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Use the Pythagorean Theorem.

a^2+b^2=c^2 is the formula.

Since a=5

          b=12

We can plug these values in.

5^2+12^2=c^2

25+144=169 (or c^2)

the square root of 169 will get us 13.

Hence, the third side length is 13 units.

Hope this helped!

Check https://brainly.com/question/12420955 

Hope this helped~!

Nice, Chris!

x + y  = 4

x^2  + y^2   =22

x^4 = y^4  - 176√7

Rearranging the last equation we have  that

x^4 - y^4  =  -176√7        factor

(x^2  - y^2) ( x^2 + y^2)  = -176√7

(x + y) ( x - y) ( x^2 + y^2)  = -176√7       subbinng into this we have  that

(4) (x - y) ( 22) = -176√7

88 ( x - y)  = -176√7         divide both sides by  88

x - y =  -2√7

So

x + y =  4

x - y  =  -2√7      add these

2x =  4 - 2√7       divide both sides by 2

x =  2 - √7

And

( 2 - √7)  +  y  = 4

y =  4 - (2 - √7)

y =  2 + √7

In the range  0.000 < x < 0.025  the value will be  -2 - (-2)  =  0.     --->     0,025 - 0.000  =  0.025

In the range  0.100 < x < 0.250  the value will be  -1 - (-1)  =  0      --->     0.250 - 0.100  =  0.150

The value won't be zero for all x in the range (0,1).

0.025 + 0.150  =  0.175

The full distance from 0.000 to 1.000  =  1.000

Probability  =  0.175 / 1.000  =  0.175

(a - 4) (b - 4)  =  

(ab)^2 -  4(a +b)  +  16       (1)

By Vieta

The  sum of  the roots   a + b =  -1/7     (2)

And the product of the roots,  ab  =  -5/7 =  -5/7      (3)

Subbing   (2)  and (3) into (1)  we get that

(-5/7)^2  - 4(-1/7)  +  16  = 

25/49  + 4/7  + 16  =

[25  + 28 + 784 ] / 49 

837 / 49

By the ratio, 5:3. (Each number)

what do you multiply 62 by confused

I added 5+3 to get 8, and did 500/8=62.5. 

Since 62.5 rounds down to 62, I knew that 62 was the number that was going to be multiplied.

Hope this helped!

so how do you work out how much he made

Good job, jfan! 

a) Since he has 500 ml total, we need to find the greatest possible amount where the ratio 5:3 will add up to 500 or less. 

5:3 times 62 will do that! 

62*5=310 parts of lime juice

62*3=186 parts of lemonade.

Does this make sense?

Here's away to prove  this

Connect BD

Since  AB  =AD.....then in triangle DAB angles ADB  and ABD  are  equal =  [180 - 110]/2  =

70/2 =  35°

So angle CDB  =180  -65 - 35 =  80°

And  angle BCD  = 20°

So...in triangle CDB  angle CBD  =   180  - 80 - 20  = 180 - 100  = 80°

But....in triangle  CDB,angles  CBD  are equal

So....this means that  CB = CD

But  since  CB = CD   and AB = AD....then ABCD is a kite  because it has two pairs of equal adjacent sides

no problem

Of course, gimme a second....

Hint:

Factor the equation, then find the roots of it (a+#)(b+#) Then, do (a-4)(b-4)

Hope this helped!

sorry i am just cofused i got 5 but can you plz recheck

thank you

Do you know how you got this equation? Could you possibly break it down for me? Thank you so much for your answer, by the way. It is very elegant.

Hint:

Since the ratio is 5:3, if we have 300ml lime juice and 200ml lemonade, we can easily create a 5:3 ratio with one of these as the base.

Hope this helped!

Anytime :D

thank you so much

1) To determine which trigonometric rule to use, identify your given values:

Given angle: 60°     Opposite side of the given angle: 21 inches     Hypotenuse: x

2) Use the trigonometric rule that will help you solve in your problem.

Sin θ = opposite side / hypotenuse

3) Plug in your values. 

Sin (60°) = 21 / x

4) Solve.

Sin (60°) = 21 / x

√ 3 / 2 = 21 / x

√ 3 x = 21 (2)

√ 3 x = 42

x = 14√ 3 or 24.24871130....

If you have any questions, just let me know!! 

Sorry I'm not CPhill... but here.

Since we know supplementary angles and vertical angles, we can solve this easily.

Angle BCD=20 degrees

Angle CDA=115 degrees.

That means Angle CBA is also 115 degrees, which makes this shape a kite.

Hope this helped!

CPHILL plz help

Equation: (2-1)((3-1)+(4-1)+(5-1)) + (2)((3)+(4)) + (12) = 35 with a total of 119 possibilities.

You can solve this now :D