Answer:
Step-by-step explanation:
Many ways to do this in the details.
All start by writing three equations with three unknowns
<em>-56 = a(3²) + b(3) + c</em>
-56 = 9a + 3b + c 1)
<em>-16 = a(-1²) + b(-1) + c</em>
-16 = a - b + c 2)
<em>-51 = a(-2²) + b(-2) + c </em>
-51 = 4a - 2b + c 3)
subtract equation 2 from equation 1
-40 = 8a + 4b
--10 = 2a + b
b = -10 - 2a 4)
subtract equation 3 from equation 1
-5 = 5a + 5b
-1 = a + b 5)
substitute 4 into 5
-1 = a + (-10 - 2a)
-1 = - a - 10
a = - 9
substitute a into 4
b = -10 - 2(-9)
b = 8
substitute a and b into any of 1, 2, or 3
-51 = 4(-9) - 2(8) + c
-51 = -36 - 16 + c
c = 1
y = -9x² + 8x + 1
We can use a plotting calculator to confirm our result.
Answer:
The domain is 
Step-by-step explanation:
Given functions 
and 
Subtract these two functions:
Plot these difference on the coordinate plane (see attached diagram). This function is defined for all vlues of x, so the domain is
Answer:
10 gallons of the 1st brand and 30 gallons of the second brand.
Step-by-step explanation:
The equation I came up with is 0.6x+0.8y=0.75(x+y), with x and y representing the total amount of mixture of each brand. Meaning, 0.6x is the amount of pure antifreeze in the first brand, 0.8y is pure antifreeze in the second brand, and 0.75(x+y) is the amount of pure antifreeze there's supposed to be when you mix the two brands together.
Now, the question also says that the mixture is 40 gallons. The total mixture of the 2 brands is basically x+y = 40, then you can minus x from both sides and get y = 40-x, then you substitute it into the original equation: 0.6x+0.8(40-x)=0.75(x+40-x), x = 10, the amount of mixture from the first brand, which also means that 30 gallons is the amount of mixture from the second brand.
<span>$8 each month
</span><span>How many months will it take him to save at least $60?
60 </span>÷ 8 = 7.5
It will take Phillip 7.5 months to save up at least $60!
