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3 years ago

Factor 4x 2 + 12x + 5 . (2x + 5)(2x + 1)

1 answer:

8 0

Factor
in form
ax²+bx+c form
use the ac method
1. mulitply a and c
2. factor the result such that the 2 factors add to b
3. split b into those 2 factors
4. group the terms
5. undistribute common factors
6. undistribute again

first multiply ac
4 times 5=20
now
what 2 numbers multiply to 20 and add to 12
2 and 10
4x²+2x+10x+5
group
(4x²+2x)+(10x+5)
undistribute
2x(2x+1)+5(2x+1)
undistribute the (2x+1)
(2x+1)(2x+5) is factored form whih you have there, nice

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PLEASE GUYS THIS IS THE HARDEST MATH PORBLEMS PLEASE ASAP PLEASE I NEED HELP PLEASE T_T

Alexandra [31]

The simplified form of R(x) is $R(x) =\frac{x^{2} -13x+42}{x^{2} -10x+25}$

<h3>Simplifying an expression </h3>

From the question, we are to simplify the expression

From the given information,

$f(x) =\frac{x^{2}-11x+28 }{x^{2}-11x+30}$

and

$g(x) =\frac{x^{2}-9x+20 }{x^{2}-12x+36}$

Also,

$R(x) = f(x) \div g(x)$

∴ $R(x) =\frac{x^{2}-11x+28 }{x^{2}-11x+30} \div \frac{x^{2}-9x+20 }{x^{2}-12x+36}$

$R(x) =\frac{x^{2}-11x+28 }{x^{2}-11x+30} \times \frac{x^{2}-12x+36 }{x^{2}-9x+20}$

Factoring each of the quadratics

$R(x) =\frac{x^{2}-7x-4x+28 }{x^{2}-6x-5x+30} \times \frac{x^{2}-6x-6x+36 }{x^{2}-4x-5x+20}$

$R(x) =\frac{x(x-7)-4(x-7) }{x(x-6)-5(x-6)} \times \frac{x(x-6)-6(x-6) }{x(x-4)-5(x-4)}$

$R(x) =\frac{(x-4)(x-7)}{(x-5)(x-6)} \times \frac{(x-6)(x-6)}{(x-5)(x-4)}$

Simplifying

$R(x) =\frac{(x-7)}{(x-5)} \times \frac{(x-6)}{(x-5)}$

$R(x) =\frac{(x-7)(x-6)}{(x-5)(x-5)}$

$R(x) =\frac{x^{2} -6x-7x+42}{x^{2} -5x-5x+25}$

$R(x) =\frac{x^{2} -13x+42}{x^{2} -10x+25}$

Hence, the simplified form of R(x) is $R(x) =\frac{x^{2} -13x+42}{x^{2} -10x+25}$

Learn more on Simplifying an expression here: brainly.com/question/1280754

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7 0

1 year ago

Graph y = -1/3x + 5<br><br> khan academy

sdas [7]

Graph the line using the slope and y-intercept, or two points.

Slope:

−1/3

y-intercept:

(0, 5)

x y

0 5

15 0

7 0

2 years ago

Carlos Martin received a statement from his bank showing a balance of $56.75 as of March 15th his check book shows a balance of

kakasveta [241]

Answer:

$48.87

Step-by-step explanation:

Let the deposited amount between the March 15th and the March 20th be x

Balance on 15th march = $56.75

The bank returned all the cancelled checks but too. One check was for $5 and the other was for $13.25

And he also deposited x amount

After deposits and deductions

So, balance = 56.75 +x - (13.25+5)

The new balance on 20th march = $87.37

⇒ $56.75 +x - (13.25+5)=87.37$

⇒ $56.75 +x - 18.25=87.37$

⇒ $38.5 +x =87.37$

⇒ $x =87.37-38.5$

⇒ $x =48.87$

Hence Carlos deposited $48.87 in his account between the March 15th and the March 20th.

6 0

2 years ago

Read 2 more answers

A hose fills an empty fish tank with 24 gallons of water in 8 minutes. At that same rate, how many minutes will it take the hose

kolezko [41]

Answer:

$\frac{8}{24} = \frac{x}{60}$

24x = 8*60

24x = 480

x = 20

Step-by-step explanation:

3 0

2 years ago

Sooo I’m a moron and reallyyy need help

boyakko [2]

You should use photo math it can help you instantly with math problems!

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2 years ago