All Answers 356017 Answers

The secant is defined to be the ratio:  hypotenuse / adjacent.

For this problem:  sec  =  32/23.

Simplify  6[-1/sqrt(2)]

              =  -6/sqrt(2)

Multiply both the numerator and the denominator by sqrt(2)

             =  [-6sqrt(2)] / [sqrt(2)·sqrt(2)]

             =  -6sqrt(2) / 2                                    since -6/2  =  -3:

             =  -3sqrt(2)

If  q  =  (x₁, y₁)   and   r  =  (x₂, y₂)     then     q - r  =  (x₁ - x₂, y₁ - y₂).

For this problem:  q - r  =  ( 56 - 83, -31 - 92 )  =  ( -27, -123 ).

Q(x) = [P(x)]²     and     P(x)  =  4x³ - 2x² + 7x - 1

--->     Q(x)  =  [ 4x³ - 2x² + 7x - 1 ]²

The y-intercept occurs when the x-value is 0; so to find the y-intercept of Q(x) substitute 0 for x:

--->     Q(0)  =  [ 4(0)³ - 2(0)² + 7(0) - 1 ]²

                      =  [ 0 - 0 + 0 - 1 ]²

                    =  [ -1 ]²

                    =  1

So, the y-intercept occurs at (0, 1)

Label the vertices of the triangle K (Kim), A (Andrea), and J (Joy).

The lengths of the sides of the triangles are:  AK = 12, AJ = 15, and KJ = 7.

Since you know the three sides of the triangle, use the Law of Cosines:  c²  =  a² + b² - 2·a·b·cos(C).

To find angle K:  AJ²  =  AK² + KJ² - 2·AK·KJ·cos(K)

--->                    15²  =  12² + 7² - 2·12·7·cos(K)   

--->                    225  =  144 + 49 - 168·cos(K)

--->                    225  =  193 - 168·cos(K)

--->                      32  =  -168·cos(K)

--->              -32/168  =  cos(K)

--->                        K  =  cos^-1(-32/168)

--->                        K  =  101º  (approximately)

To find angle J:  AK²  =  AJ² + KJ² - 2·AJ·KJ·cos(J)    (or you can use the Law of Sines)

--->                    12²  =  15² + 7² - 2·15·7·cos(J)   

--->                    144  =  225 + 49 - 210·cos(J)

--->                    144  =  274 - 210·cos(J)

--->                   -130  =  -210·cos(J)

--->             130/210  =  cos(J)

--->                        J  =  cos^-1(130/210)

--->                        J  =  52º  (approximately)

Thus A  =  27º  (approximately)

I'm just adding to CPhill's answer

14/35=2/5

Average speed=Distance / Time

A=438 / 1.55     (you must convert 33 minutes into hours by dividing 33/60 =.55 of an hour)

A=282.58 miles per hour.

If we assume that it is a right-angle triangle, then we have:

Tan(x) =Opposite/Adjacent

Tan(x) =5/3 =1 2/3, so

x=tan^-1(1 2/3), or inverse tangent

x=~59.04 degrees.

You forgot something very important!. What is the %, or the interest rate!!.

130,9

The 3rd one is correct. I dont know who wrote the sucks thing but it wasn't me who originally posted the question.

My understanding of the problem is that 100 of these patches are used to create the quilt, 10 rows of 10 patches per row.

Since the area of the quilt is 1.44 m sq, the quilt must have dimensions of 1.2 m by 1.2 m. 

Since each row contains 10 patches and each row is 1.2 m long, each patch must have a width of 0.12 m or 12 cm.

By looking at the patch shown, the each black segment must be twice as wide as a yellow segment, so each yellow segment must be 3 by 3 cm, each black segment must be 3 by 6 cm and each white segment must be 6 by 6 cm.

To find how much of each color is needed, notice that the area of each patch is divided into four 3 x 3 yellow areas (= 36 cm sq), four 3 x 6 black areas ( = 72 cm sq) and one 6 x 6 white area ( = 36 cm sq). This means that 1/4 of each patch is yellow, 1/4 of each patch is white, and 1/2 of each patch is black.

