Complete the following proofs.

Given: Points R, S, T, Q on circle O



Prove: m Arc RS + m Arc ST + m Arc TQ = m Arc RQ

In a convex pentagon, the measure of angle D is 132°.

If a planar polygon has all the line segments connecting any given pair of its points, it is said to be convex pentagon.

Properties of a Convex Polygon are-

Calculation for the measure of angle D.

The sum of the interior angles  = 540°

Let A, B , C  =   D - 40

And let  E  = D

So we have

A + B + C + D + E  = 540

(D - 40) + (D - 40)  + (D - 40)  + D + D  =  540

5D  - 120  = 540

5D = 660

D = 660 / 5  

D =  132°

Therefore, the measure of angle D is 132°.

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Answer:

The interval of the decreasing function is (-∞ , -1) ⇒ g(x)

The interval of the decreasing function is (-∞ , 0) ⇒ f(x)

Step-by-step explanation:

* Lets explain how to solve it

- Decreasing function means a function with a graph that moves

downward as it is followed from left to right.

- For example, any line with a negative slope is decreasing function

- Lets look to the attached graph to understand the meaning of the

decreasing function

∵ f(x) = IxI ⇒ green graph

∵ g(x) = Ix + 1I - 7 ⇒ purple graph

- From the graph f(x) translated 1 unit to the left and 7 units down to

form g(x)

- The domains of f(x) and g(x) are all real numbers {x : x ∈ R}

- The range of f(x) is {y : y ≥ 0}

- The range of g(x) is {y : y ≥ -7}

# For f(x)

- The slope of the green line from (-∞ , 0) is negative

- The slope of the green line from (0 , ∞) is positive

# For g(x)

- The slope of the purple line from (-∞ , -1) is negative

- The slope of the purple line from (-1 , ∞) is positive

∵ The line with negative slope represent decreasing function

∴ The interval of the decreasing function is (-∞ , -1) ⇒ g(x)

∴ The interval of the decreasing function is (-∞ , 0) ⇒ f(x)

Answer: a

/////////////////

Answer:

The correct answer is  A.

Step-by-step explanation:

The absolute value of any number is always positive.

Answer: 16x - 2

Step-by-step explanation:

The perimeter of a figure is the total length of all sides of the figure. Since this figure is a rectangle, opposite sides have the same length.

Therefore, the perimeter of the picture frame can be modeled by

[tex]6x+3+2x-4+6x+3+2x-4[/tex]

Moving all like terms together, we get

[tex]6x+2x+6x+2x+3-4+3-4[/tex]

Finally, combining these terms, we get

[tex]16x -2[/tex]

Answer:

C

Step-by-step explanation:

[tex]\frac{x+1}{x-4}[/tex] × [tex]\frac{5x}{x+1}[/tex] ← cancel x + 1 on numerator and denominator

= [tex]\frac{1}{x-4}[/tex] × [tex]\frac{5x}{1}[/tex]

= [tex]\frac{5x}{x-4}[/tex]

Answer:

5x/(x-4)

Step-by-step explanation:

To multiply fractions, all we have to do is multiply the numerators together and the denominators together. If we do that, we get the following:

[tex]\frac{x+1}{x-4}*\frac{5x}{x+1}=\frac{(x+1)(5x)}{(x-4)(x+1)}[/tex]

We notice that both the numerator and the denominator have an (x+1) term. Whenever you have something divided by itself, you get 1. In other words, they cancel out. As such, we can remove them from our answer to simplify it:

[tex]\frac{5x}{x-4}[/tex]

If we do that, we get the expression above. 5x/(x-4) is the reduced product of the rational expression given.

The total surface area of the can of coke is 641.143 cm².

A can of coke has the shape of a cylinder. A cylinder is a three-dimensional object that is made up of a prism and two circular bases. The total surface area of a closed cylinder can be determined by adding the area of all its faces.

Total surface area of the closed cylinder = 2πr(r + h)

Where:

Total surface area of the closed cylinder = (2 x 22/7 x 6) x (6 + 11)

(264 / 7) x (17)

37.714 x 17 = 641.143 cm²

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The next line after computing the sample standard deviation is to; determine the 2.5th and 97.5th percentiles of the values.

