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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

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What is the center of the circle for this equation: (x + 3)² + (y - 2)² = 25

Ksju [112]

The formula for the equation of a circle is (x - h)² + (y - k)² = r²

where (h, k) is the center of the circle and r is the radius.

So we need to find the values of (h, k) in order to find the center of the circle.

If we simply line up the equation of our given circle with our formula,

we can see that -h = 3 or h = -3 and -k = -2 so k = 2.

So now we have our answer.

center ⇒ (-3, 2)

8 0

3 years ago

What's the surface area of this figure? (figure shown on picture)

KIM [24]

Answer:

800 in²

Step-by-step explanation:

Let’s find the area of all the shapes in the net.

10 · 10 = 100

100 · 2 = 200

15 · 10 = 150

150 · 4 = 600

200 + 600 = 800

3 0

3 years ago

10 plus 10 divided and rounded to next 20

BartSMP [9]

10.5 I looked it up OKAY

7 0

3 years ago

<1 and <2 form a linear pair. The measure of <2 is six more than twice the measure of <1. Find the measure of <2

MrMuchimi

Answer:

122 Degrees

Step-by-step explanation:

Since we are given that angle 1 and 2 make a linear pair:

angle 1 + angle 2 = 180 degrees ----------------------------(1)

We have also been told that angle 2 is 6 more than twice the measure of angle 1

Which means: angle 2 = (2*angle1) + 6 -------------------(2)

From putting the value of angle 2 in (1) from (2)

angle 1 + 2*angle 1 + 6 = 180

3*angle 1 = 174

angle 1 = 58 degrees -----------------------(3)

From (1) and (3):

angle 2 + 58 = 180

angle 2 = 122 degrees

Therefore, the measure of angle 2 is 122 degrees

7 0

3 years ago

olchik [2.2K]

The correct answer is: [B]: " 25 a²⁵ b²⁵ " .
_________________________________________________________
Explanation:
_________________________________________________________
Given the expression:
_________________________________________________________
→ " (−5a⁵b⁵)² (a³b³)⁵ " ; Simplify.
_________________________________________________________
Let us being by examining:
______________________________________
→ "(−5a⁵b⁵)² " .

→ "(−5a⁵b⁵)² = (-5)² * (a⁵)² * (b⁵)² = (-5)(-5) * a⁽⁵ˣ²⁾ * b⁽⁵ˣ²⁾ = 25a⁽¹⁰⁾b⁽¹⁰⁾ ;

{Note the following properties of exponents:
(xy)ⁿ = xⁿ * yⁿ ;

(xᵃ)ᵇ = x⁽ᵃ * ᵇ) ;

(xᵃ) * (xᵇ) = x⁽ᵃ ⁺ ᵇ⁾ .}.
______________________________________

Then, we examine:
______________________________________
→ "(a³b³)⁵ " .

→ "(a³b³)⁵ = a⁽³ˣ⁵⁾b⁽³ˣ⁵⁾ = a⁽¹⁵⁾b⁽¹⁵⁾ .
______________________________________

So: " (−5a⁵b⁵)² (a³b³)⁵ = (-5)a⁽¹⁰⁾b⁽¹⁰⁾ * a⁽¹⁵⁾b⁽¹⁵⁾ " ;
________________________________________
Now, we simplify:

→ " 25a⁽¹⁰⁾b⁽¹⁰⁾ * a⁽¹⁵⁾b⁽¹⁵⁾ " ;

→ " 25a⁽¹⁰⁾b⁽¹⁰⁾ * a⁽¹⁵⁾b⁽¹⁵⁾ ;

= 25a⁽¹⁰⁾ a⁽¹⁵⁾b⁽¹⁰⁾ b⁽¹⁵⁾ ;

= 25a⁽¹⁰ ⁺¹⁵⁾ b⁽¹⁰⁺¹⁵⁾ ;

= 25a⁽²⁵⁾ b⁽²⁵⁾ ;
_______________________________________________
→ which is: Answer choice: [B]: " 25 a²⁵ b²⁵ " .
______________________________________________

5 0

3 years ago