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
alina1380 [7]
3 years ago
11

Please Help! Factor the following trinomial

x^2-24x+16" alt="9x^2-24x+16" align="absmiddle" class="latex-formula">
Please show work
Mathematics
2 answers:
Dmitrij [34]3 years ago
8 0

=> 9x² - 24x + 16

Split the middle term(term with x) in such a manner so that the product of those parts is equal to the product of term with x² and constant. Here, those parts are 12 & 12 as 12*12 = 9*16.

=> 9x² - 24x + 16

=> 9x² - (12 + 12)x + 16

=> 9x² - 12x - 12x + 16

=> 3x(3x - 4) - 4(3x - 4)

=> (3x - 4)(3x - 4)

Method 2

=> 9x² - 24x + 16

=> (3x)² - 2(3x*4) + 4²

=> (3x - 4)²

=> (3x - 4)(3x - 4)

Method 3

In case if you can't find the factors of the middle term.

Say f(x) = 0, find the zeroes using quadratic formula. Zeroes of this eqⁿ are [-(-24) ± √24²-4(9)(16)] / 2(9) = 4/3 & 4/3

Therefore, f(x) = (x - 4/3)(x - 4/3) = (3x - 4)(3x - 4)/9

Ignore the numeric constant.

f(x) = (3x - 4)(3x - 4)

AlexFokin [52]3 years ago
5 0

\huge\colorbox{pink}{Hey \: panda!}

The answer=>

For this,we need to know what's Middle splitting method

  • In order to factorize x² + bx + c we have to find numbers p and q such that p + q = b and pq = c. After finding p and q, we split the middle term in the quadratic as <em><u>px + qx and</u></em> get desired factors by grouping the terms.

Step-by-step explanation:

9x {}^{2}  - 24x + 16 \\  =  > 9x {}^{2}  - 12x - 12x + 16 \\  =  > 3x(3x - 4) - 4(3x - 4) \\  =  > (3x - 4)(3x - 4) \\ so... \\ x = eitherway \: 4

i.e

Alpha= Beta = 4

You might be interested in
4TH TIME ASKING THIS!!! Please help me! Someone pleaseeee. I need the correct answers. I don’t want to fail
Alexeev081 [22]

Answer:

The functions are inverses; f(g(x)) = x ⇒ answer D

h^{-1}(x)=\sqrt{\frac{x+1}{3}} ⇒ answer D

Step-by-step explanation:

* <em>Lets explain how to find the inverse of a function</em>

- Let f(x) = y

- Exchange x and y

- Solve to find the new y

- The new y = f^{-1}(x)

* <em>Lets use these steps to solve the problems</em>

∵ f(x)=\sqrt{x-3}

∵ f(x) = y

∴ y=\sqrt{x-3}

- Exchange x and y

∴ x=\sqrt{y-3}

- Square the two sides

∴ x² = y - 3

- Add 3 to both sides

∴ x² + 3 = y

- Change y by f^{-1}(x)

∴ f^{-1}(x)=x^{2}+3

∵ g(x) = x² + 3

∴ f^{-1}(x)=g(x)

∴ <u><em>The functions are inverses to each other</em></u>

* <em>Now lets find f(g(x))</em>

- To find f(g(x)) substitute x in f(x) by g(x)

∵ f(x)=\sqrt{x-3}

∵ g(x) = x² + 3

∴ f(g(x))=\sqrt{(x^{2}+3)-3}=\sqrt{x^{2}+3-3}=\sqrt{x^{2}}=x

∴ <u><em>f(g(x)) = x</em></u>

∴ The functions are inverses; f(g(x)) = x

* <em>Lets find the inverse of h(x)</em>

∵ h(x) = 3x² - 1 where x ≥ 0

- Let h(x) = y

∴ y = 3x² - 1

- Exchange x and y

∴ x = 3y² - 1

- Add 1 to both sides

∴ x + 1 = 3y²

- Divide both sides by 3

∴ \frac{x + 1}{3}=y^{2}

- Take √ for both sides

∴ ± \sqrt{\frac{x+1}{3}}=y

∵ x ≥ 0

∴ We will chose the positive value of the square root

∴ \sqrt{\frac{x+1}{3}}=y

- replace y by h^{-1}(x)

∴ h^{-1}(x)=\sqrt{\frac{x+1}{3}}

4 0
3 years ago
Show work on how you converted them. (also marking brainliest) &lt;3
Dmitry_Shevchenko [17]

Answer:

1. 5700mg

2. 1000cm

3. 0.0453m

4. 37.5 kg/L

Step-by-step explanation:

1. 1gram (g) =1000milligrams(mg)

5.70×1000=5700mg

2. 1 m= 100cm

10×100=1000cm

3. 1000mm=1m

45.3/1000=0.0453m

4. 1000g=1kg

37.5/1000=0.0375

1000ml=1L

1ml= 1/1000= 0.001L

0.0375/0.001= 37.5 kg/L

8 0
3 years ago
Subtract 8 y^2 − 5 y + 7 from 2 y^2 + 7 y + 1 1 <br><br> The answer is: −6y ^2 +12y+4
lys-0071 [83]

Answer:

\large\boxed{-6y^2+12y+4}

Step-by-step explanation:

(2y^2+7y+11)-(8y^2-5y+7)\\\\=2y^2+7y+11-8y^2-(-5y)-7\\\\=2y^2+7y+11-8y^2+5y-7\qquad\text{combine like terms}\\\\=(2y^2-8y^2)+(7y+5y)+(11-7)\\\\=-6y^2+12y+4

4 0
3 years ago
If the length of a leg of a triangle is 39.2 and the area of the triangle is 63 what is the length of the other leg
Nadya [2.5K]

Answer:

The length of the other leg is 3.21\ units

Step-by-step explanation:

I will assume that the triangle is a right triangle

In a right triangle the legs are perpendicular

so

The area of a right triangle is equal to

A=\frac{1}{2}(a)(b)

where

a and b are the legs of the triangle

In this problem we have

a=39.2\ units

A=63\ units^{2}

substitute the values

63=\frac{1}{2}(39.2)(b)

126=(39.2)(b)

b=126/(39.2)=3.21\ units

7 0
3 years ago
What is the arithmetic mean of the following numbers?<br> 6,4, 1,9, 3, 8, 3, 5, 10
Ronch [10]
5.4 I think I’m not sure if it correct though
6 0
2 years ago
Other questions:
  • BRAINLIEST!!! I need help ASAP how do I find the percent change from 1960 to 2000
    10·1 answer
  • Jeremy has a weekend job as a soccer referee. One weekend, he earns $140 by working 4 games. Another weekend, he earns $210 by w
    13·1 answer
  • ASAP PLZ HELP WITH THIS QUESTION I WILL MARK U AS BRAINLIST
    14·1 answer
  • How do you find the quadratic function with vertex (-2,5) and point (0,9)?
    11·1 answer
  • A circular plate has a crack along the line AB, as shown below:
    14·2 answers
  • Use the strategy to simplify 4\sqrt(576)<br> Write the prime factorization of the radicand.
    14·2 answers
  • Find the x= to the answer
    15·1 answer
  • Help help help help help help help help help help help help help help help help help help help
    14·2 answers
  • Olk-onm <br> Find the value of u.
    14·1 answer
  • Hi how’s your day ? Would you like to help me ?
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!