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3 years ago

15

Simplify. [3 • (3 – 9)] + 9 –4.5 9 45 –9

1 answer:

ArbitrLikvidat [17]3 years ago

5 0

this is your answer -45189/2000

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Help me please if you can! <br><br> Don't guess!

Alex787 [66]

Answer:

17 R 25

Step-by-step explanation:

long division. 17(15) is 510. 535-510 is 25, which is the remainder.

8 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

Convert the following units as indicated.

amid [387]

Answer: 106.63 feet

Step-by-step explanation: how this helps :)

8 0

2 years ago

WILL MARK BRAINLIEST!!!

deff fn [24]

Answer:

-3.872983346

Step-by-step explanation:

In this case we have: cos θ = 1/4 Whose possible solutions are: θ = 2 * pi * n - Acos (1/4) θ = 2 * pi * n + Acos (1/4) Where, n belongs to the natural numbers. As sin θ <0 then the solution is: θ = 2 * pi * n - Acos (1/4) For n = 1 we get: θ = 4.965069236 radians Thus: tan θ = tan (4.965069236) = - 3.872983346 Answer: tan θ = -3.872983346

3 0

3 years ago

Read 2 more answers

DISTANCE (METERS) TIME (SECONDS) SPEED (M/S) 30 6.6

LenaWriter [7]

Answer:

4.5 meters per second

Step-by-step explanation:

30/6.6 = 4.5

Assuming 30 is the meters and 6.6 is the seconds

4 0

3 years ago