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

Answers

Answer 1

Answer:

[tex]4x^2+xy-18y^2=(4x+9y)\,(x-2y)[/tex]

Step-by-step explanation:

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

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

so we want the following to happen:

[tex]a\,c = 4\\ad+bc=1\\bd--18[/tex]

Notice as well that [tex]ad+bc =1[/tex] 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 [tex]bd=-18[/tex], then we can consider the case in which one of this  (b or d) is the negative factor. So let's then assume that [tex]a\,\,and \,\,c[/tex] are positive.

We can then try combinations for  [tex]a\,\,and \,\,c[/tex]  such as:

[tex]a = 4;\,\,c=1\\a=2;\,\,c=2\\a=1;\,\,c=4[/tex]

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

we get that [tex]4d_b=1\\b=-4d-1[/tex]

and since

[tex]bd=-18\\(-4d-1)\,d=-18\\-4d^2-d=-18\\4d^2+d-18=0[/tex]

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

[tex]d=-18/(-2)\\d=9[/tex]

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

[tex]a=4; \,\,b=9;\,\,c=1;\,\,d=-2[/tex]

which makes our factorization:

[tex](4x+9y)\,(x-2y)=4x^2+xy-18y^2[/tex]


Related Questions

Which of the following represents the range of the graph below ?

Answers

Answer:

y≤0

Step-by-step explanation:

The range is the output values, or in this case the y values

Y is less than or equal to zero

y≤0

Answer:D

Step-by-step explanation:

The Value of 3^4 + 5 . 5= ___. please help!!!!!!!!!

Answers

Answer:

[tex]86.5[/tex]

Step-by-step explanation:

[tex]3^4+5.5[/tex]

[tex]81+5.5[/tex]

[tex]86.5[/tex]

Answer:

86.5

Step-by-step explanation:

3^4 + 5 . 5

Exponents first

3^4=81

81+5.5

86.5

Sorry for my first answer

|25 POINTS| Suppose you have one pyramid with a base that is 10 meters long and 10 meters wide with a slant that is 15 meters. Now, if the length of the base is increased to 15 meters, what is the difference in the surface area between the new pyramid and the old pyramid?
125 meters squared.
525 meters squared.
600 meters squared.
400 meters squared.

Answers

Answer:

125 meters squared

Step-by-step explanation:

Surface area of initial pyramid:

A= 10²+4*1/2*10*15= 400 m²

Surface area of extended pyramid:

A= 10*15+2*1/2*15*15+2*1/2*10*15= 525 m²

The difference is:

525- 400= 125 m²

Answer:

First pyramid is = 400 meters squared

A= 10²+4*1/2*10*15= 400 m²

second pyramid = 675 meters squared

A= 10*15+2*1/2*15*15+2*1/2*10*15= 525 m²

Subtract the two =

525- 400= 125 m²

What percentage of latecomers blamed delays at the security gate for their tardiness? (nearest whole percent)
A)
27%
B)
32%
0
38%
D)
42%
Submit

Answers

Answer:

C)38%

Step-by-step explanation:

Divide the # of latecomers who blame the security by the # of total latecomers.

Answer: 38 percent

Step-by-step explanation: did usa tset prep

What are the solutions to this quadratic equation? -2x^2 + x + 4 = 0

Answers

Answer:

the third one

Step-by-step explanation:

use quadratic equation

Determine the value of x. Write the answer in an inequity. Use x only once in the inequality

Answers

Answer:  1 < x < 25

Step-by-step explanation:

The sum of two sides must be GREATER than the third side.

      a +  b > c              a + c > b              b + c > a

     12 + 13 > x             12 + x > 13            13 + x > 12

          25  > x                     x > 1                      x > -1

           x < 25                     1 < x

Length cannot be negative so disregard x > -1

We are left with   1 < x  and   x < 25  

                                 1 < x < 25

Which equation represents a line which is parallel to the line y = - 3x - 1?

