Bosco

What is the easiest way to solve this without doing it in your head?  

Subtract 5 yards, 2 feet, 8 inches from 7 yards 2 feet.  

I guess the easiest way for me to solve it would be to convert everything to feet.  

                                                                                     21+2  =  23 feet   

I see inches in what we'll be going to

subtract so let's put some inches in that.                                          

                                                                   23 feet  =  22 feet  12 inches   

                                                15+2 feet  8 inches  =  17 feet    8 inches                             

Subtract   

                                                                                      5 feet   4 inches   

_.

All members of our painting team paint at the same rate. If 20 members can paint a 2000 square foot wall in 30 minutes, then how long would it take the  members to paint a 2000 square foot wall, in minutes?   

Did you actually read what you're asking there?  

If 20 members can paint 2000 sq ft in 30 minutes   

Then, how long to paint 2000 sq ft?    30 minutes   

_.

google translates  分解因式咋弄   as   How to factorize   

google translates  x的三次方+2x   as   x to the third power + 2x  

I assume they want      x³ + 2x  =  (x)(x² + 2)        

Not bad, but a simple arithmetic mistake did you in.   

Actually, there are two mistakes, both subtraction.  

So, we can conclude:

x=y+10

x+25=2y-50

x=2y-25                              x  =  2y – 75  

y+10=2y-25               y + 10  =  2y – 75  

y=2y-15                             y  =  2y – 85  

y=15                                –y  =  –85   

                                          y  =  85   

So, your brother has $85.  

_.

The total surface area of a box is 100. The length of the box is twice its width, as well as 3 less than its height. How many units are in the height of the box?   

L = 2W        ——>    W = L / 2   

L = H – 3     ——>    H  = L + 3   

                                        Total Area  =  2 • L • W  +  2 • L • H  +  2 • W • H    

Substitute equivalent  

terms for W and H  

                                         A  =  (2)(L)(L/2)  +  (2)(L)(L + 3)  +  (2)(L/2)(L + 3)    

                                         A  =  2L² / 2        +  2L² + 6L        +  2L² / 2 + 6L / 2  

                                         A  =  L²               +  2L² + 6L         +  L² + 3L    

                                         100  =  4L²  +  9L     

Rearrange as     

a quadratic     

                                         4L²  +   9L  –  100  =  0    

Factor                              (4L + 25)(L – 4)  =  0   

                                          4L = –25   Disregard.  A box can't have a negative length.   

                                            L = 4    

W = L / 2     ———>            W = 2   

H = L + 3     ———>            H = 7    

check answers    

                                         Total Area  =  2 • L • W  +  2 • L • H  +  2 • W • H    

                                                   100  =  (2)(4)(2)  +  (2)(4)(7)  +  (2)(2)(7)    

                                                   100  =  16   +  56  +  28    

                                                   100  =  100     

_.

One ordered pair (a,b) satisfies the two equations ab^4 = 48 and ab = 72. What is the value of b in this ordered pair?   

To find b, consider                                                  ab⁴  =  48  

We will divide both sides by ab.  

Since ab=72, we will divide the left side  

by "ab" and the right side by its equal 72.  

                                                                              ab⁴         48  

                                                                             ——   =   ——  

                                                                              ab           72  

Note that ab⁴ = (ab) * (b³)  

Cancel ab out of the left side.  

Reduce 48/72 on the right side.  

                                                                               b³           2  

                                                                             ——   =   ——  

                                                                                1            3  

                                                                                 b   =   cube root of (2 / 3)  

_.

Good catch, second guest.    

regarding      36/x + 8/(x^2) = 0  

                      Multiplying both sides of the equation by x2, we get:  

                      36 + 8x = 0   

Maybe if I write it like this,   

it will be easier to see   

                                                 36          8  

                                               ––––  +  ––––  =  0       

                                                  x            x²     

Multiplying both sides

by x², we get    

                                                        36x  +  8  =  0   

                                                                36x  =  –8   

                                                                                8 

                                                                    x  =  – –––  =  – 2/9      

                                                                                36         

_.

Find all values of x such that 3x^2 14x 8 = 0. If you find more than one value, then list your solutions, separated by commas.   

My monitor isn't displaying the signs between terms.   

I'm assuming that they should have been plus signs.  

Like this

                                                   3x² + 14x + 8 = 0    

Factor the equation   

                                                   (3x + 2)(x + 4) = 0   

Set each factor = zero    

                                                   3x + 2 = 0   which means   x = –3/2   

                                                     x + 4 = 0   which means   x = –4    

Separated by commas   

                                                     x =    (–3/2, –4)    

If the polarity of 14x was       

supposed to be negative,     

and polarity of 8 positive,    

then change the minuses   

in the answer to pluses.                 

_.

Will and Grace are canoeing on a lake.  Will rows at 50 meters per minute and Grace rows at 20 meters per minute. Will starts rowing at 2 p.m. from the west end of the lake, and Grace starts rowing from the east end of the lake at 2 p.m. If they always row directly towards each other, and the lake is 3800 meters across from the west side of the lake to the east side, at what time will the two meet?   

Will's rate is 50 m/min.  

Grace's rate is 20 m/min.  

They're rowing toward each other,  

so their rate of closure is 70 m/min.  

The lake is 3800 meters across.  

The time it will take them to meet is given by  

                                                                                    Distance  

                                                                            T  =  –––––––  

                                                                                       Rate  

                                                                                    3800 m  

                                                                            T  =  –––––––  

                                                                                    70 m/min  

The time it takes them to meet                             T  =  54.29 min  

Note that (0.29 min • 60 sec/min)  =  17 seconds

The time on the clock is                                             2:54:17 pm 

_.

Each face of a cube is painted randomly one of the colors red, orange, yellow, green, blue, purple, brown, black, or white. What is the probability that the cube has at least one pair of faces that share an edge and are the same color? Express your answer as a decimal to the nearest thousandth.    

The first face that we're comparing can be any of them,   

so all that needs to concern us is the second face.    

There are 4 faces that share an edge with the first face.  

All of them except the face directly opposite.  

There are 9 colors available, so the second face has a 1/9   

chance of being the same color as the first face.   

But there are 4 adjacent faces, so you have 4 shots at   

getting the same color.  This makes the probability 4/9.   

Expressed as a decimal fraction, 4/9 = 0.444.  

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