Some things we should know before we start:
- Parallel lines are lines that never meet and which are straight.
- Perpendicular lines are lines that intersect at a 90° angle.
A picture of different types of lines will be shown below
A picture of the graph will be shown below.
Looking at the graph, we can see that lines intersect and seem to have a 90°.
Therefore, they are perpendicular.
Best of Luck!
Answer:
Center: (−4,6) Radius: 5
Step-by-step explanation:
Answer:y = 2x + 4
Explanation:
1) The slope - intercept form is of the kind y = mx + b, where m is the slope and b is the y-intercept.
2) Given two points you can find the slope (using the two points) and then the equation using one of the points.
3) slope = m = Δy / Δx
points given (3,10) , (0,4)
m = [y2 - y1] / [x2 - x1] = [10 - 4] / [3 - 0] = 6 / 3 = 2
4) equation
y - y2
-------- = m
x - x2
y - 4
---------- = 2
x - 0
=> y - 4 = 2 (x - 0)
y - 4 = 2x
y = 2x + 4
Question 21
Let's complete the square
y = 3x^2 + 6x + 5
y-5 = 3x^2 + 6x
y - 5 = 3(x^2 + 2x)
y - 5 = 3(x^2 + 2x + 1 - 1)
y - 5 = 3(x^2+2x+1) - 3
y - 5 = 3(x+1)^2 - 3
y = 3(x+1)^2 - 3 + 5
y = 3(x+1)^2 + 2
Answer: Choice D
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Question 22
Through trial and error you should find that choice D is the answer
Basically you plug in each of the given answer choices and see which results in a true statement.
For instance, with choice A we have
y < -4(x+1)^2 - 3
-7 < -4(0+1)^2 - 3
-7 < -7
which is false, so we eliminate choice A
Choice D is the answer because
y < -4(x+1)^2 - 3
-9 < -4(-2+1)^2 - 3
-9 < -7
which is true since -9 is to the left of -7 on the number line.
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Question 25
Answer: Choice B
Explanation:
The quantity (x-4)^2 is always positive regardless of what you pick for x. This is because we are squaring the (x-4). Squaring a negative leads to a positive. Eg: (-4)^2 = 16
Adding on a positive to (x-4)^2 makes the result even more positive. Therefore (x-4)^2 + 1 > 0 is true for any real number x.
Visually this means all solutions of y > (x-4)^2 + 1 reside in quadrants 1 and 2, which are above the x axis.
