9514 1404 393
Answer:
- d
- 4x^2 +4x +6
- n=2
- b
- c
- x-2
- 12g^2 -11g +2
Step-by-step explanation:
1. The rules of exponents are ...
(a^b)(a^c)/(a^d) = a^(b+c-d)
(a^b)^c = a^(bc)
So, the only expression not equal to x^36 is ...
(x^3)^4·x^3 = x^(3·4+3) = x^15
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2. The shaded area is the difference between the rectangle area and the trapezoid area:
(13x^2 -4x +10) -(9x^2 -8x +4)
= (13 -9)x^2 +(-4+8)x +(10 -4)
= 4x^2 +4x +6
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3. The rules of exponents are shown above.
((x^-5)^2·x^15)/x^3 = x^(-5·2+15-3) = x^2
n = 2
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4. The desired product is the difference of squares, so has a special factoring.
25x^2 -4 = (5x)^ -2^2 = (5x -2)(5x +2)
The second binomial is 5x+2.
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5. The leading coefficient is the product of the leading coefficients of the binomials. All are correct.
The linear term coefficient is the sum of the constants in the binomials.
Aroon: -5-2 = -7 ≠ +10; Hallie: 8+3 = 11; Phoenix: 4-6 = -2
Hallie and Phoenix only are correct
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6. When you know the trinomial has binomial factors, you can find the terms of the second factor by looking at the leading term and the constant.
The second factor has a first term of (2x^2)/(2x) = x, and a constant of (-2)/(1) = -2. The other factor of the trinomial is (x-2).
The width of the desk is x-2.
Check: (2x+1)(x-2) = 2x^2 -4x +1x -2 = 2x^2 -3x +2 . . . . as required
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7. The expression is difficult to read with the reflection. We think it might be ...
g^2 + (1/4)(44g^2 -12g +8) -8g
= g^2 +11g^2 -3g +2 -8g
= (1 +11)g^2 +(-3-8)g +2
= 12g^2 -11g +2
