Maddie scored 2 fewer than triple the number of points Crystal scored in their basketball game. Together the girls scored 30 points. Let
m = the points Maddie scored, and c = the points Crystal scored. Which system can be used to find the number of points each girl
scored?

If A is between B and C, and AB=x+2, BC=4x-7 and AC=2x-1,  then the x=8 and AC=15 units.

Given,

That A is between B and C.

AB= x+2

BC= 4x-7

AC= 2x-1

Then,

BC = AB+AC

4x-7= x+2+2x-1

4x-7= 3x+1

4x-3x=1+7

x=8

Then the length of the line AC is

AC= 2x-1

AC= 2×8-1 =15 units

Hence, If A is between B and C, and AB=x+2, BC=4x-7 and AC=2x-1,  then the x= 8 and AC= 15 units

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Answer:

#3: -2 = 2y - 8

#7: 3 = y

#8: y = 3

#4: Angle1 + Angle2 = Angle ABC

#6: Angle 1 and Angle 2 are supplementary

Step-by-step explanation:

6y - 2 = 8y - 8

 8 - 2 = 8y - 6y

     6/2 = 2y/2

       3 = y

       y = 3

Answer: c=[tex]\sqrt{A/\pi}[/tex]

Step-by-step explanation:

πc²=A​

c²=A/π

c=[tex]\sqrt{A/\pi}[/tex]

Part (a)

S1 = 1/2 since we only have one term, i.e. we aren't really summing anything here.

S2 = (1/2) + (1/4) = (2/4) + (1/4) = (2+1)/4 = 3/4

S3 = (1/2) + (1/4) + (1/8) = (4/8) + (2/8) + (1/8) = (4+2+1)/8 = 7/8

Or,

S3 = S2 + 1/8 = (3/4) + (1/8) = (6/8) + (1/8) = (6+1)/8 = 7/8

S4 = S3 + 1/16 = (7/8) + (1/16) = (14/16) + (1/16) = (14+1)/16 = 15/16

S5 = S4 + 1/32 = (15/16) + (1/32) = (30/32) + (1/32) = (30+1)/32 = 31/32

Here's the summary:

=============================================================

Part (b)

Through trial and error, the formula is

Sn = ( (2^n) -1 )/(2^n)

For example, if n = 4, then,

Sn = ( (2^n) -1 )/(2^n)

S4 = ( (2^4) -1 )/(2^4)

S4 = (16 - 1)/(16)

S4 = 15/16

=============================================================

Part (c)

u1 = first term = 1/2

r = common ratio = 1/2

Sn = u1*( 1 - r^n)/(1 - r)

Sn = (1/2)*( 1 - (1/2)^n )/(1 - 1/2)

Sn = (1/2)*( 1 - (1/2)^n )/(1/2)

Sn = 1 - (1/2)^n

Sn = 1 - 1/(2^n)

Sn = (2^n)/(2^n) - 1/(2^n)

Sn = ( (2^n) -1 )/(2^n)

This helps confirm the formula mentioned in part b

=============================================================

Part (d)

As n gets very large, Sn approaches 1

Examples:

Try out larger values of n and the Sn value should get closer to 1.

The reason why this works is because Sn = (x - 1)/x where x = 2^n

The (x-1)/x is equivalent to 1 - (1/x) and the 1/x approaches zero when x gets larger. The x gets larger as 2^n does.

The value of Sn itself will never equal 1 exactly. It simply gets closer and closer.

=============================================================

Part (e)

The diagram is missing, so I don't have enough info to be able to answer this.

The area of one face of the fish tank in the shape of a cube is 25 ft²

The formulas and the procedures we will use are:

Where:

Information about the problem:

Applying the volume formula and isolating the edge length, we have:

v = s³

s = [tex]\sqrt[3]{}[/tex]v

s = [tex]\sqrt[3]{}[/tex](125 ft³)

s = 5 ft

With the edge length, we calculate the area of the cube of one face of the tank:

Total faces of the cube = 6

One face of the cube = 1

A= 1*s²

A= 1*(5ft)²

A= 1*25ft²

A= 25 ft²

Is the measure of the space occupied by a body bounded by an environment called perimeter, the same is expressed in units of squared side. Example: ft2, m2

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a, The value of p is 6 and 2/9

b. After solving the equation x is equal to 9

a. If the roots of a quadratic ax² + bx = c = 0, are equal then the discriminant is zero express as

b² - 4ac = 0

W have given the equation x² + 3px + (14p - 3) = 0

Here, a = 1

         b = 3p

         c = 14p - 3

So, substitute the value and we get

⇒ (3p)² - 4(14p -3) = 0

⇒ 9p² - 56p + 12 = 0

⇒ 9p² - 2p - 54p + 12

⇒ p(9p - 2) -6(9p - 2)

⇒ (9p - 2)(p - 6)

⇒ p = 6, p = 2/9

b. Lets substitute p = x in x² + 3px + (14p - 3)

⇒ x² + 3(6)x + (14(6) - 3)

⇒ x² + 18x + (84 - 3)

⇒ x² + 18x + 81

⇒ x² + 9x + 9x + 81

⇒ x(x + 9) +9(x + 9)

⇒ (x + 9)(x + 0)

⇒ x = 9

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The time taken for the two trains to pass one another at 324 mi apart is 4 hours.

What is velocity ?

velocity is defined as rate of change of displacement d of the object with respect to rate of change in time t. In mathematics It is written as :

v = d/t

here it is given that :

Robinsport and Titusville trains are 324 mi apart on a railroad line that is distance between then is 324 mi.

also,

Trains leave each of these depots at the same time headed for the other depot and one travels at v₁ = 43 mi/h , the other at v₂ = 38 mi/h in opposite direction that is relative speed will get add-up that is :

Δv = v₁ - v₂

Δv = 43-(-38)

Δv = 81 mi/h

Now, the time taken for the two trains to pass one another is calculated :

Δv = d/t

81 = 324/t

t = 324/81

t = 4 hours

Therefore, the time taken for the two trains to pass one another is 4 hours.

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Answer:

t = d/r

Step-by-step explanation:

d = rt

We are solving for t, so you need t alone on the left side.

Switch sides.

rt = d

t is being multiplied by r, so you need to divide the left side by r to get rid of r. You must do the same operation to both sides of an equation, so divide both sides of the equation by r.

rt/r = d/r

rt/r is simply t, so we get:

t = d/r

The value of x is 27

In this question, we have been given a line AB and a point O on the line AB.

From figure we can see that, there are linear angles ∠AOM, ∠MON, and ∠NOB

Also, ∠AOM = 36°,

∠MON = 90°, and

∠NOB = 2x

We need to find the value of x.

We know that the sum of linear angles is 180°

⇒ ∠AOM + ∠MON + ∠NOB = 180°

⇒ 36° + 90° + 2x = 180°

⇒ 126° + 2x = 180°

⇒ 2x = 180 - 126°

⇒ 2x = 54°

⇒ x = 27

Therefore, the value of x is 27

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Answer:

C

Step-by-step explanation:

Answer:

14/24

Step-by-step explanation:

multiply 7 x 2 and 8 x 3

Answer:

Step-by-step explanation:

7/8 * 2/3

7 * 2 = 14

8 * 3 = 24

14/24 = 7/12

answer: 7/12

The underlined part in the given case is a statistic.

Now,

In a given sample of 12000 students, the underlined part is a statistic, because:

Hence, the underlined part is a statistic.

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Answer:

-4

Step-by-step explanation:

Let's solve this step by step:

-7 + 14 = 7
7 + 10 = 17

17 - 21 = -4

Your answer would be -4

The length and the widths are 420.031 yards and 0.031 yards if a rectangular parking lot has a length that is 420 yards greater than the width.

It is defined as two-dimensional geometry in which the angle between the adjacent sides is 90 degrees. It is a type of quadrilateral.

It is defined as the area occupied by the rectangle in two-dimensional planner geometry.

