Answer:
![L=\sqrt{x^{2}+100}+\sqrt{x^{2}-34x+433} ft](https://tex.z-dn.net/?f=L%3D%5Csqrt%7Bx%5E%7B2%7D%2B100%7D%2B%5Csqrt%7Bx%5E%7B2%7D-34x%2B433%7D%20ft)
Step-by-step explanation:
let length of calble = L
distance from 10-foot pole = x ft
Moving from the top of the 10-foot pole to point x, we have
From the diagram that
![x^{2} +10^{2}=L_{1} ^{2} \\x^{2} + 100 = L_{1} ^{2}](https://tex.z-dn.net/?f=x%5E%7B2%7D%20%2B10%5E%7B2%7D%3DL_%7B1%7D%20%5E%7B2%7D%20%20%5C%5Cx%5E%7B2%7D%20%2B%20100%20%3D%20L_%7B1%7D%20%5E%7B2%7D)
Take the square root of both sides
![\sqrt{x^{2}+100}=\sqrt{L_{1} ^{2}}\\ \sqrt{x^{2}+100}= L_{1}](https://tex.z-dn.net/?f=%5Csqrt%7Bx%5E%7B2%7D%2B100%7D%3D%5Csqrt%7BL_%7B1%7D%20%5E%7B2%7D%7D%5C%5C%20%20%5Csqrt%7Bx%5E%7B2%7D%2B100%7D%3D%20L_%7B1%7D)
Moving from point x to the top of the 12-foot pole, we have
From the diagram that
![(17-x)^{2}+12^{2}=L_{2} ^{2} \\289-34x+x^{2} +144=L_{2} ^{2}\\x^{2} -34x+433=L_{2} ^{2}](https://tex.z-dn.net/?f=%2817-x%29%5E%7B2%7D%2B12%5E%7B2%7D%3DL_%7B2%7D%20%5E%7B2%7D%20%20%20%5C%5C289-34x%2Bx%5E%7B2%7D%20%2B144%3DL_%7B2%7D%20%5E%7B2%7D%5C%5Cx%5E%7B2%7D%20-34x%2B433%3DL_%7B2%7D%20%5E%7B2%7D)
Take the square root of both sides
![\sqrt{x^{2}-34x+433}=\sqrt{L_{2} ^{2}} \\\sqrt{x^{2}-34x+433}=L_{2}](https://tex.z-dn.net/?f=%5Csqrt%7Bx%5E%7B2%7D-34x%2B433%7D%3D%5Csqrt%7BL_%7B2%7D%20%5E%7B2%7D%7D%20%20%5C%5C%5Csqrt%7Bx%5E%7B2%7D-34x%2B433%7D%3DL_%7B2%7D)
Amount of cable used, L = L1 + L2
![L=\sqrt{x^{2}+100}+\sqrt{x^{2}-34x+433}](https://tex.z-dn.net/?f=L%3D%5Csqrt%7Bx%5E%7B2%7D%2B100%7D%2B%5Csqrt%7Bx%5E%7B2%7D-34x%2B433%7D)
Answer:
Step-by-step explanation:
<u>As per the graph, the line has:</u>
- y-intercept (0, -4.5)
- x-intercept (1, 0)
Substitute the values and verify each equation.
<u>This gives us one correct equation:</u>
<u>Proof:</u>
- x = 0 ⇒ -2y = 9 ⇒ y = -4.5
- y = 0 ⇒ 9x = 9 ⇒ x = 1
180
The exterior angle of a triangle + the adjacent interior angle are supplementary, that is sum to 180°, thus
the exterior angle = 180 - adjacent interior angle
There are 225 women in the race.
Step-by-step explanation:
Total people in the race = 234
Let,
x represents the number of women in race.
y represents the number of men in race.
According to given statement;
x+y=234 Eqn 1
x=25y Eqn 2
Putting x=25y in Eqn 1
![25y+y=234\\26y=234](https://tex.z-dn.net/?f=25y%2By%3D234%5C%5C26y%3D234)
Dividing both sides by 26
![\frac{26y}{26}=\frac{234}{26}\\y=9](https://tex.z-dn.net/?f=%5Cfrac%7B26y%7D%7B26%7D%3D%5Cfrac%7B234%7D%7B26%7D%5C%5Cy%3D9)
Putting y=9 in Eqn 2
![x=25(9)\\x=225](https://tex.z-dn.net/?f=x%3D25%289%29%5C%5Cx%3D225)
There are 225 women in the race.
Keywords: linear equation, substitution method
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Yes they can all have the same