A recipe for 2 dozen corn muffins calls for 3 cups of flour. The number of muffins varies directly with the amount of flour you use. Write a direct variation equation to represent this.

Answers

Answer 1
Answer:

Answer:

A direct variation equation to represent this ;  y = (2)/(3)x

Step-by-step explanation:

Direct Variation states that a relationship between two variables in which one is a constant multiple of the other one.

In other words, when one of the variable changes then the other changes in proportion to the first.

If b is directly proportional to a, then the equation is in the i.e,

form b = ka where k is the constant of variation.

Let y represents the number of muffins and x represents the amount of flour.

It is given that the number of muffins varies directly with the amount of flour you use.

As per the given statement:

y = 2 dozen corn and x = 3 cups of flour.

Then, by definition of Direct variation;

y = kx

Substitute the given values to find k;

2 = 3k

Divide both sides by 3 we get;

k = (2)/(3)

then, equation is, y = (2)/(3)x

Therefore, a direct variation equation to represent this situation is; y = (2)/(3)x


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Solve the equations 5x-8y=145x-7y=6

How do I solve this problem. 7a+2=3a+1

Answers

Answer:

- 1/4

Step-by-step explanation:

7a + 2 = 3a + 1

subtract the 1 from both sides

7a + 1 = 3a

subtract 7a from both sides

1 = - 4a

divide by - 4

A = - 1/4

Answer:

a= - 1/4

Step-by-step explanation:

A four pack of batteries cost 5.16 at this price what is the cost of

Answers

Answer:

1.29 for 1 pack

Step-by-step explanation:

5.16/4=1.29

You purchase a car in 2010 for $25,000. The value of the car decreases by 14% annually. What would the value of the car be in 2020?

Answers

The value of the car in 2020 is $5532.53

What is exponential decay?

A quantity is subject to exponential decay if it decreases at a rate proportional to its current value.

Given that, You purchase a car in 2010 for $25,000. The value of the car decreases by 14% annually.

The exponential decay is given by =

A = P(1-r)^t

A = final amount

P = principal amount

r = rate of decrease.

t = 10

Therefore,

A = 25000(1-0.14)¹⁰

A = 25000×0.86¹⁰

A = 5532.53

Hence, the value of the car in 2020 is $5532.53

For more references on exponential decay, click;

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Answer:

42,690

Step-by-step explanation:

it is the rule of LONG numbers

Which is equivalent to 3 square root 8^1/4x

Answers

(\sqrt[3]{8})^{(1)/(4)x}= 8^{(1)/(3)(1)/(4)x}=8^{(1)/(12)x}=(\sqrt[12]{8})^(x)

The 3rd choice is appropriate.

Final answer:

To simplify the equation 3 square root 8^1/4x, we can utilize the properties of exponents and roots. This converts the expression to 3 * 8^1/8x.

Explanation:

The original expression in question is 3 square root of 8 raised to the power of 1/4x. We can begin to simplify this expression by first recognizing the properties of exponents. For example, the calculation of 8 raised to the 1/4 power represents the same as taking the fourth root of 8. Furthermore, the square root of a number is the same as raising that number to the power of 1/2.

So, 3 square root (8^1/4x) can be written as 3 * (8^1/4x)^1/2, which simplifies to 3 * 8^1/8x, due to the property that multiply exponents when raising powers to a power. Using properties of exponents helps us in simplifying complex equations.

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Which trigonometric ratios are correct for triangle
ABC? Select three options.

Answers

Answer:

Options (1), (3) and (4)

Step-by-step explanation:

From ΔABC given in the picture,

By Pythagoras theorem

Hypotenuse² = (Leg 1)² + (Leg 2)²

BC² = AB² + AC²

(18)² = 9² + AC²

AC = √(324-81)

AC = 9√(3) cm  

sin(C) = \frac{\text{Opposite side}}{\text{Hypotenuse}}

         = (AB)/(BC)

         = (9√(3))/(18)

sin(C) = (√(3) )/(2)

sin(B) = (AC)/(BC)

         = (9)/(18)

         = (1)/(2)

cos(B) = \frac{\text{Adjacent side}}{\text{Hypotenuse}}

          = (9√(3))/(18)

          = (√(3) )/(2)

tan(B) = \frac{\text{Opposite side}}{\text{Adjacent side}}

          = (AC)/(AB)

          = (9)/(9√(3) )

          = (1)/(√(3) )

tan(C) = (AB)/(AC)

          = (9√(3))/(9)

          = √(3)

Therefore, Options (1), (3) and (4) are the correct options.

Answer:

Options (1), (3) and (4)

Step-by-step explanation:

From ΔABC given in the picture,

By Pythagoras theorem

Hypotenuse² = (Leg 1)² + (Leg 2)²

BC² = AB² + AC²

(18)² = 9² + AC²

AC =

AC =  cm  

sin(C) =

        =

        =

sin(C) =

sin(B) =

        =

        =

cos(B) =

         =

         =

tan(B) =

         =

         =

         =

tan(C) =

         =

         =

Therefore, Options (1), (3) and (4) are the correct options.Step-by-step explanation:

42 gallons in 8 minutes. What is the unit rate?

Answers

The unit rate would be gallons per minute.

Divide total gallons by total minutes:

42/8 = 5.25

Unit rate = 5.25 gallons per minute