The drama club is selling tickets to their play to raise money for the show's expenses. Each student ticket sells for $4 and each adult ticket sells for $8. There was a total of $640 in revenue from the sale of 100 total tickets. Graphically solve a system of equations in order to determine the number of student tickets sold, x, and the number of adult tickets sold, y.

Check out the diagram below.

Since D and E are midpoints of AB and AC this means midsegment DE is parallel to side BC. Furthermore, it means DE is parallel to PQ because PQ is entirely on BC.

---------

Note how I drew a line from A to O. This forms two triangles ABO and ACO

For triangle ABO, segment DP is a midsegment because D and P are midpoints of AB and OB respectively. This means side DP is parallel to side AO. Keep this in mind as we'll use it later.

For triangle ACO, segment EQ is parallel to AO because EQ is a midsegment for similar reasons as already mentioned (E and Q are midpoints of AC and OC respectively). So this must mean that AO is parallel to EQ

Now chain the arguments together: if DP || AO and AO || EQ, then DP || EQ by the transitive property.

-----------

In short, we've proven two things

This is enough to conclude that DEQP is a parallelogram. By definition, a parallelogram has two pairs of opposite parallel sides.

Answer:

Points

Step-by-step explanation:

Hey there!

A geometric sequence is where we use multiplication or division to get to the next term.

In this case, we use multiplication (we multiply every term by 3)

So we have

-1, -3, -9, -27, -81, -243...

Steps:

Hope everything is clear.

Let me know if you have any questions; if oyu do, kindly comment below my answer.

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[tex]\rule{200}{2}[/tex]

Answer:

A total of four people

Step-by-step explanation:

Answer:

4

Step-by-step explanation

divide 19.24 from 76.96.

and that gives you how many friends

Answer:

i guess 3 rd option is correct. ........hope it helps u ♥♥♥♥

Given -

x² + 4x + 1 = -3

To find -

the discriminant for the quadratic equation and to find how many real number solutions does the equation have. If it's discriminant = b² - 4ac

Concept applied -

As we know, Discriminant = b² - 4ac

A quadratic equation ax²+ bx + c = 0 has -

Solution -

Solving the quadratic equation to bring it in the form of ax² + bx + c = 0,

➛ x² + 4x + 1 = -3

➛ x² + 4x +3 + 1 = 0

➛ x² + 4x + 4 = 0

Here,

a = 1, b = 4 and c = 4.

Putting the values in the the formula, b²- 4ac = 0.

➙ (4)²- 4(1)(4)

➙ 16- 16

➙ 0

As, b²- 4ac = 0 hence the quadratic equation will have two equal roots (i.e., coincident roots).

Answer:

1 aka b

Step-by-step explanation:

Answer:

.99 cents. i think but for a pAck two dollars

Step-by-step explanation:

internet

Answer:

.99 cents. i think but for a pack two dollars

Step-by-step explanation:

Answer:

Find the appropriate form for your objective function Then you will describe which solvers can handle complex then, you pass the extra Parameters finally, the function argument details.

Answer:

3x+15+10

3x + 25

Step-by-step explanation:

Answer:

3x + 25

Step-by-step explanation:

Answer:

615.44 mm²

Step-by-step explanation:

Before finding the area of the circle, first, let us find the radius of the circle.

Given that,

diameter ⇒ 28 mm

Therefore,

28 = 2r

Divide both sides by 2.

14mm = radius

And now, let us find the area.

The formula to find the area of the circle is :

Let us solve now.

Area = π r²

        = 3.14 × 14 × 14

        = 43.96 × 14

        = 615.44 mm²

Answer:

Today: Sunday, 11 October 2020

Hour: 22.20 WIB (Indonesian)

_________________________

D = 14 cm

π = 3,142

Circumference = π × D

Circumference = 3,142 × 14

Circumference = 43.988 cm

Answer:

2:3 = 66%

Step-by-step explanation:

⇒ Convert the fraction 2/3 into decimal

⇒ 2/3 = 0.666

⇒ Multiply the decimal by 100: 0.66 × 100 = 66%

Therefore, the solution is 66%.

According to the graph, it is found that the percent of apartment residents who pay less than $700 per month is given by:

B. 75%

It states that:

Hence, for less than $700, we have that:

5% + 25% + 45% = 75%.

Thus option B is correct.

More can be learned about percentages at https://brainly.com/question/10491646

Answer:

10:  112.5

12:  84

13:  T F T

14:  F T T

15:  T F T

Answer:

9x^5*y^2*pi

Step-by-step explanation:

a = pi * r^2

a = pi * 9x^5y^2

a = 9x^5y^2pi

Let me know if you have questions or need help

Answer: y= 1/3x + 41

Answer:

[tex]_{\text{point-slope form}}[/tex]

[tex]\huge\boxed{y-5=\dfrac{1}{3}(x+12)}[/tex]

[tex]_{\text{slope-intercept form}}[/tex]

[tex]\huge\boxed{y=\dfrac{1}{3}x+9}[/tex]

[tex]_{\text{standard form}}[/tex]

[tex]\huge\boxed{x-3y=-27}[/tex]

Step-by-step explanation:

The point-slope form of an equation of a line:

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

where

[tex]m[/tex] - slope

[tex](x_1;\ y_1)[/tex] - a point on a line

We have

[tex]m=\dfrac{1}{3};\ (-12;\ 5)\to x_1=-12;\ y_1=5[/tex]

Substitute:

[tex]y-5=\dfrac{1}{3}(x-(-12))\\\\y-5=\dfrac{1}{3}(x+12)\\==================[/tex]

[tex]y-5=\dfrac{1}{3}(x+12)\qquad|\text{use the distributive property}\ a(b+c)=ab+ac\\\\y-5=\dfrac{1}{3}x+4\qquad|\text{add 5 to both sides}\\\\y=\dfrac{1}{3}x+9\\=======================[/tex]

[tex]y=\dfrac{1}{3}x+9\qquad|\text{multiply both sides by 3}\\\\3y=x+27\qquad|\text{subtract}\ x\ \text{from both sides}\\\\-x+3y=27\qquad|\text{change the signs}\\\\x-3y=-27[/tex]

Answer:125x^6y^6 (Red)

Step-by-step explanation: To find the answer we need to do first 5^3 which is 125. Then according to exponent rule, we multiply the exponents inside by the exponent outside, so it would be x^6 and y^6.

It would be 125x^6y^6.

Hope this helps you!

Answer:

50 ounces

Step-by-step explanation:

hope it helps you

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thanks

Answer:

3

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

For example, the absolute value of 3 is 3, and the absolute value of −3 is also 3. The absolute value of a number may be thought of as its distance from zero.

Hope this helps and good luck!

please give me brainliest!

The total percent discount offered by the merchant is 57.12%.

A discount is when the price of an items is reduced. It makes a good cheaper when a discount is applied.

The percent change in price after the first discount = 100% - 32% = 68%

The final price after the second discount = (100 - 16%) x 68%

= 57.12%

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Answer:

70%

Step-by-step explanation:

[tex]42\div60[/tex]

Calculate

[tex]\frac{42}{60}[/tex]

Cross out the common factor

[tex]\frac{7}{10}[/tex]

Multiply a number to both the numerator and the denominator

[tex]\frac{7}{10}\times\frac{10}{10}[/tex]

Write as a single fraction

[tex]\frac{7\times10}{10\times10}[/tex]

Calculate the product or quotient

[tex]\frac{70}{10\times10}[/tex]

Calculate the product or quotient

[tex]\frac{70}{100}[/tex]

Rewrite a fraction with denominator equals 100 to a percentage

[tex]70[/tex]%

I hope this helps you

:)

Answer:

8

Step-by-step explanation:

if a = -b, then -a = b.

plug that into the (b = -c) problem, and you get -a = -c, or a = c

if a and c ar equal, then and b = -c, b also equals -a.

the problem then becomes a - b +c, where a = 8, c = 8, and b = -8

a = -b -> 8 = -(-8)

b = -c -> -8 = -(8)

a = c -> 8 = 8

The expression for the area of the base is x² – 2x – 9. Therefore, the correct answer is (C) x² – 2x – 9.

