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marishachu [46]

3 years ago

10

What’s a equivalent expression using prime factorization for the number 254

1 answer:

erik [133]3 years ago

7 0

So prime factorization is what it seems, <u>finding the prime factors of a number.</u> Using prime factorization, we can break down 254 as such:

$\underbrace{254}_{\boxed{2*127}}$

Since 2 and 127 are prime,<u> the prime factorization of 254 is 2 × 127.</u>

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Determine the number of possible solutions for a triangle with B=37 degrees, a=32, b=27

vladimir1956 [14]

Answer:

Two possible solutions

Step-by-step explanation:

we know that

Applying the law of sines

$\frac{a}{sin(A)}=\frac{b}{Sin(B)}=\frac{c}{Sin(C)}$

we have

$a=32\ units$

$b=27\ units$

$B=37\°$

step 1

Find the measure of angle A

$\frac{a}{sin(A)}=\frac{b}{Sin(B)}$

substitute the values

$\frac{32}{sin(A)}=\frac{27}{Sin(37\°)}$

$sin(A)=(32)Sin(37\°)/27=0.71326$

$A=arcsin(0.71326)=45.5\°$

The measure of angle A could have two measures

the first measure-------> $A=45.5\°$

the second measure -----> $A=180\°-45.5\°=134.5\°$

step 2

Find the first measure of angle C

Remember that the sum of the internal angles of a triangle must be equal to $180\°$

$A+B+C=180\°$

substitute the values

$A=45.5\°$

$B=37\°$

$45.5\°+37\°+C=180\°$

$C=180\°-(45.5\°+37\°)=97.5\°$

step 3

Find the first length of side c

$\frac{a}{sin(A)}=\frac{c}{Sin(C)}$

substitute the values

$\frac{32}{sin(37\°)}=\frac{c}{Sin(97.5\°)}$

$c=Sin(97.5\°)\frac{32}{sin(37\°)}=52.7\ units$

therefore

the measures for the first solution of the triangle are

$A=45.5\°$ , $a=32\ units$

$B=37\°$ , $b=27\ units$

$C=97.5\°$ , $b=52.7\ units$

step 4

Find the second measure of angle C with the second measure of angle A

Remember that the sum of the internal angles of a triangle must be equal to $180\°$

$A+B+C=180\°$

substitute the values

$A=134.5\°$

$B=37\°$

$134.5\°+37\°+C=180\°$

$C=180\°-(134.5\°+37\°)=8.5\°$

step 5

Find the second length of side c

$\frac{a}{sin(A)}=\frac{c}{Sin(C)}$

substitute the values

$\frac{32}{sin(37\°)}=\frac{c}{Sin(8.5\°)}$

$c=Sin(8.5\°)\frac{32}{sin(37\°)}=7.9\ units$

therefore

the measures for the second solution of the triangle are

$A=45.5\°$ , $a=32\ units$

$B=37\°$ , $b=27\ units$

$C=8.5\°$ , $b=7.9\ units$

6 0

3 years ago

The area of the rectangle shown is 2x^2-x-15 square units. What is the width of the rectangle?

yuradex [85]

Answer:

<h2>The width is (2x + 5) or (x - 3)</h2>

Step-by-step explanation:

The formula of an area of a rectangle:

$A=lw$

l - length

w - width

We have

$A=2x^2-x-15$

$2x^2-x-15=2x^2+5x-6x-15=x(2x+5)-3(2x+5)\\\\=(2x+5)(x-3)$

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4 years ago

Someone start a convo in the comments or try and message me idk how

ivanzaharov [21]

Answer:

Brainly is a platform that is used to help students in need. There are many social networks that offer socializing with many people from every country in the world.

I suggest you install any of those apps, and try find someone to talk to.

On this platform, we offer knowledge and help when it comes to important tests, quizzes and other knowledge-related topics.

Hope I helped.

6 0

3 years ago

You are a carpenter and have a 3/16 inch piece of wood and a 5/8 inch piece of wood

Akimi4 [234]

<span>For this question you just divide 3.75 by five. This will give you an answer of 0.75 (the length of each piece of wood)</span>

8 0

3 years ago

This? .......................................................

adelina 88 [10]

Answer:

109.6

Step-by-step explanation:

3 0

3 years ago