A. 3y - x = 12
B. x + 3y = 6
C. 3y + y = -8
D. 3x - y = -2​

Answers

I would say D but not to sure

How many solutions are there to the equation below?

5x + 48 + 7x = 12 (x + 4)

A. 1
B. Infinitely many
C. 0

Answers

Answer:

B. Infinitely Many

Step-by-step explanation:

Step 1: Distribute

5x + 48 + 7x = 12x + 48

Step 2: Combine like terms

12x + 148 = 12x + 48

If the 2 lines are the same, which they are, they are the same lines. That means there are an infinite amount of solutions. If they had the same slope but different y-intercepts, there would be no solutions because the lines are parallel. Any other pair of equations would have 1 solution.

Answer:

B. Infinitely Many

Step-by-step explanation:

When you simplify the term on the left of the equation, it is exactly the same as the term on the right. Therefore, you can substitute virtually anything in for variable "x" and it would still be correct.


In AJKL, JL is extended through point L to point M, m m

Answers

Answer:

x = 15

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠ KLM is an external angle of the triangle, thus

∠ KLM = ∠ JKL + ∠ KJL , substitute values

5x - 7 = x + 20 + 2x + 3

5x - 7 = 3x + 23 ( subtract 3x from both sides )

2x - 7 = 23 ( add 7 to both sides )

2x = 30 ( divide both sides by 2 )

x = 15

Which ordered pair represents the solution to the system of equations? {4x−2y=18−3x−4y=−8 (4, −1) (5, 1) (−1, 4) (43, 1)

Answers

Answer:

b

Step-by-step explanation:

Answer:

(4,-1)

Step-by-step explanation:

I took the quiz

BD is the bisector of ∠ABC. Determine the measure of ∠ABD. ANSWERS: A) 90° B) 55° C) 40° D) 45°

Answers

Answer:

D) 45

Step-by-step explanation:

When a line bisects an angle, it cuts the angle into two equal halves. This means that ABD and DBC have the same angle measure, which is half of 90 degrees or 90/2=45. Hope this helps!

What is the equation of a line with a slope of -3 and a y-intercept of 4

Answers

Answer:

y = -3x + 4

Step-by-step explanation:

So the -3 is the slope and the slope always has an x and the y intercept is b which is 4

Answer:

y = -3x + 4

Step-by-step explanation:

slope-intercept form: y = mx + b

Note that: m = slope

y- intercept = b

m = slope = -3

y-intercept = b = 4

Plug in the corresponding number to the corresponding variables:

y = mx + b

y = -3x + 4 is your answer.

~

Which oneee ?????????

Answers

Answer:

Middle. The conflict normally builds near the middle.

Step-by-step explanation:


Through a point not in a plane are an infinite number of lines parallel to the plane.

Answers

Answer:

If two planes are parallel, a line in one plane is parallel to a line in the other plane. A line that intersects one of two parallel lines intersects the other also. Through a point not in a plane are an infinite number of lines parallel to the plane.

Step-by-step explanation:

i hoped this helped I found it on the web. couldnt really understand the question. too much planes

Which of the following angles can be trisected using only a compass and straightedge?
A. 45⁰
B. 125⁰
C. 65⁰
D. 175⁰

Answers

Answer:

i believe it is c

Step-by-step explanation:

What is the factored form of the binomial expansion x4 – 16x3 + 96x2 – 256x + 256?

