.A rectangular pool is 30 1/3 feet long and 12 1/2 feet wide. What is the area of the pool??

7. Use the quadratic formula to find the solution(s). x² + 2x - 8 = 0

morpeh [17]

Hey there!

Use the quadratic formula to find the solution(s). x² + 2x - 8 = 0

Answer :

x = -4 or x = 2 ✅

Explanation :

Quadratic formula : ax² + bx + c = 0 where a ≠ 0

The number of real-number solutions (roots) is determined by the discriminant (b² - 4ac) :

If b² - 4ac > 0 , There are 2 real-number solutions

If b² - 4ac = 0 , There is 1 real-number solution.

If b² - 4ac < 0 , There is no real-number solution.

The roots of the equation are determined by the following calculation:

$x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a}$

Here, we have :

a = 1
b = 2
c = -8

1) Calculate the discriminant :

b² - 4ac ⇔ 2² - 4(1)(-8) ⇔ 4 - (-32) ⇔ 36

b² - 4ac = 36 > 0 ; The equation admits two real-number solutions

2) Calculate the roots of the equation:

▪️ (1)

$x_1 = \frac{ - b - \sqrt{ {b}^{2} - 4ac} }{2a} \\ \\ x_1 = \frac{ - 2 - \sqrt{36} }{2(1) } \\ \\ x_1 = \frac{ - 2 - 6}{2} \\ \\ x_1 = \frac{ - 8}{2} \\ \\ \blue{\boxed{\red{x_1 = -4}}}$

▪️ (2)

$x_2 = \frac{ - b + \sqrt{ {b}^{2} - 4ac } }{2a} \\ \\ x_2 = \frac{ - 2 + \sqrt{36} }{2(1)} \\ \\ x_2 = \frac{ - 2 + 6}{2} \\ \\ x_2 = \frac{4}{2} \\ \\ \red{\boxed{\blue{x_2 = 2}}}$

>> Therefore, your answers are x = -4 or x = 2.

Learn more about quadratic equations:

brainly.com/question/27638369

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2 years ago

Read 2 more answers

BRAINLIESTTT ASAP! PLEASE HELP ME :)

kherson [118]

Answer:

b. $\displaystyle 225y^2 + 150xy + 100x^2 = 225y^2 + 150xy + 100x^2$

a. $\displaystyle [8x + 12y]^2 + [6x + 9y]^2 = [10x + 15y]^2$

Step-by-step explanation:

b. $\displaystyle 225y^2 + 150xy + 100x^2 = 225y^2 + 150xy + 100x^2$

a. $\displaystyle [8x + 12y]^2 + [6x + 9y]^2 = [10x + 15y]^2$

The two expressions are identical on each side of the equivalence symbol, therefore they are an identity.

I am joyous to assist you anytime.

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3 years ago

Does this graph represent a function? Why or why not?

Lunna [17]

Answer:

Step-by-step explanation:

B. Yes, because it passes the vertical line test, is the answer.

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2 years ago

I need help with numbers 5,6,and 8

erastovalidia [21]

5) Obtuse triangle because the top angle is more than 90 degrees

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2 years ago

WRITE AN COMPOUND INEQUALITY FOR THIS SENTENCE

Mila [183]

Hello there!

Write a compound inequality for this sentence: 'w' is less than 4 and greater than or equal to -8
Only use 'w' once.

W is less than four ~ $4 \ \textgreater \ w$

W is greater than or equal to -8 ~ $w \geq -8$

If we were to put this together, it would look like:

$4 \ \textgreater \ w \geq -8$

I hope I helped!

Let me know if you need anything else!

~ Zoe

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3 years ago