The drama club is selling tickets to their play to raise money for the show's expenses. Each student ticket sells for $6 and each adult ticket sells for $9. There was a total of $747 in revenue from the sale of 98 total tickets. Write a system of equations that could be used to determine the number of student tickets sold and the number of adult tickets sold. Define the variables that you use to write the system.

Answer:

[tex]13\frac{1}{8}[/tex]

Step-by-step explanation:

Given expression:

[tex]\left(-5 \frac{5}{8}\right) \cdot \left(-2 \frac{1}{3} \right)[/tex]

Convert the mixed numbers into improper fractions by multiplying the whole number by the denominator, adding it to the numerator of the fraction, and placing this as the numerator:

[tex]\implies -\dfrac{5 \cdot 8+5}{8} \cdot -\dfrac{2 \cdot 3+1}{3}[/tex]

[tex]\implies -\dfrac{40+5}{8} \cdot -\dfrac{6+1}{3}[/tex]

[tex]\implies -\dfrac{45}{8} \cdot -\dfrac{7}{3}[/tex]

[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{b} \cdot \dfrac{c}{d}=\dfrac{a \cdot c}{b \cdot d}:[/tex]

[tex]\implies \dfrac{-45 \cdot -7}{8 \cdot 3}[/tex]

[tex]\implies \dfrac{315}{24}[/tex]

Convert the improper fraction into a mixed number:

[tex]\implies 315 \div 24 = 13\: \text{r}\:3[/tex]

[tex]\implies 13\frac{3}{24}[/tex]

[tex]\implies 13\frac{1}{8}[/tex]

Answer:

Product = 13 1/8

Step-by-step explanation:

The equation is,

→ (-5 5/8) × (-2 1/3)

Now the product of equation will be,

→ (-5 5/8) × (-2 1/3)

→ (-45/8) × (-7/3)

→ (-15 × -7)/8

→ 105/8

→ 13 1/8 {mixed fraction}

Therefore, the product is 13 1/8.

Answer:

3796 length of the box

Step-by-step explanation:4,238-26×17=3,796

Answer: 209 square inches, 182 cubic inches

Step-by-step explanation:

The lateral surface area is the sum of the areas each of the four faces.

The area of one face is [tex](1/2)(11)(9.5)[/tex]. Multiplying this by 4, we get 209 square inches.

To find the volume, we use the formula [tex]V=\frac{1}{3}Bh[/tex]. This gives us that the volume is [tex](1/3)[(1/2)(11)(11)](9)[/tex], or about 182 cubic inches.

By using the method of division,  circle=20 , triangle= 35.

One of the four fundamental mathematical operations, along with addition, subtraction, and multiplication, is division. Division is the process of dividing a larger group into smaller groups so that each group contains an equal number of things. It is a mathematical operation used for equal distribution and equal grouping. In this post, let's study more about the division operation in math. One of the fundamental mathematical operations is division, which involves breaking a bigger number into smaller groups with the same number of components.

Given that,

The circles are 3

Which have the total of 60.

So, the total value divided by total number of circles.

60/3= 20

20 is the value of each circle.

The triangles are 2 including one circle

Which have the total of 90

90 - 20(circle)= 70

So, the total value divided by total number of triangles.

70/2= 35.

35 is the value of each triangle.

Therefore, circle=20 , triangle= 35

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Answer:

B) x ≥ –2 or x < 5

Step-by-step explanation:

We can immediately rule out A) All real numbers, since that will almost never be true for an inequality like this. We can also rule out C) 2 ≤ x < 5, since this is not a compound inequality.

Let's see if B) x ≥ –2 or x < 5 works by plugging in an x value greater than -2 and then, plugging in an x value less than 5.

Plug -1 into x

–4(-1) + 1 ≤ 9

4 + 1 ≤ 9

Combine like terms

5 ≤ 9

This is true, 5 is less than 9, so x ≥ –2 works.

Plug 4 into x

4∕5 + 2 < 3

Combine like terms

2.8 < 3

This is true, 2.8 is less than 3.

