A movie theater has a seating capacity of 383. The theater charges $5.00 for children, $7.00 for students, and $12.00 of
adults. There are half as many adults as there are children. If the total ticket sales was $ 2778, How many children,
students, and adults attended?

Answer:

3x + 2y = 17

2x + 5 y = 26

Step-by-step explanation:

3x + 2y = 17 }

2x + 5 y = 26}

x - 3y = - 9

x = -9 + 3y

=> 2 (-9+3y)+5y=26

-18+6y+5y=26

-18+11y=26

11y=26+18

11y=44

y= 4

3x + 8=17

3x = 17 - 8

3x = 9

x = 9 : 3

x = 3

Final answer:

By using the elimination method to solve the system of equations, we found that the solution is x = 3 and y = 4 after eliminating y, solving for x, and then substituting x back into one of the original equations to solve for y.

Explanation:

Elimination Method: Solving the System of Equations

To solve the system of equations using the elimination method, we will manipulate the equations to eliminate one variable and solve for the other. The two equations given are:

3x + 2y = 17

2x + 5y = 26

We want to eliminate one of the variables. To do this we find a common multiple for the coefficients of either x or y and then subtract or add the equations. Let's eliminate y by multiplying the first equation by 5 and the second equation by 2, which will give us equations with the same coefficient for y but opposite signs:

5(3x + 2y) = 5(17)

2(2x + 5y) = 2(26)

Now, our two new equations are:

15x + 10y = 85

4x + 10y = 52

Subtract the second new equation from the first:

(15x + 10y) - (4x + 10y) = 85 - 52

11x = 33

Solving for x:

x = 33 / 11

x = 3

Now that we have the value for x, substitute it back into one of the original equations to find y. Let's use the first original equation:

3(3) + 2y = 17

9 + 2y = 17

2y = 17 - 9

2y = 8

y = 8 / 2

y = 4

The solution to the system of equations is x = 3, y = 4.

Answer:

m² + 8m + 7 = (m + 1) (m + 7)

m² – 6m + 8 = (m – 2) (m – 4)

Step-by-step explanation:

If a trinomial ax² + bx + c is "factorable", you can use the AC method.

1. Multiply a and c.

2. Find factors of ac that add up to b.

3. Divide the factors by a and reduce.

4. The numerators are the constants, the denominators are the coefficients.

For example:

m² + 8m + 7

a = 1, b = 8, c = 7

1. ac = 1×7 = 7

2. Factors of 7 that add up to 8 are 1 and 7.

3. Divide by 1: 1/1 and 7/1

4. The factors are (m + 1) and (m + 7).

Therefore, m² + 8m + 7 = (m + 1) (m + 7).

Let's try one with a negative coefficient:

m² – 6m + 8

a = 1, b = -6, c = 8

1. ac = 1×8 = 8

2. Factors of 8 that add up to -6 are -2 and -4.

3. Divide by 1: -2/1 and -4/1

4. The factors are (m – 2) and (m – 4)

Therefore, m² – 6m + 8 = (m – 2) (m – 4).

You can check your answers by distributing.

The equation would be y = 3x+2

Here's an explanation:

Let y represent the length of the baby flower in total, and let x represent the number of months that have passed. Since the flower grows at a rate of 3 inches every month, then for x number of months, it would grow 3 times x, which is 3x. The problem also tell us that the flower is already 2 inches tall, which now makes it 3x+2. So the total length is equal to 3x + 2 inches, so the equation would be y=3x+2

Answer:

Surface area of the fish tank [tex]332\ square\ feet[/tex]

Step-by-step explanation:

We have to find the surface area of the hospital tank.

As mentioned it does not have a cover.

The tank is in cuboid shape as it has different length [tex](l)[/tex],width [tex](w)[/tex] and height [tex](h)[/tex].

Surface area of a cuboid [tex]=2(lw+wh+hl)[/tex]

But here we have to subtract the surface area of the cover,that is [tex](lw)[/tex].

