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f(g(x))      put in g(x) which is  9-x  in for 'x' in the definition of f(x)

(1-x)^2     put in  9-x   for 'x'

(1 -   (9-x)) ^2

= (x -8)^2   =      x^2 -16x+64

You should be able to do the other one now......

q = quarters                       value = 25q

n = nickels = 30-q              value = 5(30-q)        summed  they equal 330

25q          +     5 (30-q)             = 330        solve fo q the # quarters     then nickels = 30-q

\(3x^2+4x+12=0\) Is a quadratic equation of the form \(ax^2+bx+c=0\) where r and s are roots 

By Vieta's formulas:

\(r+s=-\frac{b}{a}\) Thus \(r+s=-\frac{4}{3}\)

\(r*s=\frac{c}{a}\) Thus \(rs=4\)

Now notice that:

\(r^2+s^2=(r+s)^2-2rs\)

Substitute 

\((-\frac{4}{3})^2-2(4)=-\frac{56}{9}=-6.22\)

a) 90-24-24=42. \(x=42^{\circ}\)

(i) \(\angle q\) also has a size of \(135^{\circ}\) because they are vertical angles, and vertical angles are congruent.

(ii) \(p+q+r=360-135=\boxed{225^{\circ}}\)

I hope this helped you, guest!

If you have any questions, don't hesitate to ask!

:)

where?????

The four curved lengths of the band form one circle:  C  =  pi ·10.

The four straight line segements go from the center on one circle to the center of the next circle; each one  = 10

So:  pi · 10  +  4 · 10

This problem was recently answered; please check below.

The answer is 89.050 becuase 

   84.7128

+   4.337

---------------

   89.0498

The rule of adding for sig figs is that since 4.337 has 3 digits after the decimal point, the sum has to have 3 digits after the decimal point also. 

So, we can disregard the last 8 and we get 89.049. Now, we round it and since 8>5, and 9>5, the final answer is 89.050.

It's a straight line -- its y-intercept is 335.30 and rises (from lower-left to upper-right) very steeply; for every one unit that you move to the right, you move 60.18 units vertically.

In a 30-60-90 right triangle, the side opposite the 30^o angle is equal to one-half the hypotenuse.

Since BC = 12' and BC is the side opposite the 30^o angle, the hypotenuse = 24'.

Also, the side opposite the 60^o angle is the length of the side opposite the 30^o angle times the square root of 3.

So, to find AC:  12 · sqrt(3).

I'm assuming that the problem is with the peak.

There are four congruent triangles, each with a base of 8.

We need to find the slant height of this pyramid; this will be the height of each triangle.

To find this length, consider a right triangle from the top point to the middle of the base and over to the middle of each side.

The length from the top point straight down to the middle of the base is 8.

The length from the middle of the base to the middle of one side is 4.

Therefore the slant height is the hypotenuse of this triangle:  c²  =  4² + 8²     --->     c  =  sqrt(80)

So, each triangle has an area of  ½·8·sqrt(80) and there are four of these triangles.

The base is 8 x 8.

Each side is 8 x 13.

Now, its calculator time ...

Seven positive integers, mean = 5, median = 4, and two modes 2 and 8.

Since there are an odd number of numbers and 4 is a median, at least one of the numbers is 4 and three of the numbers must be larger than 4 and three of the numbers must be smaller than 4.

Since both 2 and 8 are modes, either both are used twice or both are used 3 times.

When I tried to use them three times, I couldn't get anything to work.

So, using them twice, I have 2, 2, 4, 8, 8, giving a sum of 24.

For seven numbers to have a mean of 5, their sum must be 7 x 5  =  35.

I need another 11, split between a number smaller than 4 and a number larger than 4.

If I try 3 for the smaller number, this means that I have to use 8 for the larger number, but I can't because that would mess up the modes.

If the number is 1, than the other number must be 10.

1, 2, 2, 4, 8, 8, 10

c = 13/2.

thank you :)

The "power of the point":     DB · DC  =  DF · DE

                                 4 · [ 4 + (x - 3) ]  =  5 · [ 5 + (x - 6) ]

                                        4 · [ x + 1 ]  =  5 · [ x - 1 ]

                                                4x + 4  =  5x - 5

                                                        x  =  9

From this, you can find all the lengths ...

Pythagorean Theorem time!

For the triangle on the left:  a² + b²  =  c²     --->     1² + b²  =  5²     --->     b  =  sqrt(24)

For the griangle on the right:  5² + (sqrt(24) ² =  c²     --->     25 + 24 =  c²     --->     c  =  sqrt(49)    (which you can simplify)

To find a revolution of 270^o, I would do this:  the y-value of the initial point becomes the x-value after rotation

                                                                       the negative of the initial x-value becomes teh y-value after rotation.

A(3, -2)   --->   A'(-2, -3)

B(8, 2)   --->   B'(2, -8)

C(5, 10)   --->   C'(10, -5)

But, graph these to check to see if this works!

I'm assuming that the notation "T_1,-6" means a translation of 1 of the x-value and -6 of the y-value:

A(3, -2)   --->   A''(4, -8)

B(8, 2)   --->   B''(9, -4)

C(5, 10)   --->   C''(6, 4)

To see whether they are congruent or not, graph them and measure. My initial response is that they will be congruent because rotations and translation preserve distance and angles.

For the box on the left:

-- front side of 4 x 7

-- back side of 4 x 7

-- top side of 3 x 7

-- bottom side of 3 x 7

-- left side of 3 x 4

For the box on the right:

-- front side of 3 x 9

-- back side of 3 x 9

-- top side of 3 x 3

-- bottom side of 3 x 3

-- right side of 3 x 9

-- left side of 3 x 5

Find all the individual area and add them together for the final answer.

The conjugate of  [ sqrt(3) -1 ]  is  [ sqrt(3) + 1 ]

Numerator:  [ 6 + 10sqrt(3) ] · [ sqrt(3) + 1 ]  =  6sqrt(3) + 6 + 10sqrt(3)sqrt(3) + 10sqrt(3)

                                                                      =  6sqrt(3) + 6 + 10·3 + 10sqrt(3)

                                                                      =  16sqrt(3) + 36

Denominator:  [ sqrt(3) - 1 ] · [ sqrt(3) + 1 ]  =  3 - 1  =  2

Answer  =  [ 16sqrt(3) + 36 ] / 2  =  8sqrt(3) + 18

FV=85000; R=0.06/12; N=13*12;PMT = FV*(((1 + R)^N - 1)^-1* R);print" PMT =$",PMT

 Monthly Pmt =$ 361.01

Thank you for leading me to the right solution.

The cube root is the same as the 1/3 power.

(10⁴x)^(1/3)  =  10^4·(1/3) · x^(1/3)  =  10^4/3x^(1/3)  

What do you mean by 3 points?

[ 2x² + 2x - 2 ] / [ x(x² - 1) ]  =  [ 2x² + 2x - 2 ] / [ x(x + 1)(x - 1) ] 

To get each term to have the common denominator of x(x + 1)(x - 1),

--  multiply the first term:  A/x  by  [ (x + 1)(x - 1) ] / [ (x + 1)(x - 1)]

        so that the numerator becomes:  A(x + 1)(x - 1)  =  Ax² - A

--  multiply the second term:  B/(x - 1)  by  [ x(x + 1) ] / [ x(x + 1) ]

        so that the numerator becomes:  B(x)(x + 1)  =  Bx² + Bx

--  multiply the third term:  C/(x + 1)  by  [ x(x - 1) ] / [ x(x - 1) ]

        so that the numerator becomes:  C(x)(x - 1)  =  Cx² - Cx

All the denominator are  (x)(x + 1)(x - 1), so all we have to do is look at the numerators:

     2x² + 2x - 2  =   Ax² - A  +  Bx² + Bx  +  Cx² - Cx

     2x² + 2x - 2  =   Ax² +  Bx² +  Cx²  + BX - Cx - A 

Therefore:  Ax² +  Bx² +  Cx²  =  2x²      --->     (A + B + C)x²  =  2x²     --->     A + B + C  =  2

                                   Bx - Cx  =  2x       --->               (B - C)x  =  2x      --->            B - C  =  2

                                            -A  =  -2                                                        --->                  A  =  2

Solving, we get:  A = 2     B = 1     C = -1