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3 years ago

Find x and y, given that line WS and line VT are parallel. Show all work!

Mathematics

1 answer:

bulgar [2K]3 years ago

7 0

In the given diagram, the traingles USW and UTV are similar triangles and thus the following ratio equality applies to them.

$\frac{VT}{WS} =\frac{VU}{WU}=\frac{TU}{SU}$ ..........(Equation 1)

Checking the diagram given, we see that:

VT=y, WS=22, VU=8, ST=x-2

WU=WV+VU=12+8=20

TU=5

SU=ST+TU=(x-2)+5=x+3

Thus, substituting the required values in (Equation 1) we get:

$\frac{y}{22}=\frac{8}{20}=\frac{5}{x+3}$

Now, as can be clearly seen, to find y we will use the first two ratios as:

$\frac{y}{22}=\frac{8}{20}$

$y=\frac{8\times 22}{20}=8.8$

In a similar manner, to find the value of x we can use the last two ratios:

$\frac{8}{20}=\frac{5}{x+3}$

After cross multiplication we get:

$5\times 20=8(x+3)$

Which can be simplified as:

$x+3=\frac{100}{8} =12.5$

Thus, $x=12.5-3=9.5$

Therefore, the required answer is:

x=9.5 and y=8.8

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A set of test scores is normally distributed with a mean of 130 and a standard deviation of 30 What score is necessary to reach

nlexa [21]

Answer:

A score of 150.25 is necessary to reach the 75th percentile.

Step-by-step explanation:

Problems of normal distributions 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.

A set of test scores is normally distributed with a mean of 130 and a standard deviation of 30.

This means that $\mu = 130, \sigma = 30$

What score is necessary to reach the 75th percentile?

This is X when Z has a pvalue of 0.75, so X when Z = 0.675.

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

$0.675 = \frac{X - 130}{30}$

$X - 130 = 0.675*30$

$X = 150.25$

A score of 150.25 is necessary to reach the 75th percentile.

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3 years ago

Helpppppppppppppppppp

UNO [17]

Answer:

<em>2 solutions</em>

Step-by-step explanation:

Given the expression

2m/2m+3 - 2m/2m-3 = 1

Find the LCM of the expression at the left hand side:

2m(2m-3)-2m(2m+3)/(2m+3)(2m-3) = 1

open the bracket

4m²-6m-4m²-6m/(4m²-9) = 1

Cross multiply

4m²-6m-4m²-6m = 4m² - 9

-12m = 4m² - 9

4m² - 9+12m = 0

4m² +12m-9 = 0

<em>Since the resulting equation is a quadratic equation, it will have 2 solutions since the degree of the equation is 2</em>

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3 years ago

I need help with #61 to #64 ASAP please and thank you …. Could someone please help me with it… I need to get it done ASAP

aivan3 [116]

Problem 61

The nth triangular number is

T(n) = n(n+1)/2

I'll rewrite this into

T(n) = 0.5n(n+1)

The triangular number right after this is

T(n+1) = 0.5(n+1)(n+2)

I replaced every n with n+1 and simplified

Let's see what we get when we add up the two expressions

T(n) + T(n+1)

0.5n(n+1) + 0.5(n+1)(n+2)

0.5n^2+0.5n + 0.5(n^2+3n+2)

0.5n^2 + 0.5n + 0.5n^2 + 1.5n + 1

n^2+2n+1

(n+1)^2

This shows that the sum of any two consecutive triangular numbers results in a square number

Here's a few examples

0+1 = 1
1+3 = 4
3+6 = 9
6+10 = 16
10+15 = 25

Note each sum is a perfect square, which visually would plot out a square figure.

For quick reference, the set of the first few triangular numbers is {0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55,...}

<h3>Answer: Square number</h3>

==========================================================

Problem 64

Let's say we go with n = 5.

This means,

T(n) = 0.5n(n+1)

T(n-1) = 0.5(n-1)(n-1+1)

T(n-1) = 0.5n(n-1)

T(5-1) = 0.5*5(5-1)

T(4) = 10

This says that when n = 5, the 4th triangular number is 10

Triple that result and add on n = 5

3*T(4) + n = 3*10+5 = 35

This result is beyond obvious which category of figurate number it belongs to. It's not a triangular number since it's not in the form n(n+1)/2. It's not a square number either.

Through a bit of trial and error, you should find it's a pentagonal number

Pentagonal numbers are of the form n(3n-1)/2

If you plugged n = 5 into that, it leads to 35

n(3n-1)/2 = 5*(3*5-1)/2 = 5*14/2 = 70/2 = 35

The diagram shown below represents the first few pentagonal numbers. The number of blue dots corresponds to the pentagonal number itself. Note the equal spacing when dealing with dots on each segment (eg: some interior blue dots are midpoints, others are quarter points, etc.)

<h3>Answer: Pentagonal number</h3>

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2 years ago

PLS HELP. BRAINLIEST/5 STARS TO CORRECT ANSWER

fenix001 [56]

Where p is the distance the focus is above the vertex, the equation of a parabola with vertex (h, k) can be written as

... y = 1/(4p)·(x -h)² +k

The vertex is halfway between the focus and directrix. The focus of your parabola is on the y-axis at y=6, and the directrix of your parabola is at y=-6, so the vertex of your parabola is on the y-axis at y=0. That is, the vertex is

... (h, k) = (0, 0).

The distance p from the focus at y=6 to the vertex at y=0 is 6 units, so

... p = 6.

Filling these values into the equation gives

... y = 1/(4·6)·(x -0)² +0

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3 years ago

Find the equivalent exponential expression (7^2)^5

VladimirAG [237]