If x + 2 and x - 3 are factors of the following polynomial, then find the values of a and b. F(x) = x^2 + ax^2- 7x + b

If X + 2 And X - 3 Are Factors Of The Following Polynomial, Then Find The Values Of A And B. F(x) = X^2

Answers

Answer 1

[tex]\text{Given that,}\\\\f(x) = x^3+ax^2-7x+b \\\\\text{Since}~ (x+2)~ \text{and}~ (x-3)~ \text{are factors of f(x),}\\\\f(-2) = 0 ~ \text{and}~ f(3)=0\\\\\\ \text{Now,}\\\\f(-2)=0\\\\\ \implies (-2)^3+a(-2)^2-7(-2)+b =0\\\\\implies -8 +4a +14+b =0\\\\\implies 4a +b +6 =0~~~....(i)\\\\\\f(3) = 0\\\\\implies 3^3+a(3^2) -7(3) +b =0\\\\\implies 27 +9a -21 +b =0\\\\\implies 9a +b +6 =0~~....(ii)\\\\\\(ii)-(i):\\\\9a+b+6 - 4a-b - 6 = 0\\\\\implies 5a =0\\\\\implies a = 0\\[/tex]

[tex]\text{Substitute a=0 in equation (i):}\\\\4(0) +b +6 =0\\\\\implies b+6 =0\\\\\implies b =-6\\\\\text{Hence, a = 0 and}~ b =-6[/tex]


Related Questions

4/7 divided by 1 1/3 =

Answers

Answer:

i think probably 3/7 is answer

i’m pretty sure the answer is 12/77

help I suck at math..

Answers

Answer:

The correct answers are:

B

D and

F

Step-by-step explanation:

Hope it can help you lovelots

#LEARN WITH BRAINLY

What of the following exponential functions is represented by the data in the table?
A) f(x)=(1/3)^3
B) f(x)=3^x
C) f(x)=x^3
D) f(x)=x1/3

Answers

Answer:

f(x) = ( 1/3) ^ (x)

Step-by-step explanation:

The function is

f(x) = (1/3) ^ (x)

When x = 1  f(x) = 1/3

when x=2    f(x) = 1/9

When x = -1  f(x) = ( 1/3) ^ -1 = 3/1 =3

Answer:

f(x)=(1/3)^x

Step-by-step explanation:

Plug in the given values of x in the function above and match the answers with f(x) which is y.

help me plssssss
ssssssssss

Answers

Answer:

The answer is going to be A

Step-by-step explanation:

Try changing these improper fractions to mixed numbers.
16/5?

( teach me how to solve this please!)

Answers

Answer:

3 1/5

Step-by-step explanation:

The improper fraction 16/5 is called improper because the top number(the numerator) is bigger than the bottom number(the denominator) we "fix" this by dividing and creating a mixed number (it is called mixed because there is a whole part and a fraction part):

As 16÷5 >>> doing this division gives you 3 wholes and 1/5 leftover. We write this as

3 1/5 (in handwriting the three is big and the 1/5 is a fraction, it is the mixed number they are asking you for)

Find the slope of the line on the graph. Write your answer as a fraction or whole number, but a mixed number or decimal.

Answers

Answer:

-1/4

Step-by-step explanation:

Rise over run

Rises -1 runs 4

slope = -1/4

6. Rachael is married with 2 dependents. Her salary as a dental hygienist is $47,650 paid
in 26 pay periods. Find the state tax withheld per pay period.

Answers

Answer:1.2389 million US$

Step-by-step explanation:

Need help

Every week a company provides fruit for its office employees. They can choose from among five kinds of fruit. What is the probability distribution for the 30 pieces of fruit, in the order listed?

Answers

Answer:

it is A bacause the fractions for that one are correct

Step-by-step explanation:

Let f(x) = x+2/x+6
f^-1(-6) =

Answers

We can explicitly find the inverse. If [tex]f^{-1}(x)[/tex] is the inverse of [tex]f(x)[/tex], then

[tex]f\left(f^{-1}(x)\right) = \dfrac{f^{-1}(x)+2}{f^{-1}(x)+6} = x[/tex]

Solve for the inverse :

[tex]\dfrac{f^{-1}(x) + 2}{f^{-1}(x) + 6} = x[/tex]

[tex]\dfrac{f^{-1}(x) + 6 - 4}{f^{-1}(x) + 6} = x[/tex]

[tex]1 - \dfrac4{f^{-1}(x) + 6} = x[/tex]

[tex]1 - x = \dfrac4{f^{-1}(x) + 6}[/tex]

[tex]f^{-1}(x) + 6 = \dfrac4{1-x}[/tex]

[tex]\implies f^{-1}(x) = \dfrac4{1-x} - 6[/tex]

Then when x = -6, we have

[tex]f^{-1}(-6) = \dfrac4{1-(-6)} - 6 = \dfrac47-6 = \boxed{-\dfrac{38}7}[/tex]

Alternatively, we can first solve for x such that [tex]f(x) = -6[/tex]. Then taking the inverse of both sides, [tex]x = f^{-1}(-6)[/tex]. (The difference in this method is that we don't compute the inverse for all x.)

