In general, the sum of the inner angles of an n-sided polygon is given by the formula below

[tex]\begin{gathered} sum\text{ of inner angles}=(n-2)*180\degree \\ n\rightarrow\text{ number of sides of the polygon} \end{gathered}[/tex]12) In the case of a 5-sided polygon,

[tex]\begin{gathered} (n-2)*180=3*180=540 \\ \Rightarrow5x+5x+7x+8x+7x=540 \\ \Rightarrow32x=540 \\ \Rightarrow x=16.875 \\ \Rightarrow x\approx16.88 \end{gathered}[/tex]13) The polygon has 6 sides; then,

[tex]\begin{gathered} (6-2)*180=720 \\ \Rightarrow5x+4x+2x+7x+x+4x=720 \\ \Rightarrow23x=720 \\ \Rightarrow x=\frac{720}{23} \\ \Rightarrow x\approx31.30 \end{gathered}[/tex]The exact answer to question 13) is x=720/23, rounded to 2 decimal places the answer is 13.30Construct a difference table to predict the next term of sequence. 6, 1, 0, 10, 38, 91,.......

Number..................Difference1........... Difference 2.....Difference 3

6...........................................................................................

1................................ -5......................................................

0.............................. -1....................................4..............

10.............................. 10..................................11......................7

38.............................. 28................................18..................... 7

91.............................. 53................................25................... 7

**176............................85..............................32**

**Answer:**

**Next number in sequence 176**

5

一堆

2

If log₁/2x = -1, then the value of x is

a) 2

b) 1/2

c)-1

The value of the variable 'x' in **logarithmic **expression is: 2

**What is logarithm?**

In mathematics, the term **logarithmic **expression can be explained as the exponent or the power which is raised on the base value of the **logarithmic **expression.

According to the question, the given **logarithmic **expression are as follows:

[tex]log_{1/2}x = -1[/tex]

Using standard **logarithmic **property, we get

x = (1/2)^-1

⇒x = 2

Hence, the **logarithmic **value of the variable 'x' is: 2

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If there is more then one element in the set, separate them with commas

**Answer:**

**Sample space = {1A, 1B, 1C, 2A, 2B, 2C, 3A, 3B, 3C}**

**Event that the number chosen is 2 = {2A, 2B, 2C}**

**Explanation:**

The sample space is the set with all the possible outcomes, if she can select any number from 1, 2, or 3 and she can select any letter of A, B, or C, we get that the sample space is

Sample space = {1A, 1B, 1C, 2A, 2B, 2C, 3A, 3B, 3C}

Then, the outcome for the event that the select number is 2 is

Event that the number chosen is 2 = {2A, 2B, 2C}

Therefore, the answers are:

Sample space = {1A, 1B, 1C, 2A, 2B, 2C, 3A, 3B, 3C}

Event that the number chosen is 2 = {2A, 2B, 2C}

2. Tony's bill at a restaurant was $47.24. He planned to leave an 18% tip for the waiter. How muchdid he pay overall? (2 points)

Determine the amount paid by the Tony overall.

[tex]undefined[/tex]Write the linear inequalities that this graph represent in slope - intercept form

**Solution**

For the solid line we can select two points:

(0,2) and (1,0)

We can calculate the slope and we have:

[tex]m=\frac{0-2}{1-0}=-2[/tex]Then we can find the intercept and we got:

0= -2*1+ b

b =2

Then the equation is:

**y= -2x +2**

For the dashed line we can select (0,1) and (1,2) then the slope is:

[tex]m=\frac{2-1}{1-0}=1[/tex]The intercept is:

2= 1*1 +b

b=1

Then the equation is:

**y= x +1**

which representation shows y as a function of x?if you can't see c, is says: -1,0 -1,5-1,10-1,15

At first ,we should know that :

The relation between x and y will be a function when each value of x appeared one time

We will check the options:

A. for the figure of option A, each value of x connected one time to a value of y

B . there are 2 arrows from 0 and 1

C. the values of x = -1 , connected four times to the value of y

So, the answer is option A

What can you conclude from the information in the diagram?

**Answer:**

Triangle UVT and TSR are isosceles triangles (two equal sides).

Angle WUV = Angle WTV (base angles of isosceles triangle)

Angle RTS = Angle TRS (base angles of isosceles triangle)

Line VW is perpendicular to line UT.

Angle WTV = Angle RTS (vertically opposite angles)

Angle WTR = Angle VTS (vertically opposite angles)

Let f(x)=(x−7)(x+6)(x−5). Find the y-intercept(s), the x-intercept(s), the values of x where f(x)>0, and the values of x where f(x)<0. Do not sketch the graph.

