Diana arrives late at the theater for a play.
Her ticket entitles her to sit anywhere in Circle
G. She had hoped to sit in Seat D, which she
thought would give her the widest viewing
angle of the stage. But Seat D is taken, as
are all the other nearby seats in Circle G. The
seating chart for the theater is shown.
Identify two other spots where Diana can sit
that will give her the same viewing angle she
would have had in Seat D. Explain how you
know how your points would provide the
same viewing angle, and support your claim
by showing the viewing angles on the
drawing.

The expressions that are equal to the distance between point A and point B would be

| 3 | + | -2 |

| -3 - 2 |

3 - ( -2 )

| 3 - ( -2 ) |

What is a number line?

In elementary mathematics, a number line is a picture of a graduated straight line that serves as visual representation of the real numbers.

In the given number line, the distance between point A and point B is 5.

Now we have to check each option

| 3 | + | -2 | = 3 + 2  = 5

| -2 + 3 | = | 1 | = 1

| -3 - 2 | = | -5 | =5

3 - ( -2 ) = 3+ 2 = 5

| 3 - ( -2 ) | = |3 + 2| = 5

Hence, the expressions that are equal to the distance between point A and point B would be

| 3 | + | -2 |

| -3 - 2 |

3 - ( -2 )

| 3 - ( -2 ) |

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Answer:

Step-by-step explanation:

set the height function = 0 and solve for t-16t2+6400=0t2 = -6400/(-16)=

Answer:

2.8

Step-by-step explanation:

First you need to divide the cost by the number of gallons dollars/number of gallons =cost per gallon

And then round it . I hope it helped

Answer:

bother = 6 years ; sister = 12 years

Step-by-step explanation:

s = sister

b = brother

s - b =  6

s * b = 4(s+b)

s = b + 6

b(b+6) = 4(b+6 + b)

b² + 6b = 4(2b + 6)

b² + 6b = 8b + 24

b² + 6b - 8b - 24 = 0

b² - 2b - 24 = 0

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

b = 6

b = -4 (impossible because an age can’t be negative)

s = 6 + 6

s = 12

Answer:

{-1, 0, 1, 3}

Step-by-step explanation:

A relation is a set of ordered pairs of numbers. The domain of a relation is the set of all the first elements (or x-values) in the ordered pairs. In this case, the relation is (-1,5) , (0,4), ( 1,2) , (3,-2), so the domain is the set of all the x-values in these ordered pairs, which is the set {-1, 0, 1, 3}. Therefore, the domain of the relation is {-1, 0, 1, 3}.

If the amount borrowed at 7.5% is four times the amount borrowed at 8.5%. The amount borrowed is: $200,000, $800,000, $1,000,000.

Now let find the amount borrowed

Let X+Y+Z = 2000000

0.06X + 0.075Y + 0.085Z = 137000

Y = 4Z

Substituting Y=4Z into the first and second equations:

X + 5Z = 2000000

0.06X + 0.075(4Z) + 0.085Z = 137000

X = 2000000 - 5Z

0.06X + 0.385Z = 137000

0.06(2000000 - 5Z) + 0.385Z = 137000

120000 - 0.3Z +  0.385Z = 137000

0.085Z + 120000 = 137000

0.085Z = 17000

Divide both side by  0.085Z

Z= 17,000/0.085

Z = 200000

So,

Y = 4Z

Y = 800000

X= 200,000 + 800,000

X = 1000000

Hence,

Z = 200000

Y = 800000

X = 1000000

Therefore the amount borrowed is: $200,000, $800,000, $1,000,000.

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The probability to get the numbers greater than 2 from the outcomes of  the event of rolling a single fair die is equal to P(A) = 2/3.

As given in the question,

Event is rolling a single fair die.

Number of fair die to be rolled = 1

Possible outcomes =  { 1, 2, 3, 4, 5, 6 }

Total number of possible outcomes = 6

Numbers greater than 2 on rolling a single fair die = { 3, 4. 5,6 }

Number of favourable outcomes = 4

Probability of getting a number greater than 2

= (Number of favourable outcomes) / (Total number of outcomes)

= 4 / 6

= 2 / 3

Therefore, the probability of getting a number greater than 2 while rolling a single fair die is equal to 2 / 3.

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Answer:

wheres the photo?

Step-by-step explanation:

Answer:

I think it’s 4/n and 4 divided by n. Sorry if it’s wrong!

Step-by-step explanation:

In the proof of given identity, cos(π - A) = -cos A. Therefore, step 1 is error made.

Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions. There are numerous distinctive trigonometric identities that relate a triangle's side length and angle.

The given identity is,

cos(π - A) = -cos A.

Use formula for cos(a − b) = cosa . cosb + sina . sinb

cos(π - A) = cosπcosA + sinAsinπ

                = (−1)(cosA) + (sinA)(0)

                = −1.cosA + (sinA)(0)

                = −cosA + 0

                 = −cosA

Since, in the step 1 the formula is wrongly used,

Therefore, step 1 is error made.

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Using system of linear equation the number of popcorn and drinks bought are 5 and  3 respectively

In solving a system of linear equation, we have two unknown variables which we are to find. However, we can use either substitution, elimination or graphical method to solve them.

In this case, to solve this problem, we have to write out two equations and solve for the unknown variable;

let;

x + y = 8 ...eq(i)

6x + 4y = 42 ...eq(ii)

From eq(i)

x + y = 8

x = 8 - y ...eq(iii)

Put eq(iii) into (ii)

6(8 - y) + 4y = 42

y = 3

put y = 3 into eq(i)

x + 3 = 8

x = 5

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For the system of equations y = 2x -2 and y = 2x - 1, There is no solution.

An equation is a combination of different variables, in which two mathematical expressions are equal to each other.

The given pair of set of equations,

y = 2x -2,

y = 2x - 1.

The graph of the equations is shown below,

To find the solution for the equations,

The value of x and y can not be determined because lines are parallel to each other.

Therefore, Equations have no solution.

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Answer: its is 12

Step-by-step explanation:

Answer:

The answer for f(g(3)) is 65.

There are 2 hours of television must you watch in the eighth week to meet your goal.

What is television?

The transmission of audio and video data electronically between a source and a recipient.

The primary use of television is to transmit shows for entertainment, information, and education. Television is a system for transmitting visual images and sound that are reproduced on screens.

Given: You want to limit the amount of television you watch to an average of at most 1.5 hours per week during an 8-week period.

Suppose x is the hours of watching television in the 8th week.

Let the average of watching television per week is 1.5.

⇒

[tex]\frac{1 + 1.5 + 0.5 + 3 + 1.5 + 2 + 0.5 + x}{8} = 1.5\\ \frac{10+x}{8}=1.5 \\10+x = 12\\x = 12-10\\x = 2[/tex]

Hence, there are 2 hours of television must you watch in the eighth week to meet your goal.

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Answer: 60%

Step-by-step explanation:

Take 42 divided by 70, then times 100% = 60%

Yoko has ridden 60% so far!

Answer:

Below

Step-by-step explanation:

Slope , m, is calculated  (y1-y2) / ( x1-x2) =

   Using the first two points :   (-5-0) / (-3 -0) = 5/3

slope = 5/3

The coordinates of the midpoint of line segment  A (-4,6) and B (2,-3) is M (-1 , 3/2).

A line segment is a measurable route between two points. Line segments can make up any polygon's sides because they have a set length.

Given:

Points A (-4,6), and B (2,-3)

Calculate the midpoint of the line segment by the formula given below,

[tex]M [(x_1 + x_2) / 2 \ \ , (y_1 + y_2)/2][/tex]

Substitute the values,

M [(-4 + 2) / 2 , (6 + (-3) / 2)]

M [(-2 / 2) , (3 / 2)]

M (-1 , 3/2)

Therefore, the coordinates of the midpoint of line segment  A (-4,6) and  B (2,-3) is M (-1 , 3/2).

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Answer: y=13\3 or 4 1\3

Step-by-step explanation:

Answer:

Hope this helps : )

You should shade in 1 whole rectangle on the the bottom left corner and the top half of the second rectangle the bottom right corner.