We have

[tex]\dfrac{x+2}{x+6} = -6[/tex]

[tex]x + 2 = -6 (x + 6)[/tex]

[tex]x + 2 = -6x - 36[/tex]

[tex]7x = -38[/tex]

[tex]\implies x = \boxed{-\dfrac{38}7}[/tex]

Which value of a makes the equation true?

Answers

Answer:

a = -2

Step-by-step explanation:

3(a + 1.5) = -1.5

3a + 4.5 (-4.5) = -1.5 (-4.5)

3a = -6

a = -2

Sam saved $40 each month for 3 years. Then, he spent 65% of his savings on a cruise. How much of his savings was left? A. $420 B. $588 C. $1,092 D. $1,260​

Answers

Answer:

$588 was left

Step-by-step explanation:

Since it was $40 for 3.5 years, and there are 12 months in a year, we do: (3*12+6)*40=168065%= 13/2013/20  * 1680Sam paid $10921680 - 1092 = 588

Which of the following is not a factor of 9 ?

Answers

Answer:

2, 4, 5, 6, 7, 8

Step-by-step explanation:

The number 2 is not a factor of 9. The correct option is D.

What is factor?

A number or algebraic expression that evenly divides another number or expression—i.e., leaves no remainder—is referred to as a factor in mathematics.

The given number is 9.

To find the factor of 9:

Number m that evenly divides another number 9.

In simple words, when we divide the number 9 by a number m.

We should get a whole number.

From the options,

9/1 = 9

9/3 = 3

9/9 = 1

9/2 = 4.5

Therefore, the number 2 is not the factor of 9.

To learn more about the factor;

https://brainly.com/question/18187355

#SPJ2

The complete question is:

Which of the following is not a factor of 9?

Options:

1 , 3, 9, 2.

Which inequality matches the graph?

Answers

Answer:

x < 2/3 y + 2 1/3

Step-by-step explanation:

put it in a graphing calculator and they matched, I do not know

You have two right triangles that are similar. The base of the first is 8 and the height is 12.
If the base of the second triangle is 22, what is the height of the second triangle?
A. 33 units
B. 26 units
C. 14.7 units
D. 4.4 units

Answers

Let the height be x

[tex]\\ \sf\longmapsto \dfrac{8}{12}=\dfrac{22}{x}[/tex]

[tex]\\ \sf\longmapsto 12x=22(8)[/tex]

[tex]\\ \sf\longmapsto 12x=176[/tex]

[tex]\\ \sf\longmapsto x=14.7units[/tex]

Step-by-step explanation:

X :

8/12 = 22/x

x • 12 = 22 • 8

12x = 176

x = 14.7units (C.)

f(x) = {(1,0),(2,1),(3,-1),(4, -2),(-1,-2)
Find the inverse of the function

Answers

See attached picture please

how do i get the answer for this problem. 2x+2x+2=4x+2

Answers

Combine like terms

Subtract 2 from both sides of the equation

Simplify

Subtract 4 from both sides of the equation

Simplify

Then your answer should be 0=0

Wildcat Pizza, Inc. is trying to decide whether to revise its target capital structure. Currently, it targets a 50-50% mix of debt and equity, but it is considering a target capital structure with 70% debt. Wildcat currently has 6% after-tax cost of debt and a 12% cost of common stock. The company does not have any preferred stock outstanding

Answers

I don’t understand, explain further.

LAST ATTEMPT IM MARKING AS BRAINLIEST!! (Draw a dilation of the figure using the given scale factor )

Answers

A' = (0,0)
B' = (1,1)
C' = (3,0)
D' = (1,-1)

how many more seconds does it take to drive 1 mile at 40 miles per hour than 60 miles per hour​

Answers

Answer:

165 seconds

Step-by-step explanation:

If you were going steadily 60 miles per hour, you would go one mile in one minute. So, if you were going steadily 40 miles per hour, without your speed going up or down, you would get through one mile in 3 3/4 minutes (which is 165 seconds more than 1 minute).

Hope this helps. Pls give brainliest! Also, pls sub to kgirl633 on yt!

Angles A,D and G are congruent, and angles c, f and j are congruent. What is the mesure of angle E?​

Answers

Answer:

60

Step-by-step explanation:

Since the angles A, D, and G are congruent then sum of given angles is eaqual to 180 degrees

x + 20 + 2x + x  = 180 add like terms

4x + 20 = 180 subtract 20 from both sides

4x = 160 divide both sides by 4

x = 40

Angles B, E, and H are congruent so E is also  = x + 20 and x = 40 so angle E = 60

Describe the functions plz and thank u<3also 50pts

Answers

Answer:

See below

Step-by-step explanation:

Given function:

y = 1/2|x + 3| + 2

This is a transformation of the absolute value function y = |x|.