So the equation for the surface area of the cuboid can be re-framed as [tex]2(wh+hl)+(lw)[/tex]

Plugging the values of [tex]h=8\ ft[/tex] and [tex]l=12\ ft[/tex] and [tex]w=5\ ft[/tex]

Now

Surface area of the tank:

[tex]2(wh+hl)+(lw)[/tex]

[tex]2(5\times 8+8\times 12)+(12\times 5)[/tex]

[tex]2(40+96)+(60)[/tex]

[tex]2(136)+60[/tex]

[tex](272+60)=332\ ft^{2}[/tex]

So the surface area of the fish tank in the hospital is [tex]332\ ( ft)^{2}[/tex]

The value of x when y = -14 is 7

Step-by-step explanation:

Direct variation is a relationship between two variables that can

be expressed by an equation in which one variable is equal to a

constant times the other

If y varies directly with x, then

∵ y varies directly with x

∴ y ∝ x

∴ y = k x

To find k substitute x and y by their initial values

∵ y = 16 and x = -8

- Substitute y by 16 and x by -8 in the equation above

∴ 16 = k(-8)

- Divide both sides by -8

∴ -2 = k

∴ The value of k is -2

- Substitute the value of k in the equation above

∴ y = -2 x ⇒ equation of variation

∵ y = -14

- To find x substitute y by -14 in the equation of variation

∵ -14 = -2 x

- Divide both sides by -2

∴ 7 = x

∴  The value of x is 7

The value of x when y = -14 is 7

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The distance required for a speed 59 mph is 243.67 feet

Step-by-step explanation:

The direct variation is a relation ship between two quantities, the

ratio between them is constant

∵ The distance it takes stop a car varies directly at the square

   of the speed of the car

∴ d = k v², where d is the distance in feet and v is the speed in mph

∵ it takes 112 feet for a car traveling at 40 mph to stop

∴ d = 112 feet , v = 40 mph ⇒ initial values

- Substitute these values in the rule above to find k

∵ 112 = k (40)²

∴ 112 = 1600 k

- Divide both sides by 1600

∴ k = 0.07

∴ d = 0.07 v² ⇒ equation of variation

∵ The speed v = 59 mph

- To find the distance required for this speed substitute v in

   the equation of variation by 59

∵ d = 0.07 (59)²

∴ d = 243.67 feet

The distance required for a speed 59 mph is 243.67 feet

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Applying the direct variation formula between the speed and stopping distance of a car, we deduce that a car traveling at 59mph would require approximately 245 feet to stop.

In this problem, we use the relation that the distance it takes to stop a car varies directly with the square of the speed- this is an example of a direct variation. Given the initial condition we can establish an equation to relate the speed and the stopping distance: D = kV² where D represents the stopping distance, V is the speed, and k is a constant of variation.

First, we utilize the given information (D=112 feet and V=40 mph) to determine the constant k: 112 = k(40²), yielding k = 112/(40²) = 0.07. This factor remains constant for the car irrespective of its speed.

With the constant k determined, we then substitute V=59 and the constant k into our original equation to calculate the distance required to stop at this speed: D = 0.07*(59²), resulting in D approximately equal to 245 feet. Therefore, a car traveling at 59 mph would require approximately 245 feet to stop.

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Good evening ,

Answer:

35+7x = 63

Step-by-step explanation:

35+7x = 63

then 7x = 63 - 35

then 7x = 28

then x = 28/7

then x = 4.

:)

Answer:19.25

Step-by-step explanation:

Answer:

9⅝cm²

Step-by-step explanation:

So the formula is

A=1/2bh

A=1/2(5 1/2)(3 1/2)

Turn to improper so it'll be easier

A=1/2(11/2)(7/2)

A=11/4(7/2)

A=77/8

a=9 5/8 cm²

your welcome

Answer:

Step-by-step explanation:

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

Substitute the coordinates of the given points:

for A(3, 5) and B(-2, 6):

[tex]m_{AB}=\dfrac{6-5}{-2-3}=\dfrac{1}{-5}=-\dfrac{1}{5}[/tex]

for B(-2, 6) and C(-5, 7):

[tex]m_{BC}=\dfrac{7-6}{-5-(-2)}=\dfrac{1}{-5+2}=\dfrac{1}{-3}=-\dfrac{1}{3}[/tex]

[tex]\large\boxed{m_{AB}\neq m_{BC}}[/tex]

Answer:

12

Step-by-step explanation:

The perimeter of an equilateral triangle is 12 unit.

Let us consider that, each side of equilateral triangle is a . Because in equilateral triangle each sides are equal in length.

