For a circle with a radius of 15 cm, what is the length of an arc intercepted by an angle measuring 120°?

Answer:

61 miles.

Step-by-step explanation:

Given: driving north for 11 miles and drive east for another 60 miles.

As given in the question, the travelling pattern show a right angle triangle, where hypotenuse line is the way to return back directly to starting point. As shown in picture attached.

∴ we can say, adjacent (a) is 11 miles and opposite (b) is 60 miles

Now, using Pythagoras theorem to get distance to return.

[tex]h^{2} = a^{2} +b^{2}[/tex]

⇒ [tex]h^{2} = 11^{2} +60^{2}[/tex]

⇒ [tex]h^{2} = 121+3600= 3721[/tex]

⇒ [tex]h= \sqrt{3721}[/tex]

∴[tex]h= 61[/tex]

∴ 61 miles need to be travel to return back directly to starting point.

Answer:

x =15°

Step-by-step explanation:

Given that the horizontal line is 90° to the vertical line, then both the angles have to necessarily add up to 90° i.e

(5x-10)° + 25° = 90°

5x - 10 + 25 = 90

5x + 15 = 90  (subtract 15 from both sides)

5x = 90 - 15

5x = 75   (divide both sides by 5)

x = 75 / 5 = 15°

Answer:

The percentage change in volume between cylinder A and cylinder B is 50%

Step-by-step explanation:

The volume of a cylinder is given by the formula

V= πr^2h

For cylinder A, where r=7 and h= 5, π=22/7

V= π * 7^2 * 5

V= π * 49 * 5

V= 769.69 cubic inch

For cylinder B

V= 490π

V= 1539.3804 cubic inch

The percentage change in volume between cylinder A and cylinder B

=[ (VA- VB)/VB] *100

=( 1539.3804 - 769.69) / 1539.3804

= 0.5000 * 100

= 50%

The percentage change in the volume between cylinder A and cylinder B is 50%

A cylinder is a three-dimensional object. It is a prism with a circular base.

volume of a cylinder = πr²h

π=  22/7

r = radius

h = height

Volume of cylinder A = π(7² x 5) = 245π

Percentage change in volume = (245 / 490) - 1 = 50%

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Answer:

3(6y-11)+2y=7

18y-33+2y=7

20y-33=7

20y=40

y=40/20

y=2

Put equation 1 into equation 2.

3(6y - 11) + 2y = 7

18y - 33 + 2y = 7

18y + 2y = 40

20y = 40

y = 2

x = 6(2) - 11

x = 12 - 11

x = 1

The coordinate pair is (1, 2) (x = 1, y = 2.)

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Answer:

d=125

Step-by-step explanation

edge 2020

The value of d, which is the bottom right angle formed on line s when cut by transversal q, is 125 degrees due to the alternate exterior angles being congruent on parallel lines.

When two parallel lines are crossed by a transversal, certain angles are equal due to the properties of parallel lines. The upper left angle on line s when intersected with the transversal q is given as 125 degrees; this is the alternate exterior angle relative to the bottom right angle formed on line s also intersected by q, which is known as d degrees in the question.

According to the alternate exterior angles theorem, these two angles are equal because the lines r and s are parallel. Therefore, the bottom right angle on line s, or d degrees, is also 125 degrees, because alternate exterior angles are congruent when two parallel lines are cut by a transversal.

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Answer:

Hi here is your answer

an=5n-3

an-1= -3+5n

an-1= -3+5(n-1)

an-1= -3+5n-5

an-1= 5n-7

d= an- an-1

d=(5n-3)-(5n-7)

d=5n-3-5n+7

d=4

Answer: d = 4

Hope this helps you.

Answer:

d = 5

Step-by-step explanation:

an = 5n -3

a1 = 5 -3 = 2

a2 = 5*2 -3 = 10 - 3 = 7

d = a2 - a1 = 7 - 2 = 5

Answer:

Step-by-step explanation:

a + p = 165......a = 165 - p

1.75a + 2.5p = 337.50

1.75(165 - p) + 2.5p = 337.50

288.75 - 1.75p + 2.5p = 337.50

-1.75p + 2.5p = 337.50 - 288.75

0.75p = 48.75

p = 48.75 / 0.75

p = 65 <==== 65 lbs of peaches were sold

a + p = 165

a + 65 = 165

a = 165 - 65

a = 100 <=== there were 100 lbs of apples sold

check...

1.75a + 2.5b = 337.50

1.75(100) + 2.5(65) = 337.50

175 + 162.50 = 337.50

337.50 = 337.50 (correct)

The inequalities that require flipping the sign are:

-5x - 10 > 5

[tex]\frac{x}{-7} + 3 \leq 4[/tex]

Solution:

Let us the inequalities one by one

You can perform on operations on both sides of inequality, and have its truth value unchanged

But if we multiply or divide by a negative number , we must flip the sign

-5x - 10 > 5

Move -10 from L.H.S to R.H.S

-5x > 5 + 10

-5x > 15

Divide the above expression by 5

[tex]-x > 3[/tex]

Divide the above inequality by -1, so we must flip the sign

x < -3

[tex]7x - 5 \leq 16[/tex]

Move the constant term from L.H.S to R.H.S

[tex]7x \leq 16 + 5\\\\7x \leq 21\\\\[/tex]

Divide the above inequality by 7

[tex]x \leq 3[/tex]

This does not required flipping the symbol

[tex]\frac{x}{5} - 6 > -11[/tex]

Move the constant term from L.H.S to R.H.S

[tex]\frac{x}{5} > -11 + 6\\\\\frac{x}{5} > -5[/tex]

Multiply both the sides by 5

[tex]x > -25[/tex]

This does not required flipping the symbol

[tex]x + 12 \leq 29[/tex]

Move the constant term from L.H.S to R.H.S

[tex]x \leq 29 - 12\\\\x \leq 17[/tex]

This does not required flipping the symbol

[tex]\frac{x}{-7} + 3 \leq 4[/tex]

Move the constant term from L.H.S to R.H.S

[tex]\frac{x}{-7} \leq 4-3\\\\\frac{x}{-7} \leq 1\\\\[/tex]

Multiply both the sides by -7, so we must flip the sign

[tex]x \geq -7[/tex]

Thus this requires flipping the sign

Answer: -5x - 10 > 5

Step-by-step explanation:

Answer:

17.25%.

Step-by-step explanation:

We have been given that last ear 225 students attended the annual school dance at CCMS. This year 211 students attended the dance. We are asked to find the percent of decrease.

We will use percent decrease formula to solve our given problem as:

[tex]\text{Percent decrease}=\frac{|\text{Final - Original}|}{\text{Original}}\times 100\%[/tex]

[tex]\text{Percent decrease}=\frac{|211-255|}{255}\times 100\%[/tex]

[tex]\text{Percent decrease}=\frac{|-44|}{255}\times 100\%[/tex]

[tex]\text{Percent decrease}=\frac{44}{255}\times 100\%[/tex]

[tex]\text{Percent decrease}=0.1725490\times 100\%[/tex]

[tex]\text{Percent decrease}=17.25490\%[/tex]

[tex]\text{Percent decrease}\approx 17.25\%[/tex]

Therefore, percent decrease is approximately 17.25%.

Answer:

C

Step-by-step explanation:

The lower quartile is the value at the left side of the box, that is

LQ = 14

The upper quartile is the value at the right side of the box, that is

UQ = 28

The median is positioned at the vertical line inside the box. that is

Median = 21

Answer: OPTION B.

Step-by-step explanation:

When parallel lines are cut by a transversal several angles are formed.

There are pairs of angles called "Alternate Interior angles".

 These angles are not adjacent and they are located between the parallel lines, and on opposite sides of the transversal.

By definition, they are are congruent, or, in other words the measure of Alternate Interior angles are equal.

In this case, you can identify that the [tex]\angle 8[/tex] and the [tex]\angle 2[/tex] are Alternate Interior angles.

Based on the data given in the exercise, you know that the measure of the angle 8 is:

 [tex]\angle 8=115\°[/tex]

So, You can determine that the angle 2 have the same measure. This is:

 [tex]\angle 2=115\°[/tex]

Answer:

1) angle bisector

2) w = 72°

3) t = 44°

4) t = 51°

5) FG = 16 units

Step-by-step explanation:

1) Given that, ∠VYW ≅ ∠WYV

The line which cuts any angle into equal halves is angular bisector of the angle

⇒ YW is angle bisector

2) In a triangle, sum of two interior angle is equal to exterior angle of other side.

⇒ w-41° + w-31° = w.