The transformations are:

1. Dilation by a scale factor of 1/22. Translation left by 3 units3. Translation up by 2 points

The locator point is the vertex:  (-3, 2)

Domain is any value: x = (- ∞, + ∞)

Range is anything not less than 2: y ≥ 2 or y = [2, + ∞)

See the graph attached

sixty students at gillette road middle school play a winter modified sport. if there are 500 students in the middle school, what percent of students play a sport

Answers

Answer:

60/500=0.12

so 12%

Hope This Helps!!!

Question
Triangle ABC is similar to triangle XYZ. Find side a.
13
39
Y
5
Z
B
Provide your

Answers

Answer:

Step-by-step explanation:

There are two great ways to set up this problem and they both get you the same answer. First you know that the triangles are similar, this means they are the same shape, but not necessarily the same size. You can use ratios to compare the sizes of the sides. Just be sure to compare like things to like things.

One way: compare the small triangle's long side to short leg with the big triangle's long side to short leg. Like this:

13/5 = 39/a

OR...compare long side(sm) to long side(big) compared to short leg(sm) to short leg(big). Like this:

13/39 = 5/a

Amazingly, these equations will give you the same answer.

13a = 39*5

13a = 195

13a/13 = 195/13

a = 15

You can maybe see that the big triangle's side is 3 times bigger than the small one (13 times 3 is 39) So it works out that the 5 on the little triangle is 3 times bigger--15--on the large triangle!

Find the allowable height for the hypotenuse if the hypotenuse catheters are 4 cm and 9 cm

Answers

Answer:

L = 9.85 cm

Step-by-step explanation:

I guess you meant length for the hypotenuse. We just apply the pythagorean theorem:

L = [tex]\sqrt{(4 cm)^2 + (9 cm)^2} = \sqrt{16 cm^2 + 81 cm^2} = \sqrt{97 cm^2} = (circa) 9.85 cm[/tex]

Answer:

solutions given;

base:9 cm

perpendicular: 4 cm

hypotenuse:?

By using pythagorus law

hypotenuse^2: perpendicular^2+base^2

hypotenuse:[tex]\sqrt {4^2+9^2}[/tex]

hypotenuse:9.84cm

A sweatshirt was on sale for 32% off and cost $40.80 without tax. What was the original price of the sweatshirt?

Answers

Answer:

The original price of the sweatshirt was $127.50

Step-by-step explanation:

$40.80 / .32(32%) = $127.50

Which inequality represents the graph? x ≥ (y + 3)2 + 1 x ≤ (y + 3)2 + 1 x ≥ (y – 3)2 + 1 x ≤ (y – 3)2 + 1

Answers

The graph of each of the inequalities are created using a graphing tool as follows;

Graph 1; x ≥ (y + 3)² + 1

The domain = 1 ≤ x ≤ ∞

The range = -∞ < y < ∞

Graph 2; x ≤ (y + 3)² + 1

The domain = -∞ ≤ x ≤

The range = -∞ < y <

Graph 3; x ≥ (y - 3)² + 1

The domain = 1 ≤ x ≤ ∞

The range = -∞ < y < ∞

Graph 4; x ≤ (y - 3)² + 1

The domain = -∞ ≤ x ≤ ∞

The range = -∞ < y < ∞

Learn more about graph of inequalities here:

https://brainly.com/question/14876994

Answer:

c or x ≥ (y-3)^2+1

Step-by-step explanation:

What is the next number
3, 4, 7, 16, 11, 64, …
Answers:
A) 55
B)14
C)39
D)15

Answers

the answer is c) 39 according to the sequence

The next number 3, 4, 7, 16, 11, 64, is: 55.

What is the number pattern?

A number pattern is a pattern in a series of numbers that represents the common relationship between the numbers.

When all the terms of a geometric sequence are added, then that expression is called geometric series.

We are given the series as;

3, 4, 7, 16, 11, 64, …

If we separate the numbers that in order are in the even place of the odd ones, we would have :

3, 4, 7, 16, 11, 64,..

If we finish in 1 then they increase by 1 in 1, while in 2.- they increase in odd numbers, the following number is: 55

The correct option is A.

Learn more about a number pattern:

brainly.com/question/14471389

#SPJ2

A triangle and a square are drawn on dotty paper with dots 1 cm apart. What is the area of the region coloured red? ​

Answers

Answer:

≈ 0.9 cm²

Step-by-step explanation:

I don't know if there is any easier way to solve this, I use 8th grade slope and line method to solve. suppose A is on origin, then the coordinates of triangle ABC are (0,0) (1,3) (4,1) and polygon DEFGH intersect line BC at F and G.

