We know: length of a rectangle is 7m less than three times the width.
So let's set the length to l, width to w.
And we can get that l = 3w-7.
We also know that the area of the rectangle is 66 m^2.
Thus, l*w= 66.
So we have:
function 1: l=3w-7
function 2: l*w=66
plug function 1 to 2.
(3w-7)*w=66
3w^2-7w-66=0
w=6 and -11/3.
And the width of a rectangle can not be negative.
So: w=6.
Plug w=6 back to function 1 or 2, either way is correct and can give you the length. In this case, I will plug it back to function 1.
l=3*6-7=11.
So: the width of the rectangle is 6, and the length of the rectangle is 11.
Step-by-step explanation:
66. Δy = -3.4 Δx
Δy/Δx = -3.4
The slope of the line is -3.4. Slope-intercept equation of the line is:
y = -3.4x + b
Plug in the given point to find b:
2 = -3.4(4) + b
b = 15.6
Therefore, the equation is y = -3.4x + 15.6.
Use the equation to find the y coordinates.
![\left[\begin{array}{cc}x&y\\-4&29.2\\4&2\\6&-4.8\\18&-45.6\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Dx%26y%5C%5C-4%2629.2%5C%5C4%262%5C%5C6%26-4.8%5C%5C18%26-45.6%5Cend%7Barray%7D%5Cright%5D)
68. Repeat the same steps as 66.
Δy = -1.7 Δx
Δy/Δx = -1.7
The slope of the line is -1.7. Slope-intercept equation of the line is:
y = -1.7x + b
Plug in the given point to find b:
3 = -1.7(-7) + b
b = -8.9
Therefore, the equation is y = -1.7x − 8.9.
Use the equation to find the x or y coordinates.
![\left[\begin{array}{cc}x&y\\-19&23.4\\-7&3\\-2.412&-4.8\\3.2&-14.34\\9.1&-24.37\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Dx%26y%5C%5C-19%2623.4%5C%5C-7%263%5C%5C-2.412%26-4.8%5C%5C3.2%26-14.34%5C%5C9.1%26-24.37%5Cend%7Barray%7D%5Cright%5D)
Answer:
c
Step-by-step explanation:
Your classmate is correct, though this is not explicitly what the midpoint formula is necessarily set out to do. If one is given two sets of endpoints, one can discover the midpoint by finding the mean distance between these two endpoints. For example, if two points are 10 and 2, all you need do to find the midpoint is add the two poles and divide them by 2 (that is, find the average). The same applies for coordinate geometry, except with additional variables, the formula to find the coordinates of a midpoint is: M= (x1+x2/2, y1+y2/2). Thus, two averages (of both the x coordinates and y coordinates are taken). Your classmate is correct if two endpoints are given, think of a line with two poles, the middle of this line must be the midpoint.
