MATHEMATICS MIDDLE SCHOOL

7k^2-16k+100=0 using completing the square ?

Answers

Answer 1

Answer:

$7k^2-16k+100=0$

$7k^2-16k=-100$

Add a squared constant to both sides:

$7k^2-16k+c^2=c^2-100$

On the left, we wish to condense the quadratic into a squared binomial,

$(\sqrt7\,k-c)^2$

Expanding this gives

$7k^2-2c\sqrt7\,k+c^2$

which tells us

$-2c\sqrt7=-16\implies c=\frac8{\sqrt7}$

Then $c^2=\frac{64}7$ , and

$\left(\sqrt7\,k-\frac8{\sqrt7}\right)^2=\frac{64}7-100$

$\left(\sqrt7\,k-\frac8{\sqrt7}\right)^2=-\frac{636}7$

If you're looking for real-valued solutions, there are none, since the square root of a negative number doesn't exist... but if you're allowing complex-valued solutions, we can take the square root of both sides to get

$\sqrt7\,k-\frac8{\sqrt7}=\pm 2i\sqrt{\frac{259}7}$

Multiply both sides by $\sqrt 7$ to eliminate denominators, then solve for $k$ :

$7k-8=\pm 2i√(259)$

$7k=8\pm 2i√(259)$

$\boxed{k=\frac{8\pm2i√(259)}7}$

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PLZ HELP Kim wants to know how many families in her small neighborhood of 70 homes would participate in a neighborhood sports event. She put all the addresses in a bag and drew a random sample of 35 addresses. She then asked those families if they would participate in the sports event. She found that 15% of the families would participate in the event. She claims that 15% of the neighborhood families would be expected to participate in the sports event. Is this a valid inference? A. Yes, this is a valid inference because she took a random sample of the neighborhood
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Answers

C. No because she only asked 35 families

claudio will decorate his bedroom he can choose tan, blue, or gray paint and striped or plaid curtains how many ways can he decorate his room with different paint and curtains

Answers

5×5×5×5×5=3125

3,125 ways he can decorate his room with different paint and curtains.

Answer: 5×5×5×5×5=3125

Step-by-step explanation:this is the answer

Destiny is doing a science fair project about ant population growth. She has a very young ant colony, and to estimate the population, she captures 25 ants and marks them with special paint. Destiny then releases them into the colony, waits a few days, and then captures 240 ants. She notices that 10 of these ants are marked. To the nearest whole number, what is the best estimate for the ant population?

Answers

Answer:resume

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The absolute value of -5 and 5 are ?

Answers

Hey!

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Absolute Value - the enormity of a number regarding its sign.

|-5| = 5

|5| = 5

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Hope This Helped! Good Luck!

The absolute value of both of them would be 5 because the absolute value sign makes negative numbers positive and positive numbers stay the same

Rename the number 82000

Answers

a few ways to rename 82 thousands is 82,000 or eighty-two thousands.

the answer would be 82 because if u rename 82000 it would be 82 rename means r=that to give a new name to something so we can give 82 to 82000 I HOPE THIS HELPS=)

The number of frogs that the princess has kissed at most 4

Answers

Answer:

$x \le 4$

Step-by-step explanation:

"At most 4" means it can be 4 or less.

That is the same as "less than or equal to 4"

Let x = number of frogs the princess kissed.

$x \le 4$

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