It follows from the task content that the 95% confidence interval for the population standard deviation using the bootstrap method in which case, after numerous sampling, the 2.5th and 97.5th percentiles of the standard deviations are determined.

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The amount of packing material is 1506 cubic inches

The given parameters are:

Can

Radius, r = 7 inches

Height, h = 18 inches

Box

Base dimension, l = 15 inches

Height, h = 19 inches

The volume of the can is:

[tex]V = \pi r^2h[/tex]

So, we have:

[tex]V_1 = 3.14 * 7^2 * 18[/tex]

[tex]V_1 = 2769[/tex]

The volume of the box is

[tex]V =l^2h[/tex]

So, we have:

[tex]V_2 =15^2 * 19[/tex]

[tex]V_2 =4275[/tex]

The amount of packing material is;

Amount = V2 - V1

This gives

Amount = 4275 - 2769

Evaluate

Amount = 1506

Hence, the amount of packing material is 1506 cubic inches

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The value of a is 6 and the value of b is 7

The function is given as:

h(x) = a . sin(x - π/2) + b

From the table of values, we have:

x = π/2 when y = 7

So, we have:

a . sin(π/2 - π/2) + b = 7

Evaluate the difference

a . sin(0) + b = 7

Evaluate the value of sin(0)

a . 0 + b = 7

Evaluate the product of a and 0

b = 7

Substitute b = 7 in h(x) = a . sin(x - π/2) + b

h(x) = a . sin(x - π/2) + 7

From the table of values, we have:

x = π when y = 13

So, we have:

a . sin(π - π/2) + 7 = 13

Evaluate the difference

a . sin(π/2) + 7 = 13

Subtract 7 from both sides

a . sin(π/2)  = 6

Evaluate sin(π/2)

a . 1 = 6

Divide both sides by 1

a = 6

Hence, the value of a is 6 and the value of b is 7

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Answer:

Step-by-step explanation:

1 1/6 + (x/3 · 1/4) = 1 3/4

solve for x

1 1/6 + x/12 = 1 3/4

1 1/6 - 1 3/4 = -x/12

-7/12 = -x/12

-7 = -x

x = 7

----------------

check

1 1/6 + (7/12 * 1/4) = 1 3/4

1 1/6 + 7/48 = 1 3/4

1 15/16 = 1 3/4

1 3/4 = 1 3/4

the answer is good

[tex]\frac{119}{780}[/tex] fraction of the whole piece you play middle C.

To find  for what fraction of the whole piece do you play middle C:

Since 7 out of every 13 beats in the finale are played at middle C, [tex]\frac{7}{13}[/tex] the finale is played at middle C.

The finale is 17 measures out of a 60-measure piece or [tex]\frac{17}{60}[/tex] of the whole piece.

[tex]\frac{7}{13}[/tex] of [tex]\frac{17}{60}[/tex] is [tex]\frac{7}{13}[/tex] x [tex]\frac{17}{60} = \frac{119}{780}[/tex]

Therefore,  [tex]\frac{119}{780}[/tex] for a fraction of the whole piece you play middle C.

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Answer:

298

Step-by-step explanation:

All perfect squares from 100-200 inclusive:

100, 121, 144, 169, 196

100+1=101, 101 is prime

121+2=123, 123=41*3 so its not prime

144+1=145 145=29*5 so its not prime

169+2=171 171=9*19 so its not prime

196+1=197, 197 is prime

101+197=298

Notice that I excluded all even numbers because they are obviously composite.

The third pair [(1+2i)(1-2i)] have a real number product and other pairs have complex number.

According to the statement

we have given Following are the pairs of the complex number:

(1+2i)(8i),

(1 + 2i)(2 – 5i)

(1+2i)(1-2i) and (1+2i)(4i)

We have to check which pair out of these is a real number product, which means which pair do not contain terms consisting of "i".

So, For this purpose

we have to multiply these pairs with each other.

