1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
spayn [35]
3 years ago
12

An expression is shown below:

Mathematics
1 answer:
PolarNik [594]3 years ago
8 0
Notation
I imagine that the expression you are asked to work with is:
3 x^{3}y+15xy-9 x^{2} y-45y

When you use a keyboard it is customary to use "^" to denote an exponent is coming so you could have written: 3x^3y+15xy-9x^2y-45y just to be clear.

PART A
To factor out the GCF we are looking for the greatest factor among the terms. Looking at the coefficients (the numbers) the largest number they can all be divided by is 3 so we will pull out a 3. Notice also that each term has a y in it so we can pull out that.

This gives us: 3 x^{3}y+15xy-9 x^{2} y-45y=3y( x^{3}+5x-3 x^{2} -15)

To factor is to write as a product (something times something else). It undoes multiplication so in this case if you take what we got and multiplied it back you should get the expression we started with.

PART B
Start with the answer in part A. Namely, 3y( x^{3}+5x-3 x^{2} -15). For now let's focus only on what is in the parenthesis. We have four terms so let's take them two at a time. I am separating the expression in two using square brackets. [( x^{3}+5x)]-[3 x^{2} -15]

Let's next factor what is in each bracket:
[( x^{3}+5x)]-[3 x^{2} -15] = [x( x^{2} +5)]-[3( x^{2} +5)]

Notice that both brackets have the same expression in them so now we factor that out: [x( x^{2} +5)]-[3( x^{2} +5)] = (x-3)( x^{2} +5)

Our original expression (the one we started the problem with) had a 3y we already pulled out. We need to include that in the completely factored expression. Doing so we get: 3 x^{3}y+15xy-9 x^{2} y-45y =(3y) (x-3)( x^{2} +5)

You might be interested in
Refer to the Exhibit Student Grades. The professor has informed the class that 7.93 percent of her students received grades of A
Marta_Voda [28]

This question is incomplete, the complete question is;

Refer to the Exhibit Student Grades. A professor at a local university noted that the grades of her students were normally distributed with a mean of 73 and a standard deviation of 11.

The professor has informed the class that 7.93 percent of her students received grades of A. What is the minimum score needed to receive a grade of A

Answer:

the minimum score needed to receive a grade of A is 88.51

Step-by-step explanation:

Given the data in the question;

Let x represent the grades of the students that were normally distributed with mean μ = 73 and standard deviation σ = 11.

so, The professor has informed the class that 7.93 percent of her students received grades of A

the minimum score needed to receive a grade of A will be:

P( X > x ) = 7.93 %

P( X > x ) = 0.0793

1  - P( X ≤ x ) = 0.0793

- P( X ≤ x ) = 0.0793 - 1

- P( X ≤ x ) = - 0.9207

P( X ≤ x ) = 0.9207

⇒ P( X-μ/σ ≤ x-μ/σ ) = 0.9207

so, x-μ/σ = InvNormal( 0.9207 )  

x-μ/σ = 1.41

(x - 73) / 11 = 1.41

(x - 73) = 1.41 × 11

(x - 73)  = 15.51

x = 15.51 + 73

x = 88.51

Therefore, the minimum score needed to receive a grade of A is 88.51

7 0
2 years ago
Yo someone help i'm lost
kompoz [17]

Answer:

convert the task into ratios

(1) if $24 = 4 walks

how many $ for a walk

= (24/4) $/walk

= $6 per walk

•the first one is correct

•the second is wrong, cause it interprete $12/3 walks, which is rationalized to $3 per walk

•the third one is correct, cause it can also be rationalized ($30/5walks) to $6 per walk.

also, rationalizing this would equate to 3 miles per hour (6miles/2hrs)

• one is wrong cause it's 4 miles per hour

•two is correct, it's saying 3 miles per hour (12/4)

• third, likewise is correct 3 miles per hour (9/3) miles/hrs

5 0
2 years ago
What is 15 divided by 63.0
Keith_Richards [23]

Answer:

its 5/21 or about .24

Step-by-step explanation:

plz mark me as brainliest

5 0
3 years ago
A circle has a radius of 11 in. Find the length s of the arc intercepted by a central angle of 11°.
Travka [436]

Answer:

Step-by-step explanation:

11 degrees to radians: 1 degree =57.296 radians

L = (11 degrees)/(57.296) x (11 in) = 2.111848 in

7 0
2 years ago
a city doubles its size every 64 years. if the population is currently 225,000 what will the population be in 128 years
ale4655 [162]

Answer:

450,000

Step-by-step explanation:

128/64:2

225,000 X 2: 450,000

4 0
2 years ago
Read 2 more answers
Other questions:
  • Find the retail sale price if the original price is $65 discount by 12%
    10·2 answers
  • How do you find the curve of best fit?
    5·1 answer
  • Area of a rectangle: A=bh
    6·2 answers
  • If two coins are tossed together, then the chance for falling with heads up is 1/2. The chance for tails is also 1/2. Therefore,
    10·1 answer
  • 1) Arjun baked 15 cookies with 3 scoops of flour. With 5 scoops of flour, how many cookies
    12·1 answer
  • Can I get help with this please I am so stuck in here
    11·1 answer
  • How do I solve for d(real answers only please)
    13·1 answer
  • Find Find the value of y when x=-5, y=15x+1, When x=-5 , y=...
    13·1 answer
  • 2.) Which is an equation? *
    15·1 answer
  • What is the image point of (2, -5) after a rotation of 90 degrees counterclockwise about the origin?
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!