The area of a rectangle can be calculated using the following formula:

Rectangle area = length x width

Let L be the length and W be the width of the rectangle.

From the question:

L = 420 + W (based on the data given in the question)

LW  = 13

(420 + W)W = 13

W² + 420W - 13 = 0

After solving the above quadratic equation:

W = 0.031, W = -420.03 (width cannot be negative)

W = 0.031 yards (which is not practical but from a mathematical point of view it can be considered)

L = 420 + 0.031 = 420.031 yards

Thus, the length and the widths are 420.031 yards and 0.031 yards if a rectangular parking lot has a length that is 420 yards greater than the width.

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If three points (2,4), (6,3), (10,2) are correct, the line -4y = x - 18 will appear.

If all the three points are plotted correctly then the line obtained will be -4y = x - 18.

The form of equation of line is the slope intercept form of line. In this form of line, the line is represented with the slope of line and the intercept of the y axis.

By using the equation of the line, all the three correct points can be found out easily,

By assuming any three values of x, we can find the value of y.

1. Let us assume x = 2.

Putting value of x we get,

-4y = 2 - 18

-4y = -16

y = 4.

So, the first point is (2,4).

2. Let us assume x = 6.

Putting value of x we get,

-4y = 6-18

-4y = -12

y = 3.

So, the second point is (6,3).

3. Let us assume x = 10.

Putting value of x we get,

-4y = 10-18

-4y = -8

y = 2.

So, the third point is (10,2).

The three points to obtain the equation of line -4y = x -18, are (2,4), (6,3) and (10,2).

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Answer:

8. Supplementary means that two angles add up to 180 degrees (straight line). For the justification, I would simply write "def. of supplementary angles."

9. Equilateral means that all sides equal. For the justification, I would simply write "def. of equilateral triangle."

10. In a circle, all radiuses equal in length. TC and ZC are both radiuses. For the justification, I would simply write "def. of radius."

11. A midpoint divides a line segment in half. For the justification, I would simply write "def. of midpoint."

Answer:

2x^2+4x−13

Step-by-step explanation:

We need to know about domain and range of a graph to solve this problem. The domain is (-∞,5) and the range is (-∞,2).

The domain of a function is the input values that the function can take. The range is the set of values that can be the possible output of the function. The domain of a graph are the values that are on the x-axis and the range is on the y-axis. The arrow means that the graph goes on till infinity, a solid sphere means that the graph ends at that point and the ending point is included in the function, a hollow sphere means the graph ends at that point and the ending point is not included in the function. In the graph in the question, along x-axis the values on left goes on till negative infinity and on right the domain is open at 5. For range along y-axis, the range on the left side goes on till negative infinity and on the right it is open at 2.

Therefore we see that the domain of the graph is (-∞,5) and the range is (-∞,2).

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Distance travelled in January, February and March are 348 miles, 2436 miles and 3480 miles respectively.

Ax + b = 0, where a and b are two integers, and x is a variable, is an equation expressed in the form of linear equation with one variable. This equation has only one solution.

Let the miles travelled in January be x.

Miles travelled in February = 7x.

Miles travelled in March = 10x.

Total distance covered in three months = 6,264 miles.

Hence, the linear equation formed for given data will be:

X+7x+10x = 6264

18x = 6264

X=6264/18

X=348

So,

miles travelled in January = x

miles travelled in January = 348 miles.

Miles travelled in February = 7x

Miles travelled in February = 7*348

Miles travelled in February =2436 miles

Miles travelled in March = 10x

Miles travelled in March =1 0 * 348

Miles travelled in March=3480 miles

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The 8th term of the geometric sequence is 13122x^22

The explicit form of a geometric sequence is expressed according to the equation;

Tn = ar^n-1

where

r is the common ratio

a is the first term

n is the number of terms

Given the sequence below;

6x,18x^4,54x^7

r = 18x^4/6x

r = 3x^3

a = 6x

n = 8

Substitute to have:

T8 = 6x(3x^3)^8-1

T8 = 6x (3x^3)^7

T8 = 13122x^22

Hence the 8th term of the geometric sequence is 13122x^22

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Answer:

In a election of municipality two candidates P and Q stood for the post of mayor and 35000 people were in voter list. Voters were supposed to cast for a single candidate .22000 people cast vote for P, 5500 people cast for Q and 1500 cast vote even for both. How many people didn't cast vote find it

The answers to all the parts of the question are:

(A)  Before we begin, consider the cartesian plane, where the x-axis represents the cover charge and the y-axis represents the number of guests per night.

