Adult tickets to the fall play cost 6 and student tickets cost 3 . The drama class sold 25 more student tickets than adult tickets to the fall play. If the class collected 660 from ticket sales, how many student tickets were sold?

By graphing both functions, we will see that there are two intersections at (-1.41, -2.12) and (3.28, 7.27).

Here we must solve:

[tex]2^x - 2.5 = 2x + 0.7[/tex]

To do it, we can graph the functions:

[tex]y = 2^x - 2.5\\\\y = 2x + 0.7[/tex]

And see where do the curves intersect.

The graph can be seen below, in there we can see two intersections.

One at (-1.41, -2.12) and (3.28, 7.27).

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8π is the circumference

Answer: 1, 2, 5

Step-by-step explanation:

The first equation is true because angles in a triangle add to 180 degrees.

The second equation is true because both sides equal 180 degrees (left hand side is a straight angle, right hand side is the sum of angles in a triangle)

The third equation is not true because z = 180 - y, and 180-y+w+z is not 180.

The fourth equation is not true because z=180-y, and 180-y=w+y is not always true.

The fifth equation is true by the exterior angle theorem.

a = amount invested at 7%

b = amount invested at 9%

we know the amount invested was ₹36000, thus we know that whatever "a" and "b" are, a + b = 36000.  We can also say that

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{7\% of a}}{\left( \cfrac{7}{100} \right)a}\implies 0.07a~\hfill \stackrel{\textit{9\% of b}}{\left( \cfrac{7}{100} \right)b}\implies 0.09b[/tex]

since we know the interest earned from the invested was ₹2920, then we say that 0.07a + 0.09b = 2920.

[tex]\begin{cases} a + b = 36000\\\\ 0.07a+0.09b=2920 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{using the 1st equation}}{a + b = 36000\implies \underline{b = 36000-a}}~\hfill \stackrel{\textit{substituting on the 2nd equation}}{0.07a~~ + ~~0.09(\underline{36000-a})~~ = ~~2920} \\\\\\ 0.07a+3240-0.09a=2920\implies 3240-0.02a=2920\implies -0.02a=-320 \\\\\\ a=\cfrac{-320}{-0.02}\implies \boxed{a=16000}~\hfill \boxed{\stackrel{36000~~ - ~~16000}{20000=b}}[/tex]

Answer:

6

Step-by-step explanation:

8 * 3/4 = 24/4  = 6 WATER BOTTLES

Answer:

The student is incorrect and for parallelograms to be equal, included angles between them too should be equal.Explanation:When two quadrilaterals MNOP=TQRS, then not only all corresponding sides are equal, all corresponding angles too are equal.As MNOP and TQRS are parallelograms their diagonals bisect each other. And as MO=TR and NP=QS, it is apparent (see figure below) that MX=XO=TY=YR and NX=XP=SY=YQ. And hence two sides of all the four triangles (in each of the parallelogram) are equal.However, the angles included between the two diagonals can change (as is seen from the figure below),and hence MNOP≠TQRS

Step-by-step explanation:

Answer: [tex]\frac{- 1}{11}[/tex]

Step-by-step explanation:

Note: the "." symbol stands for multiplication

Given,

[tex]\frac{2x+4}{3} \\[/tex]  - [tex]\frac{5x-7}{2}[/tex] = 5

First we the LCM = 6,

[tex]\frac{2(2x+4)}{2.3}[/tex] - [tex]\frac{3(5x-7)}{3.2}[/tex]= 5

Then, we join both sides, since they have same denominator

[tex]\frac{2(2x+4) - 3(5x-7)}{6}[/tex] = 5

Multiply again

[tex]\frac{4x+8 - 15x+21}{6}[/tex] = 5

Add the same numbers

[tex]\frac{-11x + 29}{6}[/tex] = 5

Transpose 6 to the other side

-11x + 29 = 5.6

-11x + 29 = 30

Transpose 29 to the other side

-11x = 30 -29

-11x = 1

Transpose 11 to the other side to get answer

x = [tex]\frac{-1}{11}[/tex]

Hope it helps! If you have any doubts, feel free to ask

The area of the shaded triangular section of the stained glass window is  72 square inches.

The first step is to determine the dimensions of each rectangle that makes up the  stained glass window.

Length of one rectangle = length of the window / number of rectangles along the length

36/4 = 9 inches

Width of one rectangle = width of the window / number of rectangles along the width

48/3 = 16 inches

Area of the shaded triangular section = 1/2 x area of one rectangle

1/2 ( length x width)

1/2 x (16 x 9) = 72 square inches.

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Answer:

144

Step-by-step explanation:

i took the test

Answer: $10.24

Step-by-step explanation: 12.95 * 0.15 = 1.94    12.95 - 1.94 = 11.01

11.01 * 0.07 = .77      11.01 - 0.77 = 10.24

Answer:

114 feet

Step-by-step explanation:

To figure out the perimeter, we also need the width

The width can be found by dividing the area by the length

800/32 = 25

to find the perimeter, we use the equation 2L + 2W = P

L is the length

W is the width

2(32) + 2(25) = 64 + 50 = 114

114 feet is the perimeter

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Step-by-step explanation:

[tex]\frac{1-\sin ^2\left(x\right)}{1+\sin \left(x\right)}=1-\frac{1}{\csc \left(x\right)}[/tex]

[tex]\frac{1-\sin ^2\left(x\right)}{1+\sin \left(x\right)}[/tex]

[tex]=1-\sin \left(x\right)[/tex]

⇒ [tex]\sin \left(x\right)=\frac{1}{\csc \left(x\right)}[/tex]

