Complete the general solution to [tex]y = arcsin - \frac{ \sqrt{3} }{2} [/tex]y=___+-2πkSelect all that apply.π/3(2π)/3(4π)/3(5π)/3

SOLUTION:

Step 1:

In this question, we are given the following:

Step 2:

The details of the proof are as follows:

Since

and

Then,

CPCTC means corresponding parts of congruent triangles are congruent

and

Thus,

VUTS is a parallelogram since diagonals of a parallelogram bisect each other

Solution:

(a) Given the functions:

Then:

Similarly,

Two functions f and g are inverses of each other if and only if f(g(x))=x for every value of x in the domain of g and g(f(x))=x for every value of x in the domain of f.

ANSWER: f and g are inverse of each other.

(b) Given:

Then:

Also,

ANSWER: f and g are not inverses of each other.

Given function is:

Now put f(x)=0

so the first point is (6,0) now for another points:

So the points are (-4,0) and (2,0) and(6,0)

Hence the correct options are 1,2 and 4.

EXPLANATION:

We are given the following coordinates for a figure on the coordinate plane;

To reflect any figure or any set of coordinates across the x-axis, we shall apply the rule;

Note that the x-coordinate remains the same whereas, the y-coordinate changes its sign.

Imagine folding a graph page in two equal halves along the horizontal axis. You'll observe the y-coordinates will switch sides from top to bottom (positive to negative) or bottom to top (negative to positive). The x-coordinate remains the same since moving the folded page does not affect values along the horizontal line.

Therefore, for the vertices given, the reflection across the x-axis would be;

ANSWER:

The coordinates of the reflection across the x-axis therefore will be;

(Question 3)

Because of the definition of a perpendicular bisector, we know that angle B is a right angle (90°) an that

Note that AB is a segment that is shared by both triangles in the image. By using SAS (Side-Angle-Side), we can find that both the triangles are congruent (they are equal). Therefore,

We know that

We'll just have to plug in the value of x we calculated to find the lenght of AE

Therefore, AE = 36

(Question 4)

Because of the definition of a perpendicular bisector, we know that XY splits TS right by the middle. So if TS = 10, RS would be worth half of that

Therefore, RS = 5

Answer: -32 is less than 15.

Step-by-step explanation: 15 is greater than zero therefore it is not a negative number. -32 is less than 0 therefore it is a negative number. Negatives will always be less than positives.

Answer:

The length EI is;

The measure of angle IFE is;

Explanation:

Given the rectangle in the attached image.

Given;

Recall that the length of the diagonals of a rectangle are equal so;

solving for x, we have;

Since we have the value of x, let us substitute to get the length of diagonal EG;

Also, note that the diagonals of a rectangle bisect each other, so the length of EI would be;

Therefore, the length EI is;

To get the measure of angle IFE;

Reason: base angles of an isosceles triangle are equal.

So;

Reason: Complementary angles.

Substituting the value of angle IFG;

Therefore, the measure of angle IFE is;

Answer:

its B

Step-by-step explanation: just took the test

EXPLANATION

Let's see the facts:

Bike Price: $99

Sold Price: $117

The percentage is given by the following relationship:

Replacing terms:

Answer: The markup was 18.18%

We will have the following:

The expression that best describes the information is:

*When viewing the data for tolling a one, as the number of rolls increases, the experimental probability becomes closer to equal to the theoretical probability.

Okay, here we have this:

Let's take the packages as (x), so we obtain:

Melissa Starts with: 4x+8 ballons (1)

Her brother gave her: 3x+20 ballons (2)

And as she now has twice the number of balloons she started with. This mean that:

2(4x+8)=(3x+20)+(4x+8)

Let's clear x in this equation:

8x+16=3x+20+4x+8

8x+16=7x+28

8x-7x=28-16

x=12

Finally we obtain that in a package are 12 ballons, now let's calculate How many balloons did Melisa start with?:

Remember that Melissa Starts with: 4x+8 ballons, so replacing x with 12, we obtain that Melissa Starts with: 4(12)+8=48+8=56.

Finally we obtain that Melissa Starts with 56 ballons.

The triangles that are similar is A and B

A. ∠4 is congruent to ∠5; True.

B. Two lines are parallel; True.

C. The measure of ∠6 = 90.5°; False.

D. ∠2 and ∠3; True.

For the give question;

Two line are cut by the transversal.

∠1 =  90.5° and ∠7  =  89.5°

Thus the result for the given statement are-

A. ∠4 is congruent to ∠5 because they are alternate interior angles; True.

B. Two lines are parallel; True.

C. The measure of ∠6 = 90.5°; False.

∠6 = ∠7 =  89.5°.(correct)

D. ∠2 and ∠3 are supplementary because they are same-side exterior Angeles; True.

Thus, the result for the given statement are found.

To know more about the parallel lines, here

https://brainly.com/question/4954460

#SPJ1

Given the expression:

8(x + 4)

Let's simplify using distributive property.

Use distributive property to distribute 8 into x + 4:

8(x) + 8(4)

Evaluate:

8x + 32

ANSWER:

8x + 32

Answer

Explanation

The total charge on the car = (Charge based on number of days) + (Charge based on the number of miles)

Charge based on number of days = (23.95) (x) = (23.95x) dollars

Charge based on the number of miles = (0.08) (400) = 32 dollars

(The total charge on the car) ≤ 440

23.95x + 32 ≤ 440

23.95x + 32 - 32 ≤ 440 - 32

23.95x ≤ 408

Divide both sides by 23.95

(23.95x/23.95) ≤ (408/23.95)

x ≤ 17.04

Hope this Helps!!!

A account 8% B account 12%

A+$450 = B (1)

Ax8% +Bx12%= $220

Ax0.08 + Bx0.12 = 220

Now we replace (1) on B:

Ax0.08 + (A+450)x0.12 = 220

Ax0.08 + Ax0.12 + 54 = 220

Ax0.2 = 166

A= 830.

Now we replace the value of A on equation (1):

830 + 450 = B

B = 1280

The given situation is about the value of quarters and the number of quarters. If we think this through, we would deduct that the value of quarters depends on the number of quarters there are, for example, if there are 4 quarters, then the value is 1 dollar, and so on.

Hence,

The independent variable is the number of quarters.

The dependent variable is the value of the quarters.

The equation would be v = 0.25n.

If the input is 10, it means n = 10.

The output would be 2.5.

Answer:

Frankie is incorrect.

Step-by-step explanation:

Change 4/5 to 8/10.

You are comparing 10 7/10 to 10 8/10.

10 4/5 (which is also 10 8/10) can be written as 10.8

10 7/10 can be written as 10.7

10.8 > 10.7, so 10 4/5 > 10 7/10 is correct,

and 10 7/10 > 10 4/5 is incorrect.

Frankie is incorrect.

On a number line, show 10 and 11.

Make 10 equal spaces between 10 and 11. Each space is 1/10.

10 7/10 is one space to the left of 10 4/5, so 10 7/10 is less than 10 4/5.

The given situation can be illustrated as follow:

In order to determine the distance x between the roller coaster and the tower. Use the law of cosines, as follow:

By simplifying the previous expression, you obtain:

Hence, the distance between the tower and the roller coaester is approximately 469.5m

Step 1

Given; The area of a rectangle is given by a=6x^2y+4y^2x and the width of the rectangle is w=2xy. what is the length, l, of the rectangle if l=a/w?

Step 2

Thus;

Answer;

Given the inequality:

• You can solve it as follows:

1. Apply the Addition Property of Inequality by adding 7 to both sides of the inequality:

2. Apply the Division Property of Inequality by dividing both sides of the inequality by -4 (since you are dividing both sides by a negative number, the direction of the inequality symbol changes):

• In order to graph the solution on the Number Line, you can follow these steps:

1. Since the symbol is:

You need to draw an open circle over the number -5.

2. Draw a line from the circle to the right.

Then, you get:

Hence, the answer is:

• Solution:

• Number Line:

We're told from the question that Sarah needs atleast $1975, that means that she can either have exactly $1975 or more but not less;

Let x represent the number times she mows a lawn;

Let y represent the number of times she walks a dog;

The inequality can be modelled thus;

The Perimeter of a Rectangle

Given a rectangle of width w and length l, the perimeter is calculated as the sum of the side lengths, that is:

P = w + w + l + l

Or, equivalently

P = 2w + 2l

Hermann was calculating the perimeter of a rectangle and built the expression:

P = x + x + 4x + 4x feet

Note this expression is similar to the first one. This means that the width of the rectangle is x and the length is 4x.

a) We'll draw a rectangle with such dimensions:

b) Assuming the base is the length and the height is the width, the relationship between the base and the height is

4x / x = 4

This means the base is four times the height

c) We are given the perimeter as P = 60 feet.

We need to solve the equation

x + x + 4x + 4x = 60

Simplifying:

10x = 60

Dividing by 10:

x = 60/10

x = 6 feet

The base is 4x = 24 feet.

The base of Herman's rectangle is 24 feet

The height of Herman's rectangle is 6 feet

The prime factorization of 54 is

54 = 2 × 3 × 3 ×3

Using the exponential form of the prime factorization that is

54 = 2 × 3³

Answer:

B. (19/24)

Step-by-step explanation:

 1          1          5

------ + ------ + -------

 4         8         12

 1(6)     1(3)     5(2)

------ + ------ + -------

 4(6)   8(3)     12(2)

 6         3        10         19

------ + ------ + ------- = -------

 24      24       24        24

I hope this helps!

We are given the expression:

To get the answer, we will have to apply exponents rules

The rule is:

Thus

we will have

Therefore,

The answer is 4

a)

In order to find the list of all potential rational roots, let's find the factors of the division between the constant term and the leading term.

Since the constant term is zero, so the only potential rational root in the list is 0.

b)

Since the constant term is zero, so 0 is a root of the polynomial. Then, let's factor it to find the remaining roots:

Solving this quadratic equation using the quadratic formula, we have:

Therefore the actual roots of P(x) are:

0 (multiplicity 1) and -5 (multiplicity 2).

Explanation:

The graph shows a ine crossing the parabola. The solution of the systems is the point where both system of equations intersect.

The line crosses the parabola at two point:

At x = 2, y = 2

This point is applicable to both. Since both have same values at this point, (2, 2) is one of the solution

At x = -2, y = -6

Both graphs have this point . This shows point (-2, -6) is also a solution

Hence, the solutions of the systems are (2, 2) and (-2, -6)

Answer

Dealer's cost = $499

Explanation

The markup percent is given as

Markup percent = 10%

Selling Price = 548.90 dollars

Cost = ?

0.1 (Cost) + Cost = 548.90

1.1 (Cost) = 548.90

Divide both sides by 1.1

Cost = (548.90/1.1)

Cost = 499 dollars

Hope this Helps!!!

Step-by-step explanation:

Given that f(x) is reflected across the y-axis to create the graph of function g.

i.e. f is reflected on the line x=0

Hence x will become -x in g.

When domain of f is x>=0 the domain of g can only be x less than or equal to 0.

Hence answer is option 3,The domain of f is x ≥ 0, while the domain of g is x ≤ 0

Answer:

The third one

Step-by-step explanation: