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3 years ago

What are the factors of the equation 24x^2=9-30x?

Mathematics

1 answer:

Dennis_Churaev [7]3 years ago

7 0

Answer:

3(4x - 1)(2x + 3)

Step-by-step explanation:

Rearrange the equation into standard form

Subtract 9 - 30x from both sides

24x² + 30x - 9 = 0 ← in standard form

Take out 3 as a common factor

3(8x² + 10x - 3) = 0 ← factor the quadratic

Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x term

product = 8 × - 3 = - 24, sum = 10

The factors are - 2 and + 12

Use these factors to replace the x- term, that is

8x² - 2x + 12x - 3 ( factor the first/second and third/fourth terms )

2x(4x - 1) + 3(4x - 1) ← take out the common factor (4x - 1)

(4x - 1)(2x + 3)

24x² + 30x - 9 = 3(4x - 1)(2x + 3) ← in factored form

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PLEASE HELP

lisabon 2012 [21]

Step-by-step explanation:

The figure below shows a portion of the graph of the function $j\left(x\right) \ = \ 4^{x-2}$ , hence the average rate of change (slope of the blue line) between the $x$ and $x+h$ is

$\text{Average rate of change} \ = \ \displaystyle\frac{\Delta y}{\Delta x} \\ \\ \rule{3.7cm}{0cm} = \dsiplaystyle\frac{f\left(x+h\right) \ - \ f\left(x\right)}{\left(x \ + \ h \right) \ - \ x} \\ \\ \\ \rule{3.7cm}{0cm} = \displaystyle\frac{f\left(x + h\right) \ - \ f\left(x\right)}{h} \\ \\ \\ \rule{3.7cm}{0cm} = \displaystyle\frac{4^{x+h-2} \ - \ 4^{x-2}}{h} \\ \\ \\ \rule{3.7cm}{0cm} = \displaystyle\frac{4^{x-2+h} \ - \ 4^{x-2}}{h}$

$\\ \\ \\ \rule{3.7cm}{0cm} = \displaystyle\frac{\left(4^{x-2}\right)\left(4^{h}\right) \ - \ 4^{x-2}}{h} \\ \\ \\ \rule{3.7cm}{0cm} = \displaystyle\frac{\left(4^{x-2}\right)\left(4^{h} \ - \ 1 \right)}{h}$

7 0

2 years ago

5 (2x – 1) –7 = 2 (x – 3)

Sladkaya [172]

Answer:

x−3=x−3

Step-by-step explanation:

Evaluate (2x−1)−7, then set it equal to 2.

Subtract 7 from −1 = 2x−8

Solve 2x−8=2.

Move all terms not containing x to the right side of the equation.

Add 8 to both sides of the equation=2x=2+8

Add 2 and 8=2x=10

Divide each term by 2 and simplify.

Divide each term in 2x=10 by 2=2x/2=10/2

Cancel the common factor of 2

Cancel the common factor=10/2

Divide x by 1=x=10/2

Divide 10 by 2=x=5

Remove parentheses=x−3

List all of the solutions.

(2x−1)−7=2=x=5

x−3=x−3

7 0

3 years ago

A bank account has an balance of 1,000. If the owner withdraws 125, what is the new balance? What is the balance now?

AveGali [126]

Answer:

$875

Step-by-step explanation:

1000-125=875

6 0

3 years ago

Read 2 more answers

Lydia is buying cupcake ls for he brother birthday party. She brought 36 cupcakes total.Of the cupcakes she bought,5/6 of them w

quester [9]

Answer:

58.50

Step-by-step explanation:

First find out how many were vanilla and chocolate

vanilla: 5/6 * 36 = 30

Chocolate = total - vanilla = 36-30 =6

Cost for vanilla = 1.50*30 =45

Cost for chocolate 2.25*6 =13.5

Add the cost together

45+13.50

58.50

3 0

4 years ago

Which expression is the factored form of −1.5w+7.5 ?

tresset_1 [31]

The correct answer is C) -1.5(w-5).

Both numbers are divisible by 1.5. Since there is a negative in the first term, we will factor that out as well. This means we are dividing both terms by -1.5:

-1.5( )

Taking -1.5 out of -1.5w, we have w left:

-1.5(w )

Dividing 7.5 by -1.5, we have -5:

-1.5(w-5)

5 0

3 years ago