Apply Pythagoras theorem,

            [tex](2\sqrt{3} )^{2}+(\frac{a}{2} )^{2}=a^{2} \\\\12+\frac{a^{2} }{4} =a^{2}\\\\a^{2}-\frac{a^{2} }{4} =12\\\\\frac{3}{4}a^{2}=12\\\\a^{2}=16\\\\a=4[/tex]

 The perimeter of an equilateral triangle = [tex]3*a[/tex]

                                                                  = [tex]3*4=12unit[/tex]

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The calculated area of the bigger square is 22.5 square cm

How to determie the area of the larger square

From the question, we have the following parameters that can be used in our computation:

The square

Where, we have

Area of smaller square = 10 cm²

Using the above as a guide, we have the following:

Area of bigger square  = Area of smaller square * Scale factor²

In this case, we have

Scale factor = 1.5

Substitute the known values into the equation

Area of bigger square = 10 * 1.5²

Evaluate

Area of bigger square = 22.5

Hence, the area of the bigger square is 22.5 square cm

Answer: $7.50 per ticket

Step-by-step explanation: To solve this problem, we can rewrite the given statement using fractions.

All my work will be attached in the image provided.

to find out what will go in the blank, notice that we have a 1 in the denominator of our second fraction so we want to find a fraction that is equivalent to 37.50/5 that has a 1 in the denominator.

If we divide the numerator and the denominator of 37.50/5 by 5, we get the equivalent fraction 7.50/1 or $7.50 for 1 movie ticket.

This means that the unit rate for $37.50 for 5 movie tickets is $7.50 per ticket.

Answer:187.50 cents

Step-by-step explanation:37.50*5=187.5 so it would be 187.50 cents

Answer:

y = -1/3x + 8

Step-by-step explanation:

If two lines are perpendicular, the signs of the slope must be opposite and the slopes are reciprocals.

(basically if one is say -2/3, the other is 3/2. just flip it upside down)

So this slope is 3, so the new slope should be -1/3

The equation is now y = -1/3x + b

To find b, substitute (-9,5) in the equation

y = -1/3x + b

5 = -1/3(9) + b

5 = -3 + b

8 = b

So the equation is y = -1/3x + b

Answer:

y = -1/3x + 2

Step-by-step explanation:

I dont know who verified the other guy but he is wrong

Final answer:

The system of linear equations x + y = 75 and 10x + y = 48 is solved using the elimination method, resulting in the solution x = 3 and y = 72.

Explanation:

The student is given a system of two linear equations:

To solve this system, we can use the method of elimination or substitution. Here, elimination appears to be the more straightforward method. We'll subtract the second equation from the first to eliminate the variable y, as they both have the same coefficient in y. Subtracting the second equation from the first gives us:

9x = 27

Solving for x, we find:

x = 27 / 9 = 3

Now that we have the value for x, we can substitute it back into either of the original equations to find the value for y. Substituting into the first equation:

3 + y = 75 => y = 75 - 3 => y = 72

So the solution to the system is x = 3 and y = 72. This method remains effective even with the advent of computer algebra methods and Mathcad.

Answer: 9 cards

Step-by-step explanation:

x=27

3/9x = 1/3x = 27/3 = 9

Answer:

y=6x+22

Step-by-step explanation:

we know that the slope of a parrallel line is the same as the other line. so that gives us y=6x +b. to find b, x needs to equal 0, so to do that we must add 3 to x. we also need to add 3×6 to the y value of 4 to find the y intercept. therefore, the y intercept is 22

The slope of the given line is 6. The line parallel to this passing through the point (-3,4) would also have a slope of 6. Solving for y-intercept, we get the equation of the line as y = 6x + 22.

To find the equation of a line that is parallel to the given line and passes through a particular point, we need to use the fact that parallel lines have the same slope.

Given the equation y=6x-1, we can observe that the slope of this line is 6. As such, the line parallel to this one will also have a slope of 6.

Given the point (-3,4), the equation of the line parallel to the given line and passing through the indicated point in the form y=mx+c, where m is the slope and c is the y-intercept, can be found by substituting the x and y values from the point and the known slope m=6 into the equation to solve for c.

4 = 6*(-3) + c.

After solving, c = 22.

Therefore, our desired equation of the line is y = 6x + 22.

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Answer:

The difference between their weekly earning is $(1097.25 - 926.25) = $171.

Step-by-step explanation:

In 7 hours Bri has 13 clients and he earns $14.25 per client.

So, in 35 hours working in a week, Bri will get [tex]\frac{13 \times 35}{7} = 65[/tex] clients and he earns $(14.25 × 65) =$926.25 from his clients.

Again, in 5 hours Ali has 11 clients and he earns $14.25 per client.

So, in 35 hours working in a week, Bri will get [tex]\frac{11 \times 35}{5} = 77[/tex] clients and he earns $(14.25 × 77) =$1097.25 from his clients.

Therefore, the difference between their weekly earning is $(1097.25 - 926.25) = $171. (Answer)

$(1097.25 - 926.25) = $171  in 7 hours bri has 13 clients and he earns $14.25 per client in 5 hours ali has 11 clients and he earns $14.25 per client. the difference between their weekly earnings is 1097.25 - 926.25 = $171.

Answer:

The number of children's tickets sold was 27

Step-by-step explanation:

Let

x ----> the number of children's tickets sold

y ----> the number of adult's tickets sold

we know that

[tex]6.10x+9.40y=1,179.90[/tex] ----> equation A

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

Solve the system by substitution

Substitute equation B in equation A

[tex]6.10x+9.40(4x)=1,179.90[/tex]

solve for x

[tex]6.10x+37.6x=1,179.90[/tex]

[tex]43.7x=1,179.90[/tex]

[tex]x=27[/tex]

therefore

The number of children's tickets sold was 27

The coordinates of triangle ABC after translation according to given rule are:

A'(0,-2), B'(-1,-10) and C'(6,-4)

Step-by-step explanation:

Given vertices are:

A(-2, 1), B(-3, -7) and C(4, -1)

The translation rule is: (x,y) => (x+2, y-3)

In order to translate the vertices, 2 will be added to x-coordinate and 3 will be subtracted from y-coordinate

So,

A(-2, 1) =>  A' (-2+2, 1-3) => A'(0,-2)

B(-3,-7) = > B'(-3+2, -7-3) => B'(-1, -10)

C(4,-1) => C'(4+2, -1-3) => C' (6, -4)

Hence

The coordinates of triangle ABC after translation according to given rule are:

A'(0,-2), B'(-1,-10) and C'(6,-4)

Keywords: Triangle, Translation

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Answer:

Solution: [tex]x=-\frac{1}{5}[/tex],[tex]x=0[/tex]

Step-by-step explanation:

Given:

The rational equation to solve is given as:

[tex]\frac{x}{6}=\frac{x^2}{x-1}[/tex]

Doing cross product, we get:

[tex]x\times (x-1)=6\times x^2\\x^2-x=6x^2\\\textrm{Bringing all variables to the right side, we get:}\\6x^2-x^2+x=0\\5x^2+x=0\\x(5x+1)=0\\x=0\ or\ 5x+1=0\\x=0\ or\ x=-\frac{1}{5}[/tex]

Now, for [tex]x=0[/tex], the rational equation is equal to 0. So, [tex]x=0[/tex] is a solution.

Also, [tex]x=-\frac{1}{5}[/tex] is also a solution.

So, no extraneous solution.

Answer:

I don't know nan molla

Step-by-step explanation:

For example, Kino had a good opportunity to barely have a better life and he could have done anything to save his family but instead of doing that he refused to take the 1500 pesos.

Answer:

Neighborhoods that sheriff patrol in 5/8 of an hour is 3.125.

Step-by-step explanation:

The Time taken to patrol an entire neighborhood   = 3/ 15 hour

Total amount of time, the Sheriff  has to do patrolling = 5/ 8 of an hour.

Now, let us assume the total neighborhoods paroled in the given time  = m

So, [tex]\textrm{ Number of neighborhoods patrolled}  = \frac{\textrm{Total available time}}{\textrm{Time used in 1 paroling 1 neighborhood}}[/tex]

[tex]m = \frac{\frac{5}{8} }{\frac{3}{15} }   = {\frac{5}{8} \times {\frac{15}{3}  =3.125[/tex]

or, the number of neighborhoods covered  = 3.125

Hence, neighborhoods that sheriff patrol in 5/8 of an hour is 3.125.

To find out how many neighborhoods the sheriff can patrol in 5/8 of an hour, divide 5/8 by 3/15, which simplifies to 1/5. The calculation gives us 3.125, meaning the sheriff can complete 3 full neighborhood patrols.

The question involves determining how many neighborhoods a sheriff can patrol in 5/8 of an hour if it takes 3/15 of an hour to patrol one neighborhood. To solve this, we divide the total time available by the time it takes to patrol one neighborhood.

Thus, the sheriff can patrol 3 full neighborhoods in 5/8 of an hour, with some additional time remaining that is not enough to complete a fourth patrol.

