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Finger [1]
3 years ago
10

Write this sentence as an equation? Six less than 4 times a number gives 18

Mathematics
2 answers:
Gelneren [198K]3 years ago
7 0

Answer:

4x - 6 =15

Step-by-step explanation:

I will use "x" as our variable to represent the number we are trying to find.  

Let's take the problem piece by piece.

Six less than four times a number.

If we are using x to represent our number, we know that when we do four times that number we are multiplying x times 4, which is the same as writing "4x."

Next we know that we are taking six less than 4x. Six less than means we will be subtracting 6 from our 4x, which is the same as writing 4x - 6.

Finally, we know that six less than 4x (4x - 6) equals 15. Now we have a full equation:

4x - 6 =15

agasfer [191]3 years ago
4 0

Answer:

6-4 times x=18

btw x=9

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Match the numerical expressions to their simplified forms
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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

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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}}

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Step-by-step explanation:

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