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3 years ago

Find the value of y and simplify completely

Mathematics

1 answer:

Law Incorporation [45]3 years ago

8 0

Here we have three similar triangles

In similar triangles sides are in proportion

The altitude to the hypotenuse of a right triangle is the mean proportional between the segments into which it divides the hypotenuse.

$\frac{part of hypotenuse }{altitude} =\frac{altitude}{other part of hypotenuse}$

$\frac{16}{y} =\frac{y}{4}$

We cross multiply to solve for y

$y^{2} =64$

Taking root of both sides

y=8

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Suppose that F(x) = x2 and G(X) = 2/3 x^2. Which statement best compares the graph of G(x) with the graph of F(x)?

masha68 [24]

<h2>Answer:The graph of $G(x)$ is the graph of $F(x)$ compressed vertically.</h2>

Step-by-step explanation:

Given that $F(x)=x^{2}$ and $G(x)=\frac{2}{3}x^{2}$

$F(x)$ is always positive because $x^{2}$ is always positive.

$G(x)$ is always positive because $\frac{2}{3}x^{2}$ is always positive.

So,both are always positive.

So,there is no flipping over x-axis.

In $F(x)$ ,the height of a point at $x_{0}$ is $x_{0}^{2}$

In $G(x)$ ,the height of a point at $x_{0}$ is $\frac{2}{3}x_{0}^{2}$

So,height of any point has less height in $G(x)$ than $F(x)$

So,the graph of $G(x)$ is the graph of $F(x)$ compressed vertically.

3 0

3 years ago

In a recent contest, the mean score was 210 and the standard deviation was 25. a) Find the z-score of John who scored 190 b) Fin

denpristay [2]

Answer:

a) $Z = -0.8$

b) $Z = 2.4$

c) Mary's score was 241.25.

Step-by-step explanation:

Problems of normally distributed samples can be 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:

$\mu = 210, \sigma = 25$