A total of 937 people attend the play. Admission was $2.00 for adults and $0.75 for students. The totral ticket sales amounted to $1,109. How many students and adults attended the school play? - Applying Linear Systems in the Real World

Given:

Two chords intersect each other inside the circle.

To find:

The value of x.

Solution:

According to intersecting chords theorem, if two chords intersect each other inside the circle, then the product of two segments of one chord is equal to  the product of two segments of second chord.

In the given circle,

[tex]AE\times CE=BE\times DE[/tex]

[tex](3x-11)\times (5x-4)=(x+2)\times (-x+17)[/tex]

[tex]15x^2-12x-55x+44=-x^2+17x-2x+34[/tex]

[tex]15x^2-67x+44+x^2-15x-34=0[/tex]

[tex]16x^2-82x+10=0[/tex]

Divide both sides by 2.

[tex]8x^2-41x+5=0[/tex]

Splitting the middle term, we get

[tex]8x^2-40x-x+5=0[/tex]

[tex]8x(x-5)-1(x-5)=0[/tex]

[tex](8x-1)(x-5)=0[/tex]

Using zero product property, we get

[tex](8x-1)=0[/tex] or [tex](x-5)=0[/tex]

[tex]x=\dfrac{1}{8}[/tex] or [tex]x=5[/tex]

For [tex]x=\dfrac{1}{8}[/tex], the side AE is negative. So, [tex]x=\dfrac{1}{8}[/tex] is not possible.

Therefore, the required solution is [tex]x=5[/tex].

Answer:

4.  3 units

5. Triangle  

6.  (0,2)

Step-by-step explanation:

4. The distance between the x axis and the point (8,3) is 3 units

5. Triangle  will be formed if the points A(-3, 0), B (0,3) and C (3,0) are joined together

6. Since the point lie on the y-axis, its x co-ordinate will be zero and the point will be (0,2)

Answer:

12

Step-by-step explanation:

Since they are parallel then

(7x - 8) + (11x - 28) = 180

18x - 36 = 180

18x = 216

x = 12

Answer:

jennifer won 15 time and mark won 24

if the answer is wrong i am really sorry

Answer:

70 degrees

Step-by-step explanation:

It's a whole 540 degrees

So y = 70 degrees

Answer:   I think it is A or C

hope this helps!

Step-by-step explanation:

Answer:

where is the Venn diagram plz insert Venn diagram then I should solve

Answer:

I think it is 2 points for this .

Answer:

Step-by-step explanation:

8(1 + 2i) -  (7 - 3i) = 8*1 + 8*2i + 7*(-1) - 3i*(-1)

                          = 8 + 16i -7 + 3i

                          = 8 - 7 + 16i + 3i

                          = 1 + 19i

Daniel forgot to multiply 2i by 8

Answer:

A , He did not apply the distributive property correctly for 8(1 + 2i).

on edge

Step-by-step explanation:

Step-by-step explanation:

the lines on the graph of inequality second option

Answer:

9x20 = 180

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Answer:

C. -7 or C. Negative seven

Answer:

HCF X LCM= product of two numbers

14 x 840 = 42 x other number

other number= 14x840/42=280

Answer:

No solution is possible

Step-by-step explanation:

You didn't indicate the number of adults and children.

Answer:

(4,5)

Step-by-step explanation:

Hi there!

We are given the system of equations:

5x+2y=30

-5x+4y=0

and we need to find the solution

there are 3 ways to solve a system of equations, but let's use the elimination method, where we will add the systems together to clear one variable out, solve for the other variable, and use the value of the solved variable to find the other variable

When we clear a variable, the coefficients need to be opposites (ex. 2 and -2). In this case, the coefficients in front of x are 5 and -5 in the first and second equation respectively

5x+2y=30

-5x+4y=0

add the equations together

6y=30

divide both sides by 6

y=5

we found the value of y

now we need to find the value of x

substitute 5 as y into either one of the equations (ex. the first one) to solve for x

5x+2(5)=30

multiply

5x+10=30

subtract 10 from both sides

5x=20

divide both sides by 5

x=4

so the answer is x=4, y=5; as a point, it's (4,5)

Hope this helps! :)

The probability that the last one is not an orange if you do not replace the first and second fruits will be equal to 0.054.

Probability is calculated as the proportion of favorable events to all potential scenarios of an event. The proportion of positive results, or x, for an experiment with 'n' outcomes can be expressed.

As per the given information in the question,

The total number of fruits as per the data is,

4 apples + 6 pear + 3 oranges + 9 peaches = 21 fruits.

As per the statement, the first fruit is from 21 fruits.