Answers

Answer:

(x-4)*(x-4)*(x-4)*(x-4) or (x-4)^4

Step-by-step explanation:

x^4 – 16x^3 + 96x^2 – 256x + 256

terms with odd exponents are negative

x^4 has a coefficient of one, so the expression's GCF is 1

Thus, we need to factor out the expression as it is:

(x-4)*(x-4)*(x-4)*(x-4)

Lets multiply it out to check:

(x-4)*(x-4)*(x-4)*(x-4)=

(x^2-8x+16)*(x^2-8x+16)=

x^48x^3+16x^2−8x^3+64x^2−128x+16x^2−128x+256=

x^4 – 16x^3 + 96x^2 – 256x + 256

thus, the factored form is:

(x-4)*(x-4)*(x-4)*(x-4) or (x-4)^4

Solve for y, where y is a real number square root of y-9=8

Answers

Answer:

73

Step-by-step explanation:

First, to get rid of the square root, square both sides of the equation to get:

y-9=64

Then, move 9 to the other side to get

y=73

Answer:

y = 73

Step-by-step explanation:

sqrt(y-9) = 8

Square each side

(sqrt(y-9))^2 = 8^2

y-9 = 64

Add 9 to each side

y-9+9 = 64+9

y = 73

Since we squared each side, we have to check and see if the solution is valid

sqrt(73-9) = 8

sqrt(64) = 8

8=8

it is a valid solution

There is an 80% chance of rain tomorrow and a 20% chance the football game will be postponed. What is the probability that it will rain tomorrow and the football game will be postponed?

Answers

Answer:

4 I think

Step-by-step explanation:

I divided 80 by 40

Which of the following lies between 0 and -1?
0
-3
-2/3
-4/3

Answers

Answer:

-2/3

Step-by-step explanation:

We need a negative fraction

The numerator has to be smaller than the denominator to be between 0 and -1

Answer:3rd one

Step-by-step explanation:

the amount of pollutants that are found in waterways near large cities is normally distributed with a mean of 9.1 ppm and a standard deviation of 1.5 ppm. 9 randomly selected large cities are studies. for the 9 cities, find the probability that the average amount of pollutants is less than 9.6 ppm.?

Answers

Answer:

Step-by-step explanation:

Let x be the random variable representing the amount of pollutants that are found in waterways near large cities. Since it is normally distributed and the population mean and population standard deviation are known, we would apply the formula,

z = (x - µ)/(σ/√n)

Where

x = sample mean

µ = population mean

σ = standard deviation

n = number of samples

From the information given,

µ = 9.1

σ = 1.5

n = 9

the probability that the average amount of pollutants is less than 9.6 ppm is expressed as

P(x < 9.6)

z = (9.6 - 9.1)/(1.5/√9) = 1

Looking at the normal distribution table, the probability corresponding to the z score is 0.84

Therefore,

P(x < 9.6) = 0.84

i dont know how to do this pls help​

Answers

Answer:

≈ 8.6 cm

Step-by-step explanation:

tan= opposite leg/adjacent leg

tan 43°= 8/b

0.933= 8/b

b= 8/0.933

b= 8.57449≈ 8.6 cm

If you can please help- I need fast answers and a full description! Describe how to transform the quantity of the fifth root of x to the seventh power, to the third power into an expression with a rational exponent. Make sure you respond with complete sentences.

Answers

Answer:

[tex]x^{21/5}[/tex]

Step-by-step explanation:

Step 1: Convert [tex]\sqrt[5]{x^{7}}[/tex] into exponential form

[tex]((x^7)^{1/5})^{3}[/tex]

Step 2: Mulitply the 2 exponents together

[tex](x^{7/5})^{3}[/tex]

Step 3: Multiply the exponents again

[tex](x^{7/5})^{3}[/tex] = [tex]x^{21/5}[/tex]

Work out the area of this circle

Answers

Answer:

A = 50.3 cm²

Step-by-step explanation:

Area of a circle = [tex]\pi r^2[/tex]

Where r = 4 cm

A = π(4)²

A = 16(3.14)

A = 50.3 cm²

Find the length of side BC.
Give your answer to 1 decimal place.

