A+5=5a+5 Subtract a from each side
5=5a+5 Subtract 5 from each side
0=5a Divide each side by the number before the variable to get it alone.
--- ---
5 5
a=0
-10.3 + y = 5.2
First, regroup the terms. / Your problem should look like:
Second, add 10.3 to both sides. / Your problem should look like:
Third, add 5.2 + 10.3 to get 15.5 / Your problem should look like:
Answer:
y = 15.5 (D)
Answer:
x = 2
Step-by-step explanation:
Taking antilogs, you have ...
2³ × 8 = (4x)²
64 = 16x²
x = √(64/16) = √4
x = 2 . . . . . . . . (the negative square root is not a solution)
___
You can also work more directly with the logs, if you like.
3·ln(2) +ln(2³) = 2ln(2²x) . . . . . . . . . . . write 4 and 8 as powers of 2
3·ln(2) +3·ln(2) = 2(2·ln(2) +ln(x)) . . . . use rules of logs to move exponents
6·ln(2) = 4·ln(2) +2·ln(x) . . . . . . . . . . . . simplify
2·ln(2) = 2·ln(x) . . . . . . . . . . . subtract 4ln(2)
ln(2) = ln(x) . . . . . . . . . . . . . . divide by 2
2 = x . . . . . . . . . . . . . . . . . . . take the antilogs
Rotate one of them so the right angle is in the same orientation as the other one.
1. AB = DE
2. CB = FE
3. AC = DF
4. Compare the length of two known sides: cb and EF
CB = 3 and EF = 8
8/3 = 2 2/3 scale factor
5. Ab is side de. Multiply the length of ab by the scale factor:
4 x 2 2/3 = 10 2/3
6. FD = sqrt ( 10 2/3^2 + 8^2)
FD = 13 1/3
Answer:
C = ~50 deg
Step-by-step explanation:
Apply the cosine theorem:
cos(C) = (CA^2 + CB^2 - AB^2)/(2*CA*CB)
= (7.5^2 + 6.5^2 - 6^2)/(2*7.5*6.5)
= 0.6410
=> C = ~50 deg
Hope this helps!
