The values of x are x₁ ≈ 4.8 and x₂ ≈ - 0.8.
<h3>What is the quadratic equation behind two circular sections of equal area?</h3>
Herein we have two <em>circular</em> sections of equal area, whose expressions are described by the following geometric equations:
Semicircle
A = 0.5π · x² (1)
Half Semicircle
A = 0.25π · (x + 2)² (2)
By equalizing (1) and (2):
0.5π · x² = 0.25π · (x + 2)²
2 · x² = (x + 2)²
2 · x² = x² + 4 · x + 4
x² - 4 · x - 4 = 0
x² - 4 · x + 4 = 8
(x - 2)² = 8
x - 2 = ±√8
x = 2 ± √8
x = 2 ± 2√2
x = 2 · (1 ± √2)
x = 2 · (1 ± 1.41)
x₁ = 2 · 2.41 ∨ x₂ = 2 · (- 0.41)
x₁ = 4.82 ∨ x₂ = - 0.82
The values of x are x₁ ≈ 4.8 and x₂ ≈ - 0.8.
To learn more on quadratic equations: brainly.com/question/17177510
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10a) <u>x = 81</u> <u>y = 30.5</u>
Isolate y
2y + 20 = x
2y = x- 20
y = x/2 - 10
Plug in for y
4y - 6 + 64 + x = 180
4(x/2 - 10) - 6 + 64 + x = 180
4x/2 - 40 -6 + 64 + x = 180
4x/2 + 18 = 180
4x/2 = 162
4x = 324
x = 81
Plug in for x
2y + 20 = x
2y + 20 = 81
2y = 61
y = 30.5
10b) <u>x = 47</u>
Isolate x
4x -12 = 3x + 35
x - 12 = 35
x = 47
11)
2. definition of parallelogram
3. < ABD ≅ < BDC
4. < CBD ≅ <BDA
6. I'm not 100% sure what this one is but I think it has something to do with the line of symmetry.
Hope this helps! ;)
Answer:
i think it's c
Step-by-step explanation:
a. <u>2</u><u>/</u><u>1</u><u>00</u><u> </u><u>×</u><u> </u><u>1</u><u>5</u><u>0</u><u>=</u><u> </u><u>3</u><u>. </u><u> </u><u> </u><u> </u><u> </u><u> </u><u> </u><u> </u><u> </u><u> </u><u>b</u><u>. </u><u> </u><u>100×</u><u>4</u><u>0</u><u>0</u><u>=</u><u>4</u><u>0</u><u>0</u><u>0</u><u>0</u><u>. </u><u> </u><u> </u><u> </u><u> </u><u>c</u><u>. </u><u> </u><u> </u><u>6</u><u>/</u><u>100 </u><u>×</u><u>6</u><u>0</u><u>=</u><u> </u><u>1</u><u>.</u><u>2</u><u> </u><u>×</u><u>3</u><u>=</u><u>3</u><u>.</u><u>6</u><u>. </u><u> </u><u> </u><u> </u><u> </u><u> </u><u>d</u><u>. </u><u>6</u><u>9</u><u>×</u><u>5</u><u>0</u><u>=</u><u>3</u><u>4</u><u>0</u><u>0</u><u> </u><u> </u><u> </u><u> </u><u> </u><u> </u><u> </u><u> </u><u> </u><u> </u><u> </u><u> </u><u>so </u><u>answer</u><u> </u><u>c</u><u>. </u><u> </u><u> </u><u> </u><u> </u><u> </u>
82.50?? I think because I just multiplied them.
It is 3 and 1/14ft or 3 and 4/16 ft taller