Answer:
225 ft squared
Step-by-step explanation:
Area is length by width and since its a square the length and width are the same.
15 x 15 = 225
Let f=number of flowers in a vase, then:
5f-16=24 add 16 to both sides
5f=40 divide both sides by 5
f=8
So there were 8 flowers per vase in the beginning.
Answer:
7 quarters and 3 dimes
Step-by-step explanation:
x: quarter y: dime
25x + 10y = 205
x+y=10
y = 10-x
25x + 10*(10-x) = 205
25x+100 -10x = 205
15x = 105
x = 7
7 = 10-7 = 3
The key piece of information for these questions is the Fundamental Theorem of Algebra, which states that a degree n polynomial has n complex roots. A complex root can be either real or imaginary.
First question, regarding the polynomial y = x^3 - 3x^2 + 16x - 48:
We know there is one real root, the x-intercept.
Since it's a third degree polynomial, there are three complex roots in total.
Therefore, there is one real root and two imaginary roots.
Answer is B
Second question:
You probably can guess the answer, now that you know the Fundamental Theorem of Alegebra:
There are 3 real zeros, each with multiplicity one, meaning each root only happens once. It's a 5th degree polynomial, so there are a total of 5 roots, implying 2 imaginary roots.
Answer is C) 3 real and 2 imaginary zeroes.
I'll just factor the above equation.
x² + 18x + 80
x² ⇒ x * x
80
can be:
1 x 80
2 x 40
4 x 20
5 x 16
8 x 10 Correct pair
(x+8)(x+10)
x(x+10) +8(x+10) ⇒ x² + 10x + 8x + 80 = x² + 18x + 80
x+8 = 0
x = -8
x+10 = 0
x = -10
x = -8
(-8)² + 18(-8) + 80 = 0
64 - 144 + 80 = 0
144 - 144 = 0
0 = 0
(-10)² + 18(-10) + 80 = 0
100 - 180 + 80 = 0
180 - 180 = 0
0 = 0
I think the algebra tiles will not be a good tool to use to factor the quadratic equation because the equation is not a perfect square quadratic equation.