F is the intersect of y=2 and line BC, while G is intersect of x=3 and line BC.

Line BC: pass (1,3) and slope (m) = (1-3)/(4-1) = - 2/3,    

F(x,2)

(2-3) / (x-1) = -2/3            

2x-2 = 3       x = 2.5          

*F (2.5 , 2)

G (3,y)

(y-3) / (3-1) = -2/3     y = 5/3      

*G (3 , 5/3)

*point I (3 , 2)

segment FI = 3-2.5 = 0.5 = 1/2

segment GI = 2 - 5/3 = 1/3

area ΔFIG = (1/2 * 1/3) / 2 = 1/12 = 0.083

area of polygon  DEFGH (region colored RED) = 1 - 0.083 = 0.917 ≈ 0.9 cm²

Pls help as soon as possible thank you

Answers

Answer:

answer is b

Step-by-step explanation:

6x+10

6*-3+10=-8

4x+4

4*-3+4=-8

Sammy factored the polynomial x2 + x - 6. She came up with the factors of
(x-3) and (x-2). Describe and correct the error.

Answers

Answer:

(x+3) and (x-2) are the correct factors

Step-by-step explanation:

If we expand (x-3)(x-2), we see that it equates to x²-5x+6, which is not what we want. The correct factors would be (x+3)(x-2) since the middle term's coefficient becomes 1 as 3-2=1 whereas -3-2=-5.

Other Questions
Help help help help help help straightforward answer which pairs of polygons are congruent?A. 3 and 4 B. 1 and 3C. 1, 3, and 4D. 2, 3, and 4E. 1, 2, 3 and 4 which is an equation of the line that goes through the points (-4,7) and (-4,11) Factorize the following: 9x+6x+1-25y India is best known for its 1. During the ______, the writings and art of Ancient Greeks were rediscovered. printing press 2. ______ is the study of religious faith, practice and experience. paper 3. Renaissance thinkers promoted _______, individualism, and secularism. Italy 4. _______ is the idea that people should be more interested in advancing their lives on earth than in worrying about getting to heaven. Secularism 5. _____ is the birthplace of the Renaissance. mapmaking 6. Dissatisfied with the church, Martin Luther started the ____ Reformation. Protestant 7. Martin Luther made use of the _____ to allow people to study the bible for themselves. Theology 8. New advances in _____ helped explorers travel the world. Renaissance 9. During the Renaissance, _____ was made from cotton and linen rags mashed into a pulp. humanism 10. To make a print, Renaissance artists first carved a ____ into a surface such as wood. relief 3. ADP + Pi ATP is best classified as which type of reaction? Byron earns $11. 00 per hour. How many hours will byron have to work to earn $143. 00? 7. 7 hours 13. 0 hours 14. 3 hours 15. 7 hours. A car is traveling at a steady speed. It travels 2 1/2 miles in 3 1/3 minutes. How far will it travel in 21 minute? In 1 hour? giving brainliest !! pls help Suppose you are putting up a tent for a camping trip.The 9 foot center pole makes a right angle with the ground. If a rope goes from the top of the pole to a point on the ground 12 feet away from the base of the pole. how long of a rope is needed? In the summer reading program, a participant earns 50 stars for reading 10 books. The library tracks the number of stars(y, vertical axis) and books ( x, horizontal axis) on a graph. Which statements are correct.A: Point(5,1) Represents the unit rateB: Point(1,5) Represents the unit rateC: Point(0,50) Represents the unit rateD: Point(100,20) Represents reading 20 booksE: Point(20,100)Represents reading 20 booksPlease help, I will give you the brainliest answer John has an exhaust leak in his Acura Integra GS-R, What steps would he take to fix the leak in time for his inspection? Which functions could be represented by the graph? Check all that apply. f(x) = | x + 0.14|f(x) = |x| + 1.3f(x) = |x 7|f(x) = |x + 12|f(x) = |x| 17f(x) = |x 23| PLEASE NO LINKS AND NO NEGATIVITY 10. John is mixing paint.He uses black, green and blue in the ratio 6:3: 1. How much of black green and blue paint is needed to make a mixture of paint of 500ml. The overall condition of the way that groups of people lived is called .....A. EconomicsB. Standard of livingC. Happiness Index hand demand and private own John borrowed $5,000 from his parents to buy a car. He made a one-time payment of $1,500 and then he is going to pay his mother $250 each month. How long will it take for him to pay off the car? Fill in the blank: an important part of dashboard design is ensuring that charts, graphs, and other visual elements are cohesive. This means that they are _____ and make good use of available space. Which of the following statements is true about the Yalta and Potsdam conferences?and if anyone knows the rest of the answers that'd be amazing!100 points! please answer quickly!