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KiRa [710]
3 years ago
12

WILL MARK BRAINLIEST!!!!PLZ HELP!!!! An expression is shown below: 3pf2 − 21p2f + 6pf − 42p2 Part A: Rewrite the expression by f

actoring out the greatest common factor. Part B: Factor the entire expression completely. Show the steps of your work.
Mathematics
1 answer:
Lesechka [4]3 years ago
7 0

Answer:

See below.

Step-by-step explanation:

So, we have:

3pf^2-21p^2f+6pf-42p^2

PART A:

Find the GCF. Notice that we have a 3 in every term and a p in every term. Thus, the GCF is 3p:

3p(f^2-7pf+2f-14p)

This is the most we can do.

PART B:

Continue from where we left off. Factor the entire expression:

3p(f^2-7pf+2f-14p)\\3p(f(f-7p)+2(f-7p))\\3p((f+2)(f-7p))

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3 years ago
Find the 4th term (x-y)^12
maria [59]

Answer:

The fourth term of the expansion is -220 * x^9 * y^3

Step-by-step explanation:

Question:

Find the fourth term in (x-y)^12

Solution:

Notation: "n choose k", or combination of k objects from n objects,

C(n,k) = n! / ( k! (n-k)! )

For example, C(12,4) = 12! / (4! 8!) = 495

Using the binomial expansion formula

(a+b)^n

= C(n,0)a^n + C(n,1)a^(n-1)b + C(n,2)a^(n-2)b^2 + C(n,3)a^(n-3)b^3 + C(n,4)a^(n-4)b^4 +....+C(n,n)b^n

For (x-y)^12, n=12, k=3, a=x, b=-y, and the fourth term is

C(n,3)a^(n-3)b^3

=C(12,3) * x^(12-3) * (-y)^(3)

= 220*x^9*(-y)^3

= -220 * x^9 * y^3

3 0
3 years ago
On a coordinate plane, the segment with endpoints (10, 40) and (70, 120) is
OlgaM077 [116]

Answer:

The length of the resulting segment is 500.

Step-by-step explanation:

Vectorially speaking, the dilation is defined by following operation:

P'(x,y) = O(x,y) + k\cdot [P(x,y)-O(x,y)] (1)

Where:

O(x,y) - Center of dilation.

P(x,y) - Original point.

k - Scale factor.

P'(x,y) - Dilated point.

First, we proceed to determine the coordinates of the dilated segment:

(P(x,y) = (10, 40), Q(x,y) = (70, 120), O(x,y) = (0,0), k = 5)

P'(x,y) = O(x,y) + k\cdot [P(x,y)-O(x,y)]

P(x,y) = (0,0) +5\cdot [(10,40)-(0,0)]

P'(x,y) = (50,200)

Q'(x,y) = O(x,y) + k\cdot [Q(x,y)-O(x,y)]

Q' (x,y) = (0,0) +5\cdot [(70,120)-(0,0)]

Q'(x,y) = (350, 600)

Then, the length of the resulting segment is determined by following Pythagorean identity:

l_{P'Q'} = \sqrt{(350-50)^{2}+(600-200)^{2}}

l_{P'Q'} = 500

The length of the resulting segment is 500.

3 0
3 years ago
Rachel states that -5.5 is an integer because it is negative. is she correct why or why not
AnnyKZ [126]

Answer:

  Rachel is not correct

Step-by-step explanation:

It is true that the set of integers includes negative numbers, where the sets of whole or natural numbers do not. However, any rational, irrational, or real number can be negative. -5.5 is a rational number, but <em>it is not an integer, because it has a fractional part</em>.

6 0
3 years ago
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