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
tester [92]
3 years ago
5

Show work and Factor 4x^2+xy-18y^2

Mathematics
1 answer:
grigory [225]3 years ago
6 0

Answer:

4x^2+xy-18y^2=(4x+9y)\,(x-2y)

Step-by-step explanation:

Let's examine the following general product of two binomials with variables x and y in different terms:

(ax+by)\,(cx+dy)= ac\,x^2+adxy+bcxy+bdy^2

so we want the following to happen:

a\,c = 4\\ad+bc=1\\bd--18

Notice as well that ad+bc =1 means that those two products must differ in just one unit so, one of them has to be negative, or three of them negative. Given that the product bd=-18, then we can consider the case in which one of this  (b or d) is the negative factor. So let's then assume that a\,\,and \,\,c are positive.

We can then try combinations for  a\,\,and \,\,c  such as:

a = 4;\,\,c=1\\a=2;\,\,c=2\\a=1;\,\,c=4

Just by selecting the first one (a=4;\,\,c=1)

we get that 4d_b=1\\b=-4d-1

and since

bd=-18\\(-4d-1)\,d=-18\\-4d^2-d=-18\\4d^2+d-18=0

This quadratic equation give as one of its solutions the integer: d = -2, and consequently,

d=-18/(-2)\\d=9

Now we have a good combination of parameters to render the factoring form of the original trinomial:

a=4; \,\,b=9;\,\,c=1;\,\,d=-2

which makes our factorization:

(4x+9y)\,(x-2y)=4x^2+xy-18y^2

You might be interested in
List of all numbers less than 30 are divisible by 8?
Pavel [41]
8
16
24

Hope this helps
8 0
2 years ago
Read 2 more answers
The mass of the part of a metal rod that lies between its left end and a point x meters to the right is 3x^2 kg. Find the linear
Sav [38]

Answer:

6 kg/m

Step-by-step explanation:

mass m = 3x^2.

rho ρ= dm/dx =6x

ρ(1) =6 Kg/m

linear density is the derivative of mass (m)  with respect to position(x)

that is how fast is the mass changing at that position.

4 0
3 years ago
Can someone help me with this area question
ladessa [460]

Answer:

49.07

Step-by-step explanation:

3 0
2 years ago
In 2 days, 48,000 gallons of oil
Ann [662]

Answer:

Deepwater Horizon

good movie too btw

-Hops

5 0
3 years ago
Read 2 more answers
Find the perimeter of the figure shown above. a. 18 yds c. 20 yds b. 10 yds d. 24 yds Please select the best answer from the cho
ycow [4]
<h3>Answer: 24 yards, choice D</h3>

There are 4 sides to this figure (trapezoid). The left slanted side and the right most vertical side, combined with the top and bottom horizontal sides, will get us the perimeter.

left slanted side = 5 yards

right most vertical side = 4 yards (see note below)

bottom side = 9 yards

top side = 6 yards

Add up the four sides mentioned: 5+4+9+6 = 9+15 = 24

note: the rectangle has opposite sides that are the same length. While the right most side isn't labeled, it is the same length as the left side of the rectangle, so both are 4 yards long.

Another thing I should probably mention is that we do not add in the interior 4 yard side. The perimeter is only the outer or exterior sides we care about. Think of it like we're trying to fence around some property lot and we don't want to subdivide the property up. Finding the perimeter will help us find the amount of fencing needed to surround the property.

4 0
3 years ago
Other questions:
  • wyatt has (2x-1) one-dollar bills and (4x + 2) five dollar bills. Susan has 3 x dollars more than Wyatt. Find the total amount o
    11·2 answers
  • The question is in the photo/image
    14·1 answer
  • Please help I’ll give brainliest
    6·1 answer
  • Joanna wants to buy a backpack that costs $37.98. The sales tax rate is 8.75%. Estimate the amount of sales tax that Joanna will
    9·1 answer
  • PLEASE HELP QUICKLY : find the sum and difference of 5/6 and 1/2
    10·1 answer
  • In the following equation, what number represents the slope?
    11·2 answers
  • The product of the product of 7 and 2 and the product of 8 and p
    10·1 answer
  • 5x+3(3x−43)=............
    15·2 answers
  • Find the value of 5w+1 given that 7w-7=7.
    15·1 answer
  • Please i need help on my math
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!