Answer:
(2,1)
Step-by-step explanation:
3x+y = 7
-2x +y = -3
Solve the second equation for y by adding 2x to each side
-2x+2x +y = -3+2x
y = -3 +2x
Substitute into the first equation
3x+ (-3+2x) = 7
Combine like terms
5x -3 = 7
Add 3 to each side
5x-3+3 = 7+3
5x = 10
Divide by 5
5x/5 = 10/5
x=2
Now we need to solve for y
y = -3 +2x
y = -3 +2(2)
y = -3+4
y =1
I'm assuming each grid square= 1 square mile.
To do this, you first need to find the total distance.
The first component of his walk takes him from an x-coordinate of 2 to a coordinate of -4 1/2. Since the y-value remains the same, you're not worried about that for this part of the problem. The difference between 2 and -4 1/2 is 6 1/2, so that is your horizontal distance.
Now he walks from the (-4 1/2, -1 3/4) to (-4 1/2, 5 1/4). This time, the x-value is constant, so you only need to worry about the y. As they are on opposite sides of the x-axis, you can add the y-values to get a result of 7, which is your vertical distance.
I just realized I did those distances in reverse order, but it should be ok because the total distance is the same.
To find the total distance, add vertical to horizontal.
6 1/2 + 7 = 13 1/2. This is your total distance.
Now that you have both his speed (given), and total distance, you can find the time it will take him. If he is moving at 4 1/2 mph and the distance is 13 1/2 miles, you can use s=d/t to find the time. 3 1/2 miles divided by the time = 4 1/2 mph. To solve for t, multiply both sides by t and divide that by s, so t= d/s. we know d= 13 1/2 and s= 4 1/2, so t= 13.5 divided by 4.5 = 3. As his speed is in mph, the unit is in hours. Therefore, the answer should be 3 hours.
Answer:
9
Step-by-step explanation:
Compare your x2 + y2=81 to the following:
x^2 + y^2 = 81
The " ^ " symbol indicates exponentiation.
Now compare x^2 + y^2 = 81 to
x^2 + y^2 = r^2.
This is the standard equation of a circle of radius r centered at the origin, (0,0). You can see for yourself that 81 must equal r^2.
Taking the square root of 81, we get plus or minus 9.
But the radius must be positive, so we reject the -9 and take +9.
The radius is 9.