[tex]=1-\frac{1}{\csc \left(x\right)}[/tex]

Answer:

Addition. Add 80 + 10 so

Step-by-step explanation:

Answer:

6.96

Step-by-step explanation:

2.9 x 1.5 = 4.35

3.3 - 1.5 = 1.8

1.8 x 2.9 = 5.22

5.22 divided by 2 = 2.61

4.35 + 2.61 = 6.96

The difference of the two polynomials is 7x² + 11x. The correct option is the second option, 7x² + 11x

From the question, we are to determine the difference of the two polynomials

The given operation is

(9x²+8x) - (2x²+3x)

First, remove the brackets and collect like terms

That is,

9x²+ 8x - 2x² + 3x

9x² - 2x²+ 8x + 3x

Simplifying, we get

7x² + 11x

Hence, the difference of the two polynomials is 7x² + 11x. The correct option is the second option, 7x² + 11x

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Here is the complete and correct question:

What is the difference of the two polynomials? (9x2 + 8x) – (2x2 + 3x)
7x2 + 5x

7x2 + 11x

11x2 + 5x

11x2 + 11x

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To solve this formula, we can simply use the formula of half-life of a radioactive substance to calculate the decay rate.

The disintegration constant or decay rate is calculated as 0.385min^-1

The half-life of a radioactive substance is defined as the time taken for the initial mass of the substance to reach half it's starting mass.

The formula is given as

[tex]T_\frac{1}{2} = \frac{\ln2}{\lambda}[/tex]

Let's substitute the value into the equation and solve through

[tex]T_\frac{1}{2} = \frac{\ln2}{\lambda} \\\lambda = \frac{\ln2}{T_\frac{1}{2} } \\\lambda = \frac{0.693}{1.8} \\\lambda = 0.385[/tex]

The disintegration constant or decay rate is calculated as 0.385min^-1

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The inequality expression of the given word problem statement is;

t² - 3 ≤ 46

We are told that two numbers labelled t² and 3 have a difference that is at most 46.

Now, when we say at most, it means less than or equal to symbol.

Thus, the expression of the given statement is; t² - 3 ≤ 46

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Answer:

  16 feet

Step-by-step explanation:

The geometry of the problem can be modeled by a right triangle. The Pythagorean theorem tells us the relationship between the various distances.

  EH² +HF² = EF²

  EH² + 12² = 20²

  EH² = 400 -144

  EH = √256 = 16

The hook is 16 feet below Edna.

Answer:

8 feet

Step-by-step explanation:

Answer:

The Sum of supplementary angles is 180.

Therefore, <A + <B = 180

<A = 19<B

19<B + <B = 180

20<B = 180

<B = 9°

& <A = 19×9°

<A = 171°

The equation of a function f(x) =  x² -4x -12 in the vertex form is f(x) = (x -2)² -16 and the value of the a = 1, h = 2, and k = -16

Any equation of the form [tex]\rm ax^2+bx+c=0[/tex]  Where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

We have a quadratic equation:

f(x) =  x² -4x -12

f(x) =  x² -4x -12 + 4 -4

f(x) = (x -2)² -16

Here a = 1, h = 2, and k = -16

Thus, the equation of a function f(x) =  x² -4x -12 in the vertex form is f(x) = (x -2)² -16 and the value of the a = 1, h = 2, and k = -16

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The highlighted part is known as the center of the circle. Then the correct option is C.

It is a locus of a point drawn an equidistant from the center. The distance from the center to the circumference is called the radius of the circle.

Identify the highlighted part of circle O shown below.

The mid-point of the diameter is known as the center of the circle.

The highlighted part is known as the center of the circle.

Thus, the correct option is C.

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Answer:

−3k+6y

Step-by-step explanation:

Apply the distributive property.

5(2y)+5 (−3k)+4(3k−y)

Multiply 2 by 5.

10y+5(-3k)+4(3k−y)

Multiply −3 by 5.

10y−15k+4(3k−y)

Apply the distributive property.

10y−15k+4(3k)+4(−y)

Multiply :3 by 4

10y−15k+12k+4(−y)

Multiply: −1 by 4

10y−15k+12k−4y

Simplify by adding terms.

Subtract: 4y from 10y

−15k+12k+6y

Add: −15k and 12k

−3k+6y

Answer:

The mean hourly snowfall is 2.5 centimeters

Step-by-step explanation:

The mean hourly snowfall is the number of centimeters that fell during the period divided by the number of hours.

From 5 P.M. to 9 P.M., there are 4 hours

At 5 P.M., the total snowfall is 2 centimeters.

At 9 P.M., the total snowfall is 12 centimeters.

So in those four hours, the depth of snow increases 12-2 = 10 centimeters

10/4 = 2.5

The mean hourly snowfall is 2.5 centimeters

Answer:

The baker needs 82 boxes.

Step-by-step explanation:

326/4=81 r 2.

But, you have to fit in all the cupcakes, so you round ir up to 82.

A can is an example of a cylinder, and the volume of a cylinder is πr^2 x h. The diameter is 4, and the radius is half of a diameter so the radius is 2. The volume is π x 2^2 x 6 = 75.3982236862

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Answer:

78%

Step-by-step explanation:

a percentage is equivalent to a number over 100.

43% is 43/100

72% is 72/100

87% is 87/100

etc.

to find the percentage of students who said their favorite color is red, we need to set up a cross-multiplication equation

390/500 = ?/100

390 times 100 is 39000

39000/500 = 78

78% of the students said their favorite color is red

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