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3 years ago

Solve the equation by completing the square and then solving for x. 1. x^2-6x=122. 2x^2-24x=-20

Mathematics

1 answer:

Paraphin [41]3 years ago

8 0

Answer: (x - 3)² = 21

Step-by-step explanation:

x² - 6x + ____ = 12 + ____

↓ ↑ ↑

$\frac{-6}{2} = (-3)^{2}$

x² - 6x + 9 = 12 + 9

(x - 3)² = 21

*******************************************************

Answer: (x - 6)² = 26

Step-by-step explanation:

2x² - 24x = -20

÷2 ÷2 ÷2

x² - 12x = -10

x² - 12x + ____ = -10 + ____

↓ ↑ ↑

$\frac{-12}{2} = (-6)^{2}$

x² - 12x + 36 = -10 + 36

(x - 6)² = 26

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the captain of a boat knows that the lighthouse on the coast is 200 feet tall. he measures the angle of elevation to the top of

krek1111 [17]

Answer:

The boat is 5727.25ft far from the coast

Step-by-step explanation:

Refer the figure given.

We need to find how far is the boat from the coast = AB

Angle of elevation = 2°

The lighthouse on the coast is 200 feet tall, AC = 200 ft

We have

$tan2=\frac{AC}{AB}=\frac{200}{AB}\\\\AB=\frac{200}{tan2}=5727.25ft$

The boat is 5727.25ft far from the coast

7 0

3 years ago

What is an equation of a line that passes through the point of (-8 2) and (-4,-3)

Alex_Xolod [135]

Answer:

Step-by-step explanation:

$(-8,2)=(x_1 ,y_1)\\(-4 ,-3) = (x_2 ,y_2)\\\\\frac{y-y_1}{x-x_1} = \frac{y_2-y_1}{x_2-x_1}\\ \\\frac{y-2}{x-(-8)}= \frac{-3-2}{-4-(-8)}\\ \\\frac{y-2}{x+8}= \frac{-5}{-4+8} \\ \\\\\frac{y-2}{x+8} = \frac{-5}{4}\\ \\Cross\:Multiply \\4(y-2) = -5(x+8)\\\\4y-8 =- 5x-40\\\\4y = -5x-40+8\\\\4y =- 5x-32\\\\\frac{4y}{4} = \frac{-5x}{4} + \frac{-32}{4} \\\\y = -\frac{5}{4}x-8$

3 0

3 years ago

Let x^2−12x=61 .

Anuta_ua [19.1K]

The answer for the first blank is 36 and the answer for the second blank is 97.

To complete the square, we first take half of the value of b. The value of b in this equation is -12; -12/2 = -6.

Next we square the value we just got: (-6)² = 36.

This is what we add to both sides of the equation, giving us:
x²-12x+36=61+36

Combining like terms on the right, we have
x²-12x+36=97

4 0

3 years ago

Read 2 more answers

How many times does 3 fit into 87?

Mars2501 [29]

Answer:

29 times

Step-by-step explanation:

We can find this answer by dividing 87 by 3

87/3 = 29

We can prove this by multiplying 29 times 3 which gives us 87

4 0

2 years ago

Read 2 more answers

By 3:00 pm, the temperature had increased by another 5%F. Was the temperature at 3:00 pm positive or negative?How do you know?Wh

victus00 [196]

Answer:

Part a) The temperature at noon was -3°F

Part b) The temperature at 3:00 pm was +2°F

Part c) The temperature at 11:00 pm was -6°F

Step-by-step explanation:

The complete question is

When Leo woke up he saw that the temperature was -8°F. By noon the temperature has increased 5°F. Part a) What was the temperature at noon?

Part b) By 3:00 pm, the temperature increased by another 5 degrees Fahrenheit was the temperature at 3:00 pm positive or negative?

Part c) By 11:00 pm, the temperature had dropped 8°F. Was the

temperature at 11:00 PM positive or negative? Explain.

Part a) we know that

You can use a number line to adds the numbers

-8+5=-3°F

therefore

The temperature at noon was -3°F

Part b) we know that

the temperature increased by another 5 degrees

You can use a number line to adds the numbers

-3+5=+2°F

therefore

The temperature at 3:00 pm was +2°F

Part c) we know that

the temperature had dropped 8°F

You can use a number line to adds the numbers

2-8=-6°F

therefore

The temperature at 11:00 pm was -6°F

4 0

3 years ago