1. Find the y-intercept(s). List your answers as points in the form (a,b)

2.Find the x-intercept(s). List your answers as points in the form (a,b)

3. What are the values of x where f(x)>0?

4. What are the values of x where f(x)<0

Part 1

The y-intercept is when x=0, and [tex]f(0)=(0-7)(0+6)(0-5)=210[/tex]. So, the y-intercept is at (0, 210).

Part 2

The x-intercept(s) are when y=0, so:

[tex]f(x)=0\\\\(x-7)(x+6)(x-5)=0\\\\x-7=0, x+6=0, x-5=0\\\\x=-6, 5, 7[/tex]

So, the x-intercepts are: (-6, 0), (5, 0), (7, 0)

Using our roots from Part 2, we know that:

Part 3: [tex](-6, 5) \cup (7, \infty)[/tex]

Part 4: [tex](-\infty, -6) \cup (5, 7)[/tex]

What would the simplified form be to-√12+3√3

[tex]-\sqrt{12}\text{ + 3}\sqrt{3}[/tex][tex]\begin{gathered} -\sqrt{12}\text{ + 3}\sqrt{3} \\ -\sqrt{4\times3}\text{ + 3}\sqrt{3} \\ -2\sqrt{3}\text{ + 3}\sqrt{3} \\ \sqrt{3} \end{gathered}[/tex]

Write an equation that represents the line.

Use exact numbers.

**Answer:**

y = 0.75x + 2

**Step-by-step explanation:**

Take two distinct points on the graph

Compute the slope m and y-intercept b

Equation of line in slope-intercept form is

y = mx + b

Take points (0, 2) and (4, 5)

Slope m = (5 - 2) /(4-0) = 3/4

y-intercept from the graph is 2

So y = 3/4 x + 2 =0.75x + 2

If ∆ABC is congruent to ∆PQR, find the length of QR.

If ∆ABC is congruent to ∆PQR, find the length of QR.

Given that If ∆ABC is congruent to ∆PQR:

The simplest way to prove that triangles are congruent is to prove that all three sides of the triangle are congruent.

When all the sides of two triangles are congruent, the angles of those triangles must also be congruent.

From the triangle ABC, the side BC = 4,

Hence the PQR, the side **QR = 4 ** since they are congruent

A student is initially outside. He is given the choice with a probability of 0.4 of going to the playground, 0.3 of shopping in the mall and 0.3 of returning home. If he is in the playground, he takes 2 hrs of time and then decides to stay in the playground again or return back home. (he can continue to decide to stay in playground like a recursive process) Similarly, If he is in the mall, he takes 3 hrs of time and then decides to stay in the mall again or return back home. (he can continue to decide to stay in mall like a recursive process) For all cases, it takes 1 hr to return home. what is the expected hours the student was outside home?

Based on the **probability **values, it will take the student 2 hours to stay **outside **the home

The given parameters are:

**Probabilities**

P(1) = 0.4

P(2) = 0.3

P(3) = 0.3

**Time**

Time 1 = 2 hours

Time 2 = 3 hours

Time 3 = 1 hour

When the above are represented on a **table**, we have the following table of values

Time (x) | 2 3 1

Probability (P(x)) | 0.4 0.3 0.3

The **expected value **of the student is then calculated as

E(x) = ∑ x * P(x)

Substitute the known values in the above equation

E(x) = 2 * 0.4 + 3 * 0.3 + 1 * 0.3

Evaluate the products

E(x) = 0.8 + 0.9 + 0.3

Evaluate the sum

E(x) = 2

Hence, the **expected value **is 2

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Analyze the graph of the function f(x)=4|x+7|+8 compared to the graph of the absolute value function g(x)=|x| .

**Given:**

The functions

[tex]\begin{gathered} g(x)=|x| \\ f(x)=4|x+7|+8 \end{gathered}[/tex]**Required:**

Determine changes made in g(x) to get f(x).

**Explanation:**

The steps are:

[tex]\begin{gathered} f(x)=4|x+7|+8 \\ Shift\text{ the graph to the left }7\text{ units.} \\ Shift\text{ the graph upwards }8\text{ units.} \\ Apply\text{ a vertical stretch of }4\text{ units.} \end{gathered}[/tex]So. fourth option is describing the f(x).

The graph

**Answer:**

Completed the answer.

Find two different ways to show that one third+ one fourth is not equal to 3/7. You can use numbers words and labels sketches.

