What single decimal multiplier would you use to decrease by 3% followed by a 4% increase?

Natalija [7]

Answer:

The answer is that the measure of ∠α is ≈ 20° when rounded to the nearest °

Step-by-step explanation:

To find the measure of ∠α you need to use the reciprocal of the formula for the law of sine which says that a/Sinα = b/Sinβ = c/Sin C. The reciprocal of this gives the new equation that states Sinα/a = Sinβ/b = Sin C/c, and this will help you to find the measure of the missing angle in °'s.

In the triangle line segment BC = 5units is opposite to point A & ∠α. Line segment AC = 7units is opposite of point and ∠β which is = 28°. And finally, the hypotenuse length and the values of point C & ∠C are unknown, so they aren't important to solving the problem. Knowing all this you can plug in all the known values into the new formula, and start working on figuring things out.

To find the measure ∠α, you first write down everything, putting things into their proper places, so since you're solving for sinα you want the equation to look like this:

sinα/5 = sin28°/7

Then for the second step, you want to isolate the sinα. (To get it by itself × both left and righthand sides by 5 to begin simplifying).

This leaves you with :

sinα = sin28°÷7 · (5) [And allows you to now solve for the right side of the equation, bringing us to our third step which is to once again simplify. So what you want to do is whip out your calculator and set it to degree mode, so you can find the of sin28° which is = 0.46947156278. Then ÷ that by 7, which will get you a number = 0.06706736611. Finally, take 0.06706736611 × 5, and you will get the value = 0.33533683056, as your final answer in the third step]

Your equation should now look something like this :

sinα = 0.06706736611 × 5 or 0.33533683056

Moving onto the fourth step, you need to use the inverse of the trig function of sin to get your absolute value. (remember the inverse of sine or acrsin = sin^-1) Here you will need to multiply sin^-1 by 0.33533683056.

And also by now, you'll want to stop writing the equation as sinα = sin^-1 ×

0.33533683056, otherwise you won't get an answer, instead, you'll need to write:

α = sin^-1 × 0.33533683056

So once you do that for the fifth and final step, you'll need to simplify the equation on the righthand side one last time, and you should get the answer of α = 19.5930217327°. Which when rounded to the nearest ° is ≈ 20°.

7 0

2 years ago

PLEASE ANSWER WILL GIVE 75 POINTS!!!!!

alexdok [17]

Answer:

$\frac{4}{33}$ and $\frac{1}{27}$

Step-by-step explanation:

We require 2 equations with the repeating numbers placed after the decimal point.

let x = 0.1212...... (1) ← multiply both sides by 10

100x = 12.1212.... (2)

subtract (1) from (2) thus eliminating the repeating numbers

99x = 12 ( divide both sides by 99 )

x = $\frac{12}{99}$ = $\frac{4}{33}$ ← in simplest form

-------------------------------------------------------

let x = 0.037037....... (1) ← multiply both sides by 1000

1000x = 37.037037..... (2)

subtract (1) from (2) to eliminate the repeating numbers

999x = 37 ( divide both sides by 999 )

x = $\frac{37}{999}$ = $\frac{1}{27}$ ← in simplest form

8 0

2 years ago

Which of the following functions I which of the following functions are one to one? Select all that apply there are 3 answers

ivann1987 [24]

Answer:

The function $f(x)=\frac{x-1}{3x+3}$ is one-to-one function ⇒ 1st

The function $f(x)=\sqrt{5x+9}$ is one-to-one function ⇒ 2nd

The function $f(x)=\frac{1}{2}x^{3}$ is one-to-one function ⇒ 4th

Step-by-step explanation:

* Lets explain how to solve this problem

- One to one function is the function that has no reputation in the value

of the y-coordinates for every corresponding x-coordinates

- That means when you draw a horizontal line at any value of y, then

the horizontal line intersects the graph of the function at one point

only

- So to solve the problem look to the attached figures

# The red graph of the function $f(x)=\frac{x-1}{3x+3}$ ⇒1st graph