All Answers 358087 Answers

7 * 50 minutes = 350 minutes     =   5 hours and 50 minutes   teaching

50 + 30   = 80 minutes  of lunch  = 1 hr and 20 minutes   lunch

So

350 + 80 =   430 minutes   =  7 hours and 10 minutes [ total time]

Note that  m< BRP  and m<CRQ = 90       

And m<BRP + m<BPR  = 90

Therefore, m<BPR  = m<CRQ

And m< PBR = m <QCR = 90

Therefore, by AA congruency.....ΔPBR is similar to ΔRCQ

Then

PB/BR  = RC/CQ      

4/ BR  = RC/18       but RC  = 2BR  ...so

4/BR  = 2BR/ 18    cross-multiply

4*18  = 2BR^2

72  = 2BR^2      divide both sides by 2

36 = BR^2          take the square root of both sides

6  = BR      so.........CR  = 2BR  = 2*6   = 12

And by the Pythagorean Theorem

PR^2 =  (PB^2 + BR^2) =  4^2 + 6^2  = 16 + 36   = 52

Likewise

RQ^2  = (RC^2 + CQ^2) = 12^2 + 18^2  =  144 + 324 = 468

So, again by the Pythagorean Theorem:

PQ^2  = RQ^2 + PR^2

PQ^2 =  468 + 52

PQ^2  = 520      take the square root of both sides

PQ = sqrt(520)  = 2sqrt(130)  = about 22.8

An open square-based container is made by cutting 4cm square pieces out of a piece of tinplate. If the volume of the container is 120cm^3, find the size of the original piece of tinplate

The dimensions of the box will be, w x w x h.

 Each side will be w x h

\(\text{side area } = w h = 4 \\ \\ h = \dfrac 4 w\)

The volume is given by

\(V = w^2 h = 120 \\ \\ w^2\left(\dfrac 4 w\right) = 120 \\ \\ 4w = 120 \\ \\ w = 30 \\ h = \dfrac 4 {30} = \dfrac 2 {15}\)

So the size of the original piece of tin plate that is the bottom is w x w, or 30x30 cm²

okay thanks CPhill.

Simplify the following:
5 x-3 (2 x-4 y)-5 (3 x+4 y)

-3 (2 x-4 y) = 12 y-6 x:
5 x+12 y-6 x-5 (3 x+4 y)

-5 (3 x+4 y) = -15 x-20 y:
5 x-6 x+12 y+-15 x-20 y

Grouping like terms, 5 x-6 x+12 y-15 x-20 y = (12 y-20 y)+(5 x-6 x-15 x):
(12 y-20 y)+(5 x-6 x-15 x)

12 y-20 y = -8 y:
-8 y+(5 x-6 x-15 x)

5 x-6 x-15 x = -16 x:
-16 x-8 y

Factor 8 out of -8 y-16 x:
Answer: |   8 (-y - 2x)

the answer is 15

Solve for x:
x (x+10) = 39

Expand out terms of the left hand side:
x^2+10 x = 39

Add 25 to both sides:
x^2+10 x+25 = 64

Write the left hand side as a square:
(x+5)^2 = 64

Take the square root of both sides:
x+5 = 8 or x+5 = -8

Subtract 5 from both sides:
x = 3 or x+5 = -8

Subtract 5 from both sides:
Answer: |  x = 3           or           x = -13

The inverse of the cos function. It helps you find angles - you can look up tutorials on youtube if you want.

What you need to do is expand the brackets:

x(x+10)= 39

First mutiply each term in the brackets by x. so x times x = x^2. Then x times 10 = 10x.

Now your equation is x^2+10x = 39

You'll find that when you substitute 3 into your equation, it will equal 39. 

c = 4 because 3*4= 12 and 12+4= 16

I don't see diagram, either....but each dial has 5 possible settings  [ if we allow for repeats]....so....

5 * 5 * 5   = 5^3   = 125 possible combinations

4 times 2= 8 so w eget 9/3 + 8. 8=24/3 so now we gwt 9/3 +24/3=33/3=11

Hope that helps!!

 C=2πR

Mmmmm...I'm not sure about Guest's answer.....it could be correct......but consider

It will take Rick 18km/ [9k//hr]  = 2 hours to finish  

And runnining at his current pace, it will take D**k 2.5 hours to finish

But...he needs to cut this to 2 hours just to finish even with Rick

Call his normal rate per hour, R  and call his increased rate in order to catch Rick, (R + x)

And since R * T  = D.......we have this situation......

At his current rate, the distance he has left to run = R *2.5

And at  his his increased rate, the distance he has left to  run is the same....and this is given by:

(R + x)*2  = D     .....so.....equating the distance, we have......

R * 2.5  =  (R + x) * 2    simplify

2.5R  = 2R + 2x       subtract 2R from both sides

.5R  = 2x      divide both sides by 2

.25R   = x 

So.....he needs to run (R + .25R)    = 1.25R   = 5/4 his current rate just to tie Rick   

Consider this in light of the Guest's answer.......if 5/4  of D**k's current rate = 11.25km/hr, then his current rate must  just be 4/5 of this......but 4/5 of this = 9km/hr......the very same rate that Rick runs.....and if D**k runs at the same rate as Rick, he would be even with him, not 30 minutes behind....!!!

In my opinion.....we actually can't provide an exact numerical answer to this because we would have to know how far D**k has run and the time he has taken to do so to get his current rate.....

I may have blown a fuse, here......can some other mathematician look at  this   ????

Diameter x π

π= Pi (3.14...)

D= Diameter

R= Radius

Radius formula = D / 2

Diameter formula = (R)(2) or R x 2

-32

2 x 3.14 x radius

or 3.14 x diameter

the order of operations is always the same

looks like it is either 12 or 14...

it is a boolean algebra question T_T "A and B or C" can be written as "A && B || C" or A∧B∨C. A, B, and C might not be 1s and 0s, but you can apply the operation to every bit of the the binary version of A, B, and C (1010, 1011, and 1100). 

1010 && 1011 == 1010

1010 || 1100 == 1110

the decimal of 1110 is:

14

yes, I awnsered my own question lol. I just wanted to see if anyone knew what I was talking about.

-3(x-5)=15

-3x + 15=15

-3x=0 divide both sides by -3

x=0

y=1/2*x; For y=15 x=2*y=2*15=30

Answer:30

The probability of Landing on 4 is=1/5

The probability of NOT landing on 4 is=1 - 1/5 =4/5

the square root of a billion is 31622.7766017 and the square root of five is 2.25

6/8 + 7/8 =13/8=1 5/8