Answer:
1. (x - 3)² = 8
2. (x + 2)² = 3
3. (x + 6)² = 
4. (x + 3)² = 27
5. (x + 4)² = 13
6. 
Step-by-step explanation:
Completion of Square: 
In the following problems the terms in the RHS of the above equation may be missing. We balance the equation. Simplify it and re write it in terms of LHS.
1. x² - 6x + 1 = 0
Taking the constant term to the other side, we get:
x² - 6x = - 1
⇒ x² - 2(3)x = -1
⇒ x² -2(3)x + 9 = - 1 + 9 [Adding 9 to both the sides]
⇒ x² -2(3)x + 3² = 8
⇒ (x - 3)² = 8 is the answer.
2. 3x² + 12x + 3 = 0
Note that the co-effecient of x² is not 1. We make it 1, by dividing the whole equation by 3. And then proceed like the previous problem.
3x² + 12x = -3
Dividing by 3 through out, x² + 4x = - 1
⇒ x² + 2(2) + 4 = -1 + 4
⇒ x² +2(2) + 2² = 3
⇒ (x + 2)² = 3 is the answer.
3. 2x² + 24x = 29
x² + 12x = 
⇒ x² + 2(6)x + 36 = + 36
⇒ x² + 2(6)x + 6² = 
⇒ (x + 6)² = is the answer.
4. x² + 6x - 18 = 0
x² + 6x = 18
⇒ x² + 2(3)x = 18
⇒ x² + 2(3)x + 9 = 18 + 9
⇒ x² + 2(3)x + 3² = 27
⇒ (x + 3)² = 27 is the answer.
5. x² + 8x + 3 = 0
x² + 8x = -3
⇒ x² + 2(4)x = -3
⇒ x² + 2(4)x + 16 = - 3 + 16
⇒ x² + 2(4)x + 16 = 13
⇒ (x + 4)² = 13 is the answer.
6. 9x² - 30x + 6 = 0
9x² - 30x = - 6
⇒ x² 
x = - 6
is the answer.
Answer:292820839382
Step-by-step explanation:
282739282992
Answer:
1. 
Step-by-step explanation:
We have been given a graph of a scatter-plot and we are asked to find the correct expression than can be solved to find the slope of the trend line in the scatter-plot.
Since we know that slope of a line can be found by dividing the difference of the y-coordinates of 2 points on a line by difference of the x-coordinates of these same points.
We can see that (2,79) and (12,24) are two given points of our trend line. So let us substitute x and y-coordinates of our given points in slope formula to find the our desired expression.
Therefore, the expression can be solved to find the slope of the trend line in the scatter-plot and 1st option is the correct choice.
y=-2/3x+5
Step-by-step explanation:
From the scattered plot, it is evident that the line of best fit will have a negative slope from the way the plots are aligned.
Selecting the line of best fit that will cut the y axis at +5, the points can be estimated as;
(5,1.5) and (3.5,2.5)
The slope can be found as;
m=Δy/Δx
m=2.5-1.5/3.5-5 =1.0/ -1.5 = -0.67
Finding the equation as;
m=Δy/Δx
-0.66 = y-2.5/x-3.5
-0.66(x-3.5) = y-2.5
-0.66x+2.3=y-2.5
-0.66x+2.3+2.5=y
-0.66x+4.7=y
⇒⇒ y= -0.66 x + 4.7
⇒⇒y= -2/3 x + 5
Learn More
Linear equations:brainly.com/question/8738418
Keywords: best trend line, data set
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Step-by-step explanation:
Which of the arcs listed below represents a MAJOR ARC?
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