At a sporting event, the price for 3 cheeseburgers and 2 cups of lemonade is
$19 and the price for 2 cheeseburgers and 4 cups of lemonade is $18. How much
does it cost for 1 cheeseburger and 1 cups of lemonade?
*

Answer:

Part A:

This data is modeling an exponential function because the y-values are increasing at an increasing rate. For example, between station 1 and station 2, the time increased by 2 minutes, and between station 2 and station 3, the time increased by 4 minutes. The time between each station is increasing by a multiple of the time between the previous two stations. This indicates that the data follows an exponential curve.

Part B:

To represent this data as a function, we can use the formula y = ab^x, where a and b are constants and x is the input (station number).

Substituting in the values from the first data point, we get: 2 = ab^1

Substituting in the values from the second data point, we get: 4 = ab^2

We can then solve for a and b by dividing these equations:

4/2 = (ab^2)/(ab^1)

2 = b

Substituting this value back into the first equation, we get:

2 = a*2^1

1 = a

Therefore, the function that represents this data is y = 2^x.

Part C:

To find the average rate of change between station 2 and station 4, we can use the formula: (y2 - y1)/(x2 - x1).

Substituting in the values from the data, we get: (16 - 4)/(4 - 2) = 12/2 = 6.

Therefore, the average rate of change between station 2 and station 4 is 6.

Answer:

A. (x - 4)² + (y + 7)² = 81

Step-by-step explanation:

The general equation for a circle is given by the formula;

x² + y² + 2hx + 2ky + c = 0  ......equation 1.

Where the center is C(-h, -k)

Also, the standard form of the equation of a circle is;

(x - h)² + (y - k)² = r²  ......equation 2.

Where;

Given the following data;

h = 4

k = -7

r = 9

Substituting into eqn 2, we have;

(x - 4)² + (y - {-7})² = 9²

Simplifying further, we have;

(x - 4)² + (y + 7)² = 81

Answer:

  Truck                 Car              Total

Female           5                      35                40

Male              27                     21                48

Total              32                     56                88

P(buying a car given a male )  =  21/88 = .238 ≈ 24%

Step-by-step explanation:

Let B  = Probability of buying a car and being male    21/88

Let M = Probability of being a male  =  48/88

P(B l M)   =  P(B and M) / P(M)   =   (21/88) / (48/88)  = 21/48  = .4375  = 44%

Answer:

[tex]5h^3- h - 3[/tex]

Step-by-step explanation:

Given

[tex](2h^3 + 6h) + (3h^3 - 7h - 3)[/tex]

Required

Standard form

We have:

[tex](2h^3 + 6h) + (3h^3 - 7h - 3)[/tex]

Remove bracket

[tex](2h^3 + 6h) + (3h^3 - 7h - 3) =2h^3 + 6h + 3h^3 - 7h - 3[/tex]

Collect like terms

[tex](2h^3 + 6h) + (3h^3 - 7h - 3) =2h^3 + 3h^3+ 6h - 7h - 3[/tex]

[tex](2h^3 + 6h) + (3h^3 - 7h - 3) = 5h^3- h - 3[/tex]

Hence, the standard form is:

[tex]5h^3- h - 3[/tex]

The graph of the linear equation is attached below. After 11 months, the total savings will be $237.50.

What is a saving account?

An account in a retail bank is a savings account. Common characteristics include having a finite number of withdrawals allowed, not having check or connected debit card facilities, having few transfer choices, and not being able to become overdrawn.

Given equation is

y = 12.5x + 100

To find points on the linear equation, putting x = 0, 1 and 2 in the given equation:

y(0) = (12.5 × 0) + 100

y(0) = 100

y(1) = (12.5 × (1)) + 100

y(1) = 12.5 + 100

y(1) = 112.5

y(2) = (12.5 × 2) + 100

y(2) = 25 + 100

y(2) = 125.

The points on the linear equation are (0,100), (1, 112.5), (2,125).

Plot the points and join the points to draw the line to get graph the linear equation.

Putting y = 237.50 in the given equation y = 12.5x + 100:

237.50 = 12.5x + 100

Subtract 100 from both sides:

237.50 - 100 = 12.5x + 100 - 100

137.50 = 12.5x

Divide both sides by 12.5:

x = 137.50/12.5

x = 11

To learn more about graph of linear equation, click on the below link:

https://brainly.com/question/2601781

#SPJ1

Answer:

x = 32

Step-by-step explanation:

• any lower base angle is supplementary to any upper base angle.

here base angle = 2(x - 10) and upper base angle = 4x + 8

supplementary angles sum to 180°

sum the base and upper base angles and equate to 180

2(x - 10) + 4x + 8 = 180

2x - 20 + 4x + 8 = 180

6x - 12 = 180 ( add 12 to both sides )

6x = 192 ( divide both sides by 6 )

x = 32

Answer:

9

Step-by-step explanation:

It’s a ratio.

5/30=x/54

reduce

1/6=x/54

cross multiply

54=6x

x=9

9514 1404 393

Answer:

Step-by-step explanation:

If Anna's age is represented by A, then 12 more than Anna's age will be ...

  12 + A

Jason's age is said to be 12 more than Anna's age, so ...

  J = 12 + A

__

The sum of their ages will be J + A. That is said to be 50, so ...

  J + A = 50

_____

These equations can be solved by using the first to substitute for J in the second.

  (12 +A) +A = 50

  2A = 38 . . . . . . . . subtract 12

  A = 19 . . . . . . . . . . divide by 2

  J = 12 +19 = 31 . . . find Jason's age

Jason is 31; Anna is 19.

If the HCF is 5 and the product of the two numbers is 70, then the value of LCM is 14.

The smallest number that can be divided by both numbers is known as the least common multiple, or LCM, of two numbers. The product of the two numbers is the LCM if their greatest common divisor is 1, in which case their product is 1.

First, multiply both numbers by their prime factors to express them. Then, multiply the common factor with the highest power by the remaining factors to obtain the LCM. Take the common factors with the lowest power and multiply them to determine HCF.

To find the LCM of two numbers, you can use the formula: LCM = (a * b) / HCF.

In this case, we know that the HCF is 5, and the product of the two numbers is 70. Therefore, we can substitute these values into the formula:

LCM = (70) / 5 = 14.

So the LCM of the two numbers is 14.

To know more about HCF visit:-

brainly.com/question/29114178

#SPJ1

Answer:

16 x 12 = 192

192 x 2 = 384

10 x 8 = 80, 80 divided by 2 = 40

40 x 2 = 80

10 x 16 = 160

Add all given areas:

384 + 80 + 160 = 624 cm2 is your answer.

Answer:

B. 73°

Step-by-step explanation:

mL HLK = ½ × mL HJK = ½×146=73°

In the geometric series 2, 4, 6, 8, 10, 12,..., 24 is the 12th term. Each number in this series is separated by a factor of two.

the total of a geometric sequence's terms. Sn=a1(1rn)1r, r1 denotes the sum of the first n terms in a geometric series. an infinite geometric series whose total is provided by the expression S=a11r and where |r|1.

A geometric sequence is a set of numbers that follows a pattern in which the next term is determined by multiplying the previous one by a factor known as the common ratio, r.

To know more about geometric series visit:-

https://brainly.com/question/21087466

#SPJ1

Answer:

2.5

Step-by-step explanation:

Decimeter is 0.1 meter (10 centimeters). That means 25 decimeters is 2.5 meters.

Answer:

here

Step-by-step explanation:

180 minutes

Answer:

4

Step-by-step explanation:

How many 2/5s are in 1 1/2? To make it easier and simpler , I would change these fractions into decimals . Our answer is there are ALMOST 4 of 2/5ths in 1 and a half .

Answer: 48

Step-by-step explanation:

Answer:

The area of the rhombus is 25.83 cm².

