I need help on this question
"Find the value of the variable and GH if H is between G and I".
GI=8b+2,HI=3b-2,HI=16
Please helo me....
well, you know that GH+HI=GI
3b-2=16
b=6
GI=8*6+2=50
GH+16=50
GH=34
To find the value of the variable 'b' and the length of GH, we need to use the given information.
Given: GI = 8b + 2, HI = 3b - 2, HI = 16
Since H is between G and I, that means GH is the difference between GI and HI. So,
GH = GI - HI
Substituting the given values:
GH = (8b + 2) - (3b - 2)
GH = 8b + 2 - 3b +2
GH = 8b - 3b + 2 + 2
GH = 5b + 4
But we also know that HI = 16, so we can substitute this value:
3b - 2 = 16
Add 2 to both sides:
3b = 18
Divide both sides by 3:
b = 6
Therefore, the value of the variable b is 6.
Now we can find the length of GH using the value of b:
GH = 5b + 4
Substituting b=6:
GH = 5(6) + 4
GH = 30 + 4
GH = 34
Therefore, the value of b is 6, and the length of GH is 34.
To find the value of the variable b and the length GH, we can use the information given in the problem. Let's break down the problem step by step.
Step 1: Understand the problem
We are given that H is between G and I, and the lengths of GI and HI.
Step 2: Find the length of HI
The problem states that HI is equal to 16.
HI = 16
Step 3: Write the equation for HI in terms of b
We are given that HI is equal to 3b - 2. Substituting this value into the equation, we have:
3b - 2 = 16
Step 4: Solve the equation
To solve this equation for b, we will isolate the variable term.
Add 2 to both sides of the equation:
3b - 2 + 2 = 16 + 2
3b = 18
Divide both sides of the equation by 3:
3b/3 = 18/3
b = 6
The value of b is 6.
Step 5: Find the length of GH
To find the length of GH, we need to substitute the value of b into the equation for GI.
GI = 8b + 2
GI = 8(6) + 2
GI = 48 + 2
GI = 50
The length of GH is 50 units.
So, the value of the variable b is 6 and the length of GH is 50.