Answer:
1. ![\dfrac{44}{13}=3\dfrac{5}{13}](https://tex.z-dn.net/?f=%5Cdfrac%7B44%7D%7B13%7D%3D3%5Cdfrac%7B5%7D%7B13%7D)
2. 9.6
3. 0
Step-by-step explanation:
Thales’ Theorem: If arms of an angle are cut by parallel straight lines, then the ratio of the lengths of the line segments obtained on one arm are equal to the corresponding segments obtained on the second arm.
1. By Thales's theorem,
![\dfrac{9}{4}=\dfrac{11-x}{x}\\ \\9x=4(11-x)\ [\text{Cross multiply}]\\ \\9x=44-4x\\ \\9x+4x=44\\ \\13x=44\\ \\x=\dfrac{44}{13}](https://tex.z-dn.net/?f=%5Cdfrac%7B9%7D%7B4%7D%3D%5Cdfrac%7B11-x%7D%7Bx%7D%5C%5C%20%5C%5C9x%3D4%2811-x%29%5C%20%5B%5Ctext%7BCross%20multiply%7D%5D%5C%5C%20%5C%5C9x%3D44-4x%5C%5C%20%5C%5C9x%2B4x%3D44%5C%5C%20%5C%5C13x%3D44%5C%5C%20%5C%5Cx%3D%5Cdfrac%7B44%7D%7B13%7D)
2. By Thales's theorem,
![\dfrac{8}{12}=\dfrac{x}{24-x}\\ \\12x=8(24-x)\ [\text{Cross multiply}]\\ \\12x=192-8x\\ \\12x+8x=192\\ \\20x=192\\ \\x=9.6](https://tex.z-dn.net/?f=%5Cdfrac%7B8%7D%7B12%7D%3D%5Cdfrac%7Bx%7D%7B24-x%7D%5C%5C%20%5C%5C12x%3D8%2824-x%29%5C%20%5B%5Ctext%7BCross%20multiply%7D%5D%5C%5C%20%5C%5C12x%3D192-8x%5C%5C%20%5C%5C12x%2B8x%3D192%5C%5C%20%5C%5C20x%3D192%5C%5C%20%5C%5Cx%3D9.6)
3. By Thales's theorem,
![\dfrac{4x}{5x}=\dfrac{4x-8}{6x-10}\\ \\\dfrac{4}{5}=\dfrac{4x-8}{6x-10}\\ \\5(4x-8)=4(6x-10)\ [\text{Cross multiply}]\\ \\20x-40=24x-40\\ \\20x=24x\\ \\4x=0\\ \\x=0](https://tex.z-dn.net/?f=%5Cdfrac%7B4x%7D%7B5x%7D%3D%5Cdfrac%7B4x-8%7D%7B6x-10%7D%5C%5C%20%5C%5C%5Cdfrac%7B4%7D%7B5%7D%3D%5Cdfrac%7B4x-8%7D%7B6x-10%7D%5C%5C%20%5C%5C5%284x-8%29%3D4%286x-10%29%5C%20%5B%5Ctext%7BCross%20multiply%7D%5D%5C%5C%20%5C%5C20x-40%3D24x-40%5C%5C%20%5C%5C20x%3D24x%5C%5C%20%5C%5C4x%3D0%5C%5C%20%5C%5Cx%3D0)
Answer:
probably A
Step-by-step explanation:
Brainliest pls
I'm pretty sure the answer would be 30 people.
9514 1404 393
Answer:
51
Step-by-step explanation:
The rule gives the sequence ...
75, 69, 63, 57, 51, 45, ...
The 5th number in the sequence is 51.
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<em>Alternate solution</em>
The equation for the general term of an arithmetic sequence is ...
an = a1 +d(n -1) . . . . . for first term a1 and common difference d
Your sequence has first term 75 and common difference -6, so the equation is ...
an = 75 -6(n -1)
Then for n=5, the term is ...
a5 = 75 -6(5 -4) = 75 -24 = 51
The 5th term is 51.