⇒ w = 72°

3) Sum of interior angles in a pentagon is 540°

(For a n sided it is (n-2)180° )

⇒ 149° + 139° + t+32° + 3t +t = 540°

⇒ t = 44°

4) sum of all exterior angles taken one at each vertex = 360°

⇒ 2t-50° + 46° + 2t + 34° + 2t-50° + 34° + 40° = 360°

⇒ t = 51°

5) Here, by comparing ΔHGF and ΔHIF

   ∠GHF = ∠IHF

  ∠HGF = ∠HIF

 and HF is common side for both triangles

⇒  ΔHGF ≡ ΔHIF ;  i.e) ΔHGF , ΔHIF are congruent triangles

⇒ FG = FI = 16 units

If f(4a) = 80, then the value of "a" is 4.2

Solution:

Given that cost for the olive oil used to fill the containers on the tables in an Italian restaurant is given by the function:

f(x) = 5x – 4

where "x" represents the number of quarts of olive oil

f(x) represents the quarts of oil used

To find: value of "a" when f(4a) = 80

Substitute x = 4a in given function

f(4a) = 5(4a) - 4

80 = 20a - 4

20a = 84

10a = 42

a = 4.2

Thus the value of "a" is 4.2

We want to know the value of a factor, given that we know f(4a) = 80 and the function f(x).

The value of a is 4.2

Here we start with the function f(x) = 5x - 4

Now we know that:

f(4a) = 5*(4a) - 4 = 80

Then we can just solve the above equation to find the value of a:

5*(4a) - 4 = 80

20*a - 4 = 80

20*a = 80 + 4 = 84

a = 84/20 = 4.2

The value of a is 4.2

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You have purchased 5 weekday hours.

Step-by-step explanation:

Parking hours purchased = 26

Cost per hour on weekday = $2

Cost per hour on weekend = $10

Total spent = $220

Let,

Number of hours on weekdays = x

Number of hours on weekend = y

According to given statement;

x+y=26      Eqn 1

2x+10y=220    Eqn 2

Multiplying Eqn 1 by 10

[tex]10(x+y=26)\\10x+10y=260\ \ \ Eqn\ 3\\[/tex]

Subtracting Eqn 2 from Eqn 3

[tex](10x+10y)-(2x+10y)=260-220\\10x+10y-2x-10y=40\\8x=40[/tex]

Dividing both sides by 8

[tex]\frac{8x}{8}=\frac{40}{8}\\x=5[/tex]

You have purchased 5 weekday hours.

Keywords: linear equation, elimination method

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We are given, [tex]P_1(x_1,y_1)[/tex] and [tex]P_2(x_2,y_2)[/tex] where [tex]P_1(2,2),P_2(0,1)[/tex].

Using slope formula we obtain

[tex]m=\dfrac{\Delta{y}}{\Delta{x}}=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{1-2}{0-2}=\dfrac{-1}{-2}=\boxed{\dfrac{1}{2}}[/tex]

Hope this helps.

Answer:

1/2

Step-by-step explanation:

I took the test :)

Answer:

[tex]cos(60^o)=\frac{a}{12}[/tex]

Step-by-step explanation:

The complete question in the attached figure

we know that

In the right triangle of the figure

The cosine of the angle of 60 degrees is equal to divide the adjacent side to the angle of 60 degrees (BC) by the hypotenuse (AB)

so

[tex]cos(60^o)=\frac{BC}{AB}[/tex]

we have

[tex]BC=a\ units\\AB=12\ units[/tex]

substitute the values

[tex]cos(60^o)=\frac{a}{12}[/tex]

The correct equation that represents the side length is Cos 60 = a/12

From the triangle given, we have the following

Using the soh cah toa identity

Cos theta = adj/hyp

Cos 60 = a/12

Hence the correct equation that represents the side length is Cos 60 = a/12

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Answer:

[tex] \: \: \: \: \: \: \: \: 5h + ( - 6h) = 20 \\ = > 5h - 6h = 20 \\ = > - h = 20 \\ = > h = - 20[/tex]

The cost of adult and kid tickets, we set up two equations representing the total cost for separate groups and use the elimination method to solve the system of linear equations. Once we solve for one ticket type, we can use its value to find the cost of the other ticket type.

The problem presented is a system of linear equations where we have two unknowns: the cost of an adult ticket and the cost of a kid ticket. We can set up the two equations based on the given information:

40A + 26K = 486.70 (First group's total cost)

21A + 31K = 332.45 (Second group's total cost)

To solve this system, we can use either substitution or elimination methods. For simplification, let's use the elimination method:

Multiply the second equation by 2: (2 x 21A) + (2 x 31K) = 2 x 332.45, which gives us 42A + 62K = 664.90.

Now subtract the first equation from this new equation: (42A + 62K) - (40A + 26K) = 664.90 - 486.70, resulting in 2A + 36K = 178.20.

Divide the entire equation by 2: A + 18K = 89.10.

We now have an easier equation to work with along with our original first equation.

To find the value of one variable, we could substitute the value of A from the first equation (using the second simplified equation) into the second equation and solve for K.

Once we have the value of K, we can substitute it back into either original equation to solve for A.

These steps will give us the exact cost of an adult ticket (A) and a kid ticket (K).

Answer:

44

Step-by-step explanation:

pay for 40 hours: 7.50 * 40= 300

pay for 1 hour of overtime pay: 1.5 * 7.5= 11.25 per hour

11.25 * 4= 45

45 + 300= 345  

40 + 4= 44

Answer:

a=1 b=5 c=9

Step-by-step explanation:

Answer: answer is A

Step-by-step explanation:

Answer:

® 6(2x - 1); @ -6(-2x + 1)  

Step-by-step explanation:

12x - 6 = 6(2x- 1)  Factored out 6

12x - 6 = -6(-2x + 1)     Factored out -6

68,246 inches of road had been repaved before today.

Step-by-step explanation:

Given,

Length of road repaved so far = 97338 inches

Length repaved today = 29092 inches

Length repaved before today = Total length repaved - Length repaved today

Length repaved before today = 97338 - 29092

Length repaved before today = 68246 inches

68,246 inches of road had been repaved before today.

Keywords: subtraction

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Answer:

Option 3) (0.38, -2.85) and (2.62,3.85)

Step-by-step explanation:

we have

[tex]y=x^{2}-3[/tex] ----> equation A

[tex]y=3x-4[/tex] ----> equation B

Solve the system by graphing

Remember that the solution of the system of equations is the intersection point both graphs

using a graphing tool

The intersection points are (0.38,-2.85) and (2.62,3.85)

see the attached figure

therefore

The graphs intersect approximately at (0.38,-2.85) and (2.62,3.85)

Answer:

The rent owe by me is Rs 1435

The rent owe by roommate is Rs 1360

Step-by-step explanation:

Given as :

The total rent of the room = x = Rs 2795

Let The room rent pay by friend = Rs y

And The room rent pay by me = Rs z

Now, According to question

The room rent pay by me = Rs 75 + room rent pay by roommate

i,e Rs z = Rs 75 + Rs y

Now, Again

The total rent of the room = The room rent pay by me + room rent pay by roommate

Or, x = Rs z + Rs y

Or, Rs 2795 = (Rs 75 + Rs y) + Rs y

Or, 2795 = 75 + 2 y

Or, 2 y = 2795 - 75

Or, 2 y = 2720

∴  y = [tex]\dfrac{2720}{2}[/tex]

i.e y = Rs 1360

So, room rent pay by friend = y = Rs 1360

And,The room rent pay by me = Rs 75 + room rent pay by roommate

Or,The room rent pay by me = Rs 75 + Rs 1360

So,he room rent pay by me = Rs 1435

Hence,The rent owe by me is Rs 1435

And ,The rent owe by roommate is Rs 1360    Answer

Answer:

No.

Step-by-step explanation:

x+(-2)=-3+(-2)=-3-2=-5, not 5.

Answer:3x(45/5)-7)

(3x9)-7=27-7=20

Step-by-step explanation:

Answer:

Step-by-step explanation:

3×[(12+33)]÷5-7 ​ = 3 * 45/5 -7

=3*9 - 7 = 27 - 7 = 20

Answer:

Step-by-step explanation:

The formula for simple interest is

I = Prt,

where I is the interest earned,

P is the initial investment amount,

r is the interest rate in decimal form, and

t is the time in years.  For us,

I = 75,

P = ?

r = .05

t = 1

Filling in what we were given:

75 = P(.05)(1) and

.05P = 75 so

P = 1500

Answer:

Step-by-step explanation:

1 1/4 (or 1.25) cups to 20 servings = 1 gallon (16 cups) to x servings

 1.25        16

--------- = --------  cross multiply

 20           x

(1.25)(x) = (20)(16)

1.25x = 320

x = 320/1.25

x = 256 servings <===

Answer:

164 and one over two

Step-by-step explanation:

47 over 8 *28

=1316 over 8

=164 and four over eight

=164 and one over two

[tex] \frac{47}{8} \times 28 \\ = \frac{1316}{8} \\ = 164 \frac{4}{8} \\ = 164 \frac{1}{2} [/tex]

Hope that helps

Answer: 133.33

Just do 108/81x100 to get 133.33

Hope this helps!

Answer:

75%

Step-by-step explanation: