Given that the roots of the equation a[tex]x^{2}[/tex]+b[tex]x[/tex]+c=0 are [tex]\beta[/tex] and n[tex]\beta[/tex], show that (n+1)²ac=nb²

Answers

Answer 1

Answer:

Step-by-step explanation:

sum of roots β+nβ=-b/a

(n+1)β=-b/a

squaring

(n+1)²β²=b²/a²

product of roots β×nβ=c/a

nβ²=c/a

β²=c/na

∴(n+1)²c/na=b²/a²

multiply by na²

(n+1)²ac=nb²


Related Questions

What is the constant term of -3x(4)-7x+2 ?

Answers

Answer:

trinomials term .........................

Answer:

2

Step-by-step explanation:

Choose the congruence theorem that you would use to prove the triangles congruent

Answers

Answer:

It would be the HL theorum.

Step-by-step explanation:

The answer would be the HL theorum by just considering the name.  "HL" stands for Hypotenuse-leg.  The problem tells you that both triangles share the same length of their hypotenuse (The Hypotenuse is the line with one dash in it, or the one opposite of the 90 degree angle) and one of the legs (The legs are the lines that connect to make the 90 degree angle).  This makes the triangle congruent because if 2 sides of a triangle are the same it means that the third one is congruent as well.

please help! need answers in order to move on:)

1.) which number equals (5)^-3?
- -125
- 1/15
- 1/125
- -15

2.) find the equivalent for -(3)^-4
- -(4x4x4)
- -3x-4
- 1/-3x-3x-3x-3
- -(1/3x1/3x1/3x1/3)

3.) which of the following is equivalent to 3^-8x3^4
- 3^-12
- 3^-4
- 3^-2
- 3^-32

4.) which value is equivalent to 7^-3/7^-5
- 7^15
- 7^-2
- 7^8
- 7^2

5.) choose the equivalent expression (8^10)^2
- 8^12
- 8^20
- 8^8
- 8^5

6.) which expression is equivalent to (9x8)^4
- 9x8x4
- 9^4x8^4
- (9^8)^4
- (9^4)^8

7.) which expression is equivalent to (2/7)^5
- 2^5/7^5
- 2x5/7x5
- 2^5/7
- 2x5/7

Answers

Answer:

1.) C. - 1/125

2.) B. - -3x-4

3.) A. - 3^-12

4.) C. - 7^8

5.) D. - 8^5

6.) A.  - 9x8x4

7.) B. - 2x5/7x5 or A It's Almost the Same But I couldn't find the exact difference so Sorry.

There were 756 students enrolled in a freshman-level chemistry class. By the end of the semester, the number of students who passed was 6 times the number of students wh
failed
Find the number of students who passed and the number who failed.

Answers

Answer:

4536

Step-by-step explanation:

Answer:

630 students passed the exam and 126 students failed the exam

Need answers now. Not good with geometry or Algebra.​

Answers

Answer:

x = 4.98

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

sin theta = opp / hyp

sin 50 = x/6.5

6.5 sin 50 =x

x=4.97928

x = 4.98

I'm under the water on this problem, please help me:

question: f(x)=10x−3

answer choices:

A. f(−5)

B. f(0)

C. f(7)

D. f(t^2+2)

E. f(12−x)

F. f(x+h)

Answers

Answer:

See below

Step-by-step explanation:

Okay so...I might be interpreting the question wrong-if I am please comment! I'll fix it to the best of my ability.

A) Plug in -5 to all x values

   f(-5)=10(-5)-3

          ==50-3

    f(-5)= -53

B) f(0)=10(0)-3

    f(0)= -3

C) f(7)=10(7)-3

         =70-3

    f(7)=67

D) f(t^2+2)=10(t^2+2)-3

                 =10t^2+20-3

     f(t^2+2)=10t^2+17

E) f(12-x)=10(12-x)-3

              =120-10x-3

    f(12-x)=117-10x

F) f(x+h)=10(x+h)-3

             =10x+10h-3

what is this please tell answer​

Answers

Answer:

x=6, y=4, z=8

(c) 6

I hope this is helpful!

How do you do 9&10?

