If x=-6 then y=54.
If x=-4 then y=51.
If x=-2 then y=48.
If x=0 then y=45.
If x=2 then y=42.
If x=4 then y=39.
If x=6 then y=36.
There are an infinite variety of pairs of numbers for 'x' and 'y'
that can make that equation true.
You can use that equation to draw a line on a graph. Then
EVERY point on the line is a solution to the equation.
'x' and 'y' don't have single values unless you have TWO equations.
Answer:
The coordinate of the rest stop is: ![(5,2.5)](https://tex.z-dn.net/?f=%285%2C2.5%29)
The distance between the hotel and the stadium is 32 miles
Step-by-step explanation:
Given
--- Team hotel
--- Stadium
Solving (a): The coordinates of the rest stop
The rest stop is at half way;
So, the coordinate is:
![(x,y) = \frac{1}{2}(x_1+x_2,y_1+y_2)](https://tex.z-dn.net/?f=%28x%2Cy%29%20%3D%20%5Cfrac%7B1%7D%7B2%7D%28x_1%2Bx_2%2Cy_1%2By_2%29)
This gives:
![(x,y) = \frac{1}{2}(3+7,4+1)](https://tex.z-dn.net/?f=%28x%2Cy%29%20%3D%20%5Cfrac%7B1%7D%7B2%7D%283%2B7%2C4%2B1%29)
![(x,y) = \frac{1}{2}(10,5)](https://tex.z-dn.net/?f=%28x%2Cy%29%20%3D%20%5Cfrac%7B1%7D%7B2%7D%2810%2C5%29)
Open bracket
![(x,y) = (5,2.5)](https://tex.z-dn.net/?f=%28x%2Cy%29%20%3D%20%285%2C2.5%29)
Solving (b): Distance between the hotel and the stadium
We have:
--- Team hotel
--- Stadium
The distance (d) is:
![d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}](https://tex.z-dn.net/?f=d%20%3D%20%5Csqrt%7B%28x_1%20-%20x_2%29%5E2%20%2B%20%28y_1%20-%20y_2%29%5E2%7D)
So, we have:
![d = \sqrt{(3 - 7)^2 + (4 - 1)^2}](https://tex.z-dn.net/?f=d%20%3D%20%5Csqrt%7B%283%20-%207%29%5E2%20%2B%20%284%20-%201%29%5E2%7D)
![d = \sqrt{(-4)^2 + 3^2}](https://tex.z-dn.net/?f=d%20%3D%20%5Csqrt%7B%28-4%29%5E2%20%2B%203%5E2%7D)
![d = \sqrt{16 + 9}](https://tex.z-dn.net/?f=d%20%3D%20%5Csqrt%7B16%20%2B%209%7D)
![d = \sqrt{25}](https://tex.z-dn.net/?f=d%20%3D%20%5Csqrt%7B25%7D)
![d =5](https://tex.z-dn.net/?f=d%20%3D5)
From the question, we have:
![1\ unit = 6.4\ miles](https://tex.z-dn.net/?f=1%5C%20unit%20%3D%206.4%5C%20miles)
So:
![d =5 * 6.4\ miles](https://tex.z-dn.net/?f=d%20%3D5%20%2A%206.4%5C%20miles)
![d =32\ miles](https://tex.z-dn.net/?f=d%20%3D32%5C%20miles)
Answer:
−
8
x^
2
+
62
y
^2
+
46
Step-by-step explanation:
heheheh I do math lol
By flipping the fraction of -3/7, you will get the fraction of -7/3 or - 2 1/3.
Therefore, the reciprocal of -3/7 is - 2 1/3.
Hope this helps!
<h2><u>COMBINED OPERATIONS</u></h2><h3>Exercise</h3>
First, let's solve the subtraction (in parentheses):
![\mathsf{\dfrac{-8\left(2-6\right)}{2}}](https://tex.z-dn.net/?f=%5Cmathsf%7B%5Cdfrac%7B-8%5Cleft%282-6%5Cright%29%7D%7B2%7D%7D)
![\mathsf{\dfrac{-8(-4)}{2}}](https://tex.z-dn.net/?f=%5Cmathsf%7B%5Cdfrac%7B-8%28-4%29%7D%7B2%7D%7D)
Now, let's solve the multiplication. Remember: in multiplication, two negative numbers will give a positive number:
![\mathsf{\dfrac{-8(-4)}{2}}](https://tex.z-dn.net/?f=%5Cmathsf%7B%5Cdfrac%7B-8%28-4%29%7D%7B2%7D%7D)
![\mathsf{\dfrac{32}{2}}](https://tex.z-dn.net/?f=%5Cmathsf%7B%5Cdfrac%7B32%7D%7B2%7D%7D)
Finally, let's solve the division:
![\mathsf{\dfrac{32}{2} = 16}](https://tex.z-dn.net/?f=%5Cmathsf%7B%5Cdfrac%7B32%7D%7B2%7D%20%3D%2016%7D)
<h3><u>Answer</u>: 16</h3>