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Let's call the membership fee  " a "  and the cost per use  " b " .

Claire paid a total of  105  for the membership and for  30  uses.

105  =  a + 30b

Adrian paid a total of  123  for the membership and for  39  uses.

123  =  a + 39b

123 - 105  =  (a + 39b) - (a + 30b)

18  =  a + 39b - a - 30b

18  =  9b

2  =  b

Plug this in to one of the equations to find  a  .

105  =  a + 30(2)

105 - 30(2)  =  a

45  =  a

Solve the following system:
{x + y = 10 - x - y | (equation 1)
x - y = -2 + x + y | (equation 2)

Express the system in standard form:
{2 x + 2 y = 10 | (equation 1)
0 x - 2 y = -2 | (equation 2)

Divide equation 1 by 2:
{x + y = 5 | (equation 1)
0 x - 2 y = -2 | (equation 2)

Divide equation 2 by -2:
{x + y = 5 | (equation 1)
0 x+y = 1 | (equation 2)

Subtract equation 2 from equation 1:
{x+0 y = 4 | (equation 1)
0 x+y = 1 | (equation 2)

Collect results:
x = 4               and               y = 1

Hello, please help, I enter such an expression tg (sin (1) / sin (2)) + 2 ^ ctg (cos (2)) - 1 / (2 * 3) +3, writes the error what to do. thank you in advance.

Дорогой друг, доброе утро!

tg (sin (1) / sin (2)) + 2 ^ ctg (cos (2)) - 1 / (2 * 3) +3

\(\frac{tan\ sin(1)}{sin(2)}+2^{cot(cos(2))}-\frac{1}{2\times 3}+3\\ =\frac{tan(0.8415)}{0.9093}+2^{cot(-0.4161)}-\frac{1}{6}+3\\ =\frac{1.1190}{0.9093}+2^{-2.2629}-\frac{1}{6}+3\\ =1.23055401916+0.208388277823-0.1\overline6+3\\ \color{blue}=4.27227563031\)

До свидания    !

No..if it was  f(x) = 100 + 45x , then for year 1 the sales would be  f(1) = 100 + 45(1) = 145

But for year 1, the sales are  10 + 45(1)  =  55, which agrees with the table. 

thank you did you mean f(x)=100+45x

The radius of the circle  is

6  =  2pi * r  

r =  6 / [ 2 pi]  = [ 3/pi] m

The center of the circle will lie on the angle bisectors....so

(1/2) the length of the base....call this "d"...... is given by

tan (30)  = [ 3/pi] / d

1/√3  = 3 / [pi *d ]  rearrange as 

d = 3√3 / pi   m

And the height of the triangle, h, is given by

tan (60)  =   h / d

√3 = h / [3√3 / pi]   

√3 = pi *  h /[ 3√3]  rearrange as

9/pi  m  = h

So....the area of the triangle is : 

(1/2)b * h  =

d * h  =

[3√3 / pi] m * 9/pi m  =

[27√3] / pi^2  m ^2  ≈  4.738 m^2  ≈  4.738 * 100^2 cm^2 ≈ 47380 cm^2 

Notice how each year, the sales go up by  45 .

year 1 sales  =  55

year 2 sales  =  55 + 45

year 3 sales  =  55 + 45 + 45

year 4 sales  =  55 + 45 + 45 + 45

year 5 sales  =  55 + 45 * 4

year " x " sales  =  55 + 45 * (x - 1)

f(x)  =  55 + 45(x - 1)   where  x  is the year and  f(x)  is the sales. We can simplify the right side.

f(x)  =  55 + 45x - 45

f(x)  =  10 + 45x

13+3x=13+2x <=> 13-13=2x-3x <=> 0=-x <=> x=0/-1 <=> x=0 

thank you so much

rate  =  distance / time       ( I remember this because  speed  =  miles / hours   )

7  =  D / T       where  D  is in miles. Lets solve for  D  by multiplying both sides by  T .

D  =  7T

Is this the problem?

-9 ⋅ ( -30 ) - 9 ⋅ ( 0 / -3 )

=  -9 ⋅ ( -30 ) - 9 ⋅ 0

=  -9 ⋅ ( -30 ) - 9 ⋅ 0

=  -9 ⋅ ( -30 ) - 0

=  -9 ⋅ ( -30 ) - 0

=  270 - 0

=  270

AHAHAHA I always overthink things!

Thanks! I really don't understand functions 

Volume of the cube  = 3 x 3 x 3 =  27m^3

Volume of the cistern =  4 X 5 x 6  =  120m^3

Total volume of the cistern and added  cube =  147m^3

So.....to find the water height, h,  with the cube added, we can solve this

4 * 5  * h   =  147

20 * h  =  147     divide both sides by 20

h =  7.35 m 

y  =  kx                where  k  is a constant.

                            Plug in  -30  for  y  and  -5  for  x .

-30  =  k(-5)         Solve for  k .

-30 / -5  =  k

6  =  k

So we know that

y  =  6x           To find  y  when  x = -3 , plug in  -3  for  x .

y  =  6(-3)

y  =  -18

We don't need to use the law of sines here, since it is a right triangle.

Remember, in a right triangle... tan θ  =  opposite / adjacent

Let's call the distance (in miles) from the boat to the dock  " d ".

tan 52°  =  d / 30       Multiply both sides by  30 .

30 tan 52°  =  d        

 f(x)=kx+m

f(x+4)-f(x)=2

f(m)=6

f(x+ 4) - f(x) = [ k (x + 4) + m] -  [kx + m]  =  2

So

kx + 4k + m  - kx - m  = 2

4k =  2

k = 1/2

And   f(m)  = 6

So

f(m)  =  (1/2) (m) + m  = 6

(3/2)m  = 6

m  = 4

So....the function is

f(x)  =  (1/2)x + 4

Yes...and also you can look at it like this..if  f(-x) = -f(x)  then it is odd.

On E, it looks like (2, 8)  might be a point...

If it is odd,  f(-2)  must equal  - f(2)  =  - 8

Does  f(-2) = -8 ?  Is  (-2, -8)  a point? Yes...and it will be like this for all x values, so it is odd.

If the radius is tripled....the volume increases by a cube of this = 27 times

So...if the volume doubles....that's a 100% increase =  (2 -1) * 100%

And if it triples....that's a 200% increase  =  (3 - 1) * 100%

So......an increase of 27 times gives a % increase of  (27 - 1) * 100%  =  2600%

So whenever a function is symmetrical about the origin, it is odd?

log₂ 24 - log ₂ 3  = log₅ x

Note that  the left side can be written as

log₂ (24/3)  = log₂ 8  =  3

So  

3  =  log₅ x

This says that   5^3  =  x  = 125

E is not symmetric about the  y-axis, but it is symmetric about the origin.

So  E  is an odd function.

thanks so much that was super helpful

If 120 ohms represents 1 standard deviation,  68.2%  of the resistors fall within this

So....100 - 68.2  = 31.8%  of the resistors differ from the mean by more than 120 ohms  

 -4x + 4y = 1

First, let x  = 0

So.....  4y  = 1    →  y = 1/4

So  the point  (0, 1/4)  is on the graph

Next, let y = 0

So  ....   -4x  = 1   → x  = -1/4

So the point   ( -1/4, 0)  is also on the graph

Plot these two points and draw a line through them.......this will be your graph !!!