Question 10 please :(

To do inverse trig functions on a calculator, enter the value and press either the arcsin, arccos and arctan buttons OR [tex]sin^{-1}, cos^{-1}, tan^{-1}[/tex] buttons.  The functions arcsin(x), arccos(x) and arctan(x) are the inverse functions of the 3 main trigonometric functions sin(x), cos(x), and tan(x) formed by a reflection across the line y=x. This results in the (x,y) points of sin(x), cos(x) and tan(x) switching their order (y,x) in each inverse. Form a ratio of the side lengths, press the corresponding inverse function and you will find x = 35.6 degrees and y = 54.4 degrees.

Sine/ Cosine/Tangent

In trigonometry, there are three main functions sine, cosine, and tangent based on the ratios of sides corresponding to angles within a right triangle. The ratio for sine is opposite / hypotenuse. The ratio for cosine is adjacent / hypotenuse. The ratio for tangent is opposite / adjacent.

Notice in this triangle, 109 and 134 are the adjacent and hypotenuse to the angle x. This is the cosine function and thus Cos(x) = 109 / 134. 109 and 134 are also the opposite and hypotenuse to the angle y. This is the sine function and thus sin y = 109 / 134. To solve for x and y, use the inverse function arcsin and arccos.

Arcsin

As the arcsin(x) is the inverse of the sin(x) function, its function is defined as having inputs and outputs which have been reversed. The input of arcsin is the triangle side ratios (opposite / hypotenuse) and they align to the angle outputs of this function. For example, if sin (30) = 1/2 then arcsin(1/2) = 30. By pressing the arcsin button on your calculator it reverses the inputs and outputs. The expression sin y = 109/ 134 becomes arcsin (109/134) = y and y = 54.4 degrees.

Arccos

As the arccos(x) is the inverse of the cos(x) function, its function is defined as having inputs and outputs which have been reversed. The input of arccos is the triangle side ratios (adjacent / hypotenuse) and they align to the angle outputs of this function. For example, if cos (60) = 1/2 then arccos(1/2) = 60. By pressing the arccos button on your calculator it reverses the inputs and outputs. The expression cox x = 109/ 134 becomes arccos (109/134) = x and x = 35.6 degrees.

Category

Grade: High School - 10/11

Subject: Algebra 2

Chapter: Inverse Trig Functions

Answer: y= -1/2 + 1

Step-by-step explanation: To solve this problem, first determine the slope of your line. Since perpendicular lines have slopes that are opposite reciprocals of each other,we know that the slope is -1/2. Then plug your slip (-1/2) and point (6,-2) into the equation y=mx+b to solve for b. The resulting value for b is 1.

Answer:

Option C,D and E are correct.

Step-by-step explanation:

Clearly from the graph we could say that it is a graph of a quadratic function.so we will work on each of the following options:

A)

Clearly from the graph we could see that the graph is increasing on both the sides of -1.

Hence, option A is wrong. ( The function is decreasing over the interval x<-1).

B)

As the function is a quadratic function hence the range contains all the real numbers greater than or equal to 5 below 5 it won't take any value.

Hence option B is wrong.(The range of the function is all real numbers).

C)

clearly we could see that the function is increasing in the interval x<-1.

Hence, option C is correct.

D)

The function is defined for all of the real numbers.

Hence option D is correct. (The domain of the function is all real numbers).

E)

Clearly from the graph we could see that the function has minimum value at -1 and the graph is increasing before and after that.

Hence, option E is correct.( The function has a relative minimum at (-1,5) ).

Answer:

C,D,E

Step-by-step explanation:

The radius of a pizza that is 35 inches in diameter is 17.5 inches, which is found by dividing the diameter by two.

The question about Mrs. Hilt's pizza with a diameter of 35 inches is asking for the radius of the pizza. To find the radius of a circle when given the diameter, you simply divide the diameter by two. Therefore, the radius of the pizza is 17.5 inches, since 35 inches divided by 2 equals 17.5 inches. This is a basic geometry concept often covered in middle and high school math classes.

Answer: It is non-linear

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

Allow me to revise your question for a better understanding

y = 2x

y = [tex]x^{10}[/tex]

Any exponential function with a base bigger than 0 smaller than 1 will eventually be exceeded by any polynomial function. Let me give one example for this situation.

Let x = [tex]\frac{1}{2}[/tex], we have:

Obviously, y = [tex]x^{10}[/tex] <y = 2x  

Hope it will find you well.

The answer to this equation would be option C.47.25

hope this helps

:D :)

The percent of increase is 200%

Answer and the work are provided in the image attached.

The solution pairs are (8, 1), (-2, -6), and (-3, 1), as they satisfy the inequality 2x - 3y ≥ 12.

To determine which ordered pairs satisfy the inequality 2x - 3y ≥ 12, we can substitute each pair's coordinates into the inequality and check for validity.

For the first pair (1, -3):

2(1) - 3(-3) = 2 + 9 = 11 < 12 (Not valid)

For the second pair (8, 1):

2(8) - 3(1) = 16 - 3 = 13 ≥ 12 (Valid)

For the third pair (3, 2):

2(3) - 3(2) = 6 - 6 = 0 < 12 (Not valid)

For the fourth pair (-2, -6):

2(-2) - 3(-6) = -4 + 18 = 14 ≥ 12 (Valid)

For the fifth pair (2, 3):

2(2) - 3(3) = 4 - 9 = -5 < 12 (Valid)

For the sixth pair (1, 8):

2(1) - 3(8) = 2 - 24 = -22 < 12 (Not valid)

For the seventh pair (-3, 1):

2(-3) - 3(1) = -6 - 3 = -9 < 12 (Valid)

So, the ordered pairs that satisfy the inequality are (8, 1), (-2, -6), and (-3, 1).

To find which ordered pairs are solutions to the inequality 2x-3y ≥ 12, test each pair by plugging the values into the inequality and seeing if the result is greater than or equal to 12.

To select the ordered pairs that are solutions to the inequality 2x-3y ≥ 12, we can test each ordered pair to see if it satisfies the inequality. For an ordered pair (x, y) to be a solution, the expression 2x - 3y when calculated must be greater than or equal to 12.

An example of how to test an ordered pair is as follows:

Let's take the ordered pair (6, 0). Plugging these values into the inequality gives us 2(6) - 3(0) which simplifies to 12. Since 12 is equal to 12, the ordered pair (6, 0) is a solution to the inequality.

To methodically find all solutions, one would typically graph the line 2x - 3y = 12 and then shade the region above it for 2x - 3y > 12, since all the points in that region would satisfy the inequality. However, without graphing, we can still test individual pairs to check if they satisfy the inequality condition.

Answer: C is the correct answer.

Step-by-step explanation:

Answer:

C. Yes, the similarity ratio is 1:3

Step-by-step explanation:

The two triangles are similar because the corresponding sides are proportional.

The length of the side of the smaller triangle that is 3 units corresponds to the length of the side of the bigger triangle that is 9 units.

These two sides are in the ratio [tex]3:9[/tex].

When we simplify this ratio, we get [tex]1:3[/tex].

The length of the side of the smaller triangle that is 6 units corresponds to the length of the side of the bigger triangle that is 18 units.

These two sides are in the ratio [tex]6:18[/tex].

When we simplify this ratio, we get [tex]1:3[/tex].

The length of the side of the smaller triangle that is 5 units corresponds to the length of the side of the bigger triangle that is 15 units.

These two sides are in the ratio [tex]5:15[/tex].

When we simplify this ratio, we get [tex]1:3[/tex].

Therefore the similarity ratio is  [tex]1:3[/tex].