Answer:
A direct variation equation to represent this ;
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 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;
Divide both sides by 3 we get;
then, equation is,
Therefore, a direct variation equation to represent this situation is;
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:
Answer:
1.29 for 1 pack
Step-by-step explanation:
5.16/4=1.29
The value of the car in 2020 is $5532.53
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 = 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
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.
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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ABC? Select three 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.
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:
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