I will give Brainliest to whoever does all <br><br> PLEASE HELP

Given: PRST is a square

xxTIMURxx [149]

Answer:

$(1-\sqrt{2})a^2$

Step-by-step explanation:

Consider irght triangle PRS. By the Pythagorean theorem,

$PS^2=PR^2+RS^2\\ \\PS^2=a^2+a^2\\ \\PS^2=2a^2\\ \\PS=\sqrt{2}a$

Thus,

$MS=PS-PM=\sqrt{2}a-a=(\sqrt{2}-1)a$

Consider isosceles triangle MSC. In this triangle

$MS=MC=(\sqrt{2}-1)a.$

The area of this triangle is

$A_{MSC}=\dfrac{1}{2}MS\cdot MC=\dfrac{1}{2}\cdot (\sqrt{2}-1)a\cdot (\sqrt{2}-1)a=\dfrac{(\sqrt{2}-1)^2a^2}{2}=\dfrac{(3-2\sqrt{2})a^2}{2}$

Consider right triangle PTS. The area of this triangle is

$A_{PTS}=\dfrac{1}{2}PT\cdot TS=\dfrac{1}{2}a\cdot a=\dfrac{a^2}{2}$

The area of the quadrilateral PMCT is the difference in area of triangles PTS and MSC:

$A_{PMCT}=\dfrac{(3-2\sqrt{2})a^2}{2}-\dfrac{a^2}{2}=\dfrac{(2-2\sqrt{2})a^2}{2}=(1-\sqrt{2})a^2$

5 0

3 years ago

How do I solve this math problem?

nikitadnepr [17]

1,088 if you set it up as a proportion. It would be 17/20 compared to x/1280 multiply 17 by 1280 and then divide by 20.

3 0

3 years ago

Find the monthly payment for the loan. Finance $500,000 for an apartment complex with a 12.3% 10-year loan.

Marina86 [1]

Using it's formula, it is found that the monthly payments for the loan of the apartment is of $7,260.50.

<h3>What is the monthly payment formula?</h3>

It is given by:

$A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}$

In which:

P is the initial amount.

r is the interest rate.

n is the number of payments.

In this problem, the parameters are given as follows:

P = 500000, r = 0.123, n = 12 x 10 = 120.

Hence:

r/12 = 0.123/12 = 0.01025.

Then, the monthly payments will be of:

$A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}$

$A = 500000\frac{0.01025(1+0.01025)^{120}}{(1+0.01025)^{120} - 1}$

A = 7260.50.

More can be learned about the monthly payment formula at brainly.com/question/26267630

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6 0

2 years ago

COLLEGE PREP In the diagram, mLAGC = 38°, m/CGD=71°, and m/FGC = 147 °. Which of the following

Cerrena [4.2K]

The statements that are true are:

A. m<AGB = 19°

D. <BGD is a right angle

<h3>What is a Right Angle?</h3>

A right angle is an angle that measures 90 degrees.

Given the diagram, where:

m<AGC = 38°,

m<CGD = 71°,

m<FGC = 147°

We have the following measures:

1/2(m<AGC) = m<AGB

1/2(38) = 19°

m<CGD + m<AGC = m<BGD

Substitute

71 + 19 = m<BGD

90 = m<BGD

m<BGD = 90° [this is a right angle].

Therefore, the statements that are true are:

A. m<AGB = 19°

D. <BGD is a right angle

Learn more about right angle on:

brainly.com/question/64787

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5 0

1 year ago

If m∠O = 111, find the value of x in this figure.

uranmaximum [27]

The answer to this rather easy question is 69.

8 0

4 years ago

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I will give Brainliest to whoever does all PLEASE HELP