We can **show **that one third + one fourth is **not equal **to 3/7 by following two ways.

We are given to prove that the one third and one forth combination of any object/value does not equals to the 3/7 of that same value/object.

let's Consider we have value as 1.

∴ one third of value will be [tex] \frac{1}{3} [/tex]

∴ one forth of value will be [tex] \frac{1}{4} [/tex]

∴ three of seven of value will be [tex] \frac{3}{7} [/tex]

Now we can do the **mathematic calculation **on one third and one forth of the value.

As given we have to calculate the addition of one third and one forth of the value

∴ [tex] \frac{1}{3} + \frac{1}{4} [/tex]

= [tex] \frac{4}{12} + \frac{3}{12} [/tex] --(make **base **same )

= [tex] \frac{4\ + 3}{12}[/tex]

= [tex] \frac{7}{12}[/tex]

∴ By the calculation we clearly got that the addition of one third and one forth of the value is equal to the **seven **of **twelve **of the value.

We can also prove it by analysis as follows ;

Proof by analysis:-Consider a **number **say **120**.

∴ 1/3 of 120 will be **40 **

∴ 1/4 of 120 will be **30**

∴ 3/7 of 120 will be **51.42**

Now Addition of 1/3 and 1/4 of 120 will be 40 + 30 = **70**

Comparing it with 3/7 i.e** 51.42 ≠ 70**

Hence proved 1/3 + 1/4 ≠ 3/7 .

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discriminant of the equation x squared minus 5x equals -2 is

Recall that the "discriminat" of a quadratic equation of the form:

a x^2 + b x + c = 0

is given by the formula: b^2 - 4 a c

So for our equation:

x^2 - 5 x = -2, we start by adding 2 to both sides, in order to get the appropriate form equal to zero:

x^2 - 5 x + 2 = 0

Now we recognize:

a = 1

b = - 5

c = 2

and write the discriminant

b^2 - 4 a c = (-5)^2 - 4 (1) (2) = 25 - 8 = 17

Then, the discriminat of the equation is: **17**.

A total of $7000 is invested: part at 7 % and the remainder at 15 %. How much is invested at each rate if the annual interest is $510?

The total invested = $7000

Part of the money at 7% and the reminder at 15%

Let the part at 7% = x

So, the part at 15% = 7000 - x

Given the annual interest = $510

so,

7% of x + 15% of ( 7000 - x ) = 510

0.07 * x + 0.15 * ( 7000 - x ) = 510

0.07 x + 0.15 * 7000 - 0.15 x = 510

0.07 x + 1050 - 0.15x = 510

0.07 x - 0.15 x = 510 - 1050

-0.08 x = - 540

divide both sides by -0.08

x = -540/-0.08 = 6,750

7000 - x = 7000 - 6750 = 250

**So, the part that is invested at a rate of 7% = $6,750**

**And the part that invested at a rate of 15% = $250**

A teacher was helping me but I got force quite the app due to lag can you help me with question C, D, and E !!!

Parts C, D and E

Answer:

Explanation:

C) The maximum height is the highest point on the graph. On the x axis of the graph, each small square is 0.25 units. Thus, the x coordinate of the maximum height is is 1.25. **The ball reached maximum height after 1.25 seconds**

D) There were two different times when the ball was at 10m.

When y = 10 m, x = 0.5

when y = 10, x = 2

**At 0.5 and 2 seconds, the ball was at 10m**

E) A the time the when the ball hit the ground, the height is 0. Thus, **the time when the ball hits the ground is 3 seconds**

Describe the transformation of f(x)= x2 represented by g. then graph.

that’s 5636288163 x24

5. Which equation is solved for the height of the cone based on theinformation given below ?

**The equation for the Volume (V) of the cone given is,**

We are to isolate 'h' in the equation above

**SOLUTION**

Multiply both sides by 3

[tex]3V=3\times\frac{\pi}{3}r^2h[/tex]Simplify

[tex]3V=\pi r^2h[/tex]Divide both sides by πr²

[tex]\frac{3V}{\pi r^2}=\frac{\pi r^2h}{\pi r^2}[/tex]Simplify

[tex]h=\frac{3V}{\pi r^2}[/tex]**Hence, the answer is**

If 2 + √3 is a polynomial root, name another root of the polynomial, and explain how you know it must also be a root.

