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a. 

[x + (3x + 8)] / 2 = 20

(4x + 8) / 2 = 20

2x + 4 = 20

2x = 16

x = 8

Hope this helped!

f(x) would be   2x^3 + 7/2 x² + 3x + c  

                 when x = 0         this should equal 5        so  c = 5

I hope this helps....not sure what the function rule is.....  

This is NOT a right triangle ....so you'll have to  use the cos law

c^2 = a^2 + b^2 - 2ab cos x

7² =10² + 8² - 2 (10)(8) cos x        solve for cos x

11^1/2  * 11^1/4 * 11^1/8 * 11^1/16   =  11 ^15/16

FIRST JAR   300  ml juice   600 ml water

Second jar    360 ml juice    540 water

(300+ 360) / (600+540) =  660 / 1140 = ........       

What is n?

Hello Guest!

 \(11^n=\sqrt{11\sqrt{11\sqrt{11\sqrt{11}}}}= 11^{(\frac{1}{2})^{1+2+3+4}}=11^{ (\frac{1}{2})^{10}}=11^{\frac{1}{1024}}\)

 \(n=\frac{1}{1024}\)

  !

hint: \(\sqrt{11}=11^{1/2}\)

200 cm = 2m

200 x 75 x 50     x  3/4 = ........  cm³

11x^2 -44x  - 99 = 0

x^2 - 4x - 9  = 0

x^2 - 4x  =  9 

x^2 - 4x + 4  =   9 + 4  

(x - 2)^2  =  13

( x +  -2)^2  = 13

r =  -2        s  = 13

Now, I am pretty sure you can solve what r+s is.

We write the slope intercept form equation first based on the two given points. The slope is -4/9. We now have y=-4/9x+b. We then plug in one of the points to determine b. 

y=-4/9x+b

-2=-4/9(4)+b

-2=16/9+b

b=-2/9

So the equation is y=-4/9x-2/9. We then convert it to standard form.

y=-4/9x-2/9

4/9x+y=-2/9

4x+9y=-2

x^2-3x+1      complete the square     take 1/2 of the 'x' coefficient , square it and add   and subtract it from the equation

x- 3x + 2.25    -2.25 + 1

(x-1.5)²  - 1.25                You can finish this Q .....  

That equals (6y + 17)(y - 3), so then A = 2, B = 17, C = 3, and 6^2-17 = 19.

You are very welcome!

:P

Midpoint: (5, 4)

Slope: -1/3

Bisector: y = 3x+b

Substitute x=5, y=4

4 = 15+b

b = -11

Answer: y = 3x-11

You are very welcome!

:P

A bunch of these triangles are similar.

Let's take the bottom square. Name the bottom-left point B, the bottom-right point C, the point 5 units above C as D. Then BCD is right and BD = 5sqrt(10). Now, name the points on BD from left to right as E and F. Name the point under E as G. Call BF = x, then FD = 5sqrt(10)-x. Also call CF = y. Then we have two equations using Pythagoras

x^2+y^2=15^2, (5sqrt(10)-x)^2 +y^2=25. (We get these from triangles BFC and FDC.) Solving gets x = (9sqrt(10))/2 and y = (3sqrt(10))/2. That means that the area of BFC is xy/2, or in other words, 135/4. There are four of these triangles surrounding the square, so then 135/4 * 4 = 135. Subtracting from the total square area of 15^2 = 225 gets us the final answer of 225 - 135 = 90.

You are very welcome!

:P

Hey, I copied the problem wrong.  Father is 38 not 36. 

So it would be       38 – 26  =  3X – X       

                                     2X  =  12    

                                       X  =  6 

Sorry for the previous error.  

_π

Let X be the number of years 

36 + X  =  (13 + X) + (5 + X) +(8 + X)  

36 + X  =  26 + 3X 

36 – 26  =  3X – X  

        2X  =  10 

          X  =  5 

_.

If each side of a square were increased by seven feet the area would be three hundred fifteen square larger. What is the length of a side 

Call the side of the square X  

Then                                          (X + 7)²  =  X² + 315  

Multiply out the left side            X² + 14X + 49  =  X² + 315  

Subtract X² from both sides        14X + 49  =  315 

Subtract 49 from both sides          14X  =  266    

Divide both sides by 14                     X  =  19   

_.

    7/  (  1/6  + 1/8)   = 24 days

Given that f(x) = (1/pi)^x, what is the range of f(x) on the interval [0, ∞ )?
Give your answer in interval notation.

Hello Guest!

\( f(x) = ( \frac{1}{\pi})^x\\ f(0) = ( \frac{1}{\pi})^0=1\\ f(∞)= ( \frac{1}{\pi})^∞\ toward\approx 0\)

\(Range_{f(x)}|_0^∞=\{1\ge \mathbb R> 0\}\)

  !

yes, it would..........

60% play wind        that means   40% do NOT play wind instr

40% x 130    =    .4 x 130 = 52

first line can be re-arranged to    y = -5/3 x - 11/3      slope , m , = -5/3

parallel line      y = -5/3 x + b     sub in the point given

                        -5 = -5/3 (2) + b

                                                    b = - 5/3

y = -5/3 x - 5/3