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k³ · (k^7/5) ^-5

Do the exponent first:  (k^7/5) ^-5  = k^-7

k³ · k^-7  =  k^-4 

An explicit formula for a geometric sequence is:  t_n  =  t₁ · r^{n - 1}

where t₁ is the first term = -5     r is the common ratio  =  -4

         t_n is the n^th term (leave it in the formula)     n is the number of the term (leave it in the formulat)

so the formula is  t_n  =  -5 · (-4)^{n - 1}     <---   answer!

You can find the common ratio by dividing the second term by the first term:  20 ÷ -5  =  -4

75% is three-fourths  --  so multiply by 3 and divide by 4 ...

or multiply by 0.75 ...

Divide and then take the whole number part.

6²/2(3) + 4

The order of operations says to do the exponent first:

36/2(3) + 4

The order of operations says to do the multiplications and division from left to right; since the division occurs to the left of the multiplication, the division by 2 is next:

18(3) + 4

The order of operations says to do the multiplication before the addition:

54  + 4

which is 58.

Don't do the multiplication before the division! Multiplication and division are tied in importance; do the one to the left first!

3+9-3+3=12

9=-7W+12W-6

9=5W-6

15=5W

W=3

Eg

enter 5*10^6

If you want to change an answer from usual notation to scientific notation then hit equal twice.

The same as you put one negative number in.

Perhaps you mean how do you take away a negative number?

Perhaps you need to know that this is the same as adding :)

Hi Titanium

Correct, a diagonal cut will produce 2 right angled triangles.

After that your air waves got a bit scrambled.   LOL.  :)

From OP:

I knew I was on the right track but couldn't remember the next step.

Thank you!

To find the area of a sliced rectangle when cut diagonally, first we must know the facts of rectangles, or quadrilaterals as we say when it comes to measurement

Rectangle:

its angles equal 360 degrees-

basically its 2 triangles-

Triangle:

half a rectangle-

angles equal 180 degrees

so pretty much, half of a rectangle is a triangle

to find the area of one of the pieces, you must do the triangle formula, which is:

$${\frac{{\mathtt{h}}{\mathtt{\,\times\,}}{\mathtt{b}}}{{\mathtt{2}}}}$$

To combine the area of both mini rectangles and make it the original rectangle, just multiply by 2 or simply dont divide by 2 and just multiply h*b, which is l*w basically

the triangle is half of a rectangle becuz its angles equal 180 degrees, times it by 2 (both halfs), it equals 360 degrees, the amount of degrees in a quadrilateral, not only rectangles, but also squares

hope this helps!

3(2y+4) = 4(2y-1/2)   

6y + 12 = 8y -2      distribute

12 = 2y -2              move smallest y value over by substracting

14 = 2y                  get y by itself by adding two to the other side

7 = y                     simplify

15mg x 1g/1000mg x 1oz/28.3495g = 0.00053

0.00053 x 20 = 0.011 doses

this is very helpful thanks!

I'm trying to find the amplitude, period, phase shift, and midline of the following problem: y=2sinθ-2

It depends on where you want the brackets put :)

 y=(2sinθ)-2

amplitude=2, period=2pi, phase shift=0, and midline y=-2

 y=2sin(θ-2)

amplitude=2, period=2pi, phase shift=+2, and midline y=0

Thanks Alan  :)

$$\\12^2+2ab^2+4(a^6)^{-3}+5ab^2\\\\
144+2ab^2+4a^{-18}+5ab^2\\\\
144+4a^{-18}+5ab^2+2ab^2\\\\
144+4a^{-18}+7ab^2\\\\
or\\\\
144+7ab^2+\frac{4}{a^{18}}\\\\$$

$${\sqrt{{\mathtt{4}}}}{\mathtt{\,\times\,}}{\mathtt{3}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2}} = {\mathtt{8}}$$

or

$${{\sqrt{{\mathtt{4}}}}}^{\,{\mathtt{3}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2}} = {\mathtt{10}}$$

$$\\(5a^2 b - 3bc^2)^4\\\\
=^4C_0(5a^2b)^4+^4C_1(5a^2b)^3(-3bc^2)^1 +^4C_2 (5a^2b)^2 (-3bc^2)^2 +^4C_3(5a^2b)^1 (-3bc^2)^3 +^4C_4(-3bc^2)^4\\\\
=(5a^2b)^4+4(5a^2b)^3(-3bc^2)^1 +6 (5a^2b)^2 (-3bc^2)^2 +4(5a^2b)^1 (-3bc^2)^3 +(-3bc^2)^4\\\\
=(625a^8b^4)+4(125a^6b^3)(-3bc^2)+6 (25a^4b^2)(9b^2c^4)+4(5a^2b)(-27b^3c^6) +(81b^4c^8)\\\\
=(625a^8b^4)-(1500a^6b^4c^2)+(1350a^4b^4c^4)-540(a^2b^4c^6)+(81b^4c^8)\\\\
=625a^8b^4\;-\;1500a^6b^4c^2\;+\;1350a^4b^4c^4\;-\;540a^2b^4c^6\;+\;81b^4c^8\\\\$$

You can use the calculator on the home page here to do this.

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By definition, strain is just change in length divided by original length.  The size of the strain will depend on the applied stress, and if the stress is too great the material will break.  Elastic materials can get to larger strains than, say, ceramics, before breaking.

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Good one Titanium :)