A community theater sold a total of 400 for price tickets for adults and children the price was $8.00 per adult to get in $5.00 per children’s ticket and the total revenue was $2750 how many adult tickets and how many Childers tickets were sold

The equation of line perpendicular to line containing points (-3, 4) and (1, 0) and passes through (-2, 6) in point slope form is y = x + 8

Given that line m contains points (-3, 4) and (1, 0)

We are asked to find the equation of line perpendicular to line containing points (-3, 4) and (1, 0) and passes through (-2, 6)

Let us first find slope of the line "m"

Given two points are (-3, 4) and (1, 0)

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

[tex]\left(x_{1}, y_{1}\right)=(-3,4) \text { and }\left(x_{2}, y_{2}\right)=(1,0)[/tex]

[tex]m=\frac{0-4}{1-(-3)}=-1[/tex]

Thus slope of line m is -1

We know that product of slope of given line and perpendicular line are always -1

So, we get

[tex]\begin{array}{l}{\text { slope of line } m \times \text { slope of perpendicular line }=-1} \\\\ {-1 \times \text { slope of perpendicular line }=-1} \\\\ {\text { slope of perpendicular line }=1}\end{array}[/tex]

So we have got the slope of perpendicular line is 1 and it passes through (-2, 6)

Let us use the point slope form to find the required equation

The point slope form is given as:

[tex]y - y_1 = m(x - x_1)[/tex]

[tex](x_1, y_1) = (-2, 6)[/tex] and m = 1

y - 6 = 1(x - (-2))

y - 6 = x + 2

y = x + 8

Thus equation of required line in point slope form is y = x + 8

Answer:

10 yards 2 inches

Step-by-step explanation:

To get the answer, you must subtract the amount of the smaller whale from the larger one:

Gray whale. 15 yards 5 inches

beluga whale. - 5 yards 3 inches

= 10 yards 2 inches

Answer:

the numbers are 20 and 30

Answer:

Plz show the picture that goes long with the question!

Step-by-step explanation:

Answer:

726

Step-by-step explanation:

39204/54=726

Answer:

5

Step-by-step explanation:

100 books, half of them are fiction. So 50 of them are fiction. There are 50 books remaining. 10% of them are animal books. What is 10% of 50?

Convert 10% to a decimal: .10

Multiply .10 by 50

.10×50=5

5 books are animal books.

The classroom library contains 5 animal books.

The percentage is defined as a ratio expressed as a fraction of 100.

Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions.

The operator that performs the arithmetic operations is called arithmetic operators.

* Multiplication operation: Multiplies values on either side of the operator

For example 4*2 = 8

/ Division operation: Divides left-hand operand by right-hand operand

For example 4/2 = 2

Given that the classroom library has 100 books.

And half of the books are fiction.

There are 50 books remaining and a tenth is about animals

So 10% of them are animal books.

To calculate 10% of 50 :

⇒ 10% of 50

⇒ 10%(50)

Convert 10% to a decimal,

⇒ 0.10×(50)

Multiply 0.10 by 50

⇒ 5

Hence, the classroom library contains 5 animal books.

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Answer:

Step-by-step explanation:

I think that's it could be wrong

there we go ;)

Answer:

height is 21cm and the base is 14cm

Step-by-step explanation:

Take a look at the equation for the area of a triangle [tex]A = \frac{bh}{2}[/tex]

Write "height of a triangle is 7 cm greater than the base" as an equation:

h = b + 7

Substitute h and the area of the triangle, 147 into the equation for area.

[tex]A = \frac{bh}{2}[/tex]

[tex]147 = \frac{b(b+7)}{2}[/tex] distribute over brackets

[tex]147 = \frac{b²+7b)}{2}[/tex]  get rid of fractions

[tex]147*2 = b²+7b[/tex]

[tex]294 = b²+7b[/tex]

Rearrange to standard for for quadratic equations

0 = b²+7b - 294

standard form is 0 = ax² + bx + c

In this base, the x variable is replaced by "b".

Use the quadratic formula to solve for b. Substitute the other three values.

