Johnathan has a bag full of 14 balls to sell. He sells the baseballs for $2 dollars and the volleyballs for $5 and earns a total
1 answer:
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Answer:
Danielle drove 3 hours
Step-by-step explanation:
Suppose Heather moved in the x direction.
Then Danielle moved in the opposite direction, that is, she moved in the -x direction.
Let's call ,
,
at the speed, distance and time that I code Heather
Let's call ,
,
at the speed, distance and time Danielle codes.
Observe the following diagram:
(x) Heather <------ --------- hospital ----------
-----------> Danielle (-x)
So:
We know that after 4 hours the distance between Heather and Danielle was 290 km.
That is to say:
We know that
We already know , the distance from the hospital to Heather, so we can find
and thus know
So:
Then:
Answer:
The coordinates of point B are (-2, 2)
Step-by-step explanation:
We have two points: A and C.
The coordinates for A are (2, -8) and the coordinates for C are (-4, 7).
We have to find the coordinates of the point B, that satisfies the condition that the distance AB is 2 times the distance BC.
We also know that B is a point of the line AC.
We can calculate the line AC as a linear function y=mx+b.
The slope m is:
Then, the y-intercept b can be calculated using the coordinates of one of the points, in this case point A:
Then, we know that B is a point of the linear function y=-2.5x-3, within the range x ∈ (-4; 2).
To have a ratio AB to BC of 2 to 1, we can divide the length of the line AC in 3 parts, and the point B will be located in the end of the segment nearer to point C.
In the picture attached, you can see the division of the segment AC in three parts and the location of point B=(x, y).
Applying the Thales theorem, we can divide the segment in the y-axis in three and calculate y, and the same for the x-axis.
Then, the coordinate y for the point B is:
Then, the point B has coordinates (-2, 2).
We can verify the distances as:
