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Sphinxa [80]
3 years ago
8

Callie and Madison went to buy concert tickets for themselves and their five friends. The

Mathematics
1 answer:
nika2105 [10]3 years ago
5 0

Answer:

They bought 0 ticket of closest section and 7 tickets of other section

Step-by-step explanation:

- Callie and Madison went to buy concert tickets for themselves and

  their five friends

- That mean they are 7

- Tickets for the closest section were $45 each

- Tickets for other section were $30 each

- They  ended up spending a total of $210

- Assume that they buy x tickets for closest section and y tickets for

 the other section

∵ They want 7 tickets

∴ x + y = 7 ⇒ (1)

∵ The cost of the closest section ticket was $45

∵ The cost of the other section ticket was $30

∵ They spent $210 on them

∴ 45x + 30y = 210

- All terms have common factor 15, then divide them by 15

∴ 3x + 2y = 14 ⇒ (2)

* Now we have a system of equations to solve

- Multiply equation (1) by -2 to eliminate y

∴ -2x - 2y = -14 ⇒ (3)

- Add equations (2) and (3)

∴ x = 0

- substitute the value of x in equation (1) to find y

∴ 0 + y = 7

∴ y = 7

∵ x represents the number of tickets of the closest section and y

  represents the number of tickets in the other section

∴ They bought 0 ticket of closest section and 7 tickets of other

   section

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Two exponential functions are shown in the table. A 3-column table has 5 rows. The first column is labeled x with entries 2, 1,
DanielleElmas [232]

Answer:

B. The functions f(x) and g(x) are reflections over the y-axis.

Step-by-step explanation:

From the information given the table appears as;

x            f(x)=2^x              g(x)=0.5^x

2               4                            0.25

1                 2                           0.5

0                1                             1

-1                0.5                         2

-2               0.25                       4

Plotting the two graphs to view the trends;

In the graph of f(x)=2^x against x you notice a curve with increasing positive slope.

In the graph of g(x)=0.5^x against x you notice a curve with a negative slope that is increasing.

In combining both graphs you notice that f(x) and g(x) are reflections over the y-axis.

Correct answer is ;The functions f(x) and g(x) are reflections over the y-axis.

9 0
3 years ago
A rectangle has its base on the x axis and its upper two vertices on the parabola y = 9 − x2. (a) Draw a graph of this problem.
gtnhenbr [62]

Answer:

  • (a) see attached
  • (b) width: 2x; height: y = 9-x²
  • (c) A=2x(9-x²) . . . 0 ≤ x ≤ 3
  • (d) dA/dx = -6x² +18; x=±√3
  • (e) 12√3 units²

Step-by-step explanation:

(a) The attachment shows the graph of the parabola in blue. It also shows an inscribed rectangle in black.

(b) The upper right point of the rectangle is shown in the attachment as (x, y). The dimension y is the height of the rectangle. The x-dimension is half the width of the rectangle, which is symmetrical about the y-axis. Hence the width is 2x.

(c) As with any rectangle, the area is the product of length and width:

... A = (2x)(9 -x²) . . . . . the attachment shows a graph of this

... A = -2x³ +18x . . . . . expanded form suitable for differentiation

A suitable domain for A is where both x and A are non-negative: 0 ≤ x ≤ 3.

(d) The derivative of A with respect to x is ...

... A' = -6x² +18

This is defined everywhere, so the critical values will be where A' = 0.

... 0 = -6x² +18

... 3 = x² . . . . . . . divide by -6, add 3

... √3 = x . . . . . . . -√3 is also a solution, but is not in the domain of A

(e) The rectangle will have its largest area where x=√3. That area is ...

... A = 2x(9 -x²) = 2√3(9 -(√3)²) = 2√3(6)

... A = 12√3 . . . . square units . . . . ≈ 20.785 units²

7 0
3 years ago
Reka Maharis drove her vehicle to and from work last year. Her records show a total of $1,560 for fixed costs and $3,740 for var
amid [387]

Answer: 5,300

Step-by-step explanation:

5 0
3 years ago
Y=2/3(x-5)^2
Anvisha [2.4K]

Answer:

  see below

Step-by-step explanation:

The graph opens upward if the sign of the squared term is positive. If that sign is negative, the graph opens downward. The first three equations open upward; the last opens downward.

The line of symmetry is the value of x that makes the squared term zero. Here, that is x=5 for all equations.

<u>y=2/3(x-5)^2</u>:  A, D

<u>y=1/2(x-5)^2</u>:  A, D

<u>y=3/4(x-5)^2</u>:  A, D

<u>y=-4(x-5)^2</u>:  B, D

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3 years ago
Rewrite the function f(x)=-4(x-3)^2+16 in the form f(x)=ax^2+bx+c
elena55 [62]

Answer:

f(x) = - 4x² + 24x - 20

Step-by-step explanation:

Given

f(x) = - 4(x - 3)² + 16 ← expand the factor using FOIL

     = - 4(x² - 6x + 9) + 16 ← distribute parenthesis by - 4

    = - 4x² + 24x - 36 + 16 ← collect like terms

    = - 4x² + 24x - 20

4 0
3 years ago
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