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XYZ ==264

978264 mod 7==0

978264 mod 8==0

978264 mod 9==0

2x + 5 = 11   subtract 5 from both sides to get

2x = 6           now divide both sides by 2 to get

x = 3

The least positive n ==780

780^2 ==608,400 mod 1560 ==0

I think it means divides evenly (?)  

     Just sub in 0    to see

                   39245930/8 = 4905741.25     the .25 tells us that 6 more is needed to divide evenly

                    39245936/8 = 4905742      Tht will be the only value......adding 8 more would change the digit in the tens place

find the zeroes of   -6x^2 +25x-4      ......   this is a dome shaped parabola....  the area between the zeroes (including the zeroes) is greater than or equal to zeroe and is the domain   (since you are not allowed to have a negative sqrt)

x^2 - 16    needs to be > =   0    first of all   ( no sqrt of a negative)

    THEN    sqrt(x^2-16)    also needs to be >= 0

x^2 >= 16

x >= 4   <= -4               so  far       -4 >=x>=4     

   These values will result in a positive sqrt .....adding +3   will still be a positive sqrt

What does the  ' | '  symbol mean?

Your shapes are right.

The most general one is the Trapezoid  (In Australia we would call it a trapezium)

But unfortunately, your conclusion is not correct.   (unless I have made some really stupid error)

Draw your trapezoid and re-check your result     

If Q = 11 - 5i, E = 11i, and D = 2i, find Q*E*D.

Hello Guest!

\({\color{blue}QED}=(11-5i)*11i*2i\\ \color{blue} =-22(11-5i)\)

  !

Angle ACD = 18 degrees

DC = 10 - 1 

It's only C !!!

Square         ✓

Rectangle     ✓

Trapezoid      ✓

Rhombus       ✓

Parallelogram     ✓

Find the domain of the real-valued function

f(x) = -sqrt(-10x^2 - 4x + 6)

Hello Guest!

\(f(x) = -\sqrt{ -10x^2 - 4x + 6 }\\ -10x^2 - 4x + 6=0 \)

\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\\ x = {4 \pm \sqrt{16-4\cdot (-10)\cdot 6} \over 2\cdot (-10)}\\ x\in \{-1,\frac{3}{5}\}\)

\(\mathbb D:\ x\in\mathbb R\ |\ -1\leq x\leq \frac{3}{5}\)

  !

9+9+9+9+9+9+9+9 =?

Wait nevermind, you're actually correct. Sorry for the inconvenience 

Draw a pic. of a random quadrilateral.   One that does not look very special

Call it PQRS

Mark on it the things that are told to you.

Redraw it so that it looks more like it is supposed to.  But do not give it extra special features that are no specified (unless it is unavoidable)

What shape is it?

Now test all those possibilities and you will see that only one seems right.

Try drawing out the two triangles out and testing each of the cases to see if they're true. 

Remember that angle R = angle X, angle S = angle Y, and angle T = angle Z. 

=^._.^=

(a - 1/a) = 2 (note that normally we couldn't assume that it isn't -2, but since a > 1, a - 1/a has to be positive. 

(a - 1/a)^3 = 8

a^3 - 3a + 3/a - 1/a^3 = 8

a^3 - 1/a^3 - 3(a - 1/a) = 8

Can you figure it out from here?

=^._.^=

Let a, b, c be the three non negative integer sides of the triangle, where a <= b <= c. 

The triangular inequality tells us that a + b > c. 

List out the possible a, b, and c sides. :))

=^._.^=

Yep, you could also first subtract the quadratic solutions, from the quadratic equation. :))

(-b+sqrt(b^2 - 4ac))/2a - (-b-sqrt(b^2 - 4ac))/2a

sqrt(b^2 - 4ac)/a

Remember that we're looking for the positive difference.

=^._.^=

Using vieta's, a + b + c = -(-121)/24 = 121/24.

Can you take it from here?

=^._.^=

This is a good question.

One choice can be dismissed easily enough, which would that be, and why?

6t^2 -47t+30 = 0

   Use quadratic Formula    to find the roots        a = 6        b = -47         c = 30

\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)         

Final amount = 10 000 (1+.10)³

In three minutes there are 9 sets of 20 seconds

  so the original colony triples 9 times

    x 3⁹ = 275562

x = 275562 / 3⁹

x = 14  original bacteria