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The whole numbers from 1 upwards: 1, 2, 3, and so on

The wall and the ground form a right angle...so we can use the Pythagorean theorem to find  x .

x² + (x + 5)²   =  18²

                                                   Multiply out  (x + 5)²  .

x² +  (x + 5)(x + 5)  =  324

x² + x² + 10x + 25  =  324

                                                  Combine  x²  and  x²  , and subtract  324  from both sides.

2x² + 10x - 299  =  0

Now we can use the quadratic formula to solve for  x  .

\(x = {-10 \pm \sqrt{10^2-4(2)(-299)} \over 2(2)} \\~\\ x={-10 \pm \sqrt{100+2392} \over 4} \\~\\ x={-10 \pm \sqrt{2492} \over 4} \\~\\ x={-10 \pm 2\sqrt{623} \over 4} \\~\\ x={-5 + \sqrt{623} \over 2}\,\approx\,9.98 \qquad \text{ or }\qquad x={-5 - \sqrt{623} \over 2}\, \approx\, -14.98\)

Since  -14.98 causes a negative length for the side on the ground..... x must be ≈ 9.98

So, the length of the side on the wall  =  \({-5 + \sqrt{623} \over 2}+5\,\approx\,14.98\)   feet

Mass = Density * Volume

So.......divide both sides by Volume 

Density  = Mass / Volume  =  8.76 g / 3.07 cm^3  ≈  2.853 g / cm^3

What is the answer to 1+3(4-3n)=85

Hi guest!

\(1+3(4-3n)=85\)

\(3(4-3n)=85-1\\ 4-3n=(85-1)/3\\ -3n=\frac{84}{3}-4\\ -3n=24\\ \color{blue}n=-8\)

  !

Corresponding angles are equal

I think you might mean "complementary"  angle

If so.....complementary angles always sum to 90°

So.....  call the angle you're looking for, "x"

So we have that

52 + x  =  90         subtract 52 from both sides

x =  38°

    (   1 + (-8) - ( 2 - (-1)     )     *     (   -7/2   )     /     (   -1/4 - (-1)   )

I'm guessing that you meant to put another parenthesees here..

    (   1 + (-8) - ( 2 - (-1) )   )     *     (   -7/2   )     /     (   -1/4 - (-1)   )

=  (   1 -    8   - ( 2  + 1  )   )     *     (   -7/2   )     /     (   -1/4   +  1   )

=  (   1 -    8   -       3         )     *     (   -7/2   )     /     (        3/4        )

=  (             -10                 )     *     (   -7/2   )     *     (        4/3        )

=                                             140 / 3

\(4\times7y+9+1=10\)

\(28y+9+1=10\)

\(28y+10=10\)

\(28y+10-10=10-10\)

\(28y+0=10-10\)

\(28y=10-10\)

\(28y=0\)

\(\frac{28y}{28}=\frac{0}{28}\)

\(\frac{1y}{1}=\frac{0}{28}\)

\(1y=\frac{0}{28}\)

\(y=\frac{0}{28}\)

\(y=0\)

Now put the answer you came up with and put back into the original equation and solve to see if the answer you came up with is the correct answer.

\(4\times7y+9+1=10\)

\(4\times7\times0+9+1=10\)

\(28\times0+9+1=10\)

\(0+9+1=10\)

\(9+1=10\)

\(10=10\)

Because you came up with \(10=10\), that means that \(y=0\) is the correct answer.

\(4(x+1)>-4\) or \(2x-4≤-10\)

Firstly solve for x in the first inequality.

\(4(x+1)>-4\)

\(4x+4>-4\)

\(4x-4+4>-4-4\)

\(4x-0>-4-4\)

\(4x>-4-4\)

\(4x>-8\)

\(\frac{4x}{4}>\frac{-8}{4}\)

\(\frac{1x}{1}>\frac{-8}{4}\)

\(1x>\frac{-8}{4}\)

\(x>\frac{-8}{4}\)

\(x>-\frac{8}{4}\)

\(x>-\frac{2}{1}\)

\(x>-2\)

Secondly solve for x in the second inequality.

