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3 years ago

A challenge to all math experts...

Mathematics

1 answer:

earnstyle [38]3 years ago

7 0

Answer:

Step-by-step explanation:

Refer to attachment

As the first step extending the segment BC until intersection with AD.

Since ∠A + ∠B = 90° we get right triangle by extending CB

Naming the segments a, b, c, d as pictured

The are of (ABCD) is equal to sum of areas of two right triangles:

Area = 1/2c(a+b) + 1/2bd

Substitute d with a-c as a = c+d, then:

Area = 1/2(ac+bc) + 1/2b(a-c) = 1/2(ac + bc + ab - bc) = 1/2(ab + ac)
Area = 1/2(ab+ac)

Applying Pythagorean to small triangle:

10² = b² + (a-c)²
100 = b² + a² - 2ac + c²

Applying Pythagorean to bigger triangle:

20² = (a+b)² + c²
400 = a² + 2ab + b² + c²

Subtracting equations we got:

400 - 100 = a² + 2ab + b² + c² - (b² + a² - 2ac + c²)
300 = 2ab + 2ac

This gives us the 4 times of the area which is 1/2(ab + ac), so the area is

300/4 = 75

You might be interested in

A geometric progression has a third term of 20 and a sum of infinity which is 3 times the first term. Find the first term

Anna007 [38]

Answer: the first term is 45

Step-by-step explanation:

Step 1: The formular for the nth term is ar^n-1 and since we're solving for the third term ar^3-1 = ar² which is equal to 20

So ar²= 20 and we make this equation i

Step 2: the formular for the sum of infinity is Sn = a/(1-r) and according the question the sum of infinity is equals to 3 *A ( A means the first term)

Further simplification gives us

3a= a/(1-r)

We simplify Futher by multiplying both sides by (1-r)

3a.(1-r) = a/(1-r).(1-r)

3a(1-r)=a

= 3a-3ar=a

Make 3ar the subject of the formula

3ar= 2a and lets make this equation (ii)

Step 3: From the first equation since ar²=20, let's make a the subject of the formula by dividing both sides by r²

Ar²/r² = 20/r²

A=20/r²lets make this equation (iii)

Step 4: subtitle a as 20/r² into equation (ii)

Since 3ar=2a

Then 3.(20/r²).r = 2. 20/r²

= (60/r²) .r = 40/r²

60/r = 40/r2

Multiplying both sides by r² gives us

60r = 40

Divide both sides by 20 gives us

= 3r= 2

Divide both sides by 3 gives us

= r = 2/3

Step 5: substitute r for 2/3 in equation i

ar²= 20

a. (2/3)2 = 20

= a.4/9 = 20

= 4a = 180

= a = 180/4

a = 45

5 0

3 years ago

When was the last time that texas tried to become its own state

Rudik [331]

Answer:

The Texas Declaration of Independence was signed in 1836 and the Texas Republic ratified its own constitution shortly after. In 1837, the U.S. formally recognized Texas as a nation, but the new country struggled economically without any of the resources of its larger neighbors, leading most (but not all) residents to welcome statehood by the time it came through in 1845. Only a little more than a decade passed, however, before the state tried to secede from its national government again, joining with the Confederacy in 1861.

Step-by-step explanation:

3 0

3 years ago

How do you do this math??

Elis [28]

Answer:

9.6

Step-by-step explanation:

10 = 8

12 = x

then simply solve for x

3 0