To use synthetic division, we first need to set up the divisor in the correct form. Since we are looking for the expression for the area of the base of the rectangular prism, we know that the volume of the prism is given by:

volume = (area of base) × (height)

We are given that the height is x + 4, and the volume is x³ + 2x² – 17x – 36. Therefore, we can write:

x³ + 2x² – 17x – 36 = (area of base) × (x + 4)

Now we can use synthetic division to find the expression for the area of the base. The divisor is x + 4, so we write:

-4  | 1 2 -17 -36

    |   -4   8 36

    |-----------------

      1 -2 -9 0

The last number in the bottom row is 0, which means that x + 4 is a factor of the polynomial. The other numbers in the bottom row give us the coefficients of the quotient polynomial. Therefore, we can write:

x³ + 2x² – 17x – 36 = (x + 4)(x² – 2x – 9)

So the expression for the area of the base is x² – 2x – 9. Therefore, the correct answer is (C) x² – 2x – 9.

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Answer:

1 yard is 3 feet. There is 36 inches in a yard. There is 12 inches in a foot. Multiply 36 by 10 to get 360. There is 360 inches in 10 yards.

Step-by-step explanation:

Hope this helps! :)

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Answer:

Step-by-step explanation:

AC = length of flagpole = 12 ft

AB = length of shadow = 14 ft

BC = length from the top of the flagpole to the end of the shadow = x ft

Use Pythagorean theorem to find the length of x,

x² = AC² + BC²

   = 12² + 14²

  = 144 + 196

  = 340

x = √340

x = 18.4 ft

Answer:

3x - 4y + 8 = 0

Step-by-step explanation:

In figure,

When x = 0, y = 2

x = 4, y = 5

Two points on the line are (0, 2) & (4,5).

Slope = (5 - 2)/(4 - 0)= 3/4

Equation is:

=> y - 2 = (3/4)(x - 0)

=> y - 2 = 3x/4

=> 4y - 8 = 3x

=> 3x - 4y + 8 = 0

Answer:

(1,2), (2,4) (2.5,5) (3,6) (4,8) (5,10) (6,12) (15,30)

Step-by-step explanation:

2.5/2.5 = 1

5/2.5 = 2

(1,2), (2,4) (2.5,5) (3,6) (4,8) (5,10) (6,12) (15,30)

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Answer:

y = 3x - 20

Step-by-step explanation:

First, we have to find the slope of the equation. We can do by taking the opposite reciprocal of the slope of the original line.

The opposite reciprocal of-1/3 is 3/1 or 3.

So, the slope of our equation will be 3. Our equation so far is:

y = 3x + b.

To find b, or the y-intercept of the line, we can simply substitute the given coordinates into the equation. If we replace x with 6 and y with -2 and solve the equation, we can find the value of b.

-2 = 3(6) + b

-2 = 18 + b

-2 - 18 = b

b = -20

So the equation is,

y = 3x -20.

To check our equation, we can again substitute the coordinates into the equation and solve. If both sides are equal, then the equation is correct.

-2 = 6(3) - 20

-2 = 18 - 20

-2 = -2

The two lines are perpendicular if a 90° angle is formed when they

intersect.

The equation of the line that passes through point Z(6, -2) and is perpendicular to the line [tex]y = -\dfrac{1}{3} \cdot x + 2[/tex] is ; y = 3·x - 20

Reason:

The equation of the required line is, y = 3·x - 20

The given point is Z(6, -2)

Perpendicular to the line, [tex]y = -\dfrac{1}{3} \cdot x + 2[/tex]

Solution:

The slope of a line perpendicular to another line having a slope, m, is [tex]-\dfrac{1}{m}[/tex]

The slope of the given line is [tex]-\dfrac{1}{3}[/tex]

The slope of the perpendicular line is therefore;

[tex]m = -\dfrac{1}{\left(-\dfrac{1}{3}\right)} = \dfrac{3}{1} = 3[/tex]

The point and slope form of the equation of the given line is therefore;

y - (-2) = 3·(x - 6)

y + 2 = 3·x - 3×6 = 3·x - 18

y = 3·x - 18 - 2 = 3·x - 20

y = 3·x - 20

The equation of the line that passes through point Z(6, -2) and is perpendicular to the line [tex]y = -\dfrac{1}{3} \cdot x + 2[/tex] is therefore;

y = 3·x - 20

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