Answer:
<em>The coordinates of b are: B=(-7,-8)</em>
Step-by-step explanation:
We are given the coordinates of the midpoint of 
as M=(-5,-2).
We are also given the coordinates of A=(-3,4). The question requires us to calculate the coordinates of the other endpoint B.
Let (xb,yb) the coordinates of B. The coordinates of the midpoint can be calculated as follows:
We know xa=-3 and xm=-5. Solve the first equation for xb:
Substituting:
We can solve the second equation for xb and get:
Since ya=4 and ym=-2, then:
Thus, the coordinates of b are: B=(-7,-8)
The falling stone is a certain instant 230 feet above the ground. 3 seconds later it is only 14 feet above. The height that it was dropped is 32 feet. The equation for the answer is;
<span>16<span>t2</span>+<span>h0</span>=230</span>
<span>−16(t+3<span>)2</span>+<span>h0</span>=14</span>
Answer:
Step-by-step explanation:
<u><em>Using Pythagorean Theorem:</em></u>
=> 
Where c is hypotenuse, a is base and b is perpendicular and ( a, b = 4)
=> 
=> 
=> 
Taking sqrt on both sides
=> c = 5.7 units
Considering there is a function (relationship) and that it is linear, the distance will change proportionally to time constantly. In other words, we are taking the speed to be constant throughout the journey.
If we let:
t = time (min's) driving
d = distance (miles) from destination
Then we can represent the above information as:
t = 40: d = 59
t = 52: d = 50
If we think of this as a graph, we can think of the x-axis representing time and the y-axis representing the distance to the destination. Being linear, the function will be a line, i.e. it will have a constant gradient. If you were plot the two points inferred from the information and connect the two dots, you will get a declining line (one with a negative gradient) representing the inversely proportional relationship or equally, the negative correlation between the time driving and the distance to the destination. The equation of this line will be the linear function that relates time and the distance to the destination. To find this linear function, we do as follows:
Find the gradient (m) of the line:
m = Δy/Δx
In this case, the x-values are t-values and our y-values are d-values, so:
Δy = Δd
= 50 - 59
= -9
Δx = Δt
= 52 - 40
= 12
m = -9/12 = -3/4
Note: m is equivalent to speed with units: d/t
Use formula to find function and rearrange to give it in the desired format:
y - y₁ = m(x - x₁)
d - 50 = -3/4(t - 52)
4d - 200 = -3t + 156
4d + 3t - 356 = 0
Let t = 70 to find d at the time:
4d + 3(70) - 356 = 0
4d + 210 - 356 = 0
4d - 146 = 0
4d = 146
d = 73/2 = 36.5 miles
So after 70 min's of driving, Dale will be 36.5 miles from his destination.
Answer: 0,-3
Step-by-step explanation: hope this helps!!
