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Anestetic [448]
2 years ago
15

The school that Scott goes to is selling tickets to the annual dance

Mathematics
1 answer:
zalisa [80]2 years ago
4 0
Senior tickets (x)
Child tickets (y)

First day: 3x + 5y = 70

second day: 12x + 12y = 216

Solve the system of equations (use elimination)

Multiply first equation by -4 -4(3x + 5y = 70), which makes it

-12x - 20y = -280
(+)12x + 12y = 216 add to second equation

-8y = -64

divide by -8. y = 8

Plugin the y value to either equation ( I will choose first equation)

3x + 5(8) =70

3x+ 40 = 70

3x = 30

x = 10

Senior tickets are $10, child tickets are $8
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A circle with a radius of 3cm sits inside a circle with a radius of 11cm.
lozanna [386]

Answer:

Area of shaded region = 351.68 cm²

Step-by-step explanation:

Area of a circle = πr²

where r = radius = 3.14

Area of bigger circle = 3.14 × 11²

= 3.14 × 11 × 11

= 379.94cm²

Area of smaller circle = 3.14 * 3²

= 3.14 × 3 × 3

= 28.26cm²

Area of shaded region = Area of bigger circle - Area of smaller circle

= (379.94 - 28.26) cm²

= 351.68 cm²

8 0
3 years ago
A 99 ft length of wire is to be cut into 2 pieces, so that the longer piece is eight feet longer than six times the shorter piec
Serhud [2]

here's the solution,

let the length of shorter peice = x

then the lenght of longer peice = 6x + 8

now, we know that the sum of length of peices measures 99 feet,

So,

=》x + 6x + 8 = 99

=》7x = 91

=》x = 13

shorter piece length = 13 feet

longer peice length = 13 × 6 + 8 = 78 + 8 = 86 feet

5 0
3 years ago
The number of gift baskets Nikki can make varies directly with the amount of time she spends making the baskets . She can make 1
scoundrel [369]

Answer:

40

Step-by-step explanation:

The number of gift baskets Nikki can make varies directly with the amount of time she spends making the baskets .

Let n be the number of baskets and let t be the mount of time it takes to make the basket. This means that:

n α t

=> n = kt

where k = constant of proportionality

She can make 4 baskets in every 1/2 hour.

This means that:

4 = k * 1/2

=> k = 4 * 2 = 8 baskets per hour

The time is now 5 hours (t = 5). Therefore:

n = 8 * 5 = 40 baskets

She can make 40 baskets in 5 hours.

8 0
3 years ago
Use the functions h(x) = 2x - 5 and t(x) = 6x + 4 to complete the function operations listed below.
Rom4ik [11]

Answer:

See below for answers (in bold) and explanations

Step-by-step explanation:

Part A: (h+t)(x) = h(x) + t(x) = (2x-5) + (6x+4) = 2x - 5 + 6x + 4 = 8x - 1

Part B: (h*t)(x) = h(x) * t(x) = (2x-5) * (6x+4) = (2x)(6x) + (2x)(4) + (-5)(6x) + (-5)(4) = 12x² + 8x - 30x - 20 = 12x² - 22x - 20

Part C: h(t(x)) = h(6x + 4) = 2(6x + 4) - 5 = 12x + 8 - 5 = 12x + 3

3 0
2 years ago
Julie will build a rectangular pen for her dog against a barn. A wall from the barn will form one side of the pen. She has 32 m
MAXImum [283]

Answer:

<h3> The width (side perpedicular to the barn):  <u>x = 8 m</u></h3><h3>      The lenght (side parallel to the barn):  <u>y = 16 m</u> </h3>

Step-by-step explanation:

x  - the width of the barn

She has 32 m of fencing so for the lenght remain (32-2x) m of fencing:

y = 32 - 2x

Area of the fencing:  A = x•y

A(x) = x•(32 - 2x)

A(x) = -2x² + 32x             ←  quadratic function

The maximum value of quadratic function occurs at:  x=-\frac b{2a}

a = -2,  b = 32

x=-\frac b{2a}=-\frac{32}{2\cdot(-2)}=-(-8)=8

32-2x = 32 - 2•8 = 16

4 0
3 years ago
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