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∑(n, 1, 94, 15 / ((n +5)*(n+6)) ==It sums up to 47 / 20

DE = EF / tan(D)

m(6+n) = 7*8           m = 56 / (6+n)

n(6+m) = 5*8           m = (40/n) - 6

56 / (6+n) = (40/n) - 6               n = 3 ¹/₃           m = 6

XY = 15 ¹/₃

if y=12x then 6y=75x, therefore it is 75 inches.

The above solution and solution method is wrong.

...a box of berries having a total weight of 200 kg. The berries were 99% moisture, by weight. After two days in the sun, the moisture content of the berries was only 98%, by weight. What was the total weight of the berries after two days, in kg?

Solution:

\(\text {200 Kg of berries are 99% water. The weight of the water is then}\\ \left(0.99\cdot 200\right) = 198 ~ kg\\ \text {Let x be the weight of the water lost after exposure to the sun. }\\ \left(0.99 \cdot 200-0.98(200-x)\right)=x\\ \begin{aligned} 198-(196-0.98x)&=x\\ 198-196+0.98x&=x\\ 2+0.98x&=x\end{aligned}\\ \begin{aligned}1+0.98x-0.98x&=x-0.98x\\ 2&=0.02x\\ x&=100\\ \end{aligned}\\ \text { }\\ 200-x=200-100=100 ~ kg \leftarrow \text {The total weight of the berries after 2 days}\\ \)

GA

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Can the numbers 12, 16, and 18 be a Pythagorean Triple? Explain why or why not.  

No.  Because sqrt(12² + 16²) is NOT 18.  BTW, it's 20.  

_.

See https://web2.0calc.com/questions/graphing-question_40

x = 9 4/15 

$h^{-1}(5) = 8/3$.

How many apples does Alvin have initially?

Hello Guest!

x apples does Alvin have initially.

\(B= (\frac{1}{3}x+\frac{2}{3})\)

\(C=(\frac{1}{4}(x- (\frac{1}{3}x+\frac{2}{3}))+\frac{1}{2})\\ C= (\frac{1}{4}(x- \frac{1}{3}x-\frac{2}{3})+\frac{1}{2})\\ C=(\frac{1}{4}x- \frac{1}{12}x-\frac{1}{6}+\frac{1}{2})\\ \color{blue}C= (\frac{1}{6}x+\frac{1}{3})\)

\(D=(\frac{1}{2}(x- (\frac{1}{3}x+\frac{2}{3})-(\frac{1}{6}x+\frac{1}{3}))) \\ D=(\frac{1}{2}x- \frac{1}{6}x-\frac{1}{3}-\frac{1}{12}x-\frac{1}{6}) \\ \color{blue}D= (\frac{1}{4}x-\frac{1}{2})\)

\(E= (\frac{1}{2}(x-(\frac{1}{3}x+\frac{2}{3}) -(\frac{1}{6}x+\frac{1}{3})-(\frac{1}{4}x-\frac{1}{2}))+\frac{1}{2}) \\ E= (\frac{1}{2}x-\frac{1}{6}x-\frac{1}{3} -\frac{1}{12}x-\frac{1}{6}-\frac{1}{8}x+\frac{1}{4}+\frac{1}{2}) \\ \color{blue}E= (\frac{1}{8x}+\frac{1}{4})\)

\(x=(B)+(C)+(D)+(E)+5\)

\(x=((\frac{1}{3}x+\frac{2}{3})+(\frac{1}{6}x+\frac{1}{3}) + (\frac{1}{4}x-\frac{1}{2})+(\frac{1}{8}x+\frac{1}{4})+5)\\ x=0.875x+5.75\\ \frac{1}{8}x=5.75\)

\(x=46\)

46 apples does Alvin have initially.
  !

...or Dragan 

Yes jugoslav or civonamzuk

Harold loves to eat cookies. He eats 1/4 of the package on Monday. On Tuesday, he eats 13 cookies. On Wednesday, he eats 1/2 as many as he did on Monday. If there are 22 cookies left in the package on Thursday, how many cookies did he start with? 

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Mon = x/4        Tue = 13         Wed = x/8          left = 22

x/4 + 13 +x/8 + 22 = x

x = 56

Mon = 14

Tue = 13

Wed = 7

Left = 22

Total 56 cookies        (This is what he started with!)

[DMT] = 13 ¹/₃ square units

Let the number of pages ==P

P  -  1/5P ==4/5P - pages left after 1st hour

4/5P  - [4/5P  *  3/8] ==1/2P - pages left after 2nd hour.

1/2P == 45

P ==45 x 2 ==90 - pages in the book.

d => cammon difference

  A     +   B       +      C      = 180

17 + (17 + d) + (17 + 2d) = 180

d = 43

Angle C = 17 + 2d = 103 degrees

x ==2^2×3^3×4^4×5^5×6^6

Look at the exponents of x. ANY exponent that is EVEN is already a perfect square. All we need then is to make the exponent of 3 and 5 EVEN by multiplying them by: 3 x 5 ==15, which is the smallest number that will make x a perfect square: 2^2  x  3^4  x 4^4  x  5^6  x  6^6=60,466,176,000,000.

Square root of [60,466,176,000,000]==7,776,000 - whixh is a perfect square.

See https://web2.0calc.com/questions/graphing-question_40

Since f(x) is divisible by x^3, f(x) is of the form ax^5 + bx^4 + cx^3.

You then want ax^5 + bx^4 + cx^3 + 2 to be divisible by (x + 1)^3.  Using long division, you get the equations

-10a  + 6b - 3c = 0

4a - 3b + 2c = 0

-a + b - c + 2 = 0

==> a = 6, b = 16, c = 12

So f(x) = 6x^5 + 16x^4 + 12x^3.

f(x) = x² - 2x + 5

g(x) = x + 8

f(g(5)) - g(f(5))
= [(g(5))² - 2(g(5)) + 5] - [(f(5)) + 8]
= [((5) + 8)² - 2((5)) + 5] - [((5)² - 2(5) + 5) + 8]
= [169 - 10 + 5] - [25 - 10 + 5 + 8]
= 164 - 28
= 136