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Find cos C.

Hello Guest!

If the sin B = 4/9 in a right triangle, then the ratio of the sides is

a: b: c = 9: 4: 3.

So is

cos C = 4/9

  !

Subtrahiere $0.\overline{01}$ von 0,02 und drücke das Ergebnis als Bruch aus.

Hello Guest!

\(0.02-0.\overline{01}=0.00\overline{98}\)

   \(0.009898\overline{98}\)  =    x

-  \(\underline{ 0.989898\overline{98}}\)  =  100x

\(-0.98\)               = - 49/50

\(x-100x=-\frac{49}{50}\\ -99x=-\frac{49}{50}\\ x=\dfrac{49}{99\cdot 50}=\dfrac{7^2}{3^2\cdot 11\cdot 5^2\cdot 2}\)

\(0.02-0.\overline{01}=\dfrac{49}{4950}\)

  !

\(What\ is\ 0.4\overline{8} + 0.3\overline{7}?\)

Hello Guest!

\(0.4\overline{8} + 0.3\overline{7}=0.8\overline 6\)

   \(0.86666\overline 6\)   =  x

 -\(\underline{0.66666\overline 6}\)    = 2/3

  \(0.2\)                = 1/5

\(x-\frac{2}{3}=\frac{1}{5}\\ x=\frac{1}{5}+\frac{2}{3}=\frac{3+2\cdot 5}{15}\\ x=\frac{13}{15}\)

\(0.4\overline{8} + 0.3\overline{7}=\dfrac{13}{15}\)

  !

Find a.

Hello Guest!

\(y=m(x-x_p)+y_p\\y=\frac{8-11}{4-1}\cdot (x-1)+11=-x+1+11=-x+12\\ x+y=12\)

\(\dfrac{x}{12}+\dfrac{y}{12}=1\\ \)

\(a=12\)

  !

https://web2.0calc.com/questions/angle-bisectors-tx-and-uy-of-triangle-tuv-meet-at

Let r be the radius of the circle. 

The circle must have a center of (3 - r, 0).

So our formula is (x - 3 + r)^2 + y^2 = r^2

9(x - 3 + r)^2 + 9y^2 = 9r^2

x^2 /9 + y^2 /4 = 1

4x^2 + 9y^2 = 36

Subtracting the two formulas. 

9(x - 3 + r)^2 - 4x^2 = 9r^2 - 36

5x^2 + (18r - 54)x + (117 - 54r) = 0

There is one solution when the discriminant is 0. 

(18 - 54r)^2 - 4(5)(117 - 54r) = 0

r = 2(2 + sqrt(130))/27 (note that r can't be negative so it's not the other option)

Hope this was helpful. 

=^._.^=

Count on your fingers if you are unsure.

5 is just 1+1+1+1+1

1+1+1+1+1+1+1+1+1+1 is(count on your fingers) 9+1.

9+1 is 10. Carry the one one digit higher, into the tens digit

(I hope this helped)

Number of nickels = x ---> cost = $0.05x

Number of quarters = x/4 ---> cost = ($0.25 * x)/4

Cost of dimes = same as of nickels = $0,05x

No. of dimes * 0.1 = 0.05x

No. of dimes = (0.05x)/0.1 = 0.5x

Also cost of dime = Cost of quarters - $1.3

0.05x = (0.25x)/4 - 1.3

=> 1.3 = 0.0125x - 0.05x

=> 1.3 = 0.0125x

=> x = 1.3/0.0125 = 104

He have 104 nickels, 104/4 = 26 quarters and 1/2 * 104 = 52 dimes

Hope this helps:

https://drive.google.com/file/d/15jGxOK3vOHtVapUtu3FQ2TuRkMqQ9I98/view?usp=drivesdk

:)

Here's my solution. I only found one answer.

https://drive.google.com/file/d/1mnFdwXtfcPH4-ZGFjUSST-88OiC5gII5/view?usp=drivesdk

97 students

44 only spanish

53 is total people that learn Chinese (including those that learn both)

4 learn both

Here the link to my solution

https://drive.google.com/file/d/1uYDgsArHN3vg6ixQ7uKiDAIGWMeS8OZT/view?usp=drivesdk

hope this helps

Via Pythag theorem:

Distance from origin =   sqrt ( (4 + 8 cos 60 + 4)²  + (8 sin 60)² )  

1 - (22222, 22223, 22224, 22227, 22228, 22233, 1 22234, 22237, 22238, 22247, 22248, 22278, 22333, 22334, 22337, 22338, 22347, 22348, 22378, 22478, 23333, 23334, 23337, 23338, 23347, 23348, 23378, 23478, 33333, 33334, 33337, 33338, 33347, 33348, 33378, 33478)==36 combinations.

2 - Convert the above 36 combination to permutations as follows:
22222 ( 1 ) , 22223 ( 5 ) , 22224 ( 5 ) , 22227 ( 5 ) , 22228 ( 5 ) , 22233 ( 10 ) , 22234 ( 20 ) , 22237 ( 20 ) , 22238 ( 20 ) , 22247 ( 20 ) , 22248 ( 20 ) , 22278 ( 20 ) , 22333 ( 10 ) , 22334 ( 30 ) , 22337 ( 30 ) , 22338 ( 30 ) , 22347 ( 60 ) , 22348 ( 60 ) , 22378 ( 60 ) , 22478 ( 60 ) , 23333 ( 5 ) , 23334 ( 20 ) , 23337 ( 20 ) , 23338 ( 20 ) , 23347 ( 60 ) , 23348 ( 60 ) , 23378 ( 60 ) , 23478 ( 120 ) , 33333 ( 1 ) , 33334 ( 5 ) , 33337 ( 5 ) , 33338 ( 5 ) , 33347 ( 20 ) , 33348 ( 20 ) , 33378 ( 20 ) , 33478 ( 60 ) , >>Total combinations = 36
>>Total permutations = 992 [The numbers in brackets are the number of permutations for each combination.]

Not possible. Zero pairs. 

https://drive.google.com/file/d/1QJFwjlC2G-noSc299qW3-j9CXxCpR98y/view?usp=drivesdk

can you please elaborate?

Hello Guest!

(5x + 5 + 6x - 7x + 8x - 9x + 2x)(7x - 8x + 9x - 6x - 5x - 2x - 3x - 4x - x)

= - 13x(5x + 5)

  !

4 balloons = 2/8 of a smile   = 1/4 of a smile

     you want to find   2/ 4 of a smile....tiwce as much = 8 balloons

Let x-no. of cookies

John = 1/3x

Paul = (x - 1/3x) (3/4)

Paul = 1/2x

Michael = (x - 1/3x - 1/2x) (2/3)

Michael = 1/9x

Betty = 1 

Left = x - 1/3x - 1/2x - 1/9x - 1

Left = 1/18x - 1

1/18x - 1 = 1

1/18x = 1 + 1

1/18x = 2

x = 2 (18)

x = 36 (Total cookies)

Michael = 1/9 (36)

Michael = 4 cookies

Good spotting Catmg!  I missed it.

It will help if people always remember that a log is a power!

The area (rectangle) is 9 x 12  = 108 sqft

perimeter = 9 + 12 + 9 + 12

Thank you so much!

Nice work. :))

One small correction, log_2(3x) = 3, turns into 3x = 8, (2^3 = 8)

=^._.^=

Here is a similar Q   ...   put in .30   where .40 is and then solve for 'n'

https://web2.0calc.com/questions/inequality_126