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

[tex]x = \frac{-(7) ±\sqrt{7^{2}-4(1)(-294)} }{2(1)}[/tex] Simplify

[tex]x = \frac{-7 ±\sqrt{1225} }{2}[/tex]

[tex]x = \frac{-7 ±35 }{2}[/tex]

Split the equation at ±

[tex]x = \frac{-7 +35 }{2}[/tex]

[tex]x = \frac{28}{2}[/tex]

[tex]x = 14[/tex]  <=base

[tex]x = \frac{-7 -35 }{2}[/tex]

[tex]x = \frac{-42}{2}[/tex]

[tex]x = -21[/tex]  <=We know this number is not possible, so its inadmissible.

The base is 14 cm.

Substitute base = 14 in h = b + 7

h = b + 7

h = 14 + 7

h = 21

The height is 21cm.

Therefore, the height is 21cm and the base is 14cm.

Answer:

We have to choose any one from option B and option C

Step-by-step explanation:

We have to perform a subtraction of two decimal numbers.

(9.43 - 4.286) = (9.430 - 4.286) = 5.144.

Hence, the answer is 5.144 which is given both options B and C.  

In case there are two options with the same value and the value is the answer, then you choose any one of them but not both.

Here in our case, we have to choose any one from option B and option C and we will be rewarded full marks. (Answer)

Answer:

9 × 5= 45 .Frankie has 9 nickles.

Step-by-step explanation:

Because 5 divided by 45 equals to 9.

Answer:

Length of the garden = 69.28 meters.

Step-by-step explanation:

See the attached diagram.

Let CD is the pole with a height of 30 m and the elevation of the top of the pole from the endpoints of the length A and B are 60° and 30° respectively.

So, ∠ DAC = 60° and ∠ DBC = 30°  

Now, Δ ACD is a right triangle and [tex]\tan 60 = \frac{CD}{AC}[/tex]

⇒ [tex]AC = \frac{CD}{\tan 60} = \frac{30}{\tan 60} = 17.32[/tex] meters.

Now, from Δ BCD which is a right triangle, [tex]\tan 30 = \frac{CD}{CB}[/tex]

⇒ [tex]CB = \frac{30}{\tan 30} = 51.96[/tex] meters.

Hence, AB = AC + CB = 17.32 + 51.96 = 69.28 meters. (Answer)

Answer:

The length of the rectangle garden is 20 [tex]\sqrt{3}[/tex] i.e 34.64 meters .

Step-by-step explanation:

Given as :

The height of the pole = H = 30 m

The two angles of elevation as 60° and 30°

Let The length of the rectangle garden = L m

Now, From figure

The measure from pole ground to first elevation 60° = x m

The measure from pole ground to second elevation 30° = (L + x ) m

Now, from triangle BOC

Tan Ф = [tex]\dfrac{\textrm perpendicular}{\textrm base}[/tex]

I.e Tan 60° = [tex]\dfrac{\textrm 30}{\textrm x}[/tex]

Or, [tex]\sqrt{3}[/tex] = [tex]\dfrac{\textrm 30}{\textrm x}[/tex]

or, x = [tex]\frac{30}{\sqrt{3} }[/tex]

I.e x = 10[tex]\sqrt{3}[/tex] meter      ...1

Again From triangle BAC

Tan Ф = [tex]\dfrac{\textrm perpendicular}{\textrm base}[/tex]

I.e Tan 30° = [tex]\dfrac{\textrm 30}{\textrm L + x}[/tex]

Or, [tex]\frac{1}{\sqrt{3} }[/tex] = [tex]\dfrac{\textrm 30}{\textrm L + x}[/tex]

Or, L + x = 30 × [tex]\sqrt{3}[/tex]   ....2

Put the value of x from  1 into 2

i.e L + 10[tex]\sqrt{3}[/tex] meter   = 30 × [tex]\sqrt{3}[/tex]

or, L = 30 [tex]\sqrt{3}[/tex] - 10 [tex]\sqrt{3}[/tex]  

Or, L = 20 [tex]\sqrt{3}[/tex] = 34.64 meters

I.e length of garden is 20 [tex]\sqrt{3}[/tex]

Hence The length of the rectangle garden is 20 [tex]\sqrt{3}[/tex] i.e 34.64 meters . answer

Answer:

[tex]g(x)=1.5^{x}-4[/tex]

Step-by-step explanation:

Given:

The parent function is given as:

[tex]f(x)=1.5^{x}[/tex]

Let us consider a point on [tex]f(x)\ and\ g(x)[/tex] and compare their transformation.

