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2 years ago

Write the equation in standard form. Identity the center and radius. x² + y2 + 8x-4y-7=0

Mathematics

1 answer:

Masteriza [31]2 years ago

3 0

Answer:

See below

Step-by-step explanation:

<u>Given equation:</u>

x² + y² + 8x - 4y - 7 = 0

<u>Convert this to standard form by completing the square:</u>

(x - h)² + (y - k)² = r², where (h, k) - center, r - radius
x² + 2*4x + 4² + y² - 2*2y + 2² - 16 - 4 - 7 = 0
(x + 4)² + (y - 2)² - 27 = 0
(x + 4)² + (y - 2)² = 27
(x + 4)² + (y - 2)² = (√27)²

The center is (- 4, 2) and the radius is √27

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3 years ago

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When you flip a biased coin the probability of getting a tail is 0.75.

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1 year ago

An elementary school class ran 1 mile in an average of 11 minutes with a standard deviation of 3 minutes. Rachel, a student in t

Natali5045456 [20]

Answer:

a) Kenji's time had a lower z-score, which means that he is better compared to other runners on his level, and better to his peers compared to Nedda.

b) Rachel, because her time had the lowest z-score.

Step-by-step explanation:

Z-score:

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question:

The lower the time, the better the runner is. So whoever's time has a lower z-score is a better runner. So initially, we find the z-score of each student's time.

An elementary school class ran 1 mile in an average of 11 minutes with a standard deviation of 3 minutes. Rachel, a student in the class, ran 1 mile in 8 minutes.

This means that for Rachel's time, we have that $X = 8, \mu = 11, \sigma = 3$ . So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{8 - 11}{3}$

$Z = -1$

A junior high school class ran 1 mile in an average of 9 minutes, with a standard deviation of 2 minutes. Kenji, a student in the class, ran 1 mile in 8.5 minutes.

This means that for Kenji's time, we have that $X = 8.5, \mu = 9, \sigma = 2$ . So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{8.5 - 9}{2}$

$Z = -0.25$

A high school class ran 1 mile in an average of 7 minutes with a standard deviation of 4 minutes. Nedda, a student in the class, ran 1 mile in 8 minutes.

This means that for Nedda's time, we have that $X = 8, \mu = 7, \sigma = 4$ . So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{8 - 7}{4}$

$Z = 0.25$

(a) Why is Kenji considered a better runner than Nedda, even though Nedda ran faster than he?

Kenji's time had a lower z-score, which means that he is better compared to other runners on his level, and better to his peers compared to Nedda.

(b) Who is the fastest runner with respect to his or her class? Explain why

Rachel, because her time had the lowest z-score.

8 0

3 years ago

I need the answers for this one as well!

Julli [10]

For the sake of showing work I will replace the empty space with an x like so...

$\frac{9}{10} =\frac{90}{x}$

To find out what x is you must cross multiply (aka butterfly)

***Image of this step is attached below

9*x = 10*90

9x = 900

Next divide 9 to both sides to finish isolating x. Since 9 is being multiplied by x, division (the opposite of multiplication) will cancel 9 out (in this case it will make 9 one) from the left side and bring it over to the right side.

9x ÷ 9 = 900 ÷ 9

1x = 100

x = 100

To make these fractions equivalent the empty spot must be 100

$\frac{9}{10} = \frac{90}{100}$