Answer:
See below.
Step-by-step explanation:
It can really help to think when you see |expression| that it means the distance from expression to zero.
(a) |x| < 7 means the distance from x to 0 is less than 7. That puts x between -7 and 7. The solution set is -7 < x < 7.
(b) |x + 3| < 9 means that the distance from x + 3 to 0 is less than 9. That puts x + 3 between -9 and 9:
-9 < x + 3 < 9 Now subtract 3 from all three parts.
-12 < x < 6
(c) |y - 8| > 11 means that the distance from y - 8 to 0 is more than 11 units. That puts y - 8 in one of two places: left of -11 or right of 11.
(g) 
means that the distance from 3x - 1 to 0 is more than (or equal to) 18. Another way to say it is, 3x - 1 is farther from 0 than 18 units. That puts 3x - 1 in one of two places: to the left of -18 or to the right of 18.
means that 4y + 3 is closer to 0 than 13; it is between -13 and 13.
(That last fraction is 10/4 simplified.)
Answer:
1.8 miles
Step-by-step explanation:
For this case we can model the problem as a rectangle triangle.
We know:
Length of the sides of the triangle
We want to know:
Length of the hypotenuse
Using the Pythagorean theorem we have:
Then, the distance that he would have saved if he travels directly is:
Answer:
he would have saved:
1.8 miles
Steps to solve:
5(x + 1) = 20
~Distributive property
5x + 5 = 20
~Subtract 5 to both sides
5x + 5 - 5 = 20 - 5
~Simplify
5x = 15
~Divide 5 to both sides
5x/5 = 15/5
~Simplify
x = 3
Best of Luck!
Answer:
88
Step-by-step explanation:
The mean would be the sum of all the math quiz grades divided by the number of quizzes taken.
Solve for x:
Thus, Allen needs at least an 88 to obtain a mean of at least 90.
Answer:
30 m
Step-by-step explanation:
You simply add the lengths of all the sides. 3 m is not needed for this.