If 2+[tex]\sqrt{3}[/tex] is a** polynomial root**, then the another root of the polynomial will be 2 -[tex]\sqrt{3}[/tex]

The root of the **polynomial **= 2 +[tex]\sqrt{3}[/tex]

We know by using the quadratic equation we can find the solution of the polynomial

**The quadratic equation** of the polynomial

= [tex]\frac{-b+/-\sqrt{b^2-4ac} }{2a}[/tex]

Then the root of the polynomial is [tex]\frac{-b+\sqrt{b^2-4ac} }{2a}[/tex] and [tex]\frac{-b-\sqrt{b^2-4ac} }{2a}[/tex]

Here one root is given that 2 + [tex]\sqrt{3}[/tex]

Then using the quadratic equation of the polynomial, the other root of the polynomial will be the **conjugate **of the given root.

The other root of the polynomial = 2 - [tex]\sqrt{3}[/tex]

Hence, If 2 + [tex]\sqrt{3}[/tex] is a polynomial root, then the another root of the polynomial will be 2 - [tex]\sqrt{3}[/tex]

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Two ropes are attached to a wagon, one horizontal to the west with a tension force of 30N, and the other east and at an angle of 30 degrees northward and a tension force of 40 N. Find the components of the net force on the cart. Show all work.

The **net** **force** on the cart is **62N**

and the **vertical** **component** **=36.64** **N**

the **horizontal** **component=** **50N**

What is **revolution** of **vector**?

The process of splitting a **vector** into its **components** is called **resolution** of the vector. We resolve a vector into two components which are. component along the x-axis called **horizontal** **component**. component along the y-axis called **vertical** **component**

30N tension on the cart is westward which mean the vertical component will be 0 and the horizontal component will be 30N.

40N **tension** isN 30° E which means

the **vertical** **component=** 40 **sin60=36.64N**

**Horizontal** **component=** 40 cos 60= 20N

sum of vertical = 36.64N +0= **36.64N**

sum of horizontal= 30N+20N= **50N**

60° was used for tension 40N because the angle of vector must always lie on the horizontal axis

therefore the net force F is obtained by using Pythagoras theorem

F= √(50^2+36.64^2)

= **62N** to the nearest whole number.

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Calculate the total loss after 4 years if 299000 is reduced by 4% per annum

The total **loss** after 4 years is $47840.

From the information, we want to calculate the total **loss** after 4 years of 299000 is reduced by 4% per annum.

It should be noted that this simply means the calculation using the **interest** formula. In this case, the total loss will be gotten by knowing the interest.

In this case, the **interest** formula can be illustrated as:

Interest = PRT / 100

where P = **Principal** = 299000

R = Rate = 4%

T = Time = 4 years

Interest = (299000 × 4 × 4) / 100

Interest = 4784000 / 100

Interest = 47840

In this case, the calculation of the **interest** is the loss that the person gets.

Therefore, the **loss** is $47840.

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In a single throw of a fair die, what is the probability that an odd number or a perfect square greater than one shows up?

The probability** **that an** odd **number or a perfect **square **greater than one shows is 2/3.

**Probability **- The area of mathematics known as probability deals with numerical representations of the like that an event will occur or that a statement is true.

total no. of **outcomes** - 1,2,3,4,5,6

odd number = 1,3,5

or a perfect square = 4

probability - dividing the **favorable** number of outcomes by the total number of** possible **outcomes.

probability = favorable outcomes / total no. of outcomes

= 4/6

= 2/3

The probability that an **odd **number or a perfect **square **greater than one shows is 2/3.

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I really need a clear, step-by-step explanation

1) 1/6

3) -7/6

what is the difference between rational and fractional numbers?Any number with the formulaTo learn more about :** fractional numbers**

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x over 3=2

Can the value of x be 13

**Answer:**

no

**Step-by-step explanation:**

because 3*2 isnot equal to13

help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee

**Answer:**

d

**Step-by-step explanation:**

The number of years must be non-negative.

This eliminates all of the options except for d.

A triangle has side lengths measuring 10m, 24m, and 26m. Explain how you use Pythagorean Theorem to determine whether or not the triangle is a right triangle.

Hello there. To solve this question, we'll have to remember some properties about the pythagorean theorem and right triangles.

Given a triangle with side lengths 10 m, 24 m and 26 m, we have to determine whether this is a right triangle or not.

First, let's assume these are the sides lengths of a right triangle, as follows:

Notice in this case we choose the largest side to be the hypotenuse. We know that the largest side of a triangle has to be less than the sum of the legs and any combination would do, but since we'll apply the Pythagorean theorem, we already know that the hypotenuse has to be the largest side of the triangle.

