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taurus [48]
3 years ago
14

Thomas was selling tickets to his school play. The tickets cost $5.00 for adults and $2.00 for children. He sold 200 tickets and

collected $610. Which system represents the number of adult and child tickets that Thomas sold?
Mathematics
2 answers:
IRISSAK [1]3 years ago
8 0

Answer:

70, 130

Step-by-step explanation:

natta225 [31]3 years ago
4 0
Adult: $5, qty x
children: $2, qty y
total: $610, qty 200

Cost:      5x + 2y = 610
Quantity:  x +   y = 200

Using elimination method to solve the system of equations:
 1(5x + 2y = 610) →  5x + 2y = 610
-2( x  +  y  = 200) → -2x - 2y = -400
 Add both equations: 3x + 0  = 210
 Divide both sides by 3: x = 70

Substitute "x = 70" into either the Cost or Quantity equation: 
Quantity: x + y = 200 → 70 + y = 200 → y = 130

Adult tickets sold = 70
Children tickets sold = 130

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You are building a shelf that fits in a corner. In the figure, the entire shelf is △XYZ. Each unit in the coordinate plane repre
natima [27]

Complete Question: You are building a shelf that fits in a corner in the figure the entire shelf is XYZ each unit in the coordinate plane represents one inch find the area of the shelf.

Answer:

112.5 units²

Step-by-step explanation:

Area of the shelf = ½*base*height.

The base is the distance between Z(0, 5) and Y(15, 5)

The height is the distance between X(15, 20) and Y(15, 5).

Therefore area of the shelf = ½*ZY*XY

Use the distance formula to find ZY and XY.

Distance between Z(0, 5) and Y(15, 5):

ZY = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

Let,

Z(0, 5) = (x_1, y_1)

Y(15, 5) = (x_2, y_2)

ZY = \sqrt{(15 - 0)^2 + (5 - 5)^2}

AB = \sqrt{(15)^2 + (0)^2}

AB = \sqrt{225 + 0} = \sqrt{225}

AB = 15

Distance between X(15, 20) and Y(15, 5):

XY = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

Let,

X(15, 20) = (x_1, y_1)

Y(15, 5) = (x_2, y_2)

XY = \sqrt{(15 - 15)^2 + (5 - 20)^2}

XY = \sqrt{(0)^2 + (-15)^2}

XY = \sqrt{0 + 225} = \sqrt{225}

XY = 15

Area of shelf = ½*15*15 = ½*225 = 112.5 units²

4 0
3 years ago
Which pair of numbers is relatively prime? A. 42 and 77 B. 34 and 55 C. 45 and 102 D. 99 and 123
leonid [27]

Two pair of numbers are said to be relatively prime if there is no integer greater than 1, that divides them both.

Consider the given pair of the numbers to identify which pair is relatively prime.

1. Consider 42 and 77

7 is the number which divides 42 and 77 both. Therefore, they are not relatively prime.

2. Consider 34 and 55

Since, there is no number greater than 1, which divides both the numbers. So, they are relatively prime numbers.

3. Consider 45 and 102

3 is the number divides 45 and 102 both. Therefore, they are not relatively prime.

4.  Consider 99 and 123

3 is the number divides 99 and 123 both. Therefore, they are not relatively prime.

Therefore, Option B is the correct answer.

8 0
3 years ago
Find the distance between the two points. Round to the nearest tenth, if necessary. (Point 1 is at (-5,2) and point 2 is at (3,-
aivan3 [116]

Answer:

d = 9.4

Step-by-step explanation:

d=\sqrt{(3-(-5))^2 +(-3-2)^2\\

d=\sqrt{(8)^2+(-5)^2}

d=\sqrt{64+25}

d=\sqrt{89

d=9.4

3 0
3 years ago
Write the equation of the parabola in vertex form.<br><br><br>Vertex: (−4,6); Point: (−2,−2)
gtnhenbr [62]

Answer:

y = - 2(x + 4)² + 6

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Here (h, k ) = (- 4, 6 ) , thus

y = a(x - (- 4) )² + 6 , that is

y = a(x + 4)² + 6

To find a substitute (- 2, - 2) into the equation

- 2 = a(- 2 + 4)² + 6 ( subtract 6 from both sides )

- 8 = a(2)² = 4a ( divide both sides by 4 )

- 2 = a , thus

y = - 2(x + 4)² + 6 ← equation in vertex form

5 0
3 years ago
F(t) = -2t + 5 f() = 13
fomenos

Answer:

I don't know what the question is but...

Step-by-step explanation:

-2t+5-13= -2t-8

-2t+5+13=-2t+18

-2t+5*13= -2t+65

-2t+5/13= -26t-5/13

8 0
3 years ago
Read 2 more answers
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