Aaron the car wash owner had 228 quarters and 120 dimes.
<h3>
Equation</h3>
An equation is an expression used to show the relationship between two or more variables and numbers.
Let x represent the number of quarters and y represent the number of dimes. Hence:
x = 90% of y + y
x = (0.9y) + y
x - 1.9y = 0 (1)
Also:
0.25x + 0.1y = 69 (2)
From both equations:
x = 228, y = 120
Aaron the car wash owner had 228 quarters and 120 dimes.
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The GCF of 40 16 and 24 is 8
<h3>How to determine the GCF of 40 16 and 24?</h3>
The numbers are given as:
40 16 and 24
Start by listing out the factors of the numbers:
This is done as follows:
- The factors of 40 are: 1, 2, 4, 5, 8, 10, 20, 40
- The factors of 16 are: 1, 2, 4, 8, 16
- The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24
Then the greatest common factor in the above list is 8.
Hence, the GCF of 40 16 and 24 is 8
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Taking the derivative of 7 times secant of x^3:
We take out 7 as a constant focus on secant (x^3)
To take the derivative, we use the chain rule, taking the derivative of the inside, bringing it out, and then the derivative of the original function. For example:
The derivative of x^3 is 3x^2, and the derivative of secant is tan(x) and sec(x).
Knowing this: secant (x^3) becomes tan(x^3) * sec(x^3) * 3x^2. We transform tan(x^3) into sin(x^3)/cos(x^3) since tan(x) = sin(x)/cos(x). Then secant(x^3) becomes 1/cos(x^3) since the secant is the reciprocal of the cosine.
We then multiply everything together to simplify:
sin(x^3) * 3x^2/ cos(x^3) * cos(x^3) becomes
3x^2 * sin(x^3)/(cos(x^3))^2
and multiplying the constant 7 from the beginning:
7 * 3x^2 = 21x^2, so...
our derivative is 21x^2 * sin(x^3)/(cos(x^3))^2
Answer:
ax + b= ax + b
Step-by-step explanation:
Infinite many solutions when both sides are equal
so
ax + b= ax + b
i believe the answer would than have to be 17,24,31,45,52
