(Constant of Proportionality, Graphing Proportional Relationships, Real-World Proportional Problems HC) An ice cream shop serves chocolate milkshakes that are made with ice cream and milk. There is a proportional relationship between the number of scoops of ice cream and the amount of milk needed to make them. For every 1 scoop of ice cream, cup of milk is needed, and for every 5 scoops of ice cream, cups of milk are needed. Part A: Find the constant of proportionality. Show every step of your work. (4 points) Part B: Write an equation that represents the relationship. Show every step of your work. (2 points) Part C: Describe how you would graph the relationship. Use complete sentences. (4 points) Part D: How many cups of milk are needed for 18 scoops of ice cream? (2 points)

Answer:

B. 10

Step-by-step explanation:

To find the answer we would plug each given number into x to see if it makes the equation true

A. 2(5) = 20

    10 [tex]\neq[/tex] 20

B. 2(10) = 20

    20 = 20

C. 2(20) = 20

    40 [tex]\neq[/tex]20

As you can see, the only answer that makes the equation 2x=20 true, is answer B

f(x) =2(3ˣ) is an exponential function which has an initial value of 2.

Another word for "involving an exponent" in mathematics is exponential. For instance, an exponential rise in a number occurs when you raise it to the tenth power.

A mathematical function with the formula f(x) = aˣ is an exponential function. where an is a constant known as the function's base and x is a variable. The transcendental number e, or roughly 2.71828, is the exponential-function base that is most frequently seen. A variable is used as the exponent in exponential functions.

The exponential function that has an initial value of 2 is f(x) = 2ˣ.

f(x) = 2(3ˣ) can be written as f(x) = 2 × 3ˣ, so it starts at 2 × 3⁰ = 2 × 1 = 2.

f(x) = 3(2ˣ) can be written as f(x) = 3 × 2ˣ, so it starts at 3 × 2⁰ = 3 × 1 = 3

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The height of the equilateral triangle when its side length is given as 8 inches is calculated to be 6.93 inches.

The equilateral triangle has all sides and angles equal. The angles are always equal to 60 degrees.

Given that,

Side length of the equilateral triangle = 8 inches

Angles = 60 degrees

Height = ?

Therefore, let us find the height of the triangle using the Pythagoras theorem,

c² = a² + b²

8² - 4² = b²

b² = 64 - 16

b² = 48

b = 6.93 inches

Thus, the height of the equilateral triangle is calculated to be 6.93 inches.

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Answer:

4/8
3/8 + 1/8 = 4/8

Answer:

78.57cm²

Step-by-step explanation:

English

We need to find the area of the circle.

The area of the circle is given by pie r². We know the value of pie and r is given . Putting the values

Area= pie r².

Area= 22/7* 5² =  22/7*25= 78.57cm²

We are not bothered by the area of the rhombus or the rhombus because we need to find the area of the circle.

Area of the rhombus is given by the product of the length of diagonals divided by 2. So if the rhombus lies at the center the length of each of its diagonal will be 10 cm. Because the length from the center of the circle to any point on the circle is equal to its radius. And the diagonal is formed by 2 radii.

Area of rhombus= 10*10/2= 50 cm²

Area of the circle excluding the area of the rhombus= 78.57- 50 = 28.57 cm²

Answer:

A

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer:

i dont know the answer i just need points im sorry

Step-by-step explanation:

Answer:

Answer:

area of circle = πr²

22/7×8

25.14m² is the answer of your question

hope it is helpful to you

Answer:

1 1/3

Step-by-step explanation:

The number of feet is dependent on the number of yards. The table is completed as shown in the attachment.

A variable whose value can be determined only if another variable's value is known is called a dependent variable. Thus the value of the variable depends on another variable.

In the given question, the number of feet can be known when that of yards is multiplied by a multiplicative factor. The value of the factor can be determined as;

multiplicative factor = 15/ 5

                                      = 3

So that feet is related to that of yards by this expression;

feet = multiplicative factor * yards

Thus,

when yards is 2, then;

feet = 3 * 2

       = 6

when feet = 12

12 = 3 * yards

yards = 12/ 3

         = 4

Thus the complete table is herewith attached to this answer for more clarifications.

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A statement which is known as tautology is a type of compound statement in whose result is always the truth value. We don't take in consideration the other individual values in consideration , the result in tautology is always true.

It is one of the most significant part in logical mathematics if we need to find the most accurate answers or findings among a given group of answers.

In mathematics, tautology is used so as to ensure that the results which is obtained are true and exact and not false . A tautology is a compound statement and it will always returns true value. The result in tautology is always true, regardless of what the constituent parts are.

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Answer: 8:15pm

Step-by-step explanation:

9+6=15 +105 = 120, 120/60=2 hours (total duration), 6:15 + 1 hour = 7:15 + 1 hour = 8:15pm

Answer:

where are the angles or image

After solving, the length of the trains in meters is 60 meters.

In the given question, it takes a train of a certain length 15 seconds to pass under a sign, and it takes the same train 40 seconds to pass under a bridge that is 100 meters wide.

We have to find the length (in meters) of the train.

Let the length of the train is x.

The length of the bridge is 100 meters.

As we know that the formula of the speed is the ratio of distance that he traveled in the certain duration of time.

So Speed = Distance/Time

So according to the question;

(x + 100)/40 = x/15

Now solving the expression using the cross multiplication

15x + 1500 = 40x

Subtract 15x on both side, we get

25x = 1500

Divide by 25 on both side, we get

x = 60 meters

Hence, the length of the trains in meters is 60 meters.

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Answer:

Step-by-step explanation:

x = 1/2 ( arc(SF) + arc(RQ))

ARC SF = 50

Arc RQ (the large one ) = 200

Large Arc RQ = 200

Arc SF = 50

x = 1/2 (50 + 200)

x = 1/2 250

x = 125

Answer:

1

Step-by-step explanation:

2a +3b

let a=-4 and b=3

2(-4) +3(3)

Multiply

-8 +9

Add

1

Step-by-step explanation:

there are a few things from school everybody has to burn into their brains for life. one of them : Pythagoras for right-angled triangles :

c² = a² + b²

c is the Hypotenuse (the triangle side opposite of the 90° angle), a and b are the triangle legs.

now, it depends on what you teacher agreed with you regarding naming the sides of such a triangle.

sometimes "base" is the Hypotenuse (baseline), sometimes it is one of the legs, and then the height is the second leg (as the legs are standing at a 90° or right angle at each other).

we have to assume the second one, as for the first one we have not enough information to solve the question (because with just a given Hypotenuse and the height to the Hypotenuse we can draw infinitely many different triangles with different perimeters).

so, we have

Hypotenuse² = 24² + 7² = 576 + 49 = 625

Hypotenuse = sqrt(625) = 25 m

the perimeter of the triangle is then

25 + 24 + 7 = 56 m

Answer:

The top looks like a trapezoid and so does the bottom so it's a prism.

lets find the area of the base!

15(base 1) + 7(base2) = 22

22 x 5(height) = 110

110 divided by 2( x 1/2) = 55

Now we multiply by the actual height of the TOTAL prism which is 11.

55 x 11 = 605 cubic feet, is your answer.

Formula for AREA of a trapezoid:

B1(base 1) + B2(base 2) x H(height) x 1/2 (basically just dividing by 2)

Answer:

1,705 elk

Step-by-step explanation:

7,750 / 50 =  155 groups of elk

155 groups x 11 per group = 1,705 elk.

Answer:

c.3 got a 100

Step-by-step explanation:

C

Step-by-step explanation:

Answer:

C. 1

Step-by-step explanation:

I got this right on my test

Answer:

Alex deleted 37.5 selfies

Step-by-step explanation:

Let X be the number of selfies that Vic deleted.

Alex deleted 3X selfies.

After deleting selfies, Alex has 90-3X selfies left.

Vic has 75-X selfies left.

