Answer:
x = $20,000
the manufacturer's list price is $20,000
Step-by-step explanation:
Let x represent the manufacturer's list price.
And c the amount she finally paid
Given that;
She received a discount of 18% off the manufacturer's list price
= x - 18%x
= x - 0.18x
= 0.82x
then had to pay 8% state sales tax.
C = (0.82x) + 8% of (0.82x)
C = 0.82x + 0.08(0.82x)
C = 0.82x + 0.0656x
C = 0.8856x
Since she paid $17,712
C = $17,712
C = $17,712 = 0.8856x
0.8856x = $17,712
x = $17,712/0.8856
x = $20,000
the manufacturer's list price is $20,000
Answer:
y=-x+5 if parallel and perpendicular
if needed in point slope form : y-7 = -1(x+2)
Step-by-step explanation:
Answer:
16
Step-by-step explanation:
The hypotenuse = 2 times the shorter leg
The longer leg = the square root of 3 times the shorter leg
A) p + n + d = 18
B) .01p + .05n + .10d = 1.14
C) 2p = d
Substituting C) into A)
A) p + n + 2p = 18 equals
A) 3p + n = 18
Substituting C) into B)
B) .01p + .05n + .10 *2p = 1.14
B) .01p + .05n + .2p = 1.14
B) .21p + .05n = 1.14
Taking equation A)
A) 3p + n = 18 and multiplying it by -.05
A) -.15p -.05n = -.90 Then adding this to B)
B) .21p + .05n = 1.14
.06p = .24
Therefore there are 4 pennies.
(I'll leave it to you to determine the nickels and dimes.)
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Oh what the heck, I'll finish it for you.
Looking at equation C)
C) 2p = d
We know there are 4 pennies so there are:
2 *4 = eight dimes
Looking at Equation A)
A) p + n + d = 18 we can fill in the pennies and the dimes:
A) 4 + n + 8 = 18
Therefore, there are 6 nickels.
Remark
You'll see it a whole lot easier if you make a substitution so that it looks like something you have already seen
Solution
let y = x^2
x^4 = x^2 * x^2
x^4 = y * y
x^4 = y^2
Now the expression becomes
y^2 + 8 y - 9 = z
(y + 9)(y - 1) = z
Now put the x^2 back in.
(x^2 + 9) ( x^2 - 1) = z
x^2 - 1 becomes x + 1 and x - 1. At this level x^2 + 9 can't be factored.
Answer
(x^2 + 9) (x + 1)(x - 1)