Answers

Answer:

BC ≈ 11.9 cm

Step-by-step explanation:

We use sin∅ (opposite over hypotenuse) to solve for our missing length:

sin58° = BC/14

14sin58° = BC

BC = 11.8727

hi what is the answer for this

Answers

Step-by-step explanation:

first find the side length by

considering a triangle under

the square

[tex]l \: = \sqrt{ {3}^{2} + {1}^{2} } = \sqrt{10} \: cm \\ area \: = \: \sqrt{10} \times \sqrt{10} = 10 \: {cm}^{2} \: \: \: \: ans[/tex]

These triangles ARE similar! Which reason proves it?
Circle one:
AA~
SSS~
SAS~
SHOW CALCULATIONS to verify they are similar!

Answers

Answer:

I would say AA

Step-by-step explanation:

try to separate the picture to see the bigger picture and you can do it.

A line passes through the point (0,6) and is parallel to the line with the equation y =
1/5X - 5. What's the equation of the line?
O A) y = 1/5x + 6
OB) y = -5x + 6
C) y = 1/5* - 6
OD) y=1/5X

Answers

Answer:

A

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = [tex]\frac{1}{5}[/tex] x - 5 ← is in slope- intercept form

with slope m = [tex]\frac{1}{5}[/tex]

Parallel lines have equal slopes, thus parallel line has slope of [tex]\frac{1}{5}[/tex]

The line crosses the y- axis at (0, 6) ⇒ c = 6

y = [tex]\frac{1}{5}[/tex] x + 6 ← equation of parallel line → A

the equation of the line that passes through the point (0,6) and is parallel to the line with the equation y = 1/5X - 5 is y = 1/5x +6.

What is a Linear equation?

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

Given A line passes through the point (0,6) and is parallel to the line with the equation y = 1/5X - 5

Since the two lines are parallel to each other

thus, their slope would be equal

Slope intercept form of the Second line:

y = 1/5x + c

Given that line passes through (0, 6)

From above equation

6 = 1/5* 0 +c

Hence, c = 6

therefore, the equation of the line y = 1/5x +6.

Learn more about Linear equation here:

https://brainly.com/question/11897796

#SPJ2

During the second day of the school fair, Talia and Yoshi recorded 43 winners out of a total of 324 players. How does the actual number of winners compare to the expected number of winners?

Answers

Here is the complete question.

During the second day of the school fair, Talia and Yoshi recorded 43 winners out of a total of 324 players. How does the actual number of winners compare to the expected number of winners?

Theoretical probability

P (red ) = 1/8 = 12.5%

Experimental probability

( ? )/324 = ( ? )%

This experimental probability is ( ? ) than the theoretical probability.

There were ( ? ) winners than expected.

Answer:

Experimental probability = 13.27%

The experimental probability is 0.77% more than the theoretical probability,

There were approximately 2.5 more winners than expected

Step-by-step explanation:

Given that;

The Theoretical probability = 1/8 = 12.5%

The total number of players = 324 players

From these two data set; it is possible to determine the numbers of the theoretical winners by basically multiplying the Theoretical probability  by the total number of players.

i.e 12.5% × 324 players

0.125 × 324 players = 40.5 players

However; we know that Talia and Yoshi recorded 43 winners out of a total of 324 players

So;

number of recorded winners = 43

the total players = 324

The Experimental Probability can be calculated by dividing the number of recorded winners with the total number of players and multiplying the fraction by 100.

i.e

Experimental Probability = ( Numbers of recorded winners/ Total Number of players ·) × 100

Experimental Probability = (  43/324 ) × 100

Experimental Probability = 0.1327 × 100

Experimental Probability = 13.27%

The difference in comparison between Experimental and Theoretical Probability is =  13.27%  - 12.5% = 0.77%

The actual number of winners compare to the expected number of winners is: number of recorded winners  - the numbers of the theoretical winners

= 43 - 40.5

= 2.5

18y^8x^4w^6 and 30y^7w^3

Answers

Answer:

10

Step-by-step explanation:

Graph the result of the following transformation on f(x).

Answers

Answer:

mp.3

Step-by-step explanation:

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