There are 3 apples, so the probability will be,

3/21 = 1/7

The second fruit is from 20 fruits,

21 - 1 = 20

There are 9 peaches, so the probability will be,

9/20

The third fruit is from 19 fruits, so there are 16,

19 - 3 = 16

These fit the bill (not oranges), so the probability will be,

16/19.

So,

1/7 × 9/20 × 16/19

= 36/665

= 0.054

To know more about Probability:

https://brainly.in/question/54143022

#SPJ2

Answer:

27.3

Step-by-step explanation:

3.9 x 7

=>(4 - 0.1) x 7 (USING DISTRIBUTIVE PROPERTY)

=>28 - 0.7

=>27.3

Answer:

W'(10/3, 6), X'(4, 16/3), Y'(-4, 2) and Z'(2/3, -8/3)

Step-by-step explanation:

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, dilation and translation.

If a point A(x, y) is dilated by a scale factor of k, the new point is A'(kx, ky). If a point A(x, y) is reflected over line y = x, the new point is A'(y, x).

Given the vertices W(-3,5), X(8,6),  Y(3,-6), and Z(-4,1). If it is dilated by a scale factor of 2/3, the new point is at W*(-6, 10/3), X*(16/3, 4), Y*(2, -4) and Z*(-8/3, 2/3). If it is then reflected over the line y = x, the new point is W'(10/3, 6), X'(4, 16/3), Y'(-4, 2) and Z'(2/3, -8/3).

Answer:

THE ANSWER IS 54

Step-by-step explanation:

Answer:

After buying the meal and the computer game, Kristian has 43.33% of his money left.

Step-by-step explanation:

Given that Kristian buys a meal for $ 8.40, to calculate the fraction of the $ 72 after buying the computer game which cost $ 32.40 and the meal, the following calculation must be performed:

72 = 100

8.40 + 32.40 = X

72 = 100

40.80 = X

40.80 x 100/72 = X

4,080 / 72 = X

56.66 = X

100 - 56.66 = 43,333

Therefore, after buying the meal and the computer game, Kristian has 43.33% of his money left.

Answer:

4×4=16

Step-by-step explanation:

four squared is a two dimension polygon with a four equal side of four length unit.

Answer:

4×4=16

Step-by-step explanation:

B. |y| = 1.6

A sketch of the vector is attached to this response.

As shown, the vector lies on the second quadrant and its horizontal and vertical components are given by x and y respectively.

Where;

|x| = v cos θ              -----------------(i)

|y| = v sin θ               -----------------(ii)

and

v = magnitude of the vector = 2.5km/hr

θ = angle that the vector makes with the +x axis = 90° + 50° = 140°

To get the magnitude of the vector's vertical component

Substitute these values into equation(ii) as follows;

|y| = 2.5 sin 140°

|y| =  2.5 x 0.6428

|y| = 1.607

|y| ≅ 1.6 km/hr

Therefore, the vertical component of the vector has a magnitude of 1.6 km/hr.

Answer:

B. 1690.5 million VND

Step-by-step explanation:

Half of the perimeter of a rectangular piece of land is equal to 21 m

The full perimeter of the Land = 2 × 21m

= 42 m

Step 1

Find the Length and Width of the rectangle

Perimeter of a rectangle = 2L + 2W

Length is twice its width.

L = 2W

Hence:

42 = 2(2W ) + 2W

42 = 4W + 2W

42 = 6W

W = 42/6

W = Width = 7m

L = Length = 2W

L = 2 × 7

L = 14m

Step 2

Find the Area of the Land

Area of the rectangle = Length × Width

= 14m × 7m

= 98m²

Step 3

Given that 1 m² of the piece of land

costs 17.25 million VND. If someone wants to buy it, he or she has to

pay:

1m² = 17.25 million VND

98m² = x

Cross Multiply

1 m² × x = 98m² × 17.25 million VND

x = 1690.5 million VND

Option B is the correct answer

Answer:

[tex] V_{cone} = 4000\pi \: {cm}^{3} [/tex]

Step-by-step explanation:

Height of the cone (h) = 30 cm

Radius of the cone (r) = 20 cm

[tex]V_{cone} = \frac{1}{3} \pi {r}^{2} h \\ \\ = \frac{1}{3} \pi \: {(20)}^{2} (30) \\ \\ = \pi(400)(10) \\ \\ V_{cone} = 4000\pi \: {cm}^{3} [/tex]

Answer:

It would be 4 or C.

Step-by-step explanation:

Hope this helps!

Good Luck!

:)

Answer:

36

Step-by-step explanation:

9/16 = 20.25/?

16x20.25÷9= 36