| 2x + 6| - 4 = 20 has two absolute values
solution 1
2x + 6 - 4 = 20 --> 2x + 2 = 20 --> 2x = 18 --> x = 9
2 (9) + 6 - 4 = 24- 4 = 20 ✔
solution 2
2x - 6 - 4 = 20 --> 2x - 10 = 20 --> 2x = 10 --> x = 5
2 (5) - 6 - 4 = 10- 10 = 0
m∠5 = x + 1
m∠5 = 60°
Solution:
Given data:
Line a and Line b are parallel lines.
The line that crosses both a and b is a transversal line.
m∠1 = x + 1 and m∠6 = 2x + 2.
<em>If two parallel lines cut by a transversal, then their corresponding angles on the same side are congruent.</em>
∠5 and ∠1 are corresponding angles.
⇒ m∠5 = m∠1
⇒ m∠5 = x + 1
Now, ∠5 and ∠6 forms a linear pair.
m∠5 + m∠6 = 180°
x + 1 + 2x + 2 = 180°
3x + 3 = 180°
Subtract 3 from both sides.
3x = 177°
Divide by 3 on both sides.
x = 59°
m∠5 = 59° + 1° = 60°
m∠5 = 60°
In constructing the equation, you need to know the following:
1. What don't we know? How many minutes you must talk to have the same cost for both calling plans. So, let x be the number of minutes.
2. What do we know? Plan 1 charges $17.50 per month plus $0.17 per minute used and Plan 2 charges $32 per month plus $0.07 per minute used.
So the equation must look like this: 17.50 + .17x = 32 + 0.07x
Solving the equation:
1. Multiply both sides by 100
(100) 17.5 + .17x = 32 + 0.07x (100)
1750 + 17x = 3200 + 7x
2. Subtract 1750 from both sides
1750 + 17x - 1750 = 3200 + 7x - 1750
17x = 7x +1450
3. Subtract 7x from both sudes
17x - 7x = 7x + 1450 - 7x
10x = 1450
4. Divide both sides by 100
10x / 10 = 1450/10
x= 145 minutes
145 minutes is the number of minutes you must talk to have the same cost for both calling plans.
Answer:
7
Step-by-step explanation:
The triangle inequality applies.
In order for ACD to be a triangle, AC must lie between CD-DA=0 and CD+DA=8.
In order for ABD to be a triangle, AC must lie between BC-AB=3 and BC+AB=9.
The values common to both these restrictions are numbers between 3 and 8. Assuming we don't want the diagonal to be coincident with any sides, its integer length will be one of ...
{4, 5, 6, 7}