make r the subject of the formula:
s(t-r)=2(r-3)
explain your workings
To make r the subject of the formula, we need to isolate r on one side of the equation.
First, we can distribute the s on the left side of the equation:
st - sr = 2r - 6
Next, we can move all the terms with r to one side and all the other terms to the other side:
st - 2r = -6 + sr
Then, we can isolate r by dividing both sides by -2:
r = (-6 + sr) / (-2)
Therefore, the formula for r is:
r = (-6 + st) / (-2)
My workings involve manipulating the equation algebraically to isolate r on one side.
Use the Triangle Inequality Theorem to name a segment for the third side of a triangle if no segments are congruent and the first two sides are AB
and BD
. Use this key to enter the response: AB=1
, AC=2
, AD=3
, BC=5
, BD=6
, CD=7
. List them in ascending order.
According to the Triangle Inequality Theorem, in any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
In this case, we have sides AB and BD, so we can use the lengths given in the key to determine the possible lengths for the third side.
AB + BD = 1 + 6 = 7
BD - AB = 6 - 1 = 5
Therefore, the possible length for the third side is either 5 or 7.
In ascending order, the segments for the third side are AB=1, BC=5, CD=7.
this is incorrect
the correct answers are 2 and 5
re write it
I apologize for the error in my previous response.
According to the Triangle Inequality Theorem, in any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
In this case, we have sides AB and BD, so we can use the lengths given in the key to determine the possible lengths for the third side.
AB + BD = 1 + 6 = 7
BD - AB = 6 - 1 = 5
Therefore, the possible length for the third side is either 5 or 7.
In ascending order, the segments for the third side are AB=1, AC=2, BC=5, CD=7, and AD=3. Therefore, the possible segments for the third side of the triangle are AC=2 and BC=5.
To make "r" the subject of the formula, we need to isolate "r" on one side of the equation.
Step 1: Distribute s to both terms within the parentheses:
st - sr = 2r - 6
Step 2: Move the term containing "r" to the left side of the equation by adding sr to both sides:
st = sr + 2r - 6
Step 3: Group the terms containing "r" together:
st = r(s + 2) - 6
Step 4: Move the constant term (-6) to the right side of the equation by adding 6 to both sides:
st + 6 = r(s + 2)
Step 5: Divide both sides of the equation by (s + 2) to isolate "r":
r = (st + 6)/(s + 2)
So, "r" is the subject of the formula, and it can be represented as (st + 6)/(s + 2).
To make r the subject of the formula, we need to rearrange the equation so that r is isolated on one side.
Given equation: s(t - r) = 2(r - 3)
Step 1: Distribute the s to the terms inside the parentheses.
st - sr = 2r - 6
Step 2: Move all terms containing r to the left side and all other terms to the right side.
st - 2r = sr - 6
Step 3: Group the terms involving r.
st - 2r - sr = -6
Step 4: Factor out r on the left side.
r(s - 2) = st - 6
Step 5: Divide both sides by (s - 2) to isolate r.
r = (st - 6)/(s - 2)
Therefore, the subject r can be expressed as r = (st - 6)/(s - 2).