Since Alex has half as many selfies as Vic, we can set up the equation: 90-3X = (75-X)/2

Multiplying through the parentheses on the right side, we get: 90-3X = 75-X/2

Combining like terms, we get: 2X = 15

Dividing both sides by 2, we get: X = 7.5

Since X represents the number of selfies that Vic deleted, Vic deleted 7.5 selfies.

Since Alex deleted 3 times as many selfies as Vic, Alex deleted 37.5 = <<37.5=22.5>>22.5 selfies.

The number of selfies deleted by Alex is 51.

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given that Alex took 90 selfies and Vic took 75 selfies. Today, they each decided that some of these selfies were not very good and deleted them. Alex deleted three times as many selfies as Vic. Now, Alex has half as many selfies as Vic.

Let Vic deleted x selfies and number of selfies deleted by Alex is 3x,

Therefore,

Since, Alex has half as many selfies as Vic, we can set up the equation: 90-3x = (75-x)/2

180 - 6x = 75 - x

5x = 105

x = 17

3x = 51

Hence, the number of selfies deleted by Alex is 51.

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Answer:

375

Step-by-step explanation:

- 150 rooms total unoccupied

- 3/5 occupied

this means that 150 rooms is 2/5 of the total, and 150 is 2/5 of 375, so 375 total

Answer:

375

Step-by-step explanation:

First of all, let's consider the following points;

●3/5 of the rooms are occupied

●23 rooms are being reserved

●127 rooms are being remodeled

The keyword is the 1st point.

If 3/5 is occupied, then that means 5/5 or 5 parts are the fraction of all the hotel rooms.

So,

127+23= 150 rooms

5/5 - 3/5 = 2/5

Now let's apply the direct proportion rule;

2/5= 150

1/5= 150÷2= 75

5/5 (total)= 75*5=375

If the whole fraction things make you confused, here's an easier way;

2 parts= 160

1 part= 150÷2=75

5 Parts = 75*5= 375

Hope it helps :-)!

Answer:

A mi encantar el arte.

A mis padres interesar el traje.

A ti importar las botas.

A Emelio encantar los deportos.

A Nosotros interesar viajar.

The domain and scope of the identity function are the same. Equation for the identity function is  f(x) = x, or y = x.

An statement, rule, or law in mathematics that specifies the connection between an independent variable and a dependent variable (the dependent variable). A relationship between a group of inputs and one output each is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. Y=X2 is an illustration of this. You only receive one output for y if you enter anything for x. The fact that x is the input value leads us to argue that y is a function of x.

identity function are the same.

Equation for the identity function is

f(x) = x, or y = x.

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Solving provided question, we can say that the given linear equation is  y = -2x + 4 and -x -x +3(-2x + 4 ) + 9 = x = 7/3

A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept. When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.

the given linear equation is

y = -2x + 4 and -x +3y = -9

now,

-x +3(-2x + 4 ) + 9

-x - 6x - 12 +9 = 0

-7x = -3

x = 7/3

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Answer:

I think the answer is 3:1. found it by counting the no. of boxes

Answer:

79

Step-by-step explanation:

3x +16 + 5x - 4 = 180

8x +12 = 180

8x = 180 -12

8x = 168

x=21

3*21+16= 79

50-3x<20

the answer is C. 11

The triangle is an acute triangle using the Pythagorean theorem.

Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

We have,

The sides of a triangle are 68, 61, and 46.

Note:

When the sum of the squares of two sides of a triangle is equal to the square of the hypotenuse, the triangle is a right triangle.

When the sum of the squares of two sides of a triangle is less than the square of the hypotenuse, the triangle is an obtuse triangle.

When the sum of the squares of two sides of a triangle is greater than the square of the hypotenuse, the triangle is an acute triangle.

Now,

68² = 4624

46² = 2116

61² = 3721

We see that,

We can never have a right triangle or an obtuse triangle.

The possible combination.

61² + 68² > 46²

61² + 46² > 68²

68² + 46² > 61²

Thus,

The triangle is an acute triangle.

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