Answers

Answer:

Step-by-step explanation:

9) 9xt

10) r-10

What is the value of this expression when a = 7 and b = -4?

|2a|-b over 3

Answers

Answer:

6

Step-by-step explanation:

The absolute value of 2(7)=14. b=-4, so 14+4=18. 18/3=6.

Answer:

6

Step-by-step explanation:

2(7)-(-4)/3

14+4/3

18/3

6

3x?
3x?
If Ax)=
2x
and g(x)
find /(x) = g(x)

Answers

Answer:

and practice problems to learn how to find and evaluate composite functions. ... If f(x)=(1/x) and (f/g)(x)=((x+4)/(x^2+2x)), what is the function g?

[tex]\sqrt\\x^{2} - 3\\[/tex]

Answers

you can’t simplify it more than it is

If 150° and 3a are supplementary angles, find the value of a. ​

Answers

Answer:

a = 10

Step-by-step explanation:

Supplementary angles sum to 180° , so

150 + 3a = 180 ( subtract 150 from both sides )

3a = 30 ( divide both sides by 3 )

a = 10

Which is the graph of y = [x]-2?
Please please helped timed 20points

Answers

Answer:

3rd graph

Step-by-step explanation:

I need help with this one pls!

Answers

Hi there!

[tex]\large\boxed{b = \frac{a}{ac - 1}}[/tex]

We can begin by making each fraction have a common denominator:

If we make each have a common denominator of ab, we get:

[tex]\frac{b}{ab} + \frac{a}{ab} = c[/tex]

Simplify:

[tex]\frac{a + b}{ab} = c[/tex]

Multiply both sides by ab:

[tex]a + b = cab[/tex]

Move b to the opposite side:

[tex]a = cab - b[/tex]

Factor out b:

[tex]a = b(ac - 1)[/tex]

Divide by (ac - 1):

[tex]\frac{a}{ac - 1} = b[/tex]

what is twelve less than a variable​

Answers

Answer:

x-12

Step-by-step explanation:

Let the variable be x

12 less than

x-12

It’s mean you subtract 12 by that number.
X-12

If the base linear function is F(x) =-3x and 5 is added to the equation, then what best describes what happened to the base equation? 

A.nothing happened stayed the same

B. The base equation shifts up five units

C. The base equation shifts to the left five units

D. The base equation shifts down five units

E. The base equation shifts to the right to five units

Answers

Answer:

E the base equation shifts to the right to five unit from the midpoint

!!! i only need part c !!! There are 30 homes in Neighborhood A. Each year, the number of homes increases by 20%. Just down the road, Neighborhood B has 45 homes. Each year, 3 new homes are built in Neighborhood B.


Part A: Write functions to represent the number of homes in Neighborhood A and Neighborhood B throughout the years. (4 points)


Part B: How many homes does Neighborhood A have after 5 years? How many does Neighborhood B have after the same number of years? (2 points)


Part C: After approximately how many years is the number of homes in Neighborhood A and Neighborhood B the same? Justify your answer mathematically. (4 points)


(10 points)

Answers

I only need part c there are homes neighborhood homes act year the number of homes increases just down the road neighborhood

Solve the equation | 7x + 5| = |3x - 13|​

Answers

I 7X + 5 I = I 3X- 13I

7×+5 = 3x +13

7X-3x = 13-5

4x = 8

X= 8/4

X=2

The Ramirez family and the Stewart family each used their sprinklers last summer. The water output rate for the Ramirez family's sprinkler was 40 L per hour.
The water output rate for the Stewart family's sprinkler was 15 L per hour. The families used their sprinklers for a combined total of 55 hours, resulting in a total
water output of 1575 L. How long was each sprinkler used?

Answers

Answer:

15.5

Step-by-step explanation:

Yes

ABCD is a rectangle. AB = 3x+5, AC = 7x-9, BC = 2y+5, BD = 2x+62. Solve for x. (Round your answer to one decimal place, if necessary.)

Answers

Answer:

x=14.2

Step-by-step explanation:

AC = BD

The diagonals of a rectangle are equal

7x-9 =  2x+62

Subtract 2x from each side

7x-9-2x = 2x+62-2x

5x-9 = 62

Add 9 to each side

5x-9+9 = 62+9

5x= 71

Divide by 5

5x/5 = 71/5

x=14.2

Find −4^3(5^2). Express using exponents.​

Answers

Answer:

-1600

Step-by-step explanation:

−4^3(5^2)

5 × 5 = 25

-4 × -4 × -4

   -16 × -4

       -64

64 × 25 = -1600

   

The answer is -1600

Hope this helped.

Which point has the coordinates (-3.5, 7)?​

Answers

Answer:

Q

Step-by-step explanation:

The coordinates are ( x,y)

negative 3.5 goes 3.5 units to the left

7 goes 7 units up

Answer:

Q

Step-by-step explanation:

The x coordinates is - 3.5 so we go left to - 3 and half way to 4 to get 0.5

the Y coordinates is 7, so we go up the Y axis to 7. We can then see that Q is located there

What is the additive identity of -17?

Answers

Answer:

The additive identity is 0. The sum of any number with the additive identity is the number itself.

I HOPE ITS RIGHT IF NOT THEN SORRY

HAVE A GREAT DAY :)

It’s always has to be 0

Sitting on a park bench, you see a swing that is 100 feet away and a slide that
is 60 feet away. The angle between them is 30°.
distance between the swing and the slide?
What is the approximate

Answers

Answer:

50

Step-by-step explanation:

Answer:

The approximate between the swing and slide is 56.21 feet.

Step-by-step explanation:

3. the third one please answer ASAP write it on paper, please

Answers

The answer is 1/3
To 4/5+3/15-2/3

Answer:

1/3

Step-by-step explanation:

We have to make the denominator of all fractions to be 15:

Multiply both the 4 and the 5 in 4/5 by 3 to get 12/15.

Nothing has to be done to 3/15.

Next, multiply both the -2 and the 3 in -2/3 by 5 to get -10/15.

Solve:

12/15 + 3/15 - 10/15 = 5/15.

5/15 further simplifies to 1/3.

The final answer is 1/3.

Find the median of data set. Round it to the nearest tenth.​

Answers

Answer:

The median of the data set that you've provided, is 13,350.

Explanation:

13350 is the middle number from the set after writing the set in ascending order. you have 5 numbers on the left of 13350 and 5 on the right, 13350 is the middle one thus it's the median.

After Arranging it in Ascending order

The total number of items is 11

The middle one is 13,350

Therefore the range is 13,350

Must click thanks and mark brainliest

If f(x) = x3 – 1, what is the ordered pair for x = -2.?

Answers

Answer:

(-2, -9)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Algebra I

Coordinates (x, y)

Functions

Function Notation

Step-by-step explanation:

Step 1: Define

Identify

f(x) = x³ - 1

x = -2

Step 2: Evaluate

Substitute in x [Function f(x)]:                                                                          f(-2) = (-2)³ - 1Exponents:                                                                                                        f(-2) = -8 - 1Subtract:                                                                                                            f(-2) = -9Rewrite:                                                                                                             (-2, -9)

What is the nineteenth term of an arithmetic sequence with first term 9 and common difference 5?

Answers

Answer:

a₁₉ = 99

Step-by-step explanation:

The nth term of an arithmetic sequence is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 9 and d = 5 , then

a₁₉ = 9 + (18 × 5) = 9 + 90 = 99

The nineteenth term of arithmetic c sequence with first term 9 and common difference 5 is 99.

What is Arithmetic progression?

The difference between every two successive terms in a sequence is the same this is known as an arithmetic progression (AP).

The arithmetic progression has wider use in mathematics for example sum of natural numbers.

Natural number = 1,2,3,4,5,6,7,8...

Now it has the same difference between any two consecutive terms d =2-1 = 3-2

Given an AP series

First term(a) = 9

Common difference (d) = 5

The nth term is given by

⇒ a + (n - 1)d

So,

19th term = 9 + (19-1)5

⇒ 99

Hence "The nineteenth term of arithmetic c sequence with first term 9 and common difference 5 is 99".

For more about Arithmetic progression

https://brainly.com/question/20385181

#SPJ2

Write in factored form
m^2 - n^4

Answers

The answer is : [tex]\left(m+n^2\right)\left(m-n^2\right)[/tex]

Here are the steps below to help you! ^^

Name the marked angle in 2 different ways.

Answers

Answer:

Step-by-step explanation:

<CDE or <EDC

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