Hey! This is due at like 11 pm!
2 answers:
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Answer:
Step-by-step explanation:
You know how subtraction is the <em>opposite of addition </em>and division is the <em>opposite of multiplication</em>? A logarithm is the <em>opposite of an exponent</em>. You know how you can rewrite the equation 3 + 2 = 5 as 5 - 3 = 2, or the equation 3 × 2 = 6 as 6 ÷ 3 = 2? This is really useful when one of those numbers on the left is unknown. 3 + _ = 8 can be rewritten as 8 - 3 = _, 4 × _ = 12 can be rewritten as 12 ÷ 4 = _. We get all our knowns on one side and our unknown by itself on the other, and the rest is computation.
We know that ; as a logarithm, the <em>exponent</em> gets moved to its own side of the equation, and we write the equation like this:
, which you read as "the logarithm base 3 of 9 is 2." You could also read it as "the power you need to raise 3 to to get 9 is 2."
One historical quirk: because we use the decimal system, it's assumed that an expression like uses <em>base 10</em>, and you'd interpret it as "What power do I raise 10 to to get 1000?"
The expression means "the power you need to raise 10 to to get 100 is x," or, rearranging: "10 to the x is equal to 100," which in symbols is
.
(If we wanted to, we could also solve this: , so
)
The tangent ratio is an illustration of the trigonometry identity
The value of x that is not a solution of tan(x) = 1 is 3/4
The trigonometry identity is given as:
tan(x) = 1
Next, we test the x values using a calculator.
When , we have:
tan(-7/4) = 1
When x = 3/4, we have:
tan(3/4) = -1
When x = 5/4, we have:
tan(5/4) = 1
When x = /4, we have:
tan(/4) = 1
Hence, the value of x that is not a solution of tan(x) = 1 is 3/4
Read more about trigonometry identity at:
Answer:
Inequality: 22 + 5x ≥ 59
Minimum amount: 7.4
Realistic number: 8
Represented on a graph: I think it would look like a vertical line starting at the x value of 8, and continue right forever
Step-by-step explanation:
22 because that's how much she has already, 5x will represent her earnings relative to the number of driveways she pressure washes, and greater than or equal to 59 because she needs $59 or more to buy the video game.
22 + 5x ≥ 59 (subtract 22 from each side)
5x ≥ 37 (divide each side by 5)
x ≥ 7.4
