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3 years ago

The points with coordinates (x, -1), (2,2), and (4,3) lie on the same line. What is the value of x?

Mathematics

1 answer:

borishaifa [10]3 years ago

7 0

Find the slope of the line passing throught the points (2, 2) and (4, 3).

The formula of a slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

Substitute:

$m=\dfrac{3-2}{4-2}=\dfrac{1}{2}$

If the point (x, -1) lie on the same line, then the slope of line passing through the points (2, 2) and (x, -1) the same:

Substitute:

$m=\dfrac{-1-2}{x-2}=\dfrac{-3}{x-2}$

We have the equation:

$\dfrac{-3}{x-2}=\dfrac{1}{2}$ <em>cross multiply</em>

$(1)(x-2)=(-3)(2)$

$x-2=-6$ <em>add 2 to both sides</em>

$x=-4$

<h3>Answer: x = -4.</h3>

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2 years ago

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3 years ago

The nile river, the longest river in the world, is 66.7x100 kilometers long. What is the nile's length?

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Well if you multiply 66.7 x 100 you get 6,670.0. When multiplying by numbers like 10, 100, 1,000, etc, just simply transfer the 0's. So in this case, there are 2 0's in 100, so you add 2 of the 0's behind 66.7. So when you add the 2 of the 0's you get 6,670.0 which should be your answer.

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3 years ago

Complete the square to rewrite y-x^2-6x+14 in vertex form. then state whether the vertex is a maximum or minimum and give its co

ycow [4]

Answer:

$y= x^2 -6x +(\frac{6}{2})^2 +14 -(\frac{6}{2})^2$

And solving we have:

$y= x^2 -6x +9 + 14 -9$

$y= (x-3)^2 +5$

And we can write the expression like this:

$y-5 = (x-3)^2$

The vertex for this case would be:

$V= (3,5)$

And the minimum for the function would be 3 and there is no maximum value for the function

Step-by-step explanation:

For this case we have the following equation given:

$y= x^2 -6x +14$

We can complete the square like this:

$y= x^2 -6x +(\frac{6}{2})^2 +14 -(\frac{6}{2})^2$

And solving we have:

$y= x^2 -6x +9 + 14 -9$

$y= (x-3)^2 +5$

And we can write the expression like this:

$y-5 = (x-3)^2$

The vertex for this case would be:

$V= (3,5)$

And the minimum for the function would be 3 and there is no maximum value for the function

4 0

3 years ago

For bone density scores that are normally distributed with a mean of 0 and a standard deviation of 1, find the percentage of sc

gogolik [260]

Answer:

a) The percentage of bone density scores that are significantly high is 2.28%

b) The percentage of bone density scores that are significantly low is 2.28%

c) The percentage of bone density scores that are not significant is 95.44%

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.

a. significantly high (or at least 2 standard deviations above the mean).

This is 1 subtracted by the pvalue of Z = 2.

Z = 2 has a pvalue of 0.9772

1 - 0.9772 = 0.0228

2.28% of scores are signifcantly high

b. significantly low (or at least 2 standard deviations below the mean).

pvalue of Z = -2

Z = -2 has a pvalue of 0.0228

2.28% of scores are signicantly low.

c. not significant (or less than 2 standard deviations away from the mean).

pvalue of Z = 2 subtracted by the pvalue of Z = -2.

Z = 2 has a pvalue of 0.9772

Z = -2 has a pvalue of 0.0228

0.9772 - 0.0228 = 0.9544

95.44% of the scores are not significant

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3 years ago