According to the previous information, we will find the following coordinates there: (9,165)  (10,150).

Remember that the linear equation's slope-intercept form is y=mx+b, where m is the slope and b is the intercept.

The slope can be calculated using the following formula:

In this case, the first coordinate will be (9,165) and the second will be (10,150).

The order is irrelevant.

Finally, we get the same value for m.

So,

We now have the slope and two points. Find a linear demand equation using this formula and remember that the point-slope form of a line's equation is y - y1 = m(x - x1).

Any of two coordinates can be selected.

In this case, we will select the second one.

We can choose between two coordinates.

In this case, we'll go with the second option.

Solve equation (1) for y:

We defined x as the cover charge (p) and y as the number of guests above (q).

As a result, rewrite equation 1.

Its formula depicts the number of guests per night as a function of the cover charge.

(B) The nightly revenue can be calculated by multiplying the cover charge price by the number of guests.

So we simply multiply the equation 1 by p.

(C) To calculate the nightclub's cost function, multiply the cost of two non-alcoholic drinks by the number of guests (equation 1) and add nightly overheads.

(D) To calculate the profit in terms of the cover charge, subtract the nightly costs (equation 3) from the nightly revenue (equation 2).

We will use the first derivative test (y'(x)=0) to find an extremum point to determine the entrance fee we should charge for maximum profit.

P's first derivative should be computed (p)

P'(p) = -30p + 330 = 0

30p = 330

p = 330/30

p =  $11

For maximum profit, the entrance fee should be p=$11 per guest.

Therefore, the answers to all the parts of the question are:

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The complete question is given below:

You have just opened a new nightclub, Russ' Techno Pitstop, but are unsure of how high to set the cover charge (entrance fee). One week you charged $9 per guest and averaged 165 guests per night. The next week you charged $10 per guest and averaged 150 guests per night.

(a) Find a linear demand equation showing the number of guests q per night as a function of the cover charge p. q(p) =

(b) Find the nightly revenue R as a function of the cover charge p. R(p) =

(c) The club will provide two free non-alcoholic drinks for each guest, costing the club $2 per head. In addition, the nightly overheads (rent, salaries, dancers, DJ, etc.) amount to $1,000. Find the cost C as a function of the cover charge p. C(p) =

(d) Now find the profit in terms of the cover charge p. P(p) =

Determine the entrance fee you should charge for a maximum profit. p = $ per guest.

We can make a 3 set venn diagram out of the given information as shown in the figure below. Based on the venn diagram, we can answer the questions.

19.  P(Dragon Ball Z or Naruto Shippuden)

This can also be written as-

1 - P(only one piece)

P(only one piece) = 2/100

Thus, P(Dragon Ball Z or Naruto Shippuden) = 1- 2/100

= 98/100

= 0.98

20. P (Naruto Shippuden/Not DBZ)

Number of people who don't like Dragon ball z = 100 - 73

= 27

Number of people who like Naruto Shippuden but not Dragon ball z = 11 + 14

= 25

Thus, P (Naruto Shippuden/Not DBZ) = 25/27

= 0.92

21. P(One piece or Naruto Shippuden)

This can also be written as-

1 - P(only DBZ)

