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Sergio [31]
3 years ago
8

Factor each by using the GCF. a) 36x+81 b) 24a+36

Mathematics
2 answers:
Charra [1.4K]3 years ago
8 0

To find the GCF of numbers.

1. Find the prime factorizations of the numbers.

2. The GCF is the product of the common factors with lower exponent.

a. 36x + 81

Let's start with the prime factorizations.

36 = 2^2 * 3^2

81 = 3^4

The only factor in common is 3. There is a 3^2 and a 3^4. We use 3^2 since it has a lower exponent.

GCF = 3^2 = 9

36x + 81 = 9(4x + 9)

b. 24a + 36

Let's start with the prime factorizations.

24 = 2^3 * 3

36 = 2^2 * 3^2

The two numbers have factor 2 in common. There is a 2^2 and a 2^3, so use 2^2 since it has the lower exponent.

The two numbers have factor 3 in common. There is a 3^2 and a 3. Use 3 since it has the lower exponent.

GCF = 2^2 * 3 = 4 * 3 = 12

24a + 36 = 12(2a + 3)


nydimaria [60]3 years ago
5 0

The Greatest Common Factor (GCF) is very important when factoring. Later on, you will forget to pull out a GCF and the answer will be wrong. Always look for a GCF before doing anything.

Let's try factoring these:

a.) 36x+81

The greatest common factor of this expression is 9, because it is the maximum number that both can go into. Let's solve.

9(4x+9)

This is the simplest this expression can get. This would be your final answer. Let's try the other one.

b.) 24a+36

The GCF of this one is 12. Let's simplify it.

12(2a+3)

This is also the simplest you can get it. You can do nothing further. So, your final answers are:

a.) 9(4x+9)

b.) 12(2a+3)

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Match the information on the left with the appropriate equation on the right.
kiruha [24]

Answer:

See attachment below

Step-by-step explanation:

For the first option, we are given m = - 2 / 3, b = 3. This is likely in the point - slope form y = mx + b, where m = slope and b = y - intercept. Thus, the equation of the line in point - slope form given this information, should be y = - 2 / 3x + 3. It seems as if none of the following equations match this form, so let us interchange the equation a bit,

y = - 2 / 3x + 3,

y + 2 / 3x = 3,

2x + 3y = 9 - Option C

_______________________________________________________

Next we are given m = - 3 / 2, and that this line passes through the point ( 4, - 1 ). Substitute m as - 3 / 2, x as 4, y as - 1, knowing point ( 4, - 1 ), into the form y = mx + b - solving for b.

- 1 = ( - 3 / 2 )( 4 ) + b,

b = 5,

Thus the equation in point - slope form should be y = - 3 / 2x + 5. None of the choices match this, so let us again alter the equation,

y = - 3 / 2x + 5,

2y = - 3x + 10,

- 2y = 3x - 10 - Option A

_______________________________________________________

( 6, 3 ) and ( 3, 1 ) is given to lie on this line. The slope of the line should be as follows,

Slope = 3 - 1 / 6 - 3 = 2 / 3

Now let us determine the y - intercept ( b ) by substitute one of the points, say ( 6, 3 ). In this case x = 6, and y = 3,

3 = ( 2 / 3 )( 6 ) + b,

b = - 1,

y = 2 / 3x - 1 = Option D

Take a look at the attachment below for further help;

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dusya [7]
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If the rate of change (ROC) of the function is quadratic, what is the function type ? Choose the correct answer.
evablogger [386]

If the rate of change (ROC) of the function is quadratic, then the function type is cubic

<h3>What is rate of change?</h3>

The rate of change of a function is the rate at which the output values change over the input value

The rate of change of a function is one degree less than the actual function

This means that, a cubic function will have a quadratic rate of change

Hence, the correct option is (d)

Read more about rate of change at:

brainly.com/question/8728504

4 0
3 years ago
Share £480 in the ratio 2:3:7
aleksandr82 [10.1K]
£480

2:3:7 =  2+3+7  = 12

 2
--- 0f £480 = £80
12


 3
--- of £480 = £120
12

 7
--- of £480 = £280
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answer =  £80 : £120 : £280
5 0
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Given |u| = 2.5, |v| = 3.2, and the angle between the vectors is 60°, find the value of u · v?
Alenkasestr [34]

Step-by-step explanation:

u.v=|u||v|cos60°

u.v=(2.5)(3.2)(1/2)

u.v=(8)(1/2)

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