Answer:
6
Step-by-step explanation:
So we have a number (let's call it x) and it was multiplied by 8 and added by 2. Therefore:
![8x+2](https://tex.z-dn.net/?f=8x%2B2)
And we are told that the sum is equal to the product of 2 and 25 (or 50). Thus:
![8x+2=50](https://tex.z-dn.net/?f=8x%2B2%3D50)
To find the number, we just need to find x. Thus, subtract 2 from both sides:
![8x=48](https://tex.z-dn.net/?f=8x%3D48)
Divide both sides by 8:
![x=6](https://tex.z-dn.net/?f=x%3D6)
And we're done!
So, our original number was 6.
The similarity is while constructing a circle with two points as the center using an arc, then take the intersection point and the segment bisector connects two intersections with the length of the segment as the radius.
<h3>What is a segment bisector?</h3>
A segment bisector is a line, ray, line segment, or point that divides a line segment into two equal halves at its center.
The similarities: construct a circle with two points as the center using an arc, then take the intersection point.
The angle bisector connects one intersection with the corner vertex with the distance between the junctions on both sides as the radius, whereas the segment bisector connects two intersections with the length of the segment as the radius.
Thus, the similarity is while constructing a circle with two points as the center using an arc, then take the intersection point and the segment bisector connects two intersections with the length of the segment as the radius.
Learn more about the segment bisector here:
brainly.com/question/4137998
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Answer:
![x=2.\ y=1](https://tex.z-dn.net/?f=x%3D2.%5C%20y%3D1)
Step-by-step explanation:
![We\ are\ given\ the\ following\ pair\ of\ equations:\\5x+7y=17\\7x+5y=19\\Now,\\As\ the\ co-efficients\ of\ none\ of\ the\ algebraic\ terms\ match,\\We\ can\ take\ the\ LCM\ of\ their\ co-efficients;\\As\ the\ co-efficients\ of\ the\ x-terms\ are\ 5,7\ respectively;\\Their\ LCM\ is\ 35.](https://tex.z-dn.net/?f=We%5C%20are%5C%20given%5C%20the%5C%20following%5C%20pair%5C%20of%5C%20equations%3A%5C%5C5x%2B7y%3D17%5C%5C7x%2B5y%3D19%5C%5CNow%2C%5C%5CAs%5C%20the%5C%20co-efficients%5C%20of%5C%20none%5C%20of%5C%20the%5C%20algebraic%5C%20terms%5C%20match%2C%5C%5CWe%5C%20can%5C%20take%5C%20the%5C%20LCM%5C%20of%5C%20their%5C%20co-efficients%3B%5C%5CAs%5C%20the%5C%20co-efficients%5C%20of%5C%20the%5C%20x-terms%5C%20are%5C%205%2C7%5C%20respectively%3B%5C%5CTheir%5C%20LCM%5C%20is%5C%2035.)
![Hence,\\7(5x+7y)=7(17)\\-5(7x+5y)=-5(19)\\Hence,\\35x+49y=119\\-35x-25y=-95\\Hence,\\Adding\ the\ two\ equations\ we\ have:\\(35x+49y)+(-35x-25y)=(119)+(-95)\\(35x-35x)+(49y-25y)=119-95\\24y=24\\y=\frac{24}{24}=1](https://tex.z-dn.net/?f=Hence%2C%5C%5C7%285x%2B7y%29%3D7%2817%29%5C%5C-5%287x%2B5y%29%3D-5%2819%29%5C%5CHence%2C%5C%5C35x%2B49y%3D119%5C%5C-35x-25y%3D-95%5C%5CHence%2C%5C%5CAdding%5C%20the%5C%20two%5C%20equations%5C%20we%5C%20have%3A%5C%5C%2835x%2B49y%29%2B%28-35x-25y%29%3D%28119%29%2B%28-95%29%5C%5C%2835x-35x%29%2B%2849y-25y%29%3D119-95%5C%5C24y%3D24%5C%5Cy%3D%5Cfrac%7B24%7D%7B24%7D%3D1)
![Now,\\Lets\ consider\ the\ First\ Equation:\\5x+7y=17\\Substituting\ y=1,\\5x+7*1=17\\5x+7=17\\5x=17-7\\5x=10\\x=\frac{10}{5}=2\\\\Together,\\x=2.\ y=1](https://tex.z-dn.net/?f=Now%2C%5C%5CLets%5C%20consider%5C%20the%5C%20First%5C%20Equation%3A%5C%5C5x%2B7y%3D17%5C%5CSubstituting%5C%20y%3D1%2C%5C%5C5x%2B7%2A1%3D17%5C%5C5x%2B7%3D17%5C%5C5x%3D17-7%5C%5C5x%3D10%5C%5Cx%3D%5Cfrac%7B10%7D%7B5%7D%3D2%5C%5C%5C%5CTogether%2C%5C%5Cx%3D2.%5C%20y%3D1)