1. What is the slope of the line perpendicular to y-6=-2x-4?
2. Simplify 8 ^1/3. In case that doesn't make sense the problem is simplify 8 to the 1/3 exponent.
3. Solve -5<2x-7<8
1. y = 2x + 2
so in this case, the slope is 2. Perpendicular slope is a negative reciprocal, which means it would be... -1/2.
2. this is when you do a cube root of 8. You are asking yourself, what is the value of x for the equation, x^3 = 8.
So you get x = 2.
3. for this problem, using the order of operations, you would have to add 7 to each number, so you get 2<2x<15. Then you will divide the numbers by 2, and get 1<x<7.5.
On #1 why is it a negative recipricol and not 1/2? Then on #2 I don't see how you are getting that answer. Could you please explain? Thanks.
1. To find the slope of a line perpendicular to another line, we need to determine the slope of the given line first. The equation of the given line is in the form y = mx + c, where m represents the slope. So, by comparing the equation y - 6 = -2x - 4, we can see that the slope of the given line is -2.
To find the slope of the line perpendicular to the given line, we use the fact that the product of the slopes of two perpendicular lines is always -1. So, the slope of the line perpendicular to the given line is the negative reciprocal of -2, which is 1/2.
2. To simplify 8^(1/3), you need to raise 8 to the power of 1/3, which means finding the cube root of 8. The cube root of a number can be found by raising the number to the power of 1/3. In this case, 8^(1/3) is equal to the cube root of 8, which is 2.
3. To solve the compound inequality -5 < 2x - 7 < 8, we need to isolate x in the middle part of the inequality.
We can start by adding 7 to all three parts of the compound inequality:
-5 + 7 < 2x - 7 + 7 < 8 + 7
2 < 2x < 15
Next, we divide all three parts by 2 to isolate x:
2/2 < 2x/2 < 15/2
1 < x < 7.5
Therefore, the solution to the compound inequality -5 < 2x - 7 < 8 is 1 < x < 7.5.