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3 years ago

8

The school store sells 18 folders for $4.50. Select the three unit rates that describe this sale. $0.25 per folder , 4 folders p

er dollar ,36 folders per $9, $3 per dozen

1 answer:

max2010maxim [7]3 years ago

5 0

Answer:

All of your choices are correct.

Step-by-step explanation:

4.50 ÷ 18 = .25 each

.25 x 4 = 1.00

.25 x 36 = 9.00

12 x .25 = 3.00

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HELP ME IM DESPERATE

tankabanditka [31]

Answer:

#5 has an output of 14. #6 has an output of 32.

Step-by-step explanation:

3(3) +5=y 9+5=y 14=y

3(9) +5=y 27+5=y 32=y

3 0

3 years ago

Match the numerical expressions to their simplified forms

eduard

Answer:

$1.\ \ p^2q = (\frac{p^5}{p^{-3}q^{-4}})^{\frac{1}{4}}$

$2.\ \ pq^{\frac{3}{2}}} = (\frac{p^2q^7}{q^{4}})^{\frac{1}{2}}$

$3.\ \ pq^2 = \frac{(pq^3)^{\frac{1}{2}}}{(pq)^{\frac{-1}{2}}}$

$4.\ \ p^2q^{\frac{1}{2}} = (p^6q^{\frac{3}{2}})^{\frac{1}{3}}$

Step-by-step explanation:

Required

Match each expression to their simplified form

1.

$(\frac{p^5}{p^{-3}q^{-4}})^{\frac{1}{4}}$

Simplify the expression in bracket by using the following law of indices;

$\frac{a^m}{a^n} = a^{m-n}$

The expression becomes

$(\frac{p^{5-(-3)}}{q^{-4}})^{\frac{1}{4}}$

$(\frac{p^{5+3}}{q^{-4}})^{\frac{1}{4}}$

$(\frac{p^8}{q^{-4}})^{\frac{1}{4}}$

Split the fraction in the bracket

$(p^8*\frac{1}{q^{-4}})^{\frac{1}{4}}$

Simplify the fraction by using the following law of indices;

$\frac{1}{a^{-m}} = a^m$

The expression becomes

$(p^8*q^4)^{\frac{1}{4}}$

Further simplify the expression in bracket by using the following law of indices;

$(ab)^m = a^m * b^m$

The expression becomes

$(p^{8*\frac{1}{4}}\ *\ q^4*^{\frac{1}{4}})$

$(p^{\frac{8}{4}}\ *\ q^{\frac{4}{4}})$

$p^2q$

Hence,

$(\frac{p^5}{p^{-3}q^{-4}})^{\frac{1}{4}} = p^2q$

2.

$(\frac{p^2q^7}{q^{4}})^{\frac{1}{2}}$

Simplify the expression in bracket by using the following law of indices;

$\frac{a^m}{a^n} = a^{m-n}$

The expression becomes

$({p^2q^{7-4}}})^{\frac{1}{2}}$

$({p^2q^3}})^{\frac{1}{2}}$

Further simplify the expression in bracket by using the following law of indices;

$(ab)^m = a^m * b^m$

The expression becomes

${p^{2*\frac{1}{2}}q^{3*\frac{1}{2}}}}$

$pq^{\frac{3}{2}}}$

Hence,

$pq^{\frac{3}{2}}} = (\frac{p^2q^7}{q^{4}})^{\frac{1}{2}}$

3.

$\frac{(pq^3)^{\frac{1}{2}}}{(pq)^{\frac{-1}{2}}}$

Simplify the numerator as thus:

$\frac{p^{\frac{1}{2}} * q^3*^{\frac{1}{2}}}{(pq)^{\frac{-1}{2}}}$

$\frac{p^{\frac{1}{2}} * q^{\frac{3}{2}}}{(pq)^{\frac{-1}{2}}}$

Simplify the denominator as thus:

$\frac{p^{\frac{1}{2}} * q^{\frac{3}{2}}}{p^{\frac{-1}{2}}q^{\frac{-1}{2}}}$

Simplify the expression in bracket by using the following law of indices;

$\frac{a^m}{a^n} = a^{m-n}$

The expression becomes

$p^{\frac{1}{2} - (\frac{-1}{2} )} * q^{\frac{3}{2} - (\frac{-1}{2}) }$

$p^{\frac{1}{2} +\frac{1}{2} } * q^{\frac{3}{2} + \frac{1}{2} }$

$p^{\frac{1+1}{2}} * q^{\frac{3+1}{2}}$

$p^{\frac{2}{2}} * q^{\frac{4}{2}}$

$pq^2$

Hence,

$pq^2 = \frac{(pq^3)^{\frac{1}{2}}}{(pq)^{\frac{-1}{2}}}$

4.

$(p^6q^{\frac{3}{2}})^{\frac{1}{3}}$

Simplify the expression in bracket by using the following law of indices;

$(ab)^m = a^m * b^m$

The expression becomes

$p^6*^{\frac{1}{3}}\ *\ q^{\frac{3}{2}}*^{\frac{1}{3}}$

$p^{\frac{6}{3}}\ *\ q^{\frac{3*1}{2*3}}$

$p^2 *\ q^{\frac{3}{6}}$

$p^2 *\ q^{\frac{1}{2}$

$p^2q^{\frac{1}{2}$

Hence

$p^2q^{\frac{1}{2}} = (p^6q^{\frac{3}{2}})^{\frac{1}{3}}$

6 0

3 years ago

Mrs. Gomez has two kinds of flowers in her garden. The ratio of lilies to daisies in the garden is 5:2

Phantasy [73]

Answer:

28

Step-by-step explanation:

5 : 2

since this is a simplified ratio, they have a common factor. let's say it is 'x'

so now :

5x : 2x

we know that 5x is lilies, and we also know that she has 20 lilies, so:

5x = 20

x = 4

the daisies would be 2x so 2*4 = 8

total flowers is 20 + 8

28

4 0

3 years ago

Which is the equation of a line whose slope is -2 and whose y-intercept is 3?

marusya05 [52]

Answer:

y = -2x + 3

Step-by-step explanation:

The slope-intercept formula for a line is y = mx + b where m is the slope and b is the y intercept. Therefore, just sub -2 for m and 3 for b.

5 0

3 years ago

Factor 6x^4 - 5x^2+12x^2-10 by grouping. what is the resulting expression?

Alina [70]

12 goes with 6 and 5 with 10

(6x^4+12x^2)+(-5x^2-10)
(6x^2)(x^2+2)+(-5)(x^2+2)
undistribute
(x^2+2)(6x^2-5)

3 0

3 years ago

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