To find the midpoint, you're trying to bisect the line (cut it in half). The equation you'll need for this is (x1 + x2 / 2, y1 +y2 / 2). You're using the starting point of the line and the ending point of the line, and dividing it by two to get to the middle.
(3+-5/2 , -1 + -3/2)
(-2/2 , -4/2)
(-1,-2) is your midpoint
Answer:
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Step-by-step explanation:
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Answer:
$130
Step-by-step explanation:
You want to know Brenda and Hazel's combined money when the ratio of their remaining balances is 1 : 4 after Brenda spent $58 and Hazel spent $37. They had the same amount to start with.
<h3>Setup</h3>
Let x represent the total amount the two women started with. Then x/2 is the amount each began with, and their fnal balance ratio is ...
(x/2 -58) : (x/2 -37) = 1 : 4
<h3>Solution</h3>
Cross-multiplying gives ...
4(x/2 -58) = (x/2 -37)
2x -232 = x/2 -37 . . . . . . eliminate parentheses
3/2x = 195 . . . . . . . . . . . . add 232-x/2
x = (2/3)(195) = 130 . . . . . multiply by 2/3
Brenda and Hazel had $130 altogether before their purchases.
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<em>Alternate solution</em>
The difference in their spending is $58 -37 = $21. This is the same as the difference in their final balances. That difference is 4-1 = 3 "ratio units", so each of those ratio units is $21/3 = $7. Their ending total is 1+4 = 5 ratio units, or $35. The total they started with is $58 +37 +35 = $130.
In the question, it is given that
Suppose two trains leave a certain station, at the same time, traveling in opposite directions. one train travels 10 mph faster than the other. in 2.5hours, the trains are 255 miles apart.
Let the speed of the slower train be x m/h and faster train be (x+10) m /h.
Distances travelled by them are
And total distance is 255 miles, that is
So the speed of slower train is 46 MPH and of faster train is 56MPH.