The easiest point to consider is the y-intercept. At the y-intercept, the value of 'x' is 0.

The y-intercept of the function [tex]f(x)[/tex] is for [tex]x=0[/tex]. So,

[tex]f(0)=1.5^{0}=1[/tex]

The y-intercept of [tex]f(x)[/tex] is the point (0, 1).

Now, as per question, the transformed function [tex]g(x)[/tex] passes through the point (0, -3). Therefore,

The function [tex]g(x)[/tex] in the graph has the y-intercept equal to -3  as at y-intercept, the 'x' value is 0.

Therefore, the y-intercept of [tex]g(x)[/tex] is the point (0,-3).

Now, consider the transformation for the points (0, 1) and (0, -3).

[tex](0,1)\rightarrow (0,-3)[/tex]

Here, the 'x' value remains the same but the 'y' values decreases by 4 units. So, the rule will be:

[tex](x,y)\rightarrow (x,y-4)[/tex]

As per translation rules, if C units is added to 'y' value, then the graph moves up if 'C' is positive and moves down if 'C' is negative.

Also, the equation is of the form: [tex]g(x)=f(x)+C[/tex]

Here, [tex]C=-4[/tex].

Therefore, the graph shifts down by 4 units.

The equation of the function [tex]g(x)[/tex] is given as:

[tex]g(x)=f(x)+C=1.5^{x}-4[/tex]

Answer:

D

Step-by-step explanation:

Answer: About 32% of the average adult female body is made out of water.

Step-by-step explanation:

According to the data given in the exercise [tex]\frac{8}{25}[/tex] of the body of an average adult female is made out of water.

Then, you need to convert from fraction to percent. The steps are:

1. Divide the numerator of the fraction (In this case the numerator is  8) by the denominator of the fraction (In this case the denominator is 25). Then:

[tex]\frac{8}{25}=0.32[/tex]

2. Multiply the result 0.32 by 100:

[tex]0.32*100=32\%[/tex]

Therefore,  about 32% of the average adult female body is made out of water.

Answer:

x<8

Step-by-step explanation:

Open parenthesis first:

3x-6<18

Put all like terms on one side:

3x<18+6

3x<24

Simplify:

3x<24 -----> Divide both sides by 3 to cancel out the 3 in 3x.

x<8

~Stay golden~ :)

Answer: x<8

Step-by-step explanation:

3(x-2)<18

3x-6<18

+6 +6

3x<24

———-

3 3

x<8

Answer:

19 dimes and 9 nickels

Step-by-step explanation:

Model the situation using two equations, then solve the system.

let n be number of nickels and d be number of dimes.

n + d = 28     <= This equation is about the number of coins.

0.05n + 0.10d =  2.35   <=This equation is about the worth in dollars.

Rearrange n + d = 28.

n = 28 - d

Now we can substitute this equation into the other one.

Sub n =28-d at the "d" variable for the equation 0.05n + 0.10d =  2.35

0.05n + 0.10d =  2.35

Now there is only one variable.

0.05(28 - d) + 0.10d =  2.35   <=distribute this

0.05(28 - d) + 0.10d =  2.35

1.4 - 0.05d + 0.10d = 2.35   <=combine like terms

1.4 + 0.05d = 2.35    <= begin to isolate d

0.05d = 2.35 - 1.4

0.05d = 0.95

d = 0.95/0.05

d = 19

Now that we know d=19, we can substitute it into any equation.

Choose the equation n + d = 28 because the numbers are easier.

n + d = 28

n + 19 = 28    <=isolate n

n = 28 - 19

n = 9

Since n=9 and d=19, Kay has 9 nickels and 19 dimes.

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Write me here and I will give you my phone number - *pofsex.com*

My nickname - Lovely

Answer:

  y = 18

Step-by-step explanation:

Direct variation means y varies by the same factor x does. Here, x has changed by a factor of -6, so the new value of y is ...

  y = (-6)(-3) = 18

If y varies directly with x, and y = -3 when x = 1, the value of y when x = -6 is found using the formula y = kx. The value of y when x = -6 is 18.

In mathematics, if y varies directly with x, it means y = kx for some constant k. To find k, we substitute the given values of x and y into the equation, so -3 = k(1) gives k = -3.

Now that we have the value of k, we can find the value of y when x = -6. Substituting these values into our equation y = kx, we get y = -3*(-6), which simplifies to y = 18.

So when x = -6 and y varies directly with x, the value of y is 18.

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Answer:

I think it is 70.795% decrease

Hope that helps:)

I have a question for u

What is your fav?

Adrinette

LadyNoir

Marichat

Ladrien

Answer:

53/3

Step-by-step explanation:

1 5/6=11/6

3 1/6=19/6

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

11/6+5(19/6)=11/6+95/6=106/6

simplify

53/3

The algebraic equation for the line whose slope is m = 1 and passes through point (3 , 3) is y = x

Step-by-step explanation:

The algebraic equation of a line whose slope is m and passes

through point [tex](x_{1},y_{1})[/tex] is

∵ The slope of the line is m = 1

∵ The line passes through point (3 , 3)

∴ [tex]x_{1}[/tex] = 3

∴ [tex]y_{1}[/tex] = 3

- Substitute these values in the form of the equation

∵ [tex]y-y_{1}=m(x-x_{1})[/tex]

∴ y - 3 = (1)(x - 3)

- Simplify it

∴ y - 3 = x - 3

- Add 3 to both sides

∴ y = x

The algebraic equation for the line whose slope is m = 1 and passes through point (3 , 3) is y = x

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Answer:

The slope is 1

Step-by-step explanation:

Answer:

x= -9.3

Step-by-step explanation:

assuming i have to calculate x from the given equation that is

[tex]\frac{5}{6} of x= -8[/tex]

⇒[tex]5x= -48[/tex]

⇒x= -48/5= -9.3

therefore x= -9.3

Billy ate 1/6, Bob ate 1/4, and Buck ate 5/12 of the candies. To find the number of candies left, subtract the total fraction eaten from the total.

To find out how many candies were left, we need to subtract the candies that Billy, Bob, and Buck ate from the total number of candies in the bowl.

Billy ate 2/12 of the candies, which is equivalent to 1/6 of the candies because 2/12 can be simplified to 1/6.

Bob ate 3/12 of the candies, which is equivalent to 1/4 of the candies because 3/12 can be simplified to 1/4.

Buck ate 5/12 of the candies.

To find the total fraction of candies eaten, we add the fractions: 1/6 + 1/4 + 5/12. The common denominator for these fractions is 12.

Converting all the fractions to have a denominator of 12, we have: 2/12 + 3/12 + 5/12 = 10/12 = 5/6.

So, the three boys ate 5/6 of the candies.

To find the number of candies left, we subtract 5/6 from the total number of candies in the bowl:

120 - (5/6 * 120) = 120 - (5/6 * 120/1) = 120 - (5 * 120/6) = 120 - 100 = 20.

Therefore, there are 20 candies left in the bowl.

Answer:

you mean

[tex] - 7.2[/tex]

?

if so, then,

[tex] - 7.2 = - \frac{72}{10} [/tex]

[tex] - \frac{36}{5} [/tex]

...

Answer: y = 5x + 33

Step-by-step explanation:

y-2=5(x+7)

y-2 = 5*x + 35

y = 5x + 33

Answer: y = 5x + 33

Explanation:

First you must write the equation as you see it:

y-2=5(x+7)

Then do the math in side of the parentheses:

y-2 = 5*x + 35

Once you do the rest of the math, you shall have you answer:

y = 5x + 33

Hope this helps! :)

Answer:

The answer is given below.

Step-by-step explanation:

Alternate exterior angles: I is a pair of angles on the outer side of the each of two parallel lines but on opposite side of the transversal.

Vertically opposite angles: They are angles opposite each other when two lines intersect each other or cross each other.

Corresponding angles:  The angles which occupy the same relative position at each intersection where a transversal intersect the two parallel lines.

Same side interior angles: These are the angles between the parallel lines with the transversal.

