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4 years ago

How can I show that a * b = a+b+ab/100 is commutative?

1 answer:

7 0

* is commutative if a*b = b*a.

$b*a=b+a+\dfrac{ba}{100}=a+b+\dfrac{ab}{100}=a*b$

so the operation must be commutative because the component operations (addition and multiplication) are commutative.

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What is true about the solution above.

Masja [62]

ANSWER

$x = \pm \sqrt{3}$

and they are actual solutions.

EXPLANATION

The given equation is:

$\frac{ {x}^{2} }{2x - 6} = \frac{9}{6x - 18}$

Cross multiply

${x}^{2} (6x - 18) = 9(2x -6 )$

This implies;

${x}^{2} (6x - 18) - 9(2x - 6) = 0$

$3{x}^{2} (2x - 6) - 9(2x - 6) = 0$

Factor

$(3 {x}^{2} - 9)(2x - 6) = 0$

$3 {x}^{2} - 9 = 0 \: or \: 2x - 6= 0$

$3 {x}^{2} = 9 \: or \: 2x = 6$

${x}^{2} = 3\: or \: x = 3$

${x} = \pm \sqrt{3} \: or \: x = 3$

The domain of the given equation is

$x \ne3$

Therefore the actual solutions are

$x = \pm \sqrt{3}$

NB: x=3 is not in the domain of the given equation. It cannot be an extraneous solution.

7 0

3 years ago

Pamela and her friend Nicole are each baking apple pies and tarts for a bake sale, using the same recipes. Pamela baked 5 apple

valentina_108 [34]

Answer:

Each apple pie requires 8 apples, and each apple tart requires 4 apples.

Step-by-step explanation:

We see that both Pamela and Nicole bake the same amount of apple pies, but different amounts of apple tarts. Because of this, we can subtract the two to try to figure out the amount of apples for each apple tart. We subtract 68 from 76, giving us 8. Nicole baked 9 apple tarts, while Pamela baked 7, and 9-7=2. So we can bake two apple tarts with 8 apples, so one apple tart requires 4 apples (we divide by 2). Now that we know the amount of apples per each apple tart, we multiply 7 apple tarts that Pamela made by 4 apples, giving us 28. We subtract that from the total amount of apples Pamela used, which was 68, giving us 40. From this we can deduct that 5 apple pies need 40 apples, and we divide by 5, giving us 1 apple pie requires 8 apples.

3 0

3 years ago

Gymnast Clothing manufactures expensive soccer cleats for sale to college bookstores in runs of up to 500. Its cost (in dollars)

Murljashka [212]

The relationship between profit and revenue is:

Profit = Revenue - Total Cost
Since the cost is given as a function, the equation will be substituted as
Profit = Revenue - (3,250 + 5x + 0.1x²)

Now, the revenue is a linear graph because it is the number of pairs multiplied the fixed rate. So, the slope is constant.
Revenue = 110x --> this is the function for revenue
Thus, the equation for profit would be

Profit = 110x - 3,250 - 5x - 0.1x²
P = -0.1x²+105x-3,250 --> this is the function for profit

Now, to find the minimum value of x to make profit, differentiate P with respect to x and equate to 0.

dP/dx = 0 = -0.2x + 105
x = 525

Thus, the Gymnast Clothing should manufacture at least 525 pairs in order to make profit.

7 0

3 years ago

5. Simplify the expression:

Anna007 [38]

Answer:

Step-by-step explanation:

2 times 10 is 20. 2 times x is 2x. 2 times -4 is -8. So that gives you 20+2x-8. Combine like terms, so you don't have anything that matches with 2x, so you leave that aside. So you subtract/add 20-8 which gives you 12 and add the 2x on that. So the full answer is 2x+12.

5 0

3 years ago

Read 2 more answers

2 3/4 ÷ 10 in simplest form

nekit [7.7K]

Answer:

Ya Motha

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers