Answer: LMNO is a rhombus
Step-by-step explanation: Since LMNO= Mo x LN, Point M=LM x ON, given these circumstances, we know that LMNO is a rhombus from the sides and angles equation.
For this, all you have to do is create equations where all you have to do is change the x value. The equation for gym A would be 35 + 42x, where x is the number of months he has the membership, and the first number is the initial fee. The equation for gym B would be 65 + 36x, following the same rules. Now all you have to do is set both of these equations equal to each other:
65+36x=35+42x
Solving this equation results in x=5, which means that he has to have the memberships for 5 months for them to be equal. Now just plug that in to one side of the equation to get the amount he has to spend:
65+36(5) = $245
For this problem, you're going to need to use trig. More specifically, you need to use the tangent function:
tan (value) = opposite/adjacent
tan 75 = opposite/8 (Here, the opposite side is the length of the ladder)
8 * tan 75 = opposite
29.8564065 = opposite
So, the ladder is 29.9 feet.
9-t=t+3
Subtract t on both sides
-2t=-6
Divide by -2 to leave the variable by itself
t=3
Answer:
see below
Step-by-step explanation:
exponent to log: 
= c ---> logₐc = b
ie. question 6
log ₁₀(3x+1) = 2 -----> 
that will get you through questions 1 to 3, 5 to 6, and 8
in question 4, all you have to do is know that 2^2 = 4 and 2^3 = 8, by setting the bases equal, you can manipulate the exponents to get 2x+8 = 3x-3
for questions 7 and 9,
remember that:
logₐc + logₐd = logₐ(cd)
logₐc - logₐd = logₐ(
)
remember change of base is 
, this will be useful if you need your calculator since calculators only have base 10 and maybe if your calculator is good enough natural base e
