Answer:
Slope - intercept form:
B) y= x -4
Step-by-step explanation:
(3,-1) and (-1,-5)
Slope = (-5 + 1)/(-1 - 3)
Slope = -4 / -4
Slope = 1
Point slope form:
y + 1 = 1 (x - 3)
y +1 = x - 3
y = x - 4 <------------------slope - intercept form
Let's call the number you thought of n. Then what the two steps you took can be written as an equation:
![n+4\frac{5}{7}=12n](https://tex.z-dn.net/?f=n%2B4%5Cfrac%7B5%7D%7B7%7D%3D12n)
Subtract n to get all of your variables to one side:
![4\frac{5}{7}=11n](https://tex.z-dn.net/?f=4%5Cfrac%7B5%7D%7B7%7D%3D11n)
At this point, I recommend turning your mixed number into an improper fraction. It will make things easier later on:
![\frac{33}{7}=11n](https://tex.z-dn.net/?f=%5Cfrac%7B33%7D%7B7%7D%3D11n)
Now divide both sides by 11 to get the value of n:
In order to study geometry logically, it will be important to understand key mathematical properties and to know how to apply useful postulates and theorems. a postulate is a proposition that has not been proven true but is considered to be true on the basis for mathematical reasoning.
Solution:
we have been asked to find the equation of the line that passes through (7, 4) and (4, -2).
First we will find the slope of the line using the formula
![m=\frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=%20m%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D%20%20)
Plugin the given values we get
![m=\frac{-2-4}{4-7}=\frac{-6}{-3}=2](https://tex.z-dn.net/?f=%20m%3D%5Cfrac%7B-2-4%7D%7B4-7%7D%3D%5Cfrac%7B-6%7D%7B-3%7D%3D2%20%20%20)
Now using the point slope form of a straight line
![(y-y_1)=m(x-x_1)](https://tex.z-dn.net/?f=%20%28y-y_1%29%3Dm%28x-x_1%29%20)
Plugin the values
![(y-4)=2(x-7)\\ \\ y=2x-14+4\\ \\ y=2x-10\\](https://tex.z-dn.net/?f=%20%28y-4%29%3D2%28x-7%29%5C%5C%20%5C%5C%20y%3D2x-14%2B4%5C%5C%20%5C%5C%20y%3D2x-10%5C%5C%20)
Hence the correct option is a.
Answer:
4.62 cm to nearest hundredth.
Step-by-step explanation:
If the parallel sides are x and y then:
x + y = 2*8 = 16
x + y = 16
If we drop a perpendicular line from one of the upper points on the trapezoid we have the height. Let the upper point be C and the point on the base be A. Let the point on right of the base be B.
AC is the height of the trapezoid. AB is the baseline of the triangle CAB.
In triangle CAB the angle B is 30 degrees.
As this is a 30-60-90 degree triangle
AC/AB = 1/√3 so AC = AB/ √3.
As the trapezoid is isosceles:
AB = x + 0.5(y - x)
AB = 0.5x + 0.5y
So AC = 1 /√3 (0.5x + 0.5y)
= 1 /√3 (0.5x + 0.5(16 - x)) (Substituting for x)
= 1 /√3 (0.5x + 8 - 0.5x)
=8 / √3
. = 4.6188 cm