Step-by-step explanation:

The area of a rhombus is given by:

[tex] A = \frac{d_{1} \times d_{2}}{2} [/tex]

Where:      

d₁: is one diagonal      

d₂: is the other diagonal = d₁ + 4 cm

We know that one side length of the rhombus is equal to d₁. We can imagine a right triangle inside the rhombus, with the following dimensions:

h: hypotenuse of the right triangle  

a: one side of the right triangle

b: is the other side of the right triangle  

From the above we know that:

h = d₁                                

[tex] a = \frac{d_{2}}{2} = \frac{d_{1} + 4}{2} [/tex]

[tex] b = \frac{d_{1}}{2} [/tex]            

We can find d₁ with Pitagoras:

[tex] h^{2} = a^{2} + b^{2} [/tex]  

[tex] d_{1}^{2} = (\frac{d_{1} + 4}{2})^{2} + (\frac{d_{1}}{2})^{2} [/tex]

[tex] d_{1}^{2} = \frac{1}{4}(d_{1}^{2} + 8d_{1} + 16 + d_{1}^{2}) [/tex]

By solving the above quadratic equation for d₁ and taking the positive solution we have:

[tex] d_{1} = 5.46 cm [/tex]    

So, d₂ is:

[tex] d_{2} = d_{1} + 4 = 5.46 cm + 4 cm = 9.46 cm [/tex]

Now, we can find the area:

[tex] A = \frac{d_{1} \times d_{2}}{2} = \frac{5.46 cm \times 9.46 cm}{2} = 25.83 cm^{2} [/tex]

Therefore, the area of the rhombus is 25.83 cm².

I hope it helps you!  

Answer:

3

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

The equilateral triangle ABC have a side length of 2 units of the radius length of the circle tangent to the line AB.

An equilateral triangle have all its side lengths equal so;

line AB = line BC = line AC

At points B and C where the lines AB and AC are tangent to the circle is the a side length BC of the equilateral triangle

Line BC form the diameter of the circle which is 2 radius of the circle so;

line BC = 2 × radius of the circle

line BC = 2 × 1

line BC = 2

Therefore, the side length of the equilateral triangle is 2 units of the radius of the circle tangent at point B and C.

Learn more about tangent to a circle here: https://brainly.com/question/11067500

#SPJ1

Answer:

The answer will be 1.53 after dividing and rounding to the nearest tenth 3.5 divided by 2.29.

The function for position x(t) could be x(t) = 3t^2 - 2t + 10.

In mathematics, a function is a relation between two sets that assigns to each element of the first set exactly one element of the second set. In other words, it is a rule that describes how one set of values is related to another set of values. Functions are used to model real-world scenarios and to solve mathematical problems. Examples of functions include linear equations, polynomials, and trigonometric functions.

This is determined by using the equation x'(t) = a(t). Differentiating both sides of the equation, we get x'(t) = 6t - 2. Integrating this equation, we get x(t) = 3t^2 - 2t + C, where C is the constant of integration. Since x(1) = 10, we can substitute this value into the equation and solve for the constant of integration. Therefore, we get x(t) = 3t^2 - 2t + 10.

To know more about function click-
https://brainly.com/question/25638609
#SPJ1

Answer:

53

Step-by-step explanation:

https://brainly.com/question/23396982?answering=true&answeringSource=greatJob%2FquestionPage%2F1

Answer:

the answer is 9 hope this helps

Step-by-step explanation:

Answer:

x = 30

Step-by-step explanation:

24(24 + x) = 36² => tangent-secant theorem

Open the bracket

24*24 + 24*x = 36²

576 + 24x = 1,296

24x = 1,296 - 576

24x = 720

Divide both sides by 24

24x/24 = 720/24

x = 30

Answer:

C, definitely two sides are different in the triangle.

A, it looks as if the bottom is a right triangle if you look at it in a different way.

The polygons that would be used in a net isosceles triangle & right triangle

A pyramid is a structure whose outer surfaces are triangular and converge to a single step at the top,

As, we need a triangular pyramid whose base has all the three sides equal in length.

We can have a net in the form of isosceles triangle whose two are equal

i.e., two sides are different in the triangle.

and also, bottom with the right angle

i.e.,  the bottom is a right triangle if you look at it in a different way.

Learn more about this concept here:

https://brainly.com/question/18885675

#SPJ2

Answer:

x=per hour

233=42x+65

Step-by-step explanation: