There are two ways to find or determine for the value of
c. In the first method, we can use addition and subtraction to isolate the
variable c from the other variables. In the second method, we can use the
transposition of variables to isolate the variable c from the other variables.
So solving for the value of c:
<span>Using 1st method: Addition and Subtraction</span>
We are given:
240 = 6 z + c
Simply subtract 6 z on both sides:
240 – 6 z = 6 z + c – 6 z
Cancelling 6 z – 6 z on the right side:
240 – 6 z = c
or
c = 240 – 6 z
<span>Using the 2nd method: Transposition</span>
240 = 6 z + c
What we are going to do here is to simply transpose the
variable 6 z from the right side to the left side of the equation so that we
are left with c alone on the right side. Always remember that when we
transpose, the symbol becomes opposite. That is:
240 + (- 6 z) = c
240 – 6 z = c
or
<span>c = 240 – 6 z</span>
Problem 15
The general format for these types of problems is
A/B = C/D
One way to set things up is to notice how the horizontal sides are 15 and 6 for the large and small triangles respectively. So A/B = 15/6
At the same time, we can say C/D = 20/x since the longer diagonal is 20 and the shorter diagonal is x (notice how we divide in the same order of long over short)
A/B = C/D updates to 15/6 = 20/x
Cross multiply to solve for x
15/6 = 20/x
15*x = 6*20
15x = 120
x = 120/15
x = 8
<h3>Answer: x = 8</h3>
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Problem 16
A = Long horizontal side = x
B = Short horizontal side = 24
A/B = x/24
C = long diagonal side of larger triangle = 20+12 = 32
D = short diagonal side of smaller triangle = 20
C/D = 32/20
-------
A/B = C/D
x/24 = 32/20
20x = 24*32
20x = 768
x = 768/20
x = 38.4
<h3>Answer: x = 38.4</h3>
side notes:
- 38.4 = 38 & 2/5 as a mixed number
- 38.4 = 192/5 as an improper fraction
Answer:
It depends on the equation.
If the bases are equal and the variables are only in the exponents, set the exponents equal.
If there are variables in the exponents, but you cannot set the bases equal, then use logarithms.
Example 1:
Here you have the same base on both sides. The variables are in the exponents. Set the exponents equal and solve for x.
2x + 5 = 9
2x = 4
x = 2
Example 2:
The bases are different, but you can make the bases equal using laws of exponents. Remember that 9 = 3^2.
Now you have equal bases, so the exponents must be equal.
2x = 12
x = 6
Example 3:
Here you can't make the bases equal, so you take the log of both sides and use laws of logs.
Recall that:
1.) a>10
2.) a<3.5
How I got it: 1.) Subtract 3 from both sides, leaving -2a<10.
2.) Divide by -2 from both sides, remember to flip the inequality sign when dealing with negatives. This leaves you with a>10.
For number 2.) I divided both sides by 5, leaving a<3.5, though this answer may be wrong.