Answer:
The larger acute angle is equal to 50.8 degrees.
Step-by-step explanation:
Let's solve for both of the acute angles for the purpose of checking our work at the end with angle A being the top angle and angle B being the one on the base of the triangle (that's not the 90 degrees one). Determining whether to use sin/cos/tan comes from SOH-CAH-TOA.
A = cos^-1 (2√6/2√15)
However, you need to move the radical out of the denominator by multiplying √15 to the numerator and denominator. You should come up with (2√90)/30. So,
A = cos^-1 (2√90/30) = 50.768 degrees.
B = sin^-1 (2√90/30) = 39.231 degrees.
Now, we can check the work by adding the 2 angles to 90 and, if it comes to 180, it's right.
cos^-1 (2√90/30) + sin^-1 (2√90/30) + 90 = 180.
If you have any questions on where I got a formula or any step, feel free to ask in the comments!
Answer: the answer is x=36
Step-by-step explanation:
Simplify \frac{1}{8}(x-4)
8
1
(x−4) to \frac{x-4}{8}
8
x−4
.
-\frac{x-4}{8}=-4
−
8
x−4
=−4
2 Multiply both sides by 88.
-x+4=-4\times 8
−x+4=−4×8
3 Simplify 4\times 84×8 to 3232.
-x+4=-32
−x+4=−32
4 Regroup terms.
4-x=-32
4−x=−32
5 Subtract 44 from both sides.
-x=-32-4
−x=−32−4
6 Simplify -32-4−32−4 to -36−36.
-x=-36
−x=−36
7 Multiply both sides by -1−1.
x=36
x=36
Answer: Joe has initial amount of $12 ( when he played no game).
Step-by-step explanation:
Given: Joe took $12 to the arcade. Each game cost $.50 to play.
This situation can be modeled with the equation 
Here,
Money Joe has remaining is repreesnted by 'y', and the number of games he plays is represented by 'x'.
Since y-intercept gives the initial value of the function when x=0.
To find y-intercept , we out x=0 in funtion , we get

So , y-intercept of this function is at y=12.
Meaning of the y-intercept in the terms of this problem :
Joe has initial amount of $12 ( when he played no game).
Answer:

Step-by-step explanation:
We are asked to find x, a missing side in a triangle.
This is a right triangle because there is a small square in the corner representing a 90 degree or right angle. Therefore, we can use right triangle trigonometry. The three main functions are:
- sinθ= opposite/hypotenuse
- cosθ= adjacent/hypotenuse
- tanθ= opposite/adjacent
Examine the triangle. We will use angle S, measuring 54 degrees, for theta. Side QR, measuring x, is <u>opposite</u> angle S. Side QS, measuring 2.3, is the <u>hypotenuse</u> because it is opposite the right angle. Since we have the opposite and hypotenuse, we will use sine.

- θ= 54
- opposite= x
- hypotenuse = 2.3

We are solving for x, so we must isolate the variable. It is being divided by 2.3 The inverse operation of division is multiplication, so we multiply both sides by 2.3




Round to the nearest tenth. The 6 in the hundredth place to the right tells us to round the 8 up to a 9.

x is approximately <u>1.9</u>