Answer:
slope of the line is -0.5
y-intercept is 13
Explanation:
The general formula of the linear equation is:
y = mx + c
where m is the slope and c is the y-intercept
1- getting the slope:
We are given the two points:
(6,10) representing (x1 , y1)
(12,7) representing (x2 , y2)
The slope of the line will be calculated as follows:
m = (y2-y1) / (x2-x1) = (7-10) / (12-6) = -3/6 = -0.5
The equation of the line now becomes:
y = -0.5x + c
2- getting the value of the y-intercept:
To get the value of the y-intercept (c), we will use any of the given points, substitute in the equation of the line and solve for c. I will use the point (6,10) as follows:
y = -0.5x + c
10 = -0.5(6) + c
10 = -3 + c
c = 13
Based on the above, the equation of the line would be:
y = -0.5x + 13
Hope this helps :)
Answer:
Your answer is the first point
A reflection across the x-axis and then a transformation of -6 and 1.
Answer:
20 and 16
Step-by-step explanation:
Let us find x and y.
x – y = 4 _____(1)
x/2 + y/2= 18___(2)
Multiply (2) by 2 and add to (1)
x - y = 4
+<u>(x + y = 36)</u>
<u>2x = 40</u>
=> x = 40 / 2 = 20
From (1):
20 - y = 4
=> y = 20 - 4 = 16
The two numbers are 20 and 16.
First, we draw our line.
|------------------------------------------------------------------------------------|
a e
Next, break up this line into segments using the information.
|----------------------|----------------------|--------------------|------------------|
a b c d e
The entire line is 29.
ab + bc + cd + de = ae
ab + bc + cd + de = 29
You also know that
bd = bc + cd
Due to midpoint theorem,
ab = bc
cd = de
Then,
2ab + 2cd = 29
The equations we will use are
bd = bc + cd eq1
2bc + 2cd = 29 eq2
Dividing both sides of the equation in eq2 yields
bc + cd = 14.5
bd = bc + cd
bd = 14.5
PART I
Angular size of the minor arc .
Half of the chord an the radius makes a right angled triangle with the radius as the hypotenuse and half of the chord as one of the shorter side.
Therefore, using trigonometric ratio, sine = opp/hyp
sine θ = 8/10 where θ is half the minor angle
θ = 53.13
Therefore, the angular size of the minor arc will be 53.13 × 2 = 106.26°
PART II
The length of an arc is given by (θ/360 )× 2πr
where θ is the angle subtended by the arc to the center of the circle and r is the radius of the circle.
Therefore, length = (106.26/360) × 3.142 × 2×10
= 18.548 Inches
