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3 years ago

Compute the value of 9x^2 + 4y^2 if xy = 6 and 3x + 2y = 12.

Mathematics

1 answer:

Sindrei [870]3 years ago

8 0

Answer:

Consider the equation 3x + 2y = 12

Now, square both sides:

(3x + 2y)^2 = 122

=> 9x^2 + 12xy + 4y^2 = 144

=>9x^2 + 4y^2 = 144 – 12xy

From the questions, xy = 6

So,

9x^2 + 4y^2 = 144 – 72

Thus, the value of 9x^2 + 4y^2 = 72

Answered by GAUTHMATH

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The polygons that make up a solid are called its

SVETLANKA909090 [29]

Answer:

Faces

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I'm not sure how to explain it but imagine looking at a soccer ball with a smiley face drawn on it. I mean thats its definition its hard to explain it without using its word in a sentence.

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4 years ago

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A company that manufactures and sells consumer video cameras sells two versions of their popular hard disk camera, a basic came

saul85 [17]

Answer:

The percentage of customers who buy an extended warranty is 33%.

Step-by-step explanation:

In this problem, we have these following percentages.

35% of the customers select the basic camera.

This also means that:

65% of the customers select the deluxe version. (Since you can buy only two versions of the hard disk camera and the sum of the percentages is 100%).

20% of those who select the basic camera also purchase the extended warranty.

40% of those who select the deluxe version also purchase the extended warranty.

What is the percentage of customers who buy an extened warranty?

$P = P_{1} + P_{2}$

$P_{1}$ is the percentage of those who buy the basic version with the extended warranty. So it is 20% of 35%. So

$P_{1} = 0.20*0.35 = 0.07$

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4 years ago

Factor by grouping (sometimes called the ac-method).

lesya692 [45]

Answer:

Step-by-step explanation:

The arc method is basically finding what the a and c coefficients multiply to, and then finding the factors of that that add up to b.

Since we have the quadratic in the ax^2+bx+c form we don't have to adjust anything. Now, a = 8, b = 2 and c = -3. a*c = -24 so now we want to find all the factors of that.

-1 and 24

1 and -24

-2 and 12

2 and -12

-3 and 8

3 and -8

-4 and 6

4 and -6

And after that they repeat. It is important to note that you can use negative on either side, or if a*c was a positive number you could multiply two negatives like 24 can be and 12 as well as -1 and -12.

Now we want to look at all the factor pairs and find one that add together to equal 2 because b = 2. -4 + 6 does it, so there's our choice. Now we can rewrite the original quadratic as 8x^2-4x+6x-3. You can check that this is equivalent by combining like terms It's the same as rewriting it as 8x^2+2x-2-1 because -2 and -1 will combine to get -3. Anyway, now we can factor.

8x^2-4x+6x-3 You can imagine there being two sets of parenthesis.

( 8x^2-4x)+(+6x-3) Now from here we can factor something out of each parenthesis. e can factor out 4x fromt he first and 3 from the second.

4x(2x-1)+3(2x-3) Now, it may not be obvious but you can factor 2x-3 from each term. If that's not clear pretend 2x-3 = u

4xu + 3u Now hopefully it is clear you can factor out this u

u(4x+3) Then we know u = 2x-3 so

(2x-3)(4x+3) And it's factored.

I do want to mention you could have done this with 8x^2+6x-4x-3 with the +6 and -4 switched. I won't go through it here but it may help to do it yourself if you still don't quite understand. Let me know if there is something I can further explain though.

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3 years ago

20 POINTS!!! PLEASE HELP

pogonyaev

The logarithm of 10 to base 10 is 1

<h3>How to determine the logarithm?</h3>

The given parameters are: