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Schach [20]
3 years ago
11

Simply (2k-9)^2+(k+2)^2=(2k+1)^2+(k-8)^2

Mathematics
1 answer:
vova2212 [387]3 years ago
6 0

The square of a binomial expands as follows:

(a+b)^2=a^2+2ab+b^2

Expanding all the binomials, we have

4k^2-36k+81+k^2+4k+4=4k^2+4k+1+k^2-16k+64

Sum like terms:

5k^2-32k+85=5k^2-12k+65

Simplify terms appearing on both sides:

-32k+85=-12k+65

Move all terms involving k to the left and all numbers to the right:

-20k=-20

Divide both sides by -20:

k=1

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3 years ago
Which set of ordered pairs does not represent a function?
Daniel [21]

Answer:

B

Step-by-step explanation:

3 0
2 years ago
Ayesha has a theory about two digit numbers that have a larger tens digit than ones digit. she says that reversing the digits an
stira [4]
<span>Ayesha's right.  There's a good trick for knowing if a number is a multiple of nine called "casting out nines."  We just add up the digits, then add up the digits of the sum, and so on.  If the result is nine the original number is a multiple of nine.  We can stop early if we recognize if a number along the way is or isn't a multiple of nine.  The same trick works with multiples of three; we have one if we end with 3, 6 or 9.

So </span>1284673 <span>has a sum of digits 31 whose sum of digits is 4, so this isn't a multiple of nine.  It will give a remainder of 4 when divided by 9; let's check.

</span>1284673 = 142741 \times 9 + 4 \quad\checkmark<span>

</span>Let's focus on remainders when we divide by nine. The digit summing works because 1 and 10 have the same remainder when divided by nine, namely 1.  So we see multiplying by 10 doesn't change the remainder.  So 100 \times a + 10 \times b + c has the same remainder as a+b+c.

When Ayesha reverses the digits she doesn't change the sum of the digits, so she doesn't change the remainder.  Since the two numbers have the same remainder, when we subtract them we'll get a number whose remainder is the difference, namely zero. That's why her method works.
<span>
It doesn't matter if the digits are larger or smaller or how many there are. We might want the first number bigger than the second so we get a positive difference, but even that doesn't matter; a negative difference will still be a multiple of nine. Let's pick a random number, reverse its digits, subtract, and check it's a multiple of nine:

</span>813219543092195 - 591290345912318 =  221929197179877 = 9 \times 24658799686653 \quad \checkmark

6 0
3 years ago
Read 2 more answers
In the triangle below, what is the sine of 30°?
zlopas [31]

Answer:

There's no picture. Is it D.√3 / 2

Step-by-step explanation:

5 0
3 years ago
I WILL GIVE BRAINLIEST AND 50 POINTSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS
mars1129 [50]

Answer:

we get Rate of change = -3

Step-by-step explanation:

We need to calculate the rate of change for the following data:

x     y

-1     7

2     -2

7     -17

10   -26

The rate of change can be calculated using slope formula: Rate\:of\:change=\frac{y_2-y_1}{x_2-x_1}

From the table, we can take any 2 points

Suppose we take (-1,7) and (2,-2)

We have: x_1=-1, y_1=7,x_2=2, y_2=-2

Putting values in formula and finding rate of change

Rate\:of\:change=\frac{y_2-y_1}{x_2-x_1}\\Rate\:of\:change=\frac{-2-7}{2-(-1)}\\Rate\:of\:change=\frac{-9}{2+1}\\Rate\:of\:change=\frac{-9}{3}\\Rate\:of\:change=-3

So, we get Rate of change = -3

3 0
3 years ago
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