It can't be D) no solution now that B works, so B) x ≥ –2 or x < 5 is your answer.

Take care and Have a lovely rest of your day! :)

The expressions can be simplified as follows-

1. (9 − 3) 2− (5 • 4)0 = 12

2. (2 + 3)5 ÷ (5 × 2)2 = 5/4

3. 4 × 2 ÷ (6 − 2)4 = 1/2

4. [(1 + 7) 2] 2• (12 2 )0 = 0

Let us look at each expression one by one-

1. (9 − 3) 2− (5 • 4)0

Zero multiplied by any number is 0 itself. Thus, the expression becomes-

= (9 - 3) 2

= 6 × 2

= 12

2. (2 + 3)5 ÷ (5 × 2)2

According to the rules of BODMAS, we first solve the brackets-

(5)5 ÷ (10)2

= 25 ÷ 20

= 25/20

= 5/4

3. 4 × 2 ÷ (6 − 2)4

= 4 × 2 ÷ (4)4

= 8 ÷ (4)4

= 8/16

= 1/2

4. [(1 + 7) 2] 2• (12 2 )0

= [(8)2]2• 0

= 0

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Answer:

Option A

Step-by-step explanation:

When adjacent sides and angle between the adjacent sides are given, then,

 [tex]\sf \boxed{\text{\bf Area of Parallelogram = a*b * $Sin \ \theta$}}[/tex]

Here, a and b are the adjacent sides and [tex]\sf \theta[/tex] is the angle between them.

a = 16 cm ;  b = 30 cm ; [tex]\sf \theta = 45^\circ[/tex]

Area of parallelogram =  16 * 30 * Sin 45

                                     [tex]\sf = 16 * 30 * \dfrac{\sqrt{2}}{2}\\\\= 8*30*\sqrt{2}\\\\= 240\sqrt{2} \ sq.cm[/tex]

Answer:

  (b)  √(4x+2)√(25x-4)

Step-by-step explanation:

Given two functions f(x) = √(4x+2) and g(x) = √(25x-4), you want the function fg.

The product fg is a bit of shorthand notation:

  [tex]fg = fg(x) = f(x)\cdot g(x)[/tex]

Substituting the given function definitions, we have ...

  [tex]f(x)\cdot g(x) = \sqrt{4x+2}\cdot\sqrt{25x-4}[/tex]

The product of the radicals could be combined into one radical, but that has not been done in your answer choices. This means ...

  [tex]\boxed{fg=(\sqrt{4x+2})(\sqrt{25x-4})}[/tex]

Using the continuity concept, the functions are classified as follows:

1) Continuous.

2) Continuous.

3) Discontinuous.

A function f(x) is continuous at x = a if it is defined at x = a, and:

[tex]\lim_{x \rightarrow a^-} f(x) = \lim_{x \rightarrow a^+} f(x) = f(a)[/tex]

For functions 1 and 2, the functions are given by simple definitions, hence they are continuous, the limits and the numeric value will al be equal.

In item 3, the function will be discontinuous. This is because the function [x] returns the greatest integer less than x, hence:

Thus:

Due to different lateral limits, the function is not continuous at x = 2.

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By solving a system of equations, we can see that each geranium costs 3 dollars.

First, let's define the two variables:

x = price of one rose bush.

y = price of one geranium

Now, with the information on the problem we can write two equations, thus, we will have a system of equations:

$122 = 14*x + 8*y

$120 = 12*x + 12*y

We want to solve that system, if we isolate x on the first equation we will get:

x = ($122 - 8y)/14

Now we can replace this on the other equation:

$120 = 12*($122 - 8y)/14 + 12*y

Now we can solve this for y.

14*$120 = 12*($122 - 8y) + 12*14*y

$1,680 = $1,464 + 72y

($1,680 - $1,464 )/72 = y = $3

Each geranium costs 3 dollars.

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The two expressions to represent the perimeter of this rectangle include the following:

An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.