Alternate interior angles: These are those angles that are alternate to each other and lie inside the parallel lines forming in Z shape.

Linear pair angles: It is a pair of adjacent angles formed by two intersecting lines

[tex]\angle 1\ and\ \angle 6:\ \textrm{alternate exterior angles}\\\angle 1\ and\ \angle 3:\ \textrm{Vertical opposite angles}\\\angle 3\ and\ \angle 6:\ \textrm{corresponding angles}\\\angle 4\ and\ \angle 8:\ \textrm{same side interior angles}\\\angle 4\ and\ \angle 5:\ \textrm{alternate interior angles}\\\angle 5\ and\ \angle 6:\ \textrm{linear pair angles}[/tex]

Answer:

A

Step-by-step explanation:

A

Step-by-step explanation:

Paolo's expression 3(x+2)+3

Final answer:

To find how much light is transmitted through two screens that each transmit 18% of the light, multiply 18% by itself (0.18 x 0.18), which results in 3.24% of the original light being transmitted through both screens.

To determine how much light is transmitted through two light-blocking screens, we need to calculate the percentage of light that makes it through both screens. The first screen transmits 18% of the light. This means that only 18% of the initial light intensity will pass through the first screen.

When the light that has passed through the first screen encounters the second screen, again only 18% of that light will be transmitted. To find the total amount of light transmitted through two screens, we multiply the transmission rates of each screen:

Transmitted light through two screens = 18% of initial light * 18% = (0.18) * (0.18)

To get the final percentage, we multiply those two percentages:

Final transmission percentage = 0.18 * 0.18 = 0.0324 or 3.24%

Therefore, only 3.24% of the initial light is transmitted through two screens.

The area of the room that is not covered by the rug is: [tex]21x^3+26x^2-24x+9[/tex]

Step-by-step explanation:

Let L be the length of the room

and

W be the width of the room

Then

L = 3x^2

W = 7x+14

Area of the bedroom:

[tex]A_r = L*W\\=3x^2(7x+14)\\=21x^3+42x^2[/tex]

Area of Rug:

Let S be the side of rug

S = 4x+3

[tex]A_{rug} =S^2\\=(4x+3)^2\\=(4x)^2+2(4x)(3)+(3)^2\\=16x^2+24x+9[/tex]

The area of the room that is not covered by the rug will be obtained by subtracting the area of the rug from the area of the room.

So,

[tex]Area\ of\ room\ not\ covered\ by\ rug =A_r - A_{rug}\\= 21x^3+42x^2-(16x^2+24x+9)\\=21x^3+42x^2-16x^2-24x-9\\=21x^3+26x^2-24x+9[/tex]

Hence,

The area of the room that is not covered by the rug is: [tex]21x^3+26x^2-24x+9[/tex]

Keywords: Rectangle, square

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Answer:

The measure of larger angle is 180°

Step-by-step explanation:

Given as :

For the pentagon

The measure of interior angles are

∠A = x ,

∠B = x ,

∠C = 2 x ,

∠D = 2 x ,

∠E = 3 x

We know, The sum of measure of all interior angles of pentagon = 540°

So, x + x + 2 x + 2 x + 3 x =   540°

or, 9 x =  540°

∴  x = [tex]\frac{540}{9}[/tex]

I.e x = 60°

So, The measure of angles are

∠A =  60°  ,

∠B =  60° ,

∠C = 2 ×  60° = 120° ,

∠D = 2 ×  60° = 120°,

∠E = 3  ×  60° = 180°

So, the measure of larger angle is 180°

Hence The measure of larger angle is 180° Answer

Check the picture below.

Answer:

11 Test Packets

Step-by-step explanation:

151-30=121/11=11

The teacher purchased 11 packets of tests for the math competition.

The question is about calculating the number of test packets Andrew's teacher purchased for the math competition. We know that there was a basic enrollment fee of $30, and each packet of 10 tests cost an additional $11. The total cost was $151. To find out how many test packets the teacher purchased, the first step is to subtract the enrollment fee from the total amount spent. Therefore, $151 - $30 = $121 was spent on test packets.

Then, we divide this amount by the cost of each test packet. So $121/$11 gives us 11. Hence, the teacher purchased 11 packets of tests for Andrew's math competition.

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