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OK......

4^x  = 3    ⇒  (4^x)^2  = 3^2  ⇒   (4^x)^2  = 9

So....

4^(2x - 2)  =

(4^2)^(x - 1)  =  

( 4^2)^x  /  (4^2)   =

(4^x)^2  / ( 16)  =

9 / 16

Thank you

https://web2.0calc.com/questions/please-help_50163

It would be interesting to find a triangle in which F and F' share the same point. 

Since ZAX  is equilateral....then  AX  = 30  / 3  =  10

And  FLAX  is a square.....its area  =  (AX)^2  = (10)^2  = 100

b ( b^4 * b^3)^2  =  b^(3x)

b ( b^7)^2   = b^(3x)

b (b^14)  =  b^(3x)

b^15  =  b^3x

15 = 3x

x  = 15 /  3  =   5

We  have  the following relationship

(1/2) length of hypotenuse  / 6   =  6  /  (1/2) length of hypotenuse

cross - multiply

[ (1/2)lengt of hypotenuse ] ^2  =  6 * 6

[ (1/2) length of hypotenuse ] ^2   =  36          take  the postive root of both sides

(1/2) length of hypotenuse  =  6

So

Length of hypotenuse  =  2 * 6   =  12

You're welcome.....   

Welcome.....

thank you!

thank you so much!

Ways to roll a "5"  =

(1,4) (4,1) (2,3) (3,2)  =  4  ways

Ways  to roll a "9"  =

(4,5) (5,4) ( 6,3) (3,6) =  4 ways

D  Each  have  the same  chance  of  rolling their sum  = (4/36) ....the game is fair

2)   With the border the area becomes   10 x 12 = 120  m²      subtract the garden  4x6

       120 - 24 = 96 m²

2. A 3 meter wide sidewalk surrounds a rectangular garden that is 4 meters by 6 meters. Find the area of the sidewalk only.

If you can picture this......

We  have  four   3 x 3 squares at the corners =  4 * (3 * 3)   =  36 m^2

Also  we  have  two  4 x 3  rectangles on two sides  =  2 * ( 4 * 3)   =  24 m^2

And we  have two  6 x 3  rectangles on two sides  =  2 * ( 6 * 3)  = 36 m^2

Total area of sidewalk  =  (36 + 24 + 36)   =   96 m^2

First  one

Note  that  AB / DE  =  22 / 11  =  2 / 1  =  2

So  each correseponding side of ABC to that of DEF  is  twice as long

So

x  = 34 /  2   =  17

And 

y  =  2 * 13   =   26 

Number  on  any particular  square =  2^(n - 1)

On the  31st  square  we  have   2^(31 - 1) = 2^30  =  1073741824 grains

Total  cumulative  number  through  square  n  =  2^n  - 1 =  2^31 - 1  =  2147483647 grains

Total weight  =  2147483647 /  7000   ≈  306783 lbs

I have no idea which current the question is asking about......I assumed both since it did not specify.....

Should I show both values for current in my answer or should I pick just one? And thank you for your help.

I have revised my answer for "B"

thank you so much! I don't know how I would've gotten through without you! :D

4.The ratio of similar triangles △ACB to △DFE is 2/5 and  AB = 8.  What is the length of DE? 

DE / AB =  5/2

So

DE  =  (5/2)AB

DE  = (5/2) * 8   =   20

5. △ACB is similar to △DFE.  The m ∠ABC = 35 and the m∠ACB = 80. What is the measure of ∠FDE?

FDE  =  CAB   =  180 - mABC -m ACB =    180  - 35  - 80  =  180  - 115   =  65°

It appears you have "A'" correct

B) if the pump is 72 % efficient....it wastes 28% of the power supplied to it to pump the water ( friction/heat noise vibration etc)

         .72 x  = 858.37

            x = power required = 858.37/.72 = 1192.2 watts required         if 28% is wasted

2. A triangle with sides 8m, 11m and an included angle of 45°.  

How many triangles can be produced: _______

Explain:

One triangle.....we  have a SAS  situation.......the triangle  is well-defined

3. A triangle with angles 

25°, 56°, and 99°

How many triangles can be produced: _______

Explain:

An infinite  number  of similar triangles could  be  produced

1. Three segments have a total length of 26 inches. The first segment is two less than three times the second segment. The third segment is one more than five times the second segment. What are the lengths of the three segments? 

All three variables must be defined in terms of x.

(3x - 2)  +  x  +  ( 5x + 1)  =  26

9x - 1  = 26

9x  =  26 + 1

9x  =  27

x = 27 / 9  =  3

First segment  =   3(3) - 2   =   7  in

Second segment =  3  in

Third segment  =  5(3) + 1   =  16 in

If you did the first parts A and B correctly

  know that   electricl watts =   V * I        where v = volts    I = current

     858.37 w = 220 v   * I

        I = 3.9 amperes

   B)   If answer A is correct , this should be   858.37/.72 = 1192.2 watts

                    1192.2 watts = 220 v * I

                        I = 5.42 amperes

See this question for methodology to check your  'A' answer:

https://web2.0calc.com/questions/any-help-would-be-appreciated-thank-you_1