All categories

2 years ago

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

Mathematics

2 answers:

Jlenok [28]2 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]2 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.

You might be interested in

a sloth walks 2/5 mile in each 1/3 hour. write a complex fraction to represent the sloths unit rate of speed. then determine the

insens350 [35]

1 1/5 is the answer

5 0

2 years ago

Suppose that 4% of the 2 million high school students who take the SAT each year receive special accommodations because of docum

dangina [55]

Answer:

a. 0.0122

b. 0.294

c. 0.2818

d. 30.671%

e. 2.01 hours

Step-by-step explanation:

Given

Let X represents the number of students that receive special accommodation

P(X) = 4%

P(X) = 0.04

Let S = Sample Size = 30

Let Y be a selected numbers of Sample Size

Y ≈ Bin (30,0.04)

a. The probability that 1 candidate received special accommodation

P(Y = 1) = (30,1)

= (0.04)¹ * (1 - 0.04)^(30 - 1)

= 0.04 * 0.96^29

= 0.012244068467946074580191760542164986632531806368667873050624

P(Y=1) = 0.0122 --- Approximated

b. The probability that at least 1 received a special accommodation is given by:

This means P(Y≥1)

But P(Y=0) + P(Y≥1) = 1

P(Y≥1) = 1 - P(Y=0)

Calculating P(Y=0)

P(Y=0) = (0.04)° * (1 - 0.04)^(30 - 0)

= 1 * 0.96^36

= 0.293857643230705789924602253011959679180763352848028953214976

= 0.294 --- Approximated

The probability that at least 2 received a special accommodation is given by:

P (Y≥2) = 1 -P(Y=0) - P(Y=1)

= 0.294 - 0.0122

= 0.2818

d. The probability that the number among the 15 who received a special accommodation is within 2 standard deviations of the number you would expect to be accommodated?

First, we calculate the standard deviation

SD = √npq

n = 15

p = 0.04

q = 1 - 0.04 = 0.96

SD = √(15 * 0.04 * 0.96)

SD = 0.758946638440411

SD = 0.759

Mean =np = 15 * 0.04 = 0.6

The interval that is two standard deviations away from .6 is [0, 2.55] which means that we want the probability that either 0, 1 , or 2 students among the 20 students received a special accommodation.

P(Y≤2)

P(0) + P(1) + P(2)

P(0) + P(1) = 0.0122 + 0.294

Calculating P(2)

P(2) = (0.04)² * (1 - 0.04)^(30 - 2(

P(2) = 0.00051

So,

P(0) +P(1) + P(2). = 0.0122 + 0.294 + 0.00051

= 0.30671

Thus it 30.671% probable that 0, 1, or 2 students received accommodation.

The expected value from d) is .6

The average time is [.6(4.5) + 19.2(3)]/30 = 2.01 hours

8 0

2 years ago

There is a harvest festival each year on the planet Bozone. During that time, most of the Bozone residents sit down to rejoice a

Oliga [24]

Answer:

The price would be decreased by 18 bozats

Step-by-step explanation:

The following information is given in the question

x = number of kilograms of snig sold

P = Price per kilogram

And, the equation is

p = 300 - 18x

Now if an extra kilogram is sold so it should be x+1

Now the new price is

New price = 300 - 18(x + 1)

= 300 - 18x - 18

Therefore the price would be decreased by 18 bozats

8 0

2 years ago

Read 2 more answers

The rate traveled from Amarillo to Austin by a bus averages 65 miles per hour. The bus arrived in Austin after eight hours of tr

Kobotan [32]

If it takes 8 hours for a bus with an average velocity of 65mph to travel from Amarillo to Austin then,
d = 65 (8) = 520 miles

The distance from Amarillo to Austin (or vice versa) is 520 miles.

If the function to get the distance traveled by the automobile is given by:
d(x) = 80 t
Then, the inverse variation relationship would be
d-1(x) = t = d / 80
Since d = 520
t = 520 / 80
t = 6.5 hours

It takes 6.5 hours for the automobile to complete the trip

4 0

2 years ago

Joel is mailing a large envelope to his cousin. The envelope has pictures inside, so he doesn't want to bend it.

Nuetrik [128]

Answer: Put a cardboard piece inside the envelope then mail it

Step-by-step explanation: If you make the cardboard piece the exact size as the pictures then put it behind all of the pictures it would make it hard for the pictures to bend if it has support.

8 0

2 years ago