Step-by-step explanation:

This is because 1 1/2 is one whole rectangle and half of another rectangle. However, in this case the second rectangle on the bottom right corner is split into sixths. So half of it is 3/6 which is equal to 1/2.

Answer: 1, 3

Step-by-step explanation:

Answer:

P(Success1) =1/6

P(Success2) =1/6

P(2Success) =1/6 × 1/6 = 1/12

Answer: The first job seems better.

Step-by-step explanation:

If 1 month = 4 weeks:

40 x 40 = 1600 per week

40 x 160 = 6400 per month

250 per week on gas

250 x 4 = 1000 per month on gas

1600 - 250 = 1350

6400 - 1000 = 5400

You would earn $1350 per week on the first job, and $5400 on this job.

_____________________________________________________

25 x 160 = 4000 per month

25 x 40 = 1000 per week

100 per week on gas

100 x 4 = 400 per month on gas

1000 - 100 = 900

4000 - 400 = 3600

$900 per week on the second job, and $3600 per month on this job.

Hello,

I hope you and your family are doing well!

To compare the two jobs and determine which one is more financially advantageous, you need to calculate the total income and total expenses for each job on a monthly basis.

For the first job, the total income is 40 dollars per hour * 160 hours per month = 6400 dollars per month. The total expenses are 250 dollars per week * 4 weeks per month = 1000 dollars per month. The net income is 6400 dollars per month - 1000 dollars per month = 5400 dollars per month.

For the second job, the total income is 25 dollars per hour * 160 hours per month = 4000 dollars per month. The total expenses are 100 dollars per week * 4 weeks per month = 400 dollars per month. The net income is 4000 dollars per month - 400 dollars per month = 3600 dollars per month.

Based on these calculations, the first job is more financially advantageous because it has a higher net income. You would earn an additional 1800 dollars per month by working the first job instead of the second job.

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Happy Holidays!

Answer:  slope -intercept form = [tex]-\frac{3}{10} x-\frac{7}{10}[/tex] the slope = [tex]-\frac{3}{10}[/tex] and the y-intecept = [tex](0,-\frac{7}{10} )[/tex]

Step-by-step explanation: I used y=mx+b and filled it in with the infomation that I already knew. Hope this helps :)

Triangles ABC and DEF might or might not be congruent since the angle-angle-angle (AAA) postulate is not a requirement for congruency of any two triangles. This is due to the fact that the angle-angle-angle postulate only takes into account the triangles' angles and does not specify their side lengths, hence congruency for these triangles may or may not be true.

What is a congruent triangle?

Therefore, if two triangles have the same number of sides on each side, they are said to be congruent.

                   Additionally, we can determine if they are congruent if we have a side, an angle between the sides, and then another side that is congruent, in that order: side, angle, side.

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Answer:

 congruent  

(AAA) 

Step-by-step explanation:

The graph that correctly represents the function f(x) = [√(x + 3)] - 2 is; Graph D

We are given the function;

f(x) = [√(x + 3)] - 2

Remember that the argument of a square root must be zero or larger, then the minimum of the domain is the value of x such that:

x + 2 = 0

x = -2

Then the function starts at:

f(-2) = [√(-2 + 3)] - 2

f(-2) = 3

Then the graph should start at (-3, 2).

We can also identify another point by evaluating in x = 2.

f(2) = [√(2 + 3)] - 2

f(2) = -1

So the function also passes through (2, - 1).

Notice that the only graph that contains these two points is the last graph with x-intercept at 7.

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Answer:

The volume of the cube is increasing faster.

The volume of the cube with length : [x] is increasing faster.

Given is that the volume of a cube with length [x] is V(x) = x³. The volume of the sphere with radius (1/2)x is shown in the graph.

We have the volume of the cube with length : [x] is -

V{C} = x³

Volume of the sphere with radius : (1/2)x is

V{S} = (4/3)πr³ = (4/3)π(x/2)³ = πx³/6

V{S} = πx³/6

Refer to the graph of the function attached of both the function. It can be seen that the function of the volume of the cube with length [x] is increasing faster.

Therefore, the volume of the cube with length : [x] is increasing faster.

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Answer: the answer is c

Step-by-step explanation:

because Bru