each exterior angle of a regular polygon measures 45 degrees. how many sides does the polygon have

Answer:

B

Step-by-step explanation:

We can use the law of sines to form a proportion.

The law of sines state that any side length divided by the sin of the opposite angle measure will be equal.

Let's form a proportion.

[tex]\frac{25}{sin(90)}=\frac{b}{sin(35)}[/tex]

Simplify.

b ≈ 14.34

The value of b from the diagram is 14

From the given diagram we have the following

hypotenuse = 25

using the SOH CAH TOA identity, hence;

sin 35 = b/25

b = 25sin35

b = 14.34

The value of b from the diagram is 14.34

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Answer:

Step-by-step explanation:

get rid of the denominator by multiplying by x

ANSWER

Option D.

EXPLANATION

The given function is

[tex]f(x) = {x}^{2} [/tex]

The new function is

[tex]g(x) = f(5x)[/tex]

This implies that,

[tex]g(x) = {(5x)}^{2} [/tex]

This gives us:

[tex]g(x) = {25x}^{2} [/tex]

We can that the graph of g(x) will shrink by a factor of 25 compared to f(x).

The graph will open upwards and shrink towards the y-axis.

Answer:

The answer is D

Step-by-step explanation:

* Lets revise some transformations

- A horizontal compression is the squeezing of the graph toward

 the y-axis.

- If the graph is y = f(x) and its image is y = f(k•x)

∴ The graph is horizontally compressed if k > 1 that means divide

   each of its x-coordinates by k.

∴ The graph is horizontally stretched if 0 < k < 1, that means divide

   each of its x-coordinates by k.

* Now lets solve the problem

∵ f(x) = x²

∵ g(x) = f(5x)

- Substitute the value of x in f(x) by 5x

∴ f(5x) = (5x)²

∴ g(x) = (5x)²

∵ The image of f(x) = x² is g(x) = (5x)²

∴ k = 5

∵ 5 > 1

∴ The graph of f(x) is compressed horizontally

- divide each x-coordinates of the points on the graph by 5

∴ The graph becomes narrow to the y-axis

- Look to the attached graph for more understanding

# The red graph is f(x) = x²

# The blue graph is g(x) = (5x)²

* The answer is the last graph D

Answer:

Third week, 15 words per minute

Step-by-step explanation:

First week: 10 words per minute

Second week

10 * 20% = 10*.2 = 2

It is an increase, so we add the 2 to the original amount

10+2 = 12 word per minute

Third week

12 * 25% = 12 *.25 = 3

It was an increase, so we add the 3 to the amount in week 2

12+3 = 15 words per minute

For this case we have that from 2:16 am until 2:16 pm exactly 12 hours have passed. On the other hand, from 2:16 p.m. until 8:16 p.m., exactly 6 hours have elapsed.

If we add, we have that from 2:16 am to 8:16 pm have elapsed: 12 + 6 = 18 hours.

As we ask for the time elapsed between 2:16 am until 8:10 pm we must subtract 6 minutes. So, we have:

18 hours with 54 minutes

Answer:

18 hours with 54 minutes

Answer:

156 sq in

Step-by-step explanation:

If you have a rectangle measuring 13 inches by 12 inches, you will consider the side with 13 inches as the length of the rectangle and the one with 12 inches as the width of the rectangle.

The area of a rectangle is obtained by multiplying the length by the width... so, you'll get:

A = 13 in x 12 in = 156 square inches

Answer:

(y + 14)(y - 14)

Step-by-step explanation:

A difference of squares has the general form

a³ - b² and factors as

(a + b)(a - b)

Given

y² - 196

y² = (y)² ⇒ a = y and 196 = 14² ⇒ b = 14

y² - 196

= y² - 14² = (y + 14)(y - 14) ← difference of squares

Answer:

3x + 7y = 31

-3x - 2y = -1

____________________

5y = 30

y = 6

____________________

3x + 42 = 31

3x = -11

x = - 11/3

____________________

x = -11/3; y = 6

Answer:

∠2 = 52°

Step-by-step explanation:

Since 1 angle = 90° then the sum of the other 2 angles = 90°, that is

∠2 + ∠3 = 90 ← substitute values

3x + 1 + 2x + 4 = 90

5x + 5 = 90 ( subtract 5 from both sides )

5x = 85 ( divide both sides by 5 )

x = 17

Hence

∠2 = 3x + 1 = (3 × 17) + 1 = 51 + 1 = 52°

Answer:

40 students play all three games .

Step-by-step explanation:

You have universal and it says everyone likes all three games so your union is same as universal and there is no complement or any one who didn't like any games so use formule of universal = n A + n B + n C - n only interaction or who likes any two .Solve it and you will get your answer

Answer:

Step-by-step explanation:

The slope-intercept form of an equation of a line:

y = mx + b

m - slope

b - y-intercept → (0, b)

We have the equation y = 6x + 8. Therefore

m = 6

b = 8

Answer: A: (0,8)

Step-by-step explanation:

Answer: x = 6, x = -4

Step-by-step explanation:

Find two numbers whose product is the c-value (-24) and sum is the b-value (-2):

0 = x² - 2x - 24

                    ∧

                   1 -24

                   2 -12

                   3  -8

                   4  -6 = -2    This works!

0 = (x + 4)(x - 6)

Apply the Zero-Product Property (set each factor equal to zero and solve)

0 = x + 4      0 = x - 6

-4 = x            6 = x

The solutions are x = 6 and x = -4. Therefore, the zeros of the function are 6 and -4.

Finding the Zeros of the Function p(x) = x^2 – 2x – 24

To find the zeros of the function p(x) = x^2 – 2x – 24, we need to determine the values of x that make the function equal to zero. This means we solve the equation:

x^2 – 2x – 24 = 0

This is a quadratic equation and can be solved using factoring. We look for two numbers that multiply to -24 and add to -2. These numbers are 4 and -6:

(x - 6)(x + 4) = 0

Setting each factor equal to zero gives us the solutions:

So, the zeros of the function p(x) = x^2 – 2x – 24 are 6 and -4.

For this case we have that if and it varies directly with x, we can write the equation as:

[tex]y = kx[/tex]

Where:

k: It is the constant of proportionality.

According to the table:

[tex]-3 = k (1)[/tex]

Clearing k:

[tex]k = -3[/tex]

Then,[tex]y = -3x[/tex]

Answer:

Option C

Answer:

y varies directly with x

[tex]k = -3[/tex]

The equation is:

[tex]y = -3x[/tex]

Step-by-step explanation:

We can say that and it varies directly with x if it is fulfilled that

[tex]y = kx[/tex]

Where k is a constant known as the constant of variation.

So

[tex]\frac{y}{x} = k[/tex]

This means that if y varies with x then the division of y between x should always be equal to a constant value k.

We must test this for the values shown in the table

[tex]\frac{-3}{1} = -3[/tex]

[tex]\frac{-9}{3} = -3[/tex]

[tex]\frac{-15}{5} = -3[/tex]

The quotient of [tex]\frac{y}{x}[/tex] is always equal to [tex]-3[/tex]. Then [tex]k = -3[/tex] and the variation of y with x is direct

The equation is:

[tex]y = -3x[/tex]

Hello There!

The number of adult tickets sold in the school play = 225

Total Number Of Tickets = 505

Number Of Student Tickets = x + 55

Number of adult tickets sold can be represented by X

Number of student tickets = X + 55

X+X+55=505

2x+55=505

2x=505-55

2x=450

X=225

Answer:

225

Step-by-step explanation:

x+x+55 = 505

2x + 55 = 505

2x = 505-55

2x = 450

x = 225

GOOD LUCK ! ;)

Answer: The y-intercept would be 10

Step-by-step explanation:

(-2, 15), (1, 6), (2, 3), (4, -3), (7, -12) are the coordinate points, you can graph it to find the intercept. I used the graphing calculator desmos.

Answer:its 9

Step-by-step explanation:

Answer:

x = 3

Step-by-step explanation:

Given

[tex]\sqrt{-x+4}[/tex] = x - 4 ( square both sides )

- x  4 = (x - 4)² ← expand

- x + 4 = x² - 8x + 16 ( subtract - x + 4 from both sides )

0 = x² - 7x + 12 ← in standard form

0 = (x - 3)(x - 4) ← in factored form

Equate each factor to zero and solve for x

x - 3 = 0 ⇒ x = 3

x - 4 = 0 ⇒ x = 4

As a check

Substitute these values into the equation and if both sides are equal then they are the solutions

x = 3 : [tex]\sqrt{-3+4}[/tex] = [tex]\sqrt{1}[/tex] = 1

right side = 3 - 4 = - 1

left side ≠ right side ⇒ extraneous solution

x = 4 : [tex]\sqrt{-4+4}[/tex] = 0 and right side = 4 - 4 = 0

left side = right side ⇒ x = 4 is the solution

For this case we have by definition, that the equation of a line in the slope-intersection form is given by:

[tex]y = mx + b[/tex]

Where:

m: It's the slope

b: It is the cutoff point with the y axis

We need two points through which the line passes to find the slope:

[tex](0, -2)\\(-3,0)[/tex]

We found the slope:

[tex]m = \frac {y2-y1} {x2-x1}\\m = \frac {0 - (- 2)} {- 3-0} = \frac {2} {- 3} = - \frac {2} {3}[/tex]

So, the equation is of the form:

[tex]y = - \frac {2} {3} x + b[/tex]

We substitute a point to find "b":

[tex]-2 = - \frac {2} {3} (0) + b\\-2 = b[/tex]

Finally, the equation is:

[tex]y = - \frac {2} {3} x-2[/tex]

Answer:

Option C

Answer:

the first option

a = -2

b = 3

Step-by-step explanation:

See photo attached. (:

Answer:

Step-by-step explanation:

The equation is simplified by combining "like" terms. The terms "2x" and "2x" are "like" not just because they are identical, but because the only variable (x) is raised to the same power (1) in each term. We can use the distributive property to help combine those terms:

  2x +2x = (x)(2+2) = 4x

Of course, the constants on the left can be simply added: 3 + 5 = 8.