Answer:

C) [tex]\sqrt[3]{2}[/tex]

It is C because [tex]\sqrt[3]{2}=1.2599[/tex] which is the closest to [tex]1\frac{1}{3}[/tex]. Because [tex]\frac{2^{2} }{3}=1\frac{1}{3}[/tex].

Answer:

C) Cube root of 2

Step-by-step explanation:

Answer:

the son had $20 and the father had $200

Step-by-step explanation:

20 x 10 = 200

200 + 20 = 220

Cant be 22, Ah, 20!

Because 20 Times 10 is 200, and you add the 20 and you get 220!

Answer: (x-3)(x+1)(x+7)

Step-by-step explanation:

Answer:D on edge :) (x+7)(x-3)(x+1)

Step-by-step explanation:did the test

Answer:

7 games

Step-by-step explanation:

First Person:

Fixed Cost of 99.26

Variable Cost of 4.50 per game (program cost)

Second Person:

No Fixed Cost

Variable cost of 18.68 per game (ticket cost)

Now, we let the number of games be "x", so we can write 2 equations for each person. Then we equate and find at what number of games, the amount paid by both person would be same. Shown below:

First Person Equation:

99.26 + 4.50x

Second Person Equation:

18.68x

Now, equate and solve for x:

99.26 + 4.50x = 18.68x

99.26 = 18.68x - 4.50x

99.26 = 14.18x

x = 99.26/14.18

x = 7

So, the answer is 7 games

Graph of |x| = 2 is two vertical lines symmetric about the y-axis, intersecting x-axis at (2, 0) and (-2, 0).

The equation |x| = 2 represents two parallel vertical lines symmetrically positioned about the y-axis. These lines intersect the x-axis at points (2, 0) and (-2, 0), indicating the absolute value of x being equal to 2. The graph exhibits symmetry with respect to the y-axis, forming a V-shape.

It conveys that any value of x, whether positive or negative, yielding an absolute value of 2 satisfies the equation. The graph emphasizes the notion that the distance of x from the origin is fixed at 2 units, illustrating a clear geometric representation of the absolute value function.

To convert grams to pounds, divide the weight in grams by 453.6. In this case, the weight of the box of cereal is 600 grams, which is approximately 1.32 pounds.

To convert grams to pounds, divide the weight in grams by 453.6. In this case, the weight of the box of cereal is 600 grams. So, 600 grams ÷ 453.6 = 1.3228 pounds. Therefore, the weight of the box of cereal is approximately 1.32 pounds.

The balance of student loan will be $3330 at the end of two year degree.

Step-by-step explanation:

Annual cost of tuition = $3750

As it is two year degree, therefore, total cost of tuition;

Total cost of tuition = 3750*2 = $7500

Annual scholarship = $1250

Annual grant = $835

Total = 1250 + 835 = $2085

As this is one year amount, she will get same the next year.

Total amount received in 2 years = 2085*2 = $4170

Balance in student loans = Total cost of tuition - Total amount received as grant and scholarship

Balance in student loan = [tex]7500-4170 =\$3330[/tex]

The balance of student loan will be $3330 at the end of two year degree.

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Answer:

The balance of student loan will be $3330 at the end of two year degree.

Step-by-step explanation:

Answer:

1. 18.74%

2. 33.34%

3. 45.5%

4. 20%

5. 33.11%

6. 16.38%

Step-by-step explanation:

1. For Shoes, the actual price is $79.99 and the selling price is $65.00.

The discount is [tex]\frac{79.99 - 65}{79.99} \times 100 = 18.74[/tex]%.

2. For 12 pack og golf balls, the actual price is $29.99 and the selling price is $19.99.

The discount is [tex]\frac{29.99 - 19.99}{29.99} \times 100 = 33.34[/tex]%.

3. For Exercise bike, the actual price is $1099 and the selling price is $599.

The discount is [tex]\frac{1099 - 599}{1099} \times 100 = 45.5[/tex]%.

4. For Basketball, the actual price is $49.99 and the selling price is $39.99.

The discount is [tex]\frac{49.99 - 39.99}{49.99} \times 100 = 20[/tex]%.

5. For Sports socks, the actual price is $14.95 and the selling price is $10.00.

The discount is [tex]\frac{14.95 - 10}{14.95} \times 100 = 33.11[/tex]%.

6. For Hockey sticks, the actual price is $299 and the selling price is $250.

The discount is [tex]\frac{299 - 250}{299} \times 100 = 16.38[/tex]%.