Mathematically, the perimeter of a rectangle can be calculated by using this formula;

P = 2(L + W)

Where:

Substituting the given variables into the given expression, we have;

P = 2(2x + 6 + x)    ......expression 1.

For the second expression, we have:

P = 2(2x + 6 + x)

P = 2(3x + 6)        ......expression 2.

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Complete Question:

The length of a rectangle is 2x+6 and the width is x. Write two expressions to represent the perimeter.

Answer:

the answer is the 3rd to the 4th power and

The end behavior of the polynomial y=-4x+8x-21'+3 is y = -4x^3.

Degree of a polynomial is the highest power that its terms pertain (for multi-variables, the power of term is addition of power of variables in that term).

Thus, in the degree of the polynomial is 3 as the highest power in its terms is 3.

(power and exponent are same thing)

We are given that;

The functions (a) 1=3x-2x+12

(b) 1-10-8.x2

(c) y=6r-4r+x-120

(d) y=-3x+2x-4x+7

(e) y=5x+2x2

(f) y=-4x+8x-21'+3

Now,

To find the power function that best represents the end behavior of a polynomial, we need to look at the leading term (the term with the highest degree) of the polynomial.

(a) The leading term of this polynomial is 3x. So the power function that best represents its end behavior is y = 3x.

(b) The leading term of this polynomial is -8x^2. So the power function that best represents its end behavior is y = -8x^2.

(c) The leading term of this polynomial is 6r. So the power function that best represents its end behavior is y = 6r.

(d) The leading term of this polynomial is -3x^3. So the power function that best represents its end behavior is y = -3x^3.

(e) The leading term of this polynomial is 2x^2. So the power function that best represents its end behavior is y = 2x^2.

(f) The leading term of this polynomial is -4x^3. So the power function that best represents its end behavior is y = -4x^3.

Therefore, by polynomials the answer will be y = -4x^3.

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Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

There were 61 youth tickets sold and 34 general admission tickets in linear equation .

What in mathematics is a linear equation?

GA= GENERAL ADMISSION =$10

Y= YOUTH =$8

GA+Y= 95

GA=95-Y

10GA+8Y=828

10(95-Y)+8Y=828

950-10Y+8Y=828

-2Y= 122 MULTIPLY BY (-1)

2Y= 122

Y= 61

GA= 34

There were 61 youth tickets sold and 34 general admission tickets.

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Answer:

$78 700

Step-by-step explanation:

Four time periods   year 2 3 4 and 5

50 000 ( 1.12 )^4  =  50 000 ( 1.574) = 78700

           ( 1.574 is from the table for 12 % and 4 periods )

The expected foot length of an adult male who is 1.8 m tall is 30.8 cm.

Based on the information given, Jerry surveyed adult males to study the relationship between their high and the length of their footwear both are measured in centimeters and he found the equation y equals 75 + 3.4 x.

This will be illustrated as:

y = 75 + 3.4x..

y = 1.8m = 180

Therefore, y = 75 + 3.4x.

180= 75 + 3.4x

180 = 75 + 3.4x

Collect like terms

3.4x = 180 - 75

3.4x = 105.

Divide

x = 105 / 3.4

x = 30.8 cm

Therefore, the expected foot length of an adult male who is 1.8 m tall is 30.8 cm.

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From the given numbers :

Integers: -50,000,000

Rational numbers : -1/2 and -1.5

Real numbers : −√5 , -1/2, -50, 000, 000 , -1.5.

As given,

Given numbers:

A. −√5 :It is an irrational number.

Therefore belongs to real numbers.

B. -1/2 :In p/q form .

It is a rational and real number.

C. -50,000,000

It is a negative integer and real number.

D. -1.5 =-15 /10

          =3/2

It is a rational and real number.

Therefore, from the given numbers :

Integers: -50,000,000

Rational numbers : -1/2 and -1.5

Real numbers : −√5 , -1/2, -50, 000, 000 , -1.5.