For a right triangle with legs a, b and hypotenuse c, the Pythagorean theorem says that the sum of the squares of the legs is equal to the square of the hypotenuse, that is

[tex]a^2+b^2=c^2[/tex]Hence we plug a = 10, b = 24 and c = 26.

We have to see if this equality will hold for the values;

[tex]10^2+24^2=26^2[/tex]On the right hand side, square the number

[tex]676[/tex]On the left hand side, square and add the numbers

[tex]100+576=676[/tex]Notice we got the same answer, then we say that these values satisfy the Pythagorean theorem.

Therefore, this is a right triangle.

Determine the distance between M(4, 0) and N(-2, -3).

[tex]\text{distance = }\sqrt[]{45}[/tex]

**Explanation**

Step 1

the distance between 2 points P1 and P2 is given by:

[tex]\begin{gathered} \text{distance}=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ \text{where} \\ P1(x_1,y_1)andP2(x_2,y_2) \end{gathered}[/tex]Step 2

let

P1=M(4,0)

P2=N(-2,-3)

replace

[tex]\begin{gathered} \text{distance}=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ \text{distance}=\sqrt[]{(-2-4)^2+(-3-0)^2} \\ \text{distance}=\sqrt[]{(-6)^2+(-3)^2} \\ \text{distance}=\sqrt[]{36+9} \\ \text{distance}=\sqrt[]{45} \\ \end{gathered}[/tex]I hope this helps you

the recommended amount of meat to serve 1 and 1/2 dozzen people is 4 and 1/2 pounds. how many pounds of meat are recommended to feed 1 dozzen people? how many pounds are recommended to feed 4 people? and how many pounds are recommended to feed 1 person

First, 1 dozen is 12 units, so

[tex]1\frac{1}{2}\text{ dozen people }=\text{ 12 people + 6 people = 18 people}[/tex]Now, to solve the exercise you can use the rule of three. So, you have

*How many pounds of meat are recommended to feed 1 dozen people?

[tex]\begin{gathered} 18\text{ people}\rightarrow4.5\text{ pounds} \\ 12\text{ people}\rightarrow x\text{ pounds} \\ x=\frac{12\text{ people }\ast\text{ 4.5 pounds}}{18\text{ people}} \\ x=\frac{54}{18}\text{ pounds} \\ x=3\text{ pounds} \end{gathered}[/tex] Therefore, **3 pounds of meat is recommended to feed a dozen people.**

*How many pounds are recommended to feed 4 people?

[tex]\begin{gathered} 18\text{ people}\rightarrow4.5\text{ pounds} \\ 4\text{ people}\rightarrow x\text{ pounds} \\ x=\frac{4\text{ people }\ast\text{ 4.5 pounds}}{18\text{ people}} \\ x=\frac{18}{18}\text{ pounds} \\ x=1\text{ pound} \end{gathered}[/tex] Therefore,** 1 pound of meat is recommended to feed 4 people.**

*How many pounds are recommended to feed 1 person

[tex]\begin{gathered} 18\text{ people}\rightarrow4.5\text{ pounds} \\ 1\text{ person}\rightarrow x\text{ pounds} \\ x=\frac{1\text{ person}\ast4.5\text{ pounds}}{18\text{ people}} \\ x=\frac{1}{4}\text{ pounds} \end{gathered}[/tex] Therefore, **1/4 pound of meat is recommended to feed 1 person.**

Write the augmented matrix for the following system of equations.

9y-5+9z = 0

7x=-3y+7+z

5x + 7y = 5

The **augmented matrix **is [tex]\begin{bmatrix}0&9&9&|&5\\7&3&-1&|&7\\5&7&0&|&5\end{bmatrix}[/tex].

What is a **matrix**?

A **rectangular **array or table containing **numbers**, **symbols**, or phrases that are arranged in **rows **and **columns **is known as a **matrix**.

The given **system **of **equations **is:

9y - 5 +9z = 0

7x = -3y +7 + z

5x + 7y = 5

Rewrite the **equations **as:

0x + 9y + 9z = 5

7x +3y -1z = 7

5x + 7y + 0z= 5

Therefore, the **augmented** **matrix **for the system of **equations **is:

[tex]\begin{bmatrix}0&9&9&|&5\\7&3&-1&|&7\\5&7&0&|&5\end{bmatrix}[/tex]

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below to explore the central ideas and supporting details in "Escape to Freedom.1. Reread the section "A Bleak Time." Which statement below BEST expresses the central idea ofthis section?
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