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Let M be the amount that Matthew had in the beginning

Then Elvis had  M + 247.60

When Matthew spends 25% of his money he has 75% left =  .75M =  (3/4)M = (6/8)M

When Elvis spends 3/8 of his  money he has  (5/8)( M + 247.60) left

So  together, they have  506.75 left....so...in  equation form, we have

(6/8)M + (5/8)(M + 247.60) = 506.75

(6/8 + 5/8)M + (5/8)247.60 = 506.75

(11/8)M  + 154.75 = 506.75

(11/8)M = 50675 - 154.75

(11/8)M = 352

M = 352 ( 8/11) =   256  =what Matthew had at first

a)  Matthew had  .75 * 256 =  $192  left

b) Elvis had 256 + 247.60  = $503.60 at first

5^(2r-3)  = 25

Express 25  as 5^2

5^(2r-3) = 5^(2)

The bases are the same, so solve for the exponents

2r -3 =   2         add 3  to each side

2r = 5              divide both sides by 2

r = 5/2

The vertex is a point where the extremum of a parabola lies. The extrema can either be the maximum or the minimum depending on the parabola. 

For a parabola defined as \(f(x) = ax^2 + bx + c\), the point of the vertex lies at \((\frac{-b}{2a},f(\frac{-b}{2a}))\).

Convert 1357 from base 9 to base 10 =1024

Convert 100 from base 4 to base 10 =16

Convert 2460 from base 8 to base 10 =1328

Convert 5678 from base 9 to base 10 =4202

[1024 / 16] - 1328 + 4202 ==

64  -  1328  +  4202 ==e

- 1264  +  4202 ==2938 in bas 10

The admin messaged me. They said that now all new messages/questions are flagged for moderation, and within a few days, a volunteer-mod-person will check it and let the question through (something along the lines of that). Probably for safety and like making sure the question is ok

... *forgot about the moderation thing. my post is invisible for now.. hehe

p = 3 + 2q 

r = 9 + p - p 

r = 9 

q = -2 + q - 2r 

0 = -2 + -2r 

2 = -2r 

r = -1 

There are 2 different r values , thus there is no solution to this system 

It is correct, could you give us some examples of other inverse functions?

Use algebra and list the equations for each situation:

6 stamps situation : where x = number of friends 

6x + 5 

7 stamps situation : x = number of friends 

7x -2 

Set them to equal each other 

6x +5 = 7x -2 

solve : 

x = 7 

Thus he has 7 friends 

7800 / 1000 ==7.8 Liters in Car A

Let the amount of petrol used by each cars==P

10.3  -  P ==6 * [7.8 - P], solve for P

10.3  -  P ==46.8  -  6P

- P + 6P ==46.8  -  10.3

5P == 36.5

P == 36.5 / 5

P ==7.3 Liters of petrol used by each car.

Pearl writes down seven consecutive integers, and adds them up. The sum of the integers is equal to $21$ times the largest of the seven integers. What is the smallest integer that Pearl wrote down?   

Let the smallest integer be represented by x.   

Since the integers are consecutive, each following   

integer is one larger than the integer before it.  

(x)  +  (x + 1)  +  (x + 2)  +  (x + 3)  +  (x + 4)  +  (x + 5)  +  (x + 6)  =  (21) • (x + 6)    

                                                             7x + 21  =  21x + 126   

Subtract 7x from both sides   

                                                                     21  =  14x + 126               

Subtract 126 from both sides                     

                                                                  –105  =  14x   

Divide both sides by 14   

                                                                        x  =  –7.5   

check answer    

                         (–7.5) + (–6.5) + (–5.5) + (–4.5) + (–3.5) + (–2.5) + (–1.5)  =  (21) • (–1.5)        

                                                                                                           –31.5  =  –31.5  

_.

This is wrong. There are infinitely many linear functions that are an inverse of themselves.

My answers are also all flaged for moderation, but I think it is pretty obvious why. 

using y - 2x = 3 

We get that y = 2x + 3

Substitute that into the second equation 

-x = (2x+3) - 9 

-x = 2x - 6 

6 = 3x 

x = 2 

and 

y = 7 

According to the given information, the wall is 12 meters tall and 120 meters long. This means that the total area of the wall is \(12\text{m} * 120\text{m} = 1440\text{m}^2\).

Also, a gallon of paint covers \(150\text{ft}^2\). Notice how \(\text{ft}^2\) and \(\text{m}^2\) are different units, so we have to perform a conversion so that we can compare these units. Luckily, the problem provides the conversion factor, namely \(1 \text{ft} = 0.3048\text{m}\).