So,

(1+2i)(8i) = 8i +16(i)^2

And

(1 + 2i)(2 – 5i) = 2 +4i - 5i +10(i)^2

And

(1+2i)(1-2i) = 1 -4(i)^2 -2i +2i = 1+4 = 5

And

(1+2i)(4i) = 4i + 6(i)^2

From these multiplication we found that the third pair have a real number product.

So, The third pair [(1+2i)(1-2i)] have a real number product and other pairs have complex number.

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Answer:

2y+6

Step-by-step explanation:

first, pull out the 2 from the top to separate the equation

second, factor out y

third, cancel out the common factor of y-1

fourth, remove the parenthesis from 2(y+3)

answer = 2y+6

Answer:

The roof does form a right triangle.

Step-by-step explanation:

If it is a right triangle then it will obey the Pythagoras Theorem.

Now  (√186)^2 = (√93)^2 + (√93)^2

              186 = 93 + 93 = 186

So it obeys the theorem and is therefore a right triangle.

The value of x in the triangle is 9.3

The side x of a triangle can be found as follows:

The triangle ABC is similar to triangle ADE.

Therefore, corresponding sides of similar triangles are in the same ratios.

Hence,

7  / 13 = x / x + 8

cross multiply

7(x + 8) = 13x

7x + 56 = 13x

subtract 7x from both sides of the equation

7x - 7x + 56 = 13x - 7x

56 = 6x

divide both sides by 6

x = 56 / 6

x = 9.33333333333

x = 9.3

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Step-by-step explanation:

1 ----> 22 times

2 ----> 16 times

3 ----> 26 times

4 ----> 29 times

5 ----> 1 times

6 ----> 6 times

so , total ----> 100 times

so , percentage of rolls 6 is :-

(6/100 ) × 100%

= 6%

If the height of candle after 10 and 26 hours are 25 cm and 17 cm then the height of candle after 21 hours is 19.5 cm.

Given height of candle after 10 hours is 25 cm , height of candle after 26 hours is 17 cm.

We have to find the height of candle after 21 hours.

We have been given two points of linear function (10,25),(26,17).

We have to first form an equation which shows the height of candle after x hours.

let the hours be x and the height be y.

Equation from two points will be as under:

[tex](y-y_{1} )=(y_{2} -y_{1} )/(x_{2} -x_{1} )*(x- x_{1} )[/tex]

(y-25)=(17-25)/(26-10)* (x-10)

y-25=-8/16 *(x-10)

16(y-25)=-8(x-10)

16y-400=-8x+80

8x+16y=480

Now we have to put x=21 to find the height of candle after 21 years.

8*21+16y=480

168+16y=480

16y=480-168

16y=312

y=312/16

y=19.5

Hence the height of candle after 21 hours is 19.5 cm.

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Answer:

x = 2 or x = -1/4

Step-by-step explanation:

Let's solve your equation step-by-step.

4x2−7x−2=0

For this equation: a=4, b=-7, c=-2

4x^2+−7x+−2=0

Step 1: Use quadratic formula with a=4, b=-7, c=-2.

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

[tex]x=\frac{-(-7)\pm\sqrt{(-7)^2-4(4)(-2)} }{2(4)}[/tex]

[tex]x=\frac{7\pm\sqrt{81} }{8}[/tex]

x = 2 or x = -1/4

Answer:

x = 2 or x = -1/4

The function f(x) is vertically compressed to form g(x)

The functions are given as

f(x) =x^2

g(x) =3x^2

Substitute f(x) =x^2 in g(x) =3x^2

g(x) =3f(x)

This means that the function f(x) is vertically compressed to form g(x)

See attachment for the function g(x)

Also, both functions have the same domain and range

The complete table is:

x      -2    -1    0   1    2

g(x)  12    3    0    3   12

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Answer:

discriminant = b^2 - 4ac

Step-by-step explanation:

discriminant = b^2 - 4ac

2^2 - 4x 3x2 = 4-24 = 20

Step-by-step explanation:

Direct variation is essentially a linear equation, where there is a constant rate. Direct variation can be applied to many things, and we can use it to represent how much money someone has in their bank account after "x" weeks if they're depositing a constant amount of money each week.

