Can somebody please help me with 3 and 5. Please don’t answer if you are not sure. 17 points

Mathematics

1 answer:

otez555 [7]3 years ago

7 0

The Pyth. Thm. tells us the following: (hypo)^2 = (leg 1)^2 + (leg 2)^2.
Here the hypo is 75 miles. One train traveled x miles and the other x+10 miles.

applying the Pyth. Thm.,

x^2 + (x+10)^2 = 75^2

which becomes x^2 + x^2 + 20x + 400 = 5625, or
2x^2 + 20x - 5225 = 0.

Choose a method easy for you that will lead to a solution (x-value).
Using "completing the square," I obtained x= 47.8 miles and x = 57.8 miles. I

It's very important to check one's work. Suppose x = 47.8 miles. Then x+10 = 57.8 miles.

47.8^2 + 57.8^2 = 75^ must be true. Is it?

2284.84 + 3340.84 5625
5625.6 is approx equal to 5625. Close enough.

The first train traveled 47.8 miles and the second 57.8 miles.

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Write an equation of a line in slope intercept form that is parallel to y = 3x+6 and passes through the point (-10, 2.5)

TiliK225 [7]

1) Line should be parallel to y = 3x+6, so slope of this line should be =3.

y=mx +b

y=3x +b

Now we have to find b (y-intercept), using the point (-10, 2.5).

2.5 = 3*(-10)+b

b=2.5+30=32.5

y=3x + 32.5

2) The line should be perpendicular to y = -4x -2, so its slope is going to be negative reciprocal m= 1/4.

Now we have to find b (y-intercept), using the point (-16, -11).