Last one for today! Again would appreciate a breakdown on how to get to a resolution. It is multiple choice.
1. Simplify the expression using the quotient to a power property. (3y^6/z^7)^3
a. 27y^9/z^7
b. 3y^9/z^10
c. 27y^18/z^7
d. 27y^18/z^21
2. Use a descriptive variable and an inequality symbol to write a model for the statement. The Thompson family will spend more than 14,000 on home improvement.
a. Let a represent the amount. a < $14,000
b. Let a represent the amount. a < $14,000
c. Let a represent the amount. a > $14,000
d. Let a represent the amount. a > $14,000
3. Simplify and subtract (if possible). 10�ã27x-�ã75x
a. 25�ã3x
b. 10�ã48x
c. 25x�ã3
d. Cannot be subtracted
4. Rewrite the expression as a single term. 1/r-1/s+1/t
a. St+rt-rs/r-s+t
b. 1/r-s+t
c. St+rt-rs/rst
d. St-rt+rs/rst
5. Factor the difference of perfect cubes completely. 27a^3-1000
a. (3a+10)(9a^2-100)
b. (3a-10)(9a^2+100)
c. (3a+10)(9a^2-30a+100)
d. (3a-10)(9a^2+30a+100)
(3y^6/z^7)^3
3^3 (y^6)^3 / (z^7)^3
27 y^18/z^21
(D)
"more than" means greater
don't know why a&b and c&d are the same, but (C) or (D) works for me. I assume there should have been <= or >= in there. You want just ">" since we want "more," not just "at least".
10�√27x-�√75x
10√9√3x - √25√3x
10*3√3x - 5√3x
25√3x
(A)
1/r-1/s+1/t
put over a common denominator: rst
st/rst - rt/rst + rs/rst
(st-rt+rs)/(rst)
(D) assuming the usual sloppiness with parentheses
27a^3-1000
(3a)^3 - 10^3
(3a-10)(9a^2+30a+100)
(D)
Sure! Here's a breakdown of how to solve each of the multiple-choice questions:
1. The expression is (3y^6/z^7)^3. To simplify this using the quotient to a power property, you raise both the numerator and the denominator to the power of 3 separately. So, you raise 3y^6 to the power of 3, which gives you (3^3)(y^6)^3 = 27y^18. And you raise z^7 to the power of 3, which gives you (z^7)^3 = z^21. Now, we have (27y^18)/(z^21). The answer is d. 27y^18/z^21.
2. The statement says "The Thompson family will spend more than 14,000 on home improvement." To write a model for this statement, you can use a descriptive variable, let's say a, to represent the amount they will spend. Since the statement says "more than," the appropriate inequality symbol to use is ">". So, the model is a > $14,000. The answer is c. Let a represent the amount. a > $14,000.
3. The expression is 10√27x - √75x. Simplifying this, you can first simplify the square roots. √27x can be simplified to 3√3x, while √75x can be simplified to 5√3x. Now, you have 10(3√3x) - 5(√3x). Applying the distributive property, this becomes 30√3x - 5√3x. Combining like terms, you get 25√3x. The answer is a. 25√3x.
4. The expression is 1/r - 1/s + 1/t. To rewrite it as a single term, you need to find a common denominator for the fractions. The common denominator is rst. Multiplying the first fraction by st/st, the second fraction by rt/rt, and the third fraction by rs/rs, you get (st - rt + rs)/(rst). Now, the expression is rewritten as a single term. The answer is d. (st - rt + rs)/(rst).
5. The expression is 27a^3 - 1000. To factor the difference of perfect cubes, you write the expression as (cube root of a)^3 - (cube root of 10)^3. The cube root of 27a^3 is 3a, and the cube root of 1000 is 10. Using the formula for the difference of cubes, this expression can be factored as (3a - 10)(9a^2 + 30a + 100). The answer is b. (3a - 10)(9a^2 + 30a + 100).
I hope this breakdown helps! Let me know if you have any further questions.