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Distance is the same regardless of the speed for this question

rate x time = distance

40 m/h  * x      = distance

30 m/h * (x + 1/3)   = distance         1/3 = 1/3 hour = 20 minutes

40x  =  30 (x+1/3)

40x  = 30x + 10

10x = 10

x = 1 hr

40 m/hr x 1 hr = 40 miles       check   30 m/h x  1 1/3 = 40 miles   Check!

From 6:00 am to 2:00 pm is 8 hours.

Dropping 3^o per hour for 8 hours will result in a trop of 8 x 3^o  =  24^o.

Since the temperature started at 36^oC, the new temperature will be 36^o - 24^o  =  12^oC.

A diagonal from one vertex to its opposite vertex (through the middle of the box) can be found by using the 

"three-dimensional Pythagorean Theorem":

         Distance² =  Height² + Length² + Depth² 

--->   Distance²  =  8² + 16² + 13²

--->   Distance²  =  489

--->   Distance   =  sqrt(489)  cubic cm

hmm.. this looks like an aops problem. thus, i will not give you the direct answer so you can learn! :))

check out this example: it's the same type of problem, just different numbers. i hope this helps!

https://web2.0calc.com/questions/help_68175 

that is correct!

Since there is replacement, any card can be the first. Any card except the 13 of the first suit can be the secon. Any card except the 26 of the first & second suits. And theres only 13 cards left.

1*3/4*2/4*1/4=3/32

Introduce a new equation

x+y=c

let c be a slider.

now slide ist and see where the biggest value of c is.

I got the approx value of 2.72 but you can get the exact values from the equation.

212 - 14 - 58 - lettuce = 34     solve for lettuce  

   But I think some of those numbers in your question might be fractions?

See this first

https://web2.0calc.com/questions/question_65419

then we need to modify it by multiplying by -2

(x^2 - 6x + 4 ) x (-2) = -2x^2 +12x - 8        Vertex will be at  x = - b/2a =  - 12 / (2*-2) = 3

The use this value of x to find the 'y' value by substituting into the equation   y = .........

First box  4 choices ....2 are regular pencils    2/4 = 1/2

Second box  12 choices   ... 7 are color pencils   7/12

7/12  x   1/2 =    7/24

I answered this just yesterday.

The equation would look like this

(x - r1)(x-r2)    = x^2 - r1x - r2x + r1r2

                      = x^2 -3x-sqrt5x  - 3x+sqrt5x  +  9-5

                      = x^2 -6x + 4  

Graph #2  shows   |x-3|<4       It cannot include 7 or -1      Those would = 4 , hence the hollow endpoints

                                                                all of the nubers in between would result in <4

99km/9l =  11 km/l

12 l  x   11 km/l = 132 km     with 12 l

I'm am just writing the same as guest here. Thanks guest (below)

\(\begin{pmatrix} n\\ k-1 \end{pmatrix}\\=\frac{n!}{(k-1)!(n-[k-1])!}\\ =\frac{n!}{(k-1)!(n-k+1)!}\\\)

I 

I feel so stupid it all fell into place. Argh. Thank you so much.

Thank you so much!

-OP

1)  A cube with side length = 4 has an area of 16 for each of its sides; 6 x 16  =  96  for its total area.

     A cube with side length = 5, has an area of 25 for each of its sides; 6 x 25  =  150 for its total area.

    The total area for both is  96 + 150  =  246

    If you glue one of the sides of the smaller cube to one of the sides of the larger cube, you will remove 16 

    from each of the two cubes:  246 - 16 - 16  =  214

2)  length  =  L

     width   =  W

     height  =  H

     L · W  =  6                    --->   W  =  6 / L

     W · H  =  15                 --->   W  =  15 / H

     L · H  =  40

     Since  W  =  6 / L   and   W  =  15 / H     --->     6 / L.  =  15 / H     --->     6H  =  15L     --->     H  =  15L / 6

     Since  L · H  =  40     --->     L · ( 15L / 6 )  =  40     --->     15L²  =  240     --->     L²  =  16     --->     L  =  4

     Since  L  =  4     --->     L · W  =  6     --->     4 · W  =  6     --->     W  =  1.5

     Since  L · H  =  40     --->     4 · H  =  40     --->     H  =  10

To find a:  Evaluate  f(2)  =  2 - 5  =  -3

                 So:  when  x > 2, ax + 3  =  -3  

                                                 a·2  =  -6

                                                    a  =  -3

To find b:  Evaluate  f(-2)  =  -2 = 5  =  -7

                 So:  when  x < -2,  2x -  b  =  -7

                                            2(-2) - b  =  -7

                                                -4 - b  =  -7

                                                       b  =  3

Have the houses listed along the x-axis:

a)  Start the y-axis with 15, have a scale of 1, and end the y-axis at 25.

b)  Start the y-axis at 0 and have a maximum of 100; they will all be grouped closely together.

c)  I haven't the foggiest idea how to do this ...

Following the hint:  

First:  find the  slope:  m  =  ( y₂ - y₁ ) / ( x₂ - x₁ )

                                   m  =  ( 1 - 11 ) / ( - 2 - 3 )  =  -10 / -5  =  2

Using the equation:  y - y₁  =  m( x - x₁ )

                                 y - 11  =  2( x - 3 )

                                 y - 11  =  2x - 6

                                        y  =  2x + 5

Second: try each of the possibilities:

Choice 1:  (2, 1)   --->   1  =   2(2) + 5

                                      1  =  4 + 5

                                      1  =  9                  <---  Not true!

So, try the other choices until one of them is true ...

Arithmetic sequence:  9, x, 81

The middle term of three consecutive terms of an arithmetic sequence is the mean of the outside two:

     x  =  ( 9 + 81 ) / 2   --->   x  =  90 / 2   --->   x  =  45

Yes. it is B

  As an exercise    let's find the current through the 10 ohm resistor

9v/10 ohm  =   .9 A  

so the total current is thus  .45 + .9 = 1.35 A

the resultant resistance is thus    9 v/ 1.35 A = R = 6 .667 ohm

Is this true?

     Calculate the resultant resistance of the two resistors in parallel     1/ (1/10 + 1/20)  =  6.667   ohm  !    TRUE !

the answer actually ended up being B , hmm im not sure then. Maybe im not understanding this as much as i thought