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vovangra [49]
3 years ago
10

Rewrite the equation y^2 – 4y – 2x – 4 = 0 in standard form.

Mathematics
1 answer:
patriot [66]3 years ago
8 0

y² - 4y - 2x - 4 = 0

<u>            +2x +4 </u>   <u>+2x + 4 </u>

y² - 4y              = 2x + 4

<u>             +4    </u>      <u>       +4 </u>      

 (y - 2)²          = 2x + 8

<u>              -8   </u>      <u>      -8 </u>

 (y - 2)²  - 8   = 2x

\frac{(y - 2)^{2}}{2} - \frac{8}{2} = \frac{2x}{2}

\frac{1}{2}(y - 2)² - 4 = x

x = \frac{1}{2}(y - 2)² - 4

<em>Note: this is a parabola whose axis of symmetry is y = 2 and vertex is (-4, 2)</em>

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son4ous [18]

Answer:

The reading speed of a sixth-grader whose reading speed is at the 90th percentile is 155.72 words per minute.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

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 problem, we have that:

\mu = 125, \sigma = 24

What is the reading speed of a sixth-grader whose reading speed is at the 90th percentile

This is the value of X when Z has a pvalue of 0.9. So it is X when Z = 1.28.

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

1.28 = \frac{X - 125}{24}

X - 125 = 1.28*24

X = 155.72

The reading speed of a sixth-grader whose reading speed is at the 90th percentile is 155.72 words per minute.

4 0
3 years ago
Read 2 more answers
A + b·c = a + c·b is an example of the associative property.
muminat

Answer:

yes , This is an example of the associative property.

Step-by-step explanation:

8 0
2 years ago
3 soccer balls and 5 more how many are there​
vodomira [7]

Answer:

8

Step-by-step explanation:

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6 0
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Joe has one book each for algebra, geometry, history, psychology, Spanish, English and Physics in his locker. How many different
Alisiya [41]

Answer:

There are 35 different sets of 3 books Joe could choose

Step-by-step explanation:

* Lets explain how to solve the problem

- Combination is a collection of the objects where the order doesn't

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- The formula for the number of possible combinations of r objects from

 a set of n objects is nCr = n!/r!(n-r)!

- n! = n(n - 1)(n - 2)................. × 1

Lets solve the problem

- Joe has one book each for algebra, geometry, history, psychology,

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∴ He has <em>seven</em> books in the locker

- He wants to chose <em>three</em> of them

∵ The order is not important when he chose the books

∴ We will use the combination <em>nCr</em> to find how many different sets

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- The total number of books is 7

∴ n = 7

∵ He chooses 3 of them

∴ r = 3

∵ 7C3 = 7!/3!(7 - 3)! = 7!/3!(4!)

∴ 7C3=\frac{(7)(6)(5)(4)(3)(2)(1)}{[(3)(2)(1)][(4)(3)(2)(1)]}=35

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* There are 35 different sets of 3 books Joe could choose

3 0
3 years ago
(x+2)(2x+1)+(x+2)(2x-3) factorizar
koban [17]

Answer:

(x + 2)(4x - 2).

Step-by-step explanation:

(x+2)(2x+1)+(x+2)(2x-3)

Note that  (x + 2) is common to 2 parts of the expression. So we have:

(x + 2)(2x + 1 + 2x - 3)

= Ix + 2)(4x - 2)

8 0
3 years ago
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