Which of the numbers below are exactly divisible by 9?
2 answers:
You might be interested in
Answer:
1. 13 or -13
2. -5 < y < -3
3. 6 or -6
4. 1/8 or -1/8
Step-by-step explanation:
Clear the absolute-value bars by splitting the equation into its two cases, one for the Positive case and the other for the Negative case.
The Absolute Value term is |x|
For the Negative case we'll use -(x)
For the Positive case we'll use (x)
Step 3 :
Solve the Negative Case
-(x) = 13
Multiply
-x = 13
Multiply both sides by (-1)
x = -13
Which is the solution for the Negative Case
Step 4 :
Solve the Positive Case
(x) = 13
Which is the solution for the Positive Case
Step 5 :
Wrap up the solution
x=-13
x=13
But for the case of question (2) its a different pattern..
Since this is a "less than" absolute-value inequality, my first step is to clear the absolute value according to the "less than" pattern. Then I'll solve the linear inequality.
| y + 4 | < 1
–1 < y + 4 < 1
This is the pattern for "less than". Continuing, I'll subtract 3 from all three "sides" of the inequality:
–1 – 4 < y + 4 - 4 < 1 – 4
–5 < y < -3
The solution to the original absolute-value inequality, | y + 4 | < 1 , is the interval:
Distance between the top and bottom of the bridge is 76 feet
Solution:
The image of the question is attached below.
Ratio of the triangles is 1 : 1.
AC = 2x + 10 and EC = 4x − 18.
Since the two triangles ACB and DCE are in the ratio 1 : 1, so their corresponding sides are also in the ratio 1 : 1.
Therefore sides AC and EC are corresponding to each other.
AC : EC = 1 : 1
Subtract 10 from both sides of the equation.
Subtract 4x from both sides of the equation.
Divide by -2 on both sides, we get
⇒ x = 14
Distance between the top and bottom of the bridge is EA.
EA = AC + EC
= 2x + 10 + 4x - 18
= 6x - 8
= 6(14) - 8
= 84 - 8
EA = 76 feet
Distance between the top and bottom of the bridge is 76 feet.
