Answer:
p = -4 or p = 4
300 sq. ft.
Step-by-step explanation:
In the first question since it is only the first turn for the player in the game he could only have won or lost 4 points. Therefore the equation would be the following.
p = -4 or p = 4
in the second question we need to calculate the area of the living room, which can be calculated using the following equation by implementing the values given to us in the question.
... add 25 to both sides
... divide 1/5 by both sides
finally, we can see that the area of the living room is 300 sq. ft.
Longer leg = x + 4
Shorter leg = x
Hypotenuse = x + 8
Using Pythagorean Theorem:
a^2 + b^2 = c^2
(x + 4)^2 + x^2 = (x + 8)^2
x^2 + 8x + 16 + x^2 = x^2 + 16x + 64
2x^2 + 8x + 16 = x^2 + 16x + 64
2x^2 +8x = x^2 + 16x + 48
2x^2 - 8x = x^2 + 48
x^2 - 8x = 48
x^2 - 8x - 48 = 0
You can complete the square from here or use the quadratic formula.
Completing the square:
x^2 - 8x = 48
x^2 - 8x + (-8/2)^2 = 48 + (-8/2)^2
x^2 - 8x + 16 = 48 + 16
(x - 4)(x - 4) = 64 or (x - 4)^2 = 64
x - 4 = +√64 OR x - 4 = -√64
x - 4 = +8 OR x - 4 = -8
x = 12 OR x = -4
However, you can't use negative 4 as a length because your length needs to be a positive.
So x will be 12.
Shorter leg: 12
Longer leg: 12 + 4
Hypotenuse: 12 + 8
Answer:
C. Its APR, because it's less than its effective interest rate.
Step-by-step explanation:
The interest rate determines the money you must pay on the outstanding balance on the credit card.
The credit card company would advertise the lowest numbers it could truthfully use.
The APR is 15.83 %.
The formula for the effective interest rate is
where the interest rates are expressed as decimals.
If the APR is 15.83% and the interest is compounded daily,
The APR is less than the effective interest rate, so that's what the company would advertise.
Answer:
12 boys, 36 girls
Step-by-step explanation:
We can use systems of equations to solve this using substitution.
Let b = # of boys in the class
Let g = # of girls in the class
b + g = 48
g=3b
b+(3b)=48
4b=48
b=12
12*3=36
Check:
36+12=48