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3 years ago

Given that PQRS is a square, find x and y.

Mathematics

2 answers:

Dovator [93]3 years ago

4 0

Every angle of a square equals 90 degrees.

2x - 4 = 90 3y + 6 = 90
2x = 90 + 4 3y = 90 - 6
2x = 94 3y = 84
x = 94/2 y = 84/3
x = 47 y = 28

so x = 47 and y = 28

Helga [31]3 years ago

4 0

Answer:

B. x = 28, y = 47

Step-by-step explanation:

Given that PQRS is a square

We know that , In a square each vertex is a right angle that is 90 degree

So we set two equations

3y+ 6 = 90 and 2x -4 = 90

Solve for x and y

3y + 6 = 90

Subtract 6 from both sides

3y = 84

divide by 3 on both sides

y = 28

2x - 4 = 90

Add 4 on both sides

2x= 94

Divide by 2 on both sides

x= 47

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Solve the equation for the specified variable.<br> T= BA-9, for B<br> What does b=

NARA [144]

9514 1404 393

Answer:

$B=\dfrac{T+9}{A}$

Step-by-step explanation:

Add 9 to both sides of the equation, and divide by the coefficient of B.

T = BA -9

T +9 = BA

(T +9)/A = B

We can rewrite that with B on the left:

B = (T +9)/A

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3 years ago

An important factor in selling a residential property is the number of times real estate, agents show a home. A sample of 21 hom

Natalka [10]

Using the t-distribution to build the 99% confidence interval, it is found that:

The margin of error is of 3.64.

The 99% confidence interval for the population mean is (19.36, 26.64).

<h3>What is a t-distribution confidence interval?</h3>

The confidence interval is:

$\overline{x} \pm t\frac{s}{\sqrt{n}}$

In which:

$\overline{x}$ is the sample mean.

t is the critical value.

n is the sample size.

s is the standard deviation for the sample.

The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 21 - 1 = 20 df, is t = 2.086.

The other parameters are given as follows:

$\overline{x} = 23, s = 8, n = 21$

The margin of error is given by:

$M = t\frac{s}{\sqrt{n}} = 2.086\frac{8}{\sqrt{21}} = 3.64$

Hence the bounds of the interval are:

$\overline{x} - M = 23 - 3.64 = 19.36$

$\overline{x} + M = 23 + 3.64 = 26.64$

The 99% confidence interval for the population mean is (19.36, 26.64).

More can be learned about the t-distribution at brainly.com/question/16162795

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2 years ago

Look at the graph below measuring the speed of a truck and answers the following 2 question.

NemiM [27]

X would be equal to time and y be equal to distance

The y axis would be measuring distance and the x axis would be measuring time. Another name for a speed graph is the distance time graph. The y axis would be measuring the distance covered by the truck in meters and the x axis would be for the time it takes to reach that distance in second.

B) 2-6 would represent contact motion, meaning the vehicle is at rest. The time would be increasing from 2-6 to however the distance remains the same which is 20m

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3 years ago

One positive number is 14 less than another positive number. If the reciprocal of the smaller number is added to five times the

Kipish [7]

Let's call the two numbers $s$ and $l$ .

Given these variables, we can say: $s = l - 14$ , based on the first sentence in the problem.

Also, remember that the reciprocal of a number is simply 1 divided by the number. Thus, we can say that:

$\dfrac{1}{s} + 5\Big( \dfrac{1}{l} \Big) = \dfrac{1}{4}$

To solve, we can simply substitute $l -14$ in for $s$ in the second equation and solve.

$\dfrac{1}{l - 14} + \dfrac{5}{l} = \dfrac{1}{4}$

Set up

$\dfrac{l}{l(l - 14)} + \dfrac{5(l - 14)}{l(l - 14)} = \dfrac{1}{4}$

Get terms on the left side to a common denominator for easier addition

$\dfrac{l + 5l - 70}{l(l - 14)} = \dfrac{1}{4}$

Simplify

$4(6l - 70) = l(l - 14)$

Cross multiplication ( $\frac{a}{b} = \frac{c}{d} \Rightarrow ad = bc$ )

$24l - 280 = l^2 - 14l$

Simplify

$l^2 - 38l + 280 = 0$

Subtract $24l - 280$ from both sides of the equation

$(l - 10)(l - 28) = 0$

Factor left side of the equation

$l = 10, 28$

Zero Product Property

Now, notice that we have found two solutions, but the problem is only asking for one. This <em>likely </em>means that one of our solutions is extraneous. Let's take a look. Remember that the smaller positive number is equal to 14 less than the larger number. However,

$s = 10 - 14 = -4$ ,