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1 year ago

Use prime factorizations to find the GCF of 18 and 33.

Mathematics

1 answer:

Sonja [21]1 year ago

4 0

Answer:

Use prime factorizations to find the GCF of 18 and 33.

Prime factorization of 18: 2 × 3 × 3

Prime factorization of 33: 3 x 11

The GCF of 18 and 33 is

Step-by-step explanation:

Use prime factorizations to find the GCF of 18 and 33.

Prime factorization of 18: 2 × 3 × 3

Prime factorization of 33: 3 x 11

The GCF of 18 and 33 is

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Simplify 27x^7y^2/9x^6y^5

solmaris [256]

Answer: x/y^3

Step-by-step explanation:

So you divide 27/9 which is 3. Then it ix x^7-x^6=x. And then it is y^2-y^5=y3

27*x*x*x*x*x*x*x*y*y/9*x*x*x*x*x*x*y*y*y*y*y

Doing this makes it easier so you cross each variable out for each one in both sides. 3x/y^3 would be your answer.

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3 years ago

A 51-foot wire running from the top of a tent pole to the ground makes an angle of 58° with the ground. If the length of the ten

AfilCa [17]

Answer:

35.11 ft

Step-by-step explanation:

This given situation can be thought of as triangle $\triangle PQR$ where PQ is the length of pole.

PR is the length of rope.

and QR is the distance of bottom of pole to the point of fastening of rope to the ground.

And $\angle Q \neq 90^\circ$

Given that:

PQ = 44 ft

PR = 51 ft

$\angle R = 58^\circ$

To find:

Side QR = ?

Solution:

We can apply Sine Rule here to find the unknown side.

Sine Rule:

$\dfrac{a}{sinA} = \dfrac{b}{sinB} = \dfrac{c}{sinC}$

Where

a is the side opposite to $\angle A$

b is the side opposite to $\angle B$

c is the side opposite to $\angle C$

$\dfrac{PR}{sinQ}=\dfrac{PQ}{sinR}\\\Rightarrow sin Q =\dfrac{PR}{PQ}\times sinR\\\Rightarrow sin Q =\dfrac{51}{44}\times sin58^\circ\\\Rightarrow \angle Q =79.41^\circ$

Now,

$\angle P +\angle Q +\angle R =180^\circ\\\Rightarrow \angle P +58^\circ+79.41^\circ=180^\circ\\\Rightarrow \angle P = 42.59^\circ$

Let us use the Sine rule again:

$\dfrac{QR}{sinP}=\dfrac{PQ}{sinR}\\\Rightarrow QR =\dfrac{sinP}{sinR}\times PQ\\\Rightarrow QR =\dfrac{sin42.59}{sin58}\times 44\\\Rightarrow QR = 35.11\ ft$

So, the answer is 35.11 ft.

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3 years ago

Simplify the following expression. 4a^-2b A.) b/4a^2 B.)4b/a^2 C.)1/4a^b2

Sergio [31]

ANSWER

The correct answer is B

$\frac{4b}{ {a}^{2} }$

EXPLANATION

The given exponential expression is

$4 {a}^{ - 2} b$

We can rewrite this as,

$4b \times {a}^{ - 2}$

We need to simplify to obtain a positive index, so we apply the following property,

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

This implies that,

$4b \times {a}^{ - 2} = 4b \times \frac{1}{ {a}^{2} }$

This will finally simplify to,

$4b \times {a}^{ - 2} =\frac{4b}{ {a}^{2} }$

Therefore the correct answer is B

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