All Answers 352748 Answers

This problem just requires some logic to crack it. 

Both numbers have 5 digits. A must be equal to or equal to or less than 2 because, otherwise, the result would exceed the 5-digit restriction. 4E is even, so A only has one value: 2. This leaves us with 2BCDE*4=EDCB2

4E must end in a 2. Only two values achieve this: 3 and 8. E cannot be 3 because 20000*4=80000. 8 is the only option then. This leaves us with 2BCD8*4=8DCB2

B2 must be a multiple of 4 because of the divisibility rules for 4. B cannot exceed 2 because 3000*4=12000. This would cause a carry for 2BCD8*4, and the result would be impossible. Only 1 works because that makes 8DCB2 end in a 12, which is divisible by 4. This leaves us with 21CD8*4=8DC12

4D+3 must end in a 1, so 7 and 1 are the only options. D cannot be 1 because all the digits must be unique, according to the original problem; therefore, d=7. This leaves us with 21C78*4=87C21

We have a carry of 3 from 4*7+3=31, and 4c+3 must result in a carry of 3 so that the result holds true. This leaves us with a basic algebra problem:

c=9

Therefore, \(21978*4=87912\)

Ive solved the question 

24,28,36,38,40,42,46

Yes It is

So...either 2, 3, 4, 5 or 6 people show up

And the least common multiple for  2,3,4, 5 , 6  =  60

So.....the least number he could bake with one left   is  60 + 1   = 61

Thanks, X² !!!....here's another approach.....

Let  SC  be the base of triangle RSC.....and let  its length  =  8 - x

The slope of the line segment  AC   =    (0 - 8) / (8 - 0)  =  -8/8  = -1

And the equation of the line containing this segment is   y = - x + 8  ⇒  y  = 8 - x

So...let the height of  triangle  RSC = SR   = 8 - x

And we have that the area of triangle RSC =

(1/2) (8 -x) (8 -x)  =  12.5     multiply both sides by 2

(8 - x) ( 8 - x)  = 25     simplify

x^2 - 16x + 64  = 25

x^2 - 16x + 39 =  0     factor

(x - 3) ( x - 13)  = 0

Setting both factors to 0  and solving for x produces

x = 13   (reject)   or

x  = 3   (accept)

So.... since R  lies on the line  y  = 8 - x, its coordinates are  ( 3, 5)

And the positive difference of its x and  y coordinates  =  5 - 3 =  2

Thank you for catching that \(1.1*0.9\neq 9.9\)

Constructing a diagram is a crucial step here; digesting all that information visually is extremely difficult without a visual aid. I have concocted one that I am proud of. I have tried to label everything in this diagram for your convenience. This problem most likely has many avenues toward achieving the correct answer, but I will present my approach for you:
 

In the diagram above, I have added point D, which is the intersection of point A and point C. The point lies on the origin. Let's focus on some characteristics regarding \(\triangle ACD\) .

Point A and point D have the same x-coordinate, so a vertical segment connects them. Point C and point D share the same y-coordinate, so they must be connected with a horizontal segment. \(\overline{AD}\perp\overline{DC}\) because horizontal and vertical lines are always perpendicular; thus, \(m\angle ADC=90^{\circ}\).

\(AD=DC=8\), so \(\triangle ACD\) is also an isosceles triangle.

A triangle that is both right and isosceles is also known as a 45-45-90 triangle. It is possible to observe these similarities with \(\triangle RSC\).

\(\overline{AD}\parallel\overline{RS}\) because they are both vertical lines. Whenever a parallel line cuts through a triangle, the resulting triangles are similar. In this case, \(\triangle ADC\sim\triangle RSC\) . 

\(DC=8\) and \(DS=a\) , so \(CS=8-a\) . Because \(\triangle RSC\) is isosceles, \(RS=CS=8-a\) . The area of this triangle, according to the original problem, is 12.5. We know the lengths of the side lengths, so we can determine the value of a.

Yes, it is possible to solve for a here, and it is relatively simple from here on out. However, we can take a slight shortcut. The end goal is to determine the difference of x- and y-coordinates, but 8-a represents the height of the triangle. Since 8-a=5, we know that the y-coordinate is 5. 

 (3,5) is the coordinate of point R. \(|3-5|=2\)  is the positive difference.

You can use a formula like this to solve that:

FV = PV x [1 + R]^N, where FV=Future value, PV=Present value, R=Rate(of interest), N= Number of periods.

FV = 200 x [1 + 0.08]^20

FV = 200 x[1.08]^20

FV = 200 x    4.6609571........

FV = $932.19 - The price of Apple's iThing after 20 years.

If  C  is reflected over the y axis, the point  C'  is  (3, 2)

So....the distance from  C  to C'  is just the distance  from  (-3,2)  to (3,2)  =

  √ [ ( 3  -  -3)^2  +  ( 2  - 2 )^2 ]   =

√ [ 6^2  + 0^2  ] =

√ 36  =

6 units

What is the universal set???   [ Is it all the even positive integers < 50??  ]

Just a minor typo. It should read: 0.99a^2 =0.99/1 x 100/100 =99 / 100.