\(150\text{ft}^2 * \frac{0.3048^2 \text{m}^2}{1^2 \text{ft}^2} \approx 13.9355\text{m}^2\). In other words, a gallon of paints covers \(13.9355\text{m}^2\) of area.

Now, \(\frac{1440\text{m}^2}{13.9355\text{m}^2} \approx 103.3335 \text{gallons}\) of paint. However, this is not the final answer because you can only purchase whole gallons of paint. You could purchase 103 gallons of paint, but you would require 0.3335 more gallons of paint to complete the job. Therefore, you would be forced to purchase 1 more gallon of paint. In total, you would need 104 gallons of paint, which is the smallest whole number of gallons to cover the whole wall.

The equation  y=-16t^2 +80t describes the height (in feet) of a projectile launched from the ground at 80 feet per second. At what  t will the projectile reach 36 feet in height for the first time? Express your answer as a decimal rounded to the nearest tenth.    

y  =  –16t² + 80t describes the height, so let's just set y to the desired height and see what happens.   

                                                                  36  =  –16t² + 80t      

Subtract 36 from both sides.                       0  =  –16t² + 80t – 36   

Multiply both sides by –1.                         16t² – 80t + 36  =  0  

Divide both sides by 4, to get     

more manageable coefficients.                   4t² – 20t + 9  =  0   

Factor.                                                        (2t – 1)(2t – 9)  =  0    

                                                                    2t  =  1      ----->  t  =  0.5 sec   

                                                            and  2t  =  9      ----->  t  =  4.5 sec   

The problem asks for the time  

to get to 36 feet on the way up,       

so it's the smaller answer.   

check answer    

                                                          y  =  –16t² + 80t    

                                                          y  =  –(16 • 0.25) + (80 • 0.5)    

                                                          y  =  –4 + 40    

                                                          y  =  36       

_.

1600/20 = 80 square feet per person

Now since they all do it at the same time then "

8/3 sq feet per minute therefore 

15 x 8/3 = 40 ft per minute 

1800 / 40 = 45 minutes 

for proportion problems always break down the answer into per __ unit , (small as possible) 

@anitbiotics   >>> sigh, what did I do for my message to deserve moderation... <<<    

Mine have been getting flagged for moderation, too.  Like you, I also wondered what I had done to get in the doghouse, so I messaged a Moderator and asked.  It turns out that many posts are getting flagged for moderation.  I don't know how the posts are selected.  

_.

Keiko tosses one penny and Ephraim tosses two pennies. What is the probability that Ephraim gets less heads than Keiko gets?  Express your answer as a common fraction.    

For Ephraim to get fewer heads than Keiko, then Keiko has to get heads and Ephram no heads.  

If Keiko does not get heads, Ephram can't get fewer, because it would have to be fewer than zero.  

The probability that Keiko's toss comes up heads is 1 / 2.   

Ephraim's toss can come up one of four ways:  they are HH, TT, HT, or TH   

Only one of the results contains zero tails, so the probability of that is 1 / 4.   

The probability of both things happening simultaneously is  (1 / 2) • (1 / 4)  =  1 / 8       

_.

In a store window, there was a box of berries having a total weight of 200 kg.  The berries were 99% water, by weight.  After two days in the sun, the water content of the berries was only 90%, by weight.  What was the total weight of the berries after two days, in kg?   

You're starting with 200 kg of berries, and 99% of that is water.  

Since they're 99% water, that means that there's 1% of solid stuff.  

1% of 200 kg means that there are 2 kg of solid stuff.   

Some of the water evaporates in the sun, but the solid stuff doesn't.  

So, after the evaporation, there still remains the same 2 kg of solid stuff.  

Since the new water content is 90%, that means that now the solid stuff is 10%.  

So 2 kg (the solid stuff) is 10% of the total weight.  

That means the new total weight is 20 kg.  

_.

If I give my brother 5 dollars, then we will have the same amount of money. If instead he gives me 25 dollars, then I'll have twice as much money as he will have. How much money does my brother currently have (in dollars)?  

Let M stand for My original amount  

Let B stand for Brother's original amount   

                                                             (M – 5)  =  (B + 5)   

                                                             (M + 25)  =  (2)(B – 25)  

                                                              M – 5  =  B + 5   gives us  M = B + 10    (1)  

                                                              M + 25  =  2B – 50                                 (2)  

Substitute the value of M from (1)   

into the equation (2)                             B + 10 + 25  =  2B – 50   

Combine like terms                                          85  =  B    

                                                   Brother has 85 dollars .   

The problem doesn't ask for My original amount but it's B + 10 = 95  

Check answer  

If I give my brother 5, then I'll have 90 and so will he, so we have the same.  

If my brother gives me 25, then I'll have 120 and my brother will have 60.  

_.