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Answer:

Step-by-step explanation:

Answer:

4×9=36

1-3=-2

36÷2=18

Step-by-step explanation:

4×+1,9×-1.

4×9=36

1-3=-2

The missing values are x = 45, t = 90, n = 60, p = 75, m = 30, s = 15, k = 135, w = 30, f = 60 and y = 45.

Herein we have a geometrical system formed by six triangles, one of them is a equilateral triangle and other one is a right triangle. By geometry we know that the sum of the measures of a triangle is equal to 180°, the angles in a equilateral triangle have the same measure and one of the angles in a right triangle is a right angle.

Then, we have following system of linear equations:

t = 90                              (1)

t + 2 · x = 180                  (2)

3 · n = 180                       (3)

2 · p + m = 180                (4)

p + f + y = 180                 (5)

(t + 5) + w + n = 180        (6)

s + k + m = 180                (7)

x + n + p = 180                (8)

f + w = 90                        (9)

m + n = 90                      (10)

p + s = 90                        (11)

By (1) and (2):

x = 45

By (3):

n = 60

By (8):

p = 180 - 45 - 60

p = 75

By (4):

m = 180 - 2 · 75

m = 30

By (11):

s = 90 - 75

s = 15

By (7):

k = 180 - 15 - 30

k = 135

By (6) and (1):

w = 180 - 60 - 90

w = 30

By (9):

f = 90 - 30

f = 60

By (5):

y = 180 - 75 - 60

y = 45

The missing values are x = 45, t = 90, n = 60, p = 75, m = 30, s = 15, k = 135, w = 30, f = 60 and y = 45.

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Answer:

post a pic, OP, to get specific answer

Step-by-step explanation:

You can use any two points, usually uppercase letters, that are on the line, in any order. Also, lines are named with a single script or italicized lowercase letter that is written beside one end of the line. See image for example.

Answer:

Aisha is ten years old and Mpho is seven

The age of Aisha is 10 years old and the age of Mpho is 7 years old.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Aisha is three years older than Mpho. Together their ages add up to 17 years.

Let x be the age of Aisha and y be the age of Mpho. Then the equations are given as,

x = y + 3               ...1

x + y = 17             ...2

From equations 1 and 2, then we have

y + 3 + y = 17

2y = 14

y = 7

Then the value of 'x' is given as,

x = 7 + 3

x = 10

The age of Aisha is 10 years old and the age of Mpho is 7 years old.

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Answer: $ 6.50 per liter of petrol rose

Step-by-step explanation:

Answer:

[tex]1. \;\;y = \dfrac{1}{3}x - 1\\\\2.\;\;y = -\dfrac{2}{5}x\\\\3.\;\;y = x + 8[/tex]

Step-by-step explanation:

The slope intercept form equation is y = mx + b

where m = slope and b = y-intercept

So for each case, substitute for slope(m) and y-intercept(b)

Answer:

1.  y = 1/3x + (-1)

2. y = -2/5x

3. y = 1x + 8 = 1x + 8 or  y = x + 8

Step-by-step explanation:

1. First of all, we need to know the slope-intercept form. The formula is y = mx + b. M represent the slope and b represents the y-intercept. So the question asked for the slope-intercept form for the slope that is 1/3 and the interception of -1. So we need figure out how to write it. It asked for -1/3 and -1 and we use the formal y = mx + b and it'll help us on figuring out how to write it. So far we have y = 1/3x + b, b is the intercept. The intercept would be -1. So the way we'd right it out is y = 1/3x + (-1). But first you have to multiply the + with -1. When we would multiply the signs you do it like this: (+) (+) = + and (-) multiplied by (-) is +. As well as (-) multiplied by (+) is -.

So for 1 the slope would be 1/3 and the (0, -1) . But we have to write it in the given form: y = mx + b ... m = slope, b = y intercept. So the way we'd right it is y = mx + b and m = slope, b = y intercept. Therefore the answer for this one is y = 1/3x - 1.

