Write an equation of a like that passes through the points (9,5) and (6,7)
1 answer:
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Let's call that number x, twice the number will be 2x, sum of it and 5 is, 2x+5. So if this expression is at most 15, it means, it can be only less than 15 and equal to 15. Let's show this as an inequality.
Let's solve.
![x\quad \in \quad \left[ -\infty ,5 \right]](https://tex.z-dn.net/?f=x%5Cquad%20%5Cin%20%5Cquad%20%5Cleft%5B%20-%5Cinfty%20%2C5%20%5Cright%5D%20)
If the number is a natural number. The values it can take is,![x\quad \in \quad \left[ 0,1,2,3,4,5 \right]](https://tex.z-dn.net/?f=x%5Cquad%20%5Cin%20%5Cquad%20%5Cleft%5B%200%2C1%2C2%2C3%2C4%2C5%20%5Cright%5D%20)
Let's solve.
If the number is a natural number. The values it can take is,
The distance d is 9 ft and the height is 12ft.
<h3>How to find the distance and the height?</h3>
Here we can model the situation with a right triangle, where the length of the wire is the hypotenuse.
The height is one cathetus and the distance is the other catheti.
Let's define:
- h = height
- d = distance.
- hypotenuse = 15ft
We know that the height of the tower is 3 ft larger than the distance, then:
h = d + 3ft
Now we can use the Pythagorean theorem, it says that the sum of the squares of the cathetus is equal to the square of the hypotenuse.
Then:
Now we can solve this equation for d:
Then the solutions are:
We only take the positive solution:
d = (-3ft + 21ft)/2 = 9ft
And the height is 3 ft more than that, so:
h = 9ft + 3ft = 12ft
The distance d is 9 ft and the height is 12ft.
If you want to learn more about right triangles:
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