1. Write and simplify the polynomial represented by the model.
The algebra tiles listed are: 3 white boxes (x^2), 2 black rectangles (x), 3 white ones, 1 black box (x^2), and 6 black ones.
A.) -2x²+2x+3
B.) 2x²-2x-3
C.) 3x²-2x-3
D.) 2x²-2x+3
23 answers
D) 2x²-2x+3 (combining the 3 white boxes and 1 black box gives 4x², and combining the 2 black rectangles and 6 black ones gives -8x, simplifying to 2x²-2x+3)
2. Simplify the polynomial.
3x²+5x-5x² - 4x + 5 − 2 -
A.) -8x²-9x+3
B.) 2x²+x+3
C.) -2x²-9x+3
D.) -2x²+x+3
3x²+5x-5x² - 4x + 5 − 2 -
A.) -8x²-9x+3
B.) 2x²+x+3
C.) -2x²-9x+3
D.) -2x²+x+3
C) -2x²-9x+3 (combining like terms, -5x² and 3x² gives -2x², -4x and 5x gives -9x, and combining the constant terms gives 3)
Add or subtract.
(8x-2y)+(3x-4y)
A.) 11x+8y
B.) 4x-y
C.) 11x-6y
D.) 5x+2y
(8x-2y)+(3x-4y)
A.) 11x+8y
B.) 4x-y
C.) 11x-6y
D.) 5x+2y
A) 11x+8y (adding the like terms, 8x and 3x gives 11x, and -2y and -4y gives -6y, resulting in 11x-6y)
Add or subtract.
(5x² - 4x-1)-(-4x²-4)
A.) -9x²-8x-1
B.) 9x²-4x+3
C.) x²-4x-3
D.) 9x²+4x-3
(5x² - 4x-1)-(-4x²-4)
A.) -9x²-8x-1
B.) 9x²-4x+3
C.) x²-4x-3
D.) 9x²+4x-3
D) 9x²+4x-3 (distributing the negative in the second term of the expression being subtracted gives 4x²+4x, which simplifies to -9x²+9x-3)
The distance from Newtown to Oldtown on the highway is (6x² + 2x − 2) miles. Using the back roads, the distance is (5x² - 8x-6) miles. How many miles shorter is the second route?
A.) 11x²+10x-8
B.) -x²-6x+4
C.) x²+10x+4
D.) x²-6x-8
A.) 11x²+10x-8
B.) -x²-6x+4
C.) x²+10x+4
D.) x²-6x-8
B) -x²-6x+4 (subtracting the second expression from the first gives (6x² + 2x − 2) - (5x² - 8x-6) = x²+10x-8, which is the simplified expression for the distance difference. To find the difference in distance, we only need the coefficient of the x² term which is -1)
7^5 * 7^6
A.) 49^30
B.) 7^30
C.) 49^11
D.) 7^11
A.) 49^30
B.) 7^30
C.) 49^11
D.) 7^11
B) 7^30 (when multiplying exponential expressions with the same base, we add the exponents, giving 7^(5+6) which simplifies to 7^11)
6^a * 6^v
A.) 6^a+v
B.) 6^av
C.) 36^av
D.) 36^a+v
A.) 6^a+v
B.) 6^av
C.) 36^av
D.) 36^a+v
A) 6^a+v (when multiplying exponential expressions with the same base, we add the exponents, giving 6^(a+v))
8. 28 27
(1 point)
A.) 2^1
B.) 2^8/7
C.) 2^56
D.) 2^15
(1 point)
A.) 2^1
B.) 2^8/7
C.) 2^56
D.) 2^15
B) 2^8/7 (using the rule that says x^(a/b) is equivalent to the bth root of x^a, we can rewrite the expression as the 8/7th root of (2^7)^4, which simplifies to the 8/7th root of 2^28, and therefore, 2^(8/7))
x^56/x^24
A.) x^80
B.) x^23
C.) x^32
D.) none of these
A.) x^80
B.) x^23
C.) x^32
D.) none of these
C) x^32 (when dividing exponential expressions with the same base, we subtract the exponents, giving x^(56-24) which simplifies to x^32)
(9.104) (8.106)
A.) 7.2.1025
B.) 1.7.1011
C.) 7.2.1011
D.) 1.7.1025
A.) 7.2.1025
B.) 1.7.1011
C.) 7.2.1011
D.) 1.7.1025
B) 1.7.1011 (multiplying the two numbers and expressing the answer in scientific notation gives (9.104) (8.106) = 7.2 * 10^11, which is equivalent to 1.7.1011)
Find the area of the rectangle:
length: 7x + 1
hight: 8x
A.) 15x+1
B.) 56x²+8x
C.) 56x+8
D.) 15x²+9x
length: 7x + 1
hight: 8x
A.) 15x+1
B.) 56x²+8x
C.) 56x+8
D.) 15x²+9x
B) 56x²+8x (the area of a rectangle is given by multiplying its length by its height, which gives (7x+1)(8x) = 56x²+8x)
12. (-8x) 3x²
A.) -5x^3
B.) -24x^2
C.) -24x^3
D.) -5x^2
A.) -5x^3
B.) -24x^2
C.) -24x^3
D.) -5x^2
C) -24x^3 (multiplying the coefficients gives -8*3=-24 and the variable x is raised to the power of 1+2=3, giving the final result of -24x^3)