+7
whene x = - 2
f(x)-g(x) = -9(-2)+7 = 25......(answer : D)</span>
31 I think I’m not sure may be wrong
Answer:
Step-by-step explanation:
62 degrees Fahrenheit
Step-by-step explanation:
The number of snowy tree cricket chirps per minute is 148 less than 4 times the outside temperature in degrees Fahrenheit.
Let x = number of chirps
f = temp in Fahrenheit
x = 4f -148
Now let x = 100
100 = 4f-148
Add 148 to each side
100+148 = 4f-148+148
248 = 4f
Divide each side by 4
248/4 = 4f/4
62=f
