Answer:
- -1/3 < x < 3 or x = (-1/3, 3)
Step-by-step explanation:
<u>Given sides of a triangle:</u>
<u>Triangle inequality theorem:</u>
- Any side is smaller than the some of the other two.
<u>Apply to the given triangle:</u>
- 2x + 5 - x > 4 ⇒ x > -1
- 2x + 4 > 5 - x ⇒ 3x > -1 ⇒ x > -1/3
- 5 - x + 4 > 2x ⇒ 3x < 9 ⇒ x < 3
<u>Combine all the inequalities:</u>
- -1/3 < x < 3
- x = (-1/3, 3)
Answer:
The length of the shorter piece is
.
The length of the longer piece is
.
Step-by-step explanation:
The five-step method is GUESS method.
Given:
Length of steel beam, 
Length of longer piece is 1 foot longer than twice the shorter one.
Unknown:
Length of longer and shorter pieces of beam.
Let the length of shorter piece be
feet.
Therefore, the length of longer beam is equal to 
Evaluate:
Sum of lengths of longer and shorter pieces of beam is equal to the total length of beam. So,

Substitute and Solve:
Now, we have,
.
Substitute 5 for
for the lengths of shorter and longer pieces and solve for each. This gives,
Length of shorter piece = 
Length of longer piece = 
Therefore, the lengths of shorter and longer pieces are
and
respectively.
Answer:
b = 4
Step-by-step explanation:
y = mx + b represents the equation of a line
m represents the slope
b represents the y-intercept
Based on what we're given, we could determine that 4 is our y-intercept or b.
Slope=-9/12 = -3/4
y=mx+b y=-3/4x+b
3=-3/4(-6)+b
b=3+9/2=7.5
Equation is y=-0.75x+7.5