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Solve for the roots in simplest form by completing the square x^2-12x+20=0

Alex17521 [72]

Answer:

x = 10 or x = 2

Step-by-step explanation:

Solve for x:

x^2 - 12 x + 20 = 0

Hint: | Solve the quadratic equation by completing the square.

Subtract 20 from both sides:

x^2 - 12 x = -20

Hint: | Take one half of the coefficient of x and square it, then add it to both sides.

Add 36 to both sides:

x^2 - 12 x + 36 = 16

Hint: | Factor the left hand side.

Write the left hand side as a square:

(x - 6)^2 = 16

Hint: | Eliminate the exponent on the left hand side.

Take the square root of both sides:

x - 6 = 4 or x - 6 = -4

Hint: | Look at the first equation: Solve for x.

Add 6 to both sides:

x = 10 or x - 6 = -4

Hint: | Look at the second equation: Solve for x.

Add 6 to both sides:

Answer: x = 10 or x = 2

5 0

2 years ago

An automobile company wants to determine the average amount of time it takes a machine to assemble a car. A sample of 40 times y

aksik [14]

Answer:

A 98% confidence interval for the mean assembly time is [21.34, 26.49] .

Step-by-step explanation:

We are given that a sample of 40 times yielded an average time of 23.92 minutes, with a sample standard deviation of 6.72 minutes.

Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;

P.Q. = $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample average time = 23.92 minutes

s = sample standard deviation = 6.72 minutes

n = sample of times = 40

$\mu$ = population mean assembly time

Here for constructing a 98% confidence interval we have used a One-sample t-test statistics because we don't know about population standard deviation.

So, a 98% confidence interval for the population mean, $\mu$ is;

P(-2.426 < $t_3_9$ < 2.426) = 0.98 {As the critical value of z at 1% level

of significance are -2.426 & 2.426}

P(-2.426 < $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ < 2.426) = 0.98

P( $-2.426 \times {\frac{s}{\sqrt{n} } }$ < ${\bar X-\mu}$ < $2.426 \times {\frac{s}{\sqrt{n} } }$ ) = 0.98

P( $\bar X-2.426 \times {\frac{s}{\sqrt{n} } }$ < $\mu$ < $\bar X+2.426 \times {\frac{s}{\sqrt{n} } }$ ) = 0.98

98% confidence interval for $\mu$ = [ $\bar X-2.426 \times {\frac{s}{\sqrt{n} } }$ , $\bar X+2.426 \times {\frac{s}{\sqrt{n} } }$ ]

= [ $23.92-2.426 \times {\frac{6.72}{\sqrt{40} } }$ , $23.92+2.426 \times {\frac{6.72}{\sqrt{40} } }$ ]

= [21.34, 26.49]

Therefore, a 98% confidence interval for the mean assembly time is [21.34, 26.49] .

7 0

2 years ago

What is 6300kg in grams

vaieri [72.5K]

Answer:

6,300kg=6,300,000grams

multiply 6,300 and 1,000 to get 6,300,000

4 0

3 years ago

Solve for x & round the answer to the nearest tenth

diamong [38]

6/14 = 7/x
so
x = 7 * 14 / 6
x = 98/6
x = 16.3

answer
D. x = 16.3

3 0

2 years ago

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The volume of a rectangular prism is (x{3} – 3x{2} + 5x – 3), and the area of its base is (x{2} – 2). If the volume of a rectang

Gemiola [76]

Answer:

x³ - 3x² + 5x - 3 / x² - 2

Step-by-step explanation:

Given in the question,

volume of a rectangular prism = x³ - 3x² + 5x - 3

base area of a rectangular prism = x² - 2

Formula for the volume of prism

V = BA x H

here BA is base area

H is height

Formula for the height of prism

H = V / BA

plug values in the formula

x³ - 3x² + 5x - 3 / x² - 2

We will do long division

x - 1

----------------------------

x² - 2 | x³ - 3x² + 5x - 3

x³ - 2x²

---------------------------

-x² + 5x - 3

-x² + 2

----------------------

5x - 5

The remainder indicates that x³ - 3x² + 5x - 3 is not divisible by x² - 2, and that means that you cannot find the exact height.

6 0

2 years ago

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