Now, the simplified form of the equation is ...

  4x + 8 = 16

__

To solve this, we note that all the numerical values are multiples of 4, the x-coefficient. Then we can divide all of them by 4 to give ...

  x + 2 = 4

You know the value of x already at this point, since you're familiar with your addition facts. However, to complete the solution algebraically, we subtract 2 from both sides of the equation:

  x = 2

_____

Comment on this solution

You will usually get instruction to "separate the variable terms from the constant terms," so the simplified equation would usually have 8 subtracted from both sides to give ...

  4x = 8

Then, you would divide by the x-coefficient to get x=2.

I elected to do it the way shown above for a couple of reasons:

Answer:

82%

Step-by-step explanation:

Answer:

Assuming your asking what is 4.82 hours to minutes, the answer to this is 289.2 minutes

Answer:

If one factor is (x-10) then the other factor is (x+2).

Step-by-step explanation:

We need to factorize the term x^2-8x-20

For factorization we need to break the middle term.

Middle term : -8x

Product of first and last term: -20x^2

Factors: -10x, +2x

Solving:

x^2-8x-20

x^2-10x+2x-20

x(x-10)+2(x-10)

(x-10)(x+2)

So, if one factor is (x-10) then other factor is (x+2)

when a graphed line is vertical, it indicates that the relation is not a function

Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points do not matter.

We can visually identify functions by their graphs using the vertical line test. If any vertical line intersects the graph more than once, then the graph does not represent a function.

The vertical line represents a value in the domain, and the number of intersections with the graph represent the number of values to which it corresponds.

As we can see, any vertical line will intersect the graph of y=|x|−2 only once.

Therefore, it is a function.

A vertical line can cross the graph of x=|y|+1 more than once.

therefore, it is not a function.

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Answer:

60 m2

Step-by-step explanation:

Since they are congruent SQ=MP, NM=RQ, RS=NP. The formula to find the area of a triangle is  1/2 bh. So you do 8 times 15 divided by 2. 8 times 15 is 120. 120 divided by 2 is 60 m2.

Answer:60m^2

Step-by-step explanation:

MNP is a triangle and area of a triangle = 1/2* base *height

From the figure height = 15 and base = ?

So we solve for the base using Pythagoras theorem

.: MP = square root of 17^2 - 15^2

MP = 8m =the base

Area of MNP = 1/2*8*15

Area = 60m^2

Answer:

f(n) = 64(3/4)^(n-1).

Step-by-step explanation:

The common ratio  is  48/64 = 36/48 =  3/4.

For a GS  nth term = a1 r^(n-1) where r = the common ratio, a1 = the first term, and n = the number of peaks reached.

The axplicit function is   64(3/4)^(n-1).

Answer:

f(x) = 64(three-fourths) Superscript x minus 1

Step-by-step explanation:

A bouncing toy reaches a height of 64 inches at its first peak, 48 inches at its second peak, and 36 inches at its third peak. The explicit function is f(x) = 64(three-fourths) Superscript x minus 1

Answer:

Option 1

Step-by-step explanation:

Before answering the question, we should define what the like radicals are.

The radicals which have the same expression under the root and same root number. There can be numerical multiples outside the radical but we have to compare the root number and same expression under the root.

In the given question, only option one has the same root number to the radical given in the question and the same expression under the root ..

Answer: X^4 you just subtract or add with exponents

Step-by-step explanation:

In mathematics, when you multiply variables that have the same base, you add their exponents. The solution to the problem X^-3•x^7 is x^4.

To multiply the variables with the same base, you need to add their exponents. In this case, x-3 multiplied by x7 would be equal to x-3+7 or x4. Therefore, the answer is x4.

The problem given is X^-3•x^7. This problem involves the multiplication of two variables with exponents. In mathematics, when you multiply variables with the same base, you keep the base and add the exponents. This is called the 'Laws of Exponents'. Therefore, for X^-3•x^7, our base is X, so we add the exponents -3 and 7 to get 4. Hence, the result is x^4.

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Answer:

6/7

Step-by-step explanation:

One way of doing this problem is to find the square root of numerator separately (it is 6) and the square root of the denominator likewise (it is 7).  Then the value of the given expression is 6/7.

The value of the given expression is [tex]\frac{6}{7}[/tex].

What is a mathematical expression?

"A mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context."

The given mathematical expression is

[tex](\frac{36}{49})^{\frac{1}{2}} \\= (\frac{6^{2} }{7^{2} })^{\frac{1}{2}}\\= [(\frac{6}{7})^{2}]^{\frac{1}{2}}\\= \frac{6}{7}[/tex]

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