so school is starting again .0.
Could I be walked through a few practice questions? I've forgotten everything over the summer and a refresher would be nice. I'm not looking for answers, just some help/pointers!
1. Solve for x. |2x - 4| >10
(for this one don't I have to do something with making the first half a -2x and positive 4?)
2. The variables x and y vary directly. Write an equation that relates x and y. Then, find y when x=-3.
x=4, y=-12
(not quite sure how to start/deal with this one)
3. determine the x-intercept and y-intercept of the line with the given equation. 10x+3y=20
(?)
4. What is the vertex of the parabola? y=-3(x-4)^2+2
I might ask a few more if anyone is willing to help! I've just forgotten how to do a majority of these over the summer and I'm scared to get called on in class and not know how to solve the problem haha
thanks!
1. Solve for x. |2x - 4| >10
(for this one don't I have to do something with making the first half a -2x and positive 4?)
sort of
(2x-4) > 10 and -(2x-4)>10
2x >14 and 2x-4<-10
if you multiply both side of inequality by negative, reverse arrow
x > 7 and x < -3
2. The variables x and y vary directly. Write an equation that relates x and y. Then, find y when x=-3.
x=4, y=-12
(not quite sure how to start/deal with this one)
==================
y = k x
-12 = k (4)
k = -3
y = -3 x
y = -3*-3 = 9
3. determine the x-intercept and y-intercept of the line with the given equation. 10x+3y=20
(?)
x intercept when y = 0
so when x = 20/10 = 2
y intercept when x = 0
so when y = 20/3
4. What is the vertex of the parabola? y=-3(x-4)^2+2
=======================
LOL (x-4)^2 is the same as (-x+4)^2
so function symmetric about x = 4
(look at (x-4)^2 when x = 3 or x = 5)
so vertex at x = 4
then
y = 2
(4,2)
Of course, I'd be happy to help! Let's work through the practice questions together:
1. Solve for x: |2x - 4| > 10
To solve this inequality, we need to consider two cases: when the expression inside the absolute value is positive and when it is negative.
Case 1: Set the expression inside the absolute value greater than 10 and solve for x:
2x - 4 > 10 (no need to change the signs)
2x > 14
x > 7
Case 2: Set the expression inside the absolute value less than -10 and solve for x:
-(2x - 4) > 10 (flip the sign when moving the expression to the other side)
-2x + 4 > 10
-2x > 6
x < -3 (dividing by -2 and flipping the sign)
So, the solution to the inequality is x < -3 or x > 7.
2. The variables x and y vary directly. Write an equation that relates x and y. Then, find y when x = -3.
When two variables vary directly, it means they can be related by a constant multiplier. Let's call this constant multiplier "k."
The equation that relates x and y when they vary directly is: y = kx.
To find the value of k, you can use the given data:
When x = 4, y = -12. So, we can substitute these values into the equation:
-12 = k(4)
-12 = 4k
Now solve for k:
k = -12/4
k = -3
Therefore, the equation that relates x and y when they vary directly is y = -3x. Now let's find y when x = -3:
y = -3(-3)
y = 9
So, when x = -3, y = 9.
3. Determine the x-intercept and y-intercept of the line with the given equation: 10x + 3y = 20.
To find the x-intercept, we set y = 0 and solve for x:
10x + 3(0) = 20
10x = 20
x = 2
So the x-intercept is (2, 0).
To find the y-intercept, we set x = 0 and solve for y:
10(0) + 3y = 20
3y = 20
y = 20/3
So the y-intercept is (0, 20/3).
4. What is the vertex of the parabola? y = -3(x - 4)^2 + 2.
The vertex form of a parabola equation is y = a(x - h)^2 + k, where (h, k) represents the vertex.
For the given equation y = -3(x - 4)^2 + 2, the vertex is (4, 2).
I hope this helps! If you have any more questions or need further clarification, feel free to ask.