2. First we should know that we have the slope of -2/5 and the y-intercept is 0. The right form for this is y = -2/5x +. So for this one we got y = -2/5x because we said that the first one is 1/3 and -1. As well as the second is -2/5 and 0. The third is 1 and 8 as we wrote it earlier. So that's how we got our answer y = -2/5x for this question. Therefore our answer to this question is y = -2/5x.

3. For this one we first know slope = 1 and intercept =8. This equation is easier than both number 1 and 2 all we need to do is just put every given number in the right place. So we'll need to write the y as it is then add the = sign. Then write the slope which is given above. Then we have to write the x. We'll need to add the + sign and write the intercept given above next to it. After doing these steps you we'd have the answer because this is the general formula. So we would write 1 instead of m and the intercept is 8 so you need to write it instead of b. Therefore our answer would be y = 1x + 8 = 1x + 8 or another way we could write it is  y = x + 8 either way would be correct.

I hope this helps, have a blessed day! :)

The real court is 9 by 18 meters in length and width.

The length of something is its width or size measured across its entire surface. Or, to put it another way, it is the larger of a geometric shape's higher two or three dimensions.

This statement implies that the court's original dimensions have been reduced by 22.5 for every 1 centimeter in the size of the current drawing, which is 40 cm by 80 cm. To get the original dimension, we will multiply the required dimension by each 22.5 cm as shown. Original length for a 40-cm length = 40 * 22.5 originally 900 cm long 100 cm equals one meter in metres. Multiply 900cm by x to get 9m: 100x = 900*1x = 900/100x Therefore, 900cm = 9m For the 80-cm width: Original width is equal to 80 * 22.5, or 1800 cm. 100 cm equals one meter in metres. multiplying 1800cm by x yields 100x, 1800*1, 1800/100x, and 18m. So 1800cm = 9m. As a result, the real court is 9 meters long and 18 meters wide.

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a The absolute value of ax will be considered while for the second the absolute value of ax + b will be considered.

b The absolute value of ax will be considered while for the second the absolute value of ax + b will be considered.

Given data

a, b, c, and x be real numbers.

|ax| + b = c

The equation here contains the modulus sign only for ax hence only the absolute value of ax is considered.

|ax + b| = c

Here the modulus sign covers both ax and b hence the absolute values  of ax + b is considered.

|ax| + b ≤ c

The equation here contains the modulus sign only for ax hence only the absolute value of ax is considered.

|ax + b| ≥  c

Here the modulus sign covers both ax and b hence the absolute values  of ax + b is considered.

Note that absolute values do not consider the signs

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Answer: ABD=67 degrees

CBD=67 degrees

ABC=134 degrees

Step-by-step explanation:

ABC=ABD+CBD

25x+34=ABD+11x+23

14x+34=ABD+23

ABD=14x+11

ABD=CBD ==> Bisected angles are equal to each other since angle ABC is divided into two equal angles when bisected.

14x+11=11x+23

3x+11=23

3x=12

x=4

ABD=14x+11

ABD=14(4)+11

ABD=56+11

ABD=67 degrees

CBD=11x+23

CBD=11(4)+23

CBD=44+23

CBD=67 degrees

ABC=25x+34

ABC=25(4)+34

ABC=100+34

ABC=134 degrees

Answer:

∠ ABD = 67° , ∠ CBD = 67° , ∠ ABC = 134°

Step-by-step explanation:

since BD bisects ∠ ABC , then

∠ ABD = ∠ CBD = 11x + 23

∠ ABC = ∠ ABD + ∠ CBD ( substitute values )

25x + 34 = 11x + 23 + 11x + 23

25x + 34 = 22x + 46 ( subtract 22x from both sides )

3x + 34 = 46 ( subtract 34 from both sides )

3x = 12 ( divide both sides by 3 )

x = 4

Then

∠ ABD = 11x + 23 = 11(4) + 23 = 44 + 23 = 67°

∠ CBD = ∠ ABD = 67°

∠ ABC = 25x + 34 = 25(4) + 34 = 100 + 34 = 134°