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lapo4ka [179]
3 years ago
11

Helllllllpppppppp Plllleeeeaaase I have a test!!!!

Mathematics
1 answer:
Tresset [83]3 years ago
3 0
Do you still need it
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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
What is the solution to the system of equations?<br><br> y = x – 10<br><br> 2x + y = 4
Bumek [7]
2x+(x-10)=4
3x-10=4
3x=14
x=4.6 repeating
6 0
4 years ago
If you bought 4 things from Walmart (Things listed below) What would be the tax?
allochka39001 [22]
10.99 +11.67+ 3.64 + 2.83 = 29.13 SO THE TAX EQUALS 87 CENTS 
7 0
4 years ago
1 For each line
Elena-2011 [213]

Step-by-step explanation:

I'll do line A for you and you can use the formulas to solve lines B and C yourself, since its good for you to practice doing these questions yourself

a)

The gradient, m, is calculated using m = (y2-y1)/(x2-x1) where x1,x2,y1 and y2 can be any ordered pairs on the line.  I'm going to use (4,0) and (7,3) as the 2 points.

m = (3-0)/(7-4) = 3/3 = 1

b)

The y-intercept is where the line intersects with the x-axis. In this case (0,-4)

c)

The equation of a linear line is y=mx+b (or c depending on which country you are from)

y = 1x-4

y=x-4

Now try the other 2 lines yourself!

If this answer has helped you, considered making this the brainliest answer!

5 0
3 years ago
Why does beethoven now spend all his time erasing music
schepotkina [342]
He is decomposing :0
3 0
3 years ago
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