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ohaa [14]
3 years ago
12

Solve for x. write both solutions, separated by a comma.

3x%20-%209%20%3D%200" id="TexFormula1" title=" {2x}^{2} + 3x - 9 = 0" alt=" {2x}^{2} + 3x - 9 = 0" align="absmiddle" class="latex-formula">
​
Mathematics
2 answers:
gulaghasi [49]3 years ago
7 0

Answer:

x = -3 and x = 3/2

Step-by-step explanation:

2x^2 + 3x - 9 = 0

2x^2 + 6x - 3x - 9 =0

2x(x + 3) - 3(x + 3) = 0

(2x - 3)(x + 3) = 0

2x - 3 = 0; x = 3/2

x + 3 = 0; x = -3

attashe74 [19]3 years ago
5 0

Answer:

see explanation

Step-by-step explanation:

given

2x² + 3x - 9 = 0

To factor

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 = 2 × - 9 = - 18 and sum = + 3

The factors are + 6 and - 3

Use these factors to split the x- term

2x² + 6x - 3x - 9 = 0 ( factor the first/second and third/fourth terms )

2x(x + 3) - 3(x + 3) = 0 ← factor out (x + 3)

(x + 3)(2x - 3) = 0

Equate each factor to zero and solve for x

x + 3 = 0 ⇒ x = - 3

2x - 3 = 0 ⇒ 2x = 3 ⇒ x = \frac{3}{2}

Solutions are x = - 3, \frac{3}{2}

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8 0
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Zahra compares two wireless data plans. Which equation gives the correct value of n, the number of GB, for which Plans A and B c
Elden [556K]

The equation which gives the correct value of n, the number of GB, for which Plans A and B cost the same is 8n = 20 + 6(n-2)

To determine which equation gives the correct value of n, the number of GB, for which Plans A and B cost the same, we will first solve the equations.

  • For the first equation

8n = 20 + 6n

Collect like terms

8n - 6n = 20

2n = 20

Then, n = 20 ÷ 2

n = 10 GB

For Plan A

No initial fee and $8 for each GB

Here, 10GB will cost 10 × $8 = $80

For Plan B

$20 for the first 2GB and $6 for each additional GB after the first 2

Here, 10GB will cost $20 + (8 × $6) = $20 + $48 = $68

∴ Plans A and B do not cost the same here.

  • For the second equation

8n = 20(2n) + 6

First, clear the bracket

8n = 40n + 6

Now, collect like terms

40n - 8n = 6

42n = 6

∴ n = 6 ÷ 42

n = 1/7 GB

For Plan A

No initial fee and $8 for each GB

Here, 1/7GB will cost 1/7 × $8 = $1.14

For Plan B

$20 for the first 2GB and $6 for each additional GB after the first 2

Here, 1/7GB will cost $20 (Since the lowest cost is $20)

∴ Plans A and B do not cost the same here.

  • For the third equation

8n = 20 + 6(n-2)

First, clear the brackets

8n = 20 + 6n - 12

Now, collect like terms

8n - 6n = 20 - 12

2n = 8

n = 8 ÷ 2

n = 4 GB

For Plan A

No initial fee and $8 for each GB

Here, 4GB will cost 4× $8 = $32

For Plan B

$20 for the first 2GB and $6 for each additional GB after the first 2

Here, 4GB will cost $20 + (2 × $6) = $20 + $12 = $32

Plans A and B do not cost the same here.

∴ Plans A and B do cost the same here

  • For the fourth equation

8n = 20 + 2n + 6

Collect like terms

8n - 2n = 20 + 6

6n = 26

n = \frac{26}{6}

n = \frac{13}{3} GB or 4\frac{1}{3} GB

For Plan A

No initial fee and $8 for each GB

Here, \frac{13}{3} GB will cost \frac{13}{3}  × $8 = $34.67

For Plan B

$20 for the first 2GB and $6 for each additional GB after the first 2

Here, 4\frac{1}{3}GB will cost $20 + ( 2\frac{1}{3}× $6) = $20 + $14 = $34

∴ Plans A and B do not cost the same here.

Hence, the equation which gives the correct value of n, the number of GB, for which Plans A and B cost the same is 8n = 20 + 6(n-2)

Learn more here: brainly.com/question/9371507

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