Answer:
The product rule for exponents states that to multiply powers with the same base add their exponents. The term “powers” refers to numbers written in exponential form, such as 3^4. “Base” refers to the number that is being raised to the power, and it appears directly to the left of exponent. For instance, in 3^4, the 3 is the base, and the 4 is the exponent, or power.
Hope this helps
Step-by-step explanation:
Answer:
f(n) = 120 * (1/2)^n
Step-by-step explanation:
First the first number is 120, so we get y = 120, then 60/120 = 1/2
So we no the r, or constant rate is 1/2.
After that, we can finish our equation by doing
f(n) = 120 * (1/2)^n
or
y = 120*(1/2)^x
Answer:
- sin(X) = 6/7.5
- XY = 4.5
- cos(X) = 4.5/7.5
- tan(X) = 6/4.5
Step-by-step explanation:
It is convenient to use the Pythagorean theorem to find XY to start with. That theorem tells you ...
XZ² = YZ² + XY²
Solving for XY, you find ...
XY² = XZ² - YZ²
XY = √(XZ² - YZ²) = √(7.5² -6²) = √(56.25 -36) = √20.25
XY = 4.5
The mnemonic SOH CAH TOA is very helpful here. It reminds you that ...
Sin = Opposite/Hypotenuse
sin(X) = 6/7.5
Cos = Adjacent/Hypotenuse
cos(X) = 4.5/7.5
Tan = Opposite/Adjacent
tan(X) = 6/4.5
_____
<em>Comment on the triangle and ratios</em>
The side lengths of this triangle are in the ratios ...
XY : YZ : XZ = 3 : 4 : 5
If you recognize that the given sides are in the ratio 4 : 5, this tells you that you have a "3-4-5" right triangle with a scale factor of 1.5. At least, you can find XY = 1.5·3 = 4.5 with no further trouble.
The trig ratios could be reduced to sin(X) = 4/5; cos(X) = 3/5; tan(X) = 4/3, but the wording "don't simplify" suggests you want the numbers shown on the diagram, not their reduced ratios.
Answer:
360
Step-by-step explanation:
multiply 90 and 4
