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3 years ago

Which expression has the same GCF as 15x2 - 21x?

Mathematics

2 answers:

Jlenok [28]3 years ago

7 0

Answer:First, find the greatest common factor of the coefficients of the given expression.

The greatest common factor of 15 and 21 is 3. Factor this out of the polynomial.

Next, find the greatest common factor of the variables.

The greatest common factor of x2 and x is x. Factor this out of the polynomial.

So, the greatest common factor of the expression 15x2 − 21x is 3x.

Now, consider the expression 15x2 − 21.

The greatest common factor of the coefficients 15 and 21 is 3. Only one term has a variable, so there is no common variable factor. Factor 3 out of the polynomial.

So, the greatest common factor of the expression 15x2 − 21 is 3.

Consider the expression 18x2 − 24x.

The greatest common factor of the coefficients 18 and 24 is 6, and the greatest common factor of the variables x2 and x is x. Factor these out of the polynomial.

So, the greatest common factor of the expression 18x2 − 24x is 6x.

Consider the expression 12x2 − 18x.

The greatest common factor of the coefficients 12 and 18 is 6, and the greatest common factor of the variables x2 and x is x. Factor these out of the polynomial.

So, the greatest common factor of the expression 18x2 − 24x is 6x.

Consider the expression 12x2 − 15x.

The greatest common factor of the coefficients 12 and 15 is 3, and the greatest common factor of the variables x2 and x is x. Factor these out of the polynomial.

So, the greatest common factor of the expression 12x2 − 15x is 3x.

Therefore, the expression 12x2 − 15x has the same GCF as 15x2 − 21x.

there you go

Mice21 [21]3 years ago

5 0

Answer:

$15x^2 +21 x$

Step-by-step explanation:

We have the following expression:

$15x^2 -21 x$

We can find the GCF with the following steps.

1. Find the GCF for the numerical part 15 and -21

The factors for 15 are : 1,3,5,15

The factors for -21 are -21,-7,-3,-1,1,3,7,21

And the common factors are 1,3

The GCF for the numerical part is 3*1 = 3

2. Find the GCF for the variable

The factors of x^2 are : x*x

The factors of x are: x

The common factors are x for this case, so then the GCF for the variable part is x

3. Multiply the two results from steps 1 and 2

GCf= 3*x = 3x

If we consider the new expression:

$15x^2 +21x$

We can find the GCF with the following steps.

1. Find the GCF for the numerical part 15 and -21

The factors for 15 are : 1,3,5,15

The factors for -21 are 1,3,7,21

And the common factors are 1,3

The GCF for the numerical part is 3*1 = 3

2. Find the GCF for the variable

The factors of x^2 are : x*x

The factors of x are: x

The common factors are x for this case, so then the GCF for the variable part is x

3. Multiply the two results from steps 1 and 2

GCf= 3*x = 3x

And as we can see both GCF are equal. So then we satisfy the condition required.

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Step-by-step explanation:

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3 years ago

10$ is spent on 2 big pails and 1 small one. A smail pail cosf half as much as each big one. How much is spent on a big pail? Ho

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Answer:

$4 is spent on a big pail and $2 is spent on a small pail.

Step-by-step explanation:

Given:

10$ is spent on 2 big pails and 1 small one.

A small pail cost half as much as each big one.

Now, to find the amount spent on a big pail and on a small pail.

Let the cost of a big pail be $x.$

And the cost of small pail be $\frac{x}{2} .$

As given, there are 2 big pails.

And the total money spent = $10.

According to question:

$(x+x)+\frac{x}{2}=10$

$2x +\frac{x}{2}=10$

$\frac{4x+x}{2} =10$

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Multiplying both sides by 2 we get:

$5x=20$

Dividing both sides by 5 we get:

$x=4.$

The cost of a big pail = $4.

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Therefore, $4 is spent on a big pail and $2 is spent on a small pail.

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3 years ago

Which of the following applies the law of cosines correctly and could be solved to find m∠E? ANSWERS: A) cos E = 312 + 392 – 2(3

defon

This question is incomplete because the options were not properly written.

Complete Question

Which of the following applies the law of cosines correctly and could be solved to find m∠E? ANSWERS:

A) cos E = 31²+ 39² – 2(31)(39)

C) 56² = 39² – 2(39) ⋅ cos E

D) 56² = 31² + 39² – 2(31)(39) ⋅ cos E

Answer:

D) 56² = 31² + 39² – 2(31)(39) ⋅ cos E

Step-by-step explanation:

From the above diagram, we see are told to apply the law of cosines to solve for m∠E i.e Angle E

The formula for the Law of Cosines is given as:

c² = a² + b² − 2ab cos(C)

Because we have sides d , e and f and we are the look for m∠E the law of cosines would be:

e² = d² + f² - 2df cos (E)

e = 56

d = 39

f = 31

56² = 39² + 31² - (2 × 39 × 31) × cos E

Therefore, from the above calculation and step by step calculation, the option that applies the law of cosines correctly and could be solved to find m∠E

Is option D: 56² = 31² + 39² – 2(31)(39) ⋅ cos E

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4 years ago