So a practical example would be: If someone just opened a bank account and deposits $50 every week, how many weeks will it take for them to have $400 in their account.

So the slope is given in the question, it's $50, since their depositing that constant amount each week. So this gives us the equation: [tex]y=50x[/tex] where x represents the amount of weeks. The y represents the amount of money they have, and since we want to find when this equals 400, we set the y=400, and then solve for x. This gives us the equation: [tex]400=50x[/tex]. Dividing both sides by 50 you get: [tex]8=x[/tex]. So it'll take 8 weeks to have $400 dollars, if you deposit 50 dollars each week.

The least possible value of n is 27.

According to the statement

We have given that the set which is {2,4,6,8.....n} and and one set is removed from them the average of remaining integers is 28.

Then

Firstly set contain n numbers

But after that set contain n-1 numbers after removal of 1 digit from them.

and average value of remaining digit is 28 then 28th term become after removal is

28th term =28*2

28th term = 56.

then

we use the formula to calculate n

n-1 =28

then the value of n become 27.

the least possible value of n is 27.

So, The least possible value of n is 27.

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[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

There are two hemispheres in there with radius 3 cm, so we can consider it as a whole one. and the other shape in between is Cylinder with radius 3 cm and height 4 cm.

Volume of whole ahape = volume of Cylinder + volume of sphere ~

Volume of sphere :

[tex]\qquad \sf  \dashrightarrow \: \cfrac{4}{3} \pi {r}^{3} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{4}{3} \sdot3.14 \sdot {(3)}^{3} [/tex]

[tex]\qquad \sf  \dashrightarrow \: (4 )\sdot(3.14) \sdot(9)[/tex]

[tex]\qquad \sf  \dashrightarrow \: 113.04 \: \: cm {}^{3} [/tex]

Volume of Cylinder :

[tex]\qquad \sf  \dashrightarrow \: \pi {r}^{2} h[/tex]

[tex]\qquad \sf  \dashrightarrow \: 3.14 \cdot(3) {}^{2} \sdot4[/tex]

[tex]\qquad \sf  \dashrightarrow \: 3.14 \sdot(9) \sdot(4)[/tex]

[tex]\qquad \sf  \dashrightarrow \: 113.04 \: \: cm {}^{3} [/tex]

Volume of whole shape :

[tex]\qquad \sf  \dashrightarrow \: 113.04 + 113.04 = 226.08 \: \: cm {}^{3} [/tex]

[tex]\qquad \sf  \dashrightarrow \: 226.08 \: \: cm {}^{3}[/tex]

Answer:

Slope: 1

Y-intercept: -1

Step-by-step explanation:

The line passes the y-axis at -1, the rise/run, which is used to calculate the slope is 2/2, and it equals to 1, so the slope is 1.

I hope it helps! Have a great day!

bren~  

Answer:

5 apples

Step-by-step explanation:

4 friends + Robby = 5 people

25 apples in total ÷ 5 people

= 5 apples per person

Answer:

On a Sunday?

Step-by-step explanation:

Answer:

y = 4x^2 + 8x - 12

4(x^2 + 2x - 3) = 0

4(x - 1)(x + 3) = 0

x = 1, -3

Answer:

[tex]\fbox {x-intercepts : (1, 0) and (-3, 0)}[/tex]

[tex]\fbox {Roots : x = 1, x = -3}[/tex]

Step-by-step explanation:

Given :

4 cancels throughout.

Solving by quadratic formula :

∴ Hence, the x-intercepts are (1, 0) and (-3, 0). The roots of the equation are 1 and -3.

The pen is [tex]15.78[/tex] centimeters long when scale is [tex]7[/tex] inches long and pen is [tex]2cm[/tex] shorter then the scale.

How to find the how much long is the pen ?

Scale is [tex]7 inches[/tex] long and

We know that

[tex]7inches=17.78cm[/tex]

And pen is [tex]2cm[/tex] shorten then the scale

So the length of the pen is

[tex]=17.78-2\\=15.78cm[/tex]

[tex]=6.21 inches[/tex]

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Answer: 1

Step-by-step explanation: Any number raised to zero is always 1.