\(2x-4≤-10\)

\(2x-4+4≤-10+4\)

\(2x-0≤-10+4\)

\(2x≤-10+4\)

\(2x≤-6\)

\(\frac{2x}{2}≤\frac{-6}{2}\)

\(\frac{1x}{1}≤\frac{-6}{2}\)

\(1x≤\frac{-6}{2}\)

\(x≤\frac{-6}{2}\)

\(x≤-\frac{6}{2}\)

\(x≤-\frac{3}{1}\)

\(x≤-3\)

Thirdly put both answers together with the word "or" in between.

\(x>-2\) or \(x≤-3\)

Forthly, put answer in interval notation.

\((-2,∞)\) or \((-∞,-3]\)

\((-∞,-3]\) or \((-2,∞)\)

Lastly, look at the list of A. B. C. and D. and figure out which one matches the answer.

A.  (-∞,-3] or \((-2,∞)\)

-5  <  a - 4  <  2       Add  4  to each number.

-1  <  a  <  6

  a   is bigger than  -1 , but less than  6  .  On a number line, this is...

 1+3(4-3n) = 85           distribute the 3 across the terms in the parentheses

1 + 12 - 9n  = 85         simplify

13 - 9n  = 85        subtract  13 from both ides

-9n  =  72             divide both sides by 9

n = -8

4*7y+9+1=10

 10

-  1

-  9

--------

0

so then get 4*7y to 0 (so y = 0.....giving you 4*7y......4*(7*0).......4*(0)....0)

so y = 0

I could be wrong, but it may be right

log_a14

Given  log_a2=3.01, log_a6=.778 and log_a7 is .845

Note that we only need   log_a 2 = 3.01   and log_a 7  = .845     to solve this

By a log property......log m  + log n  =  log ( m * n)    ....so.....

log_a 2  +   log_a 7  =     log_a  ( 2 * 7 )  =   log_a (14)

3.01    +   .845   =    log_a (14)   =   3.855

BTW -  "a"  couldn't be a "real" base!!!

Yep, -7

And so it's -7??

0.16?

And so the other answers are right, right?

OK.....except for the last one

Think about this

(2/5) (5/2) * -7

What is the product of the first two terms ???

Wow, Gh0sty.......!!!

Very nice.....!!!!.......

whenever you are multiplying by 10, you just move the decimal over 1, so 7/8 becomes 8.75, or 8 3/4

Correct me if I'm wrong.

And I put the answer in terms of pi. Use a calculator to put the answer to decimals.

Ignore those red and orange lines. My mistake.

Correct-a-mundo, NSS!!!!!!

yes ur

Here's my best attempt at this one......whether it's the correct answer, I don't know.....!!!

Note that any four digit number can be written as

1000a + 100b + 10c + d

And let the sum of its digits be     a + b + c + d

And we're told that

1000a + 100b + 10c + d =  109 (a + b + c + d)     distribute the 109

1000a + 100b + 10c + d  = 109a + 109b + 109c + 109d       subtract the right side from both sides  

891a - 9b -99c - 108d  = 0          divide through by 9

99a - b - 11c - 12d = 0        add  12d , b to both sides

99a - 11c =  12d + b            factor the left side

11 [ 9a - c ]  = `12d + b         divide both sides by 11

9a - c  =       [ 12d + b ] / 11

Note that we need to have "a" as large as possible.......

And as large as the right side can be, 10, is when d = 9 and b = 2

And this implies that a = 2  and c =8 

And when the right side is 9, d = 8 and b = 3

And this implies that a = 2 and c = 9

And when the right side is 8, d = 7 and b = 4 

And this implies that  a =  2, but c = 10 which is impossible

So....it appears that the largest our number can be is  when a = 2, b = 3, c = 9 and d = 8

So.....the number is  2398 

P.S.  -  any corrections / additional answers by other mathematicians are welcome !!!!!!! 

The answer is 42. 

"The answer is ALWAYS 42. Unless there are pancakes involved. Then the answer would be yes." - quote from Ghosty

Me? Um...yeah...*cough* of course. 

Well...maybe on weekends.

Um..10?

Because you add 2 to both sides to get x=10.