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7x - 3 = 60

7x = 63

x = 9

11y + 5 = 60

11y = 55

y = 5

What is the ratio for Sin C in the following triangle? Make sure your answer is in simplest radical form.    

                                                                                                   opp   

I don't see a triangle, but sine is opposite over hypotenuse.     ––––  

                                                                                                    hyp  

Hello Guest! This is a great question!

For the first digit, there are 10 choices: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9

The second digit there are 26 choices, and I am not going to list them all!

The last digit has 10 choices again.

So, in all, there are 2600 possible codes.

For it to contain an odd digit, there are 10 choices for the first or second, and 5 odd choices for the other digit. This makes there be 50 choices with od numbers.

So, here is our answer. The proability is:

50/2600 or 1/52.

I really hope this helped.

The Math Whiz

You did not miss any! The answer of 16 integers that satisfy n is correct!

Thank you so much!!! 😊😊😊

Yep....hope I didn't miss any  !!!!

Thank you so much! So, just to clarify, the numbers under the "n" column are the numbers that satisfy it?

Mmmm....good question ....here's my best attempt ....

a     b         n             a       b       n               a         b       n          

1     3         1     

2     3         8            2       5       32              2        7      128       

3     3       27            3       5      243 

4     3       64            4       5     1024

5     3      125                  

6    3       216

7    3       343

8    3       512

9    3       729

10  3     1000

11   3     1331

12  3      1728

I love puzzles, I am going to try them!

Impressive, Math Whiz,   that you know all the Prezzes  !!!

I can name  them from about  Hoover on , but before his time  I'd need Wikipedia  ( or you  !!!  )

Area of rectangle  =  7  x 4   = 28  cm^2

Area of trapezoid  with height of   8  and bases of 7  and 19  =

(1/2)  ( 8) ( 7 + 19 )  =    104 cm^2

Total area =   ( 28  + 104)  =   132 cm^2

Second one

Angle  E  =  180  -  50  -  66   =  64°

Law of Sines :

8 / sin 64°  =   EF /sin 50°

EF  =  8 sin 50°  / sin 64 °  =  6.8

Area  = (1/2) ( 6.8 * 8)  sin  66°  =  24.8 cm^2

Hello,

Since I have memorized all the presidents, let me say, it was Calvin Coolidge, nicknamed Silent Cal, who hid under his desk to confuse his bodyguards.

He took office upon the death of Warren Gamaliel Harding, who he served as vice president during the term of., and both were Repulican.

The Math Whiz

\(y = {-(x+1)(x+1)(x-0)(x-2)}\)
 

Why? You can see the roots at -1, 0 and 2. The polynomial is of order 4 (it does not look like order 3), but we only found three roots. One has to be a double root. It is the one at \(-1\), as the graph "touches" the x-axis but does not cross it. Take the corresponding factor twice.

Insert a value: \(x=1\), we obtain \(-4\). It should be \(+4\). Therefore the factor \(a\) is \(-1\).

Cheers

First one

sin  F /  5  =  sin 35 / 9

sin F  =  5 sin 35  /9

arcsin  ( 5 sin 35  / 9) = F  ≈  18.58°

Angle  E  =180 -  35  -18.58   = 126.42°

Area  =  (1/2) (5 * 9) sin 126.42   ≈   18.1 cm^2

We have two  inequalities  to solve

(1/3)t  - 5 <  t  - 2                   and                 t  - 2 ≤ -3t + 7

add 2 to both sides,                                       add 2, 3t to both sides                                 

subtract 1/3t from both sides                         

-3 < t - (1/3)t                                                   4t ≤  9

-3  < (2/3)t                                                         t ≤  9/4

(-3)(3/2) < t

-9/2 < t

So  t  =   ( -9/2 , 9/4 ] 

The answer is 17.

9.17

There are 3 times the dogs as children.

So, let's say that there are 5 children.

Based on the statement, there are 3 times 5 children number of dogs.

- That's 15 dogs; or 3* the number of children(5).

In other words, the expression is 3c.

Area  =

2 * side^2  ( 1 + sqrt 2 )  =   

2 * (20)^2  ( 1 + sqrt 2)  = 

800 ( 1 + sqrt 2) ≈  1931.37 cm^2

The altitude, A,  can  be found as

cos 58° =  A / 44

A  =  44 * cos 58°

And x  can  be found as

tan 48°  =  A /  x

x = A /  tan 48°   =   44 *cos 58° / tan 48°  =  21

One  rectangle  with  dimensions of  4  x 8   =  32 ft^2

One  trapezoid  with bases of   8  and 14  and a  height  of  4

Area  =   (1/2) height  ( sum of bases)  =  (1/2) ( 4) ( 8 + 14)  = 44 ft^2

Total area=  (  32 + 44)   =   76 ft^2