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We know an angle and an opposite side.....and we are trying to find the adjacent side....the tangent seems logical, here

tan 63 = 24 / miles       rearrange as

miles =    24 / tan 63  ≈   12.2 

100 = k * (0.25)      divide both sides by 0.25

100/ 0.25  = k =  400

So

80  =  400 (x)    divide both sides by 400

80/ 400 =  x =  1/5 m =  0.2 meters

A

Remember that.....with inverse variation, the product of the variables is constant

So....x * y  =  5 * 12  =  60

So....

x * 32  =  60       divide both sides by 32

x = 60 / 32  =   15 / 8

312.50 = k * 25       divide both sides by 25

(312.50 / 25)  =  k = 12.5

So....the equation is

p = 12.5 h           where h is the number of hours worked 

Not an expert on this, NSS...I think the spring constant should be  " 0.3 N / m"

So

F =  (0.3 N/ m) (1.5 m)

F =  (0.3)(1.5)N =   0.45 N

Here's the second one

New point =

[ (1, 4) - (-3, 1) ] (2) + (-3, 1) = [ 4, 3 ](2) + (-3,1) = [ 8, 6] + (-3, 1) = ( 5, 7)

New point =

[ (2, 2) - (-3,1)](2) + (-3, 1) = [ 5,  1](2) + (-3, 1)  = [ 10,2] + (-3, 1) = (7, 3)

New point

[ (-3, 3) - (-3, 1)](2) + (-3,1) = [ 0, 2] (2) + (-3,1) = [ 0, 4] + (-3, 1) = (-3, 5)

Here's the image

See if you can do the last one....

We can do this with a "formula"

New point =  [ old point - center of dilation ] (scale factor) + center of dilation

First one

New point =  [ ( 2,4) - (0,0)] (1/2) + (0,0) =   [ 2,4](1/2) + (0,0) = (1,2)

New point  = [ ( -2, 8) - (0,0) ] (1/2) +  (0,0) = [ -2,8](1/2) + (0,0) = (-1, 4)

New point = [ (-4, 2) - (0,0)](1/2) + (0,0) = [-4,2](1/2) + (0,0) = (-2, 1)

Here's the graph:

So so....

Thank you so much you are a life saver!!

horrible

There are many examples you can find. .3 repeating is 1/3.

Good afternoon. It is a good day to play in a jazz band.

https://www.youtube.com/watch?v=-5YShgaZoNg

Example:

-2.5 x 3+(3x4+ 2^3)^2 x3 =  1192.5

It seems to do so....there was some discussion some time back about   -2^2    = -4  because it does the exponent first then does the negative     so if you want   -2  squared you have to use parens   (-2)^2 = 4

I solved the quadratic in terms of a and b (well, ok, I used a piece of software to do so!). This resulted in an expression under a square root sign that meant if b>=2-2a, two of the four roots would be real.

you would probably get that answer faster if you ask one of the moderaters directly i would suggest asking CPhill he is one of the moderaters that stay on of the longest so you would have a better shot at getting your answer

The graph of \(y=f(x)\) is shown below. Assume \(f(x)\) is defined only on the domain shown, and that the \(y\)-axis is an axis of symmetry for the graph.

For any real number \(c\), let \(g(c)\) be the number of solutions to the equation \(f(x) = c\). What is the average of all distinct values in the range of \(g(c)\). 

Thank you so much!

Density = rabbits/acre  =  960/250

+2925-1530+125-550 =         ?     If positive it is increasing

960 +970

Fewer rabbits(because of trapping) means decreasing rabbit/acre density....

Thank you!

Thank You!

Is sales tax 8.875 % in NYC?  If so then:

32.50 x 1.08875   + 3 = $ 38.38       (Tax is $ 2.88 )

thanks

Always never mindful.