P(only DBZ) = 22/100

Thus, P(One piece or Naruto Shippuden) = 1- 22/100

= 78/100

= 0.78

22. P(Dragon ball Z/Not One Piece)

Number of people who don't like one piece = 100 - 51

= 49

Number of people who like Naruto Shippuden but not one piece = 14 + 13

= 27

Thus, P(Dragon ball Z/Not One Piece) = 27/49

= 0.55

23.  Number of people who like both DBZ and Naruto Shippuden = 13 + 29

= 42

Thus, probability of students that like Dragon Ball Z and Naruto Shippuden = 42/100

= 0.42

24. Number of people who like one piece but not naruto = 51 - 29 - 11

= 11

Thus, the probability of students that like One Piece and do not like Naruto Shippuden = 11/100

= 0.11

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The angles that are marked congruent to each other on the diagram are : angle ZVY and angle ZYV

In this question, we need to identify two angles that are marked congruent to each other on the diagram.

We know that two angles are congruent means the measure of these angles is equal to each other.

These angles are identical to each other.

In given diagram we can observe that, angle ZVY and angle ZYV are identical.

This means, angle ZVY and angle ZYV are marked congruent to each other.

Therefore, two angles that are marked congruent to each other on the diagram are : angle ZVY and angle ZYV

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Answer:

x= -9/5

Step-by-step explanation:

I hope this helps!

Parallel to the line:

[tex]{\sf{2y = x + 1}}[/tex]

[tex]{\sf{y = \frac{x}{2} + \frac{1}{2 }}} [/tex]

Hence Slope:

[tex]{\sf{\large{\frac{1}{2}}}}[/tex]

The slope of line of which equation we need is parallel to the line given. Therefore, it's slope also is (m):

[tex]{\sf{\large{\frac{1}{2}}}} [/tex]

Also, the line passes through the points (4, 1)

Therefore by the formula of

[tex]{\sf{(y - y1) = m(x - x1)}}[/tex]

we have:

[tex]{\sf{(y - 1) = \frac{1}{2} (x - 4) }}[/tex]

[tex]{\sf{2y - 2 = x - 4}}[/tex]

[tex]{\sf{x - 4 - 2y + 2 = 0}}[/tex]

[tex]{\sf{\red{\boxed{\sf{x - 2y - 2 = 0}}}}}[/tex]

Answer: The answer for question 6 is 20,  The answer for question 7 is 7,

The answer for question 9 is 72, and the answer for question 8 is 12

Step-by-step explanation: Here is how you solve question 6!

4(3+5)-3(6-2) (You multiply 4 within the parentheses and the same for 3.)

12+20-18+6

32-18+6

14+6

20

Here is how you solve question 7

6+1/4(12-8) I multiply 1/4 with 12 to get 3 and -8 to get -2

6+3-2

7

Here is how you solve question 8

8(7.3+3.7-8)/2 You multiply within the 8 parentheses

58.4+29.6-64/2

24/2

12

Here is how you solve question 9

6^2(3+5)/4 This time you do not multiply anything over!

36(8)/4 I multiplied 36 with 8 to get 288

288/4

72

Hope this Helped :D

Answer:

6.

4(3 + 5) - 3(6-2)

= 4(8) - 3(4)

= 32 - 12

= 20

7.

6 + 1/4(12 - 8)

= 6 + 1/4(4)

= 6 + 1

= 7

8.

8(7.3 + 3.7 - 8) ÷ 2

= 8(3) ÷ 2

= 24 ÷ 2

= 12

9.

(6^2(3+5)/4)

= (36(8)/4)

= 288/4

= 72

10.

8 + 5(4) - 3(2)

= 8 + 20 - 6

= 22

The required average speed of the triathlon is 0.02 miles per minute.

Given that,
Total distance swim in the triathlon = 0.5 miles
Total time consumed to swim = 25 minutes
To determine the average speed of swimming in the triathlon.

Here,

Total time consumed to complete the swim portion of the triathlon = 25 minute
Distance swim = 0.5 miles
Speed of swim or average speed of swim = distance swim \time
= 0.5 / 25
= 0.02 miles / minute.

Thus, the required average speed of the triathlon is 0.02 miles per minute.

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Answer:

here's the answer I have in the photo and solution too