Thus, 1/4 of the total quilt is yellow (1/4 of 1.44 m sq is 0.36 m sq) as is also the white area (another 0.36 m sq) but the black area is twice as much (o.72 m sq).

I do not understand this statement.     

An interesting feature is created when the blocks are sewn together: each colour forms a shape. The shape and its area are exactly the same for each colour. (The feature appears throughout the quilt, except at the edges.)

Do you understand it?    

What is the smallest number that leaves a remainder of 5 when divided by 12, 14, and 18?

First, find the smallest number that is divisible by 12, 14, and 18:

   ---  factor each of the numbers:

                   12  =  2 x 2 x 3

                   14  =  2 x 7

                   18  =  2 x 3 x 3

  ---  the least common multiple of these numbers is  2 x 2 x 3 x 3 x 7  =  252

Thus, 252 is divisible by 12, 14, and 18.

If you want a remainder of 5, add 5 to that number:  252 + 5  =  257.

M.A.T.H

Mental Abuse To Humans

=(x+1)^2

(x+1)(x+1)

x^2+1x+1x+1

=x^2+2x+1

only factors of 1 are 1 and 1

1+1 = 2

1*1 = 1

Did you mean: Why is maths difficult?

Well, it is a way of describing systems and these systems can be complex, requiring complex solutions.

Or did you mean: Why does society make me do maths?

Because they hate you.

(substitution)       (go down before going to the next column)                 x+2((6-2z)/2)=z+2

x+2y=-z+2                                                                                               x+2((6-6)/2)=3+2      

z-8=-x                                                                                                     x+0=5

y-z=-5                                                                                                     x=5

x=-z+8          (x=5)                                                                                  y=(6-2(3))/2

z=-x+8          (z=3)                                                                                  y=6-6/2

y=(6-2z)/2     (y=0)                                                                                  y=0

(-z+8)+2y=z+2                                                                                      Check by substituting back into the forumulas

-2z+6+2y=0                                                                                           z-8=-x

-2z+2y=-6                                                                                             3-8=-(5)

2y=6-2z                                                                                                 -5=-5

-z+8+2((6-2z)/2)=z+2

-z+8+(12-4z)/4=z+2

-2z+11=z+2

-3z+11=2

-3z=-9

z=3

Three fair dice is rolled. Calculate the probability that the sum of the numbers on the dice are even, given that the numbers on the dice are all the same.

Could be

2 odd and 1 even   or    3 even

\(3C2*0.5^3+3C3*0.5^3 = 3*0.5^3+0.5^3=4*0.5^3\)

4*0.5^3 = 0.5

Lets think about this answer..

Can't be

2 even and 1 odd   or  3 odd

So 50% makes perfect sense :))

Here are your possible rolls

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

8 are even out of 16     8/16 = 50%

Hmmm.... I got the correct answer.....but I am not sure I did it correctly...I'd go with Melody's answer!

Thank You

From third equation   y = z-5    sunstitute into first equation to get

x + 2(z-5) = -z +2

x + 2z -10 = -z+2

x = 12 - 3z                 Sub into Second eq

z-8 = -(12-3z) 

z-8 = -12 + 3z

z=2                            Sub into Third equation

y-2= -5         to get y= -3      and  x=6     z = 2   

F

\({2*10^{-3}}*1000000={2*10^{-3}}*10^6=2*10^{-3+6}=2*10^3=2000\)

Write down the equations as follows.

x + 2y + z =  2

x         + z =  8

        y - z  = -5

Then you can create the matrix for this system

1  2  1  2

1  0  1  8

0  1 -1 -5

Subtract row 2 from row 1, then interchange these two rows.

1  0  1  8

0  2  0 -6

0  1 -1 -5

Divide row 2 by two, then subtract row 2 from row 3.

1  0  1  8

0  1  0 -3

0  0 -1 -2

Add row 3 to row 1 then multiply row 3 by -1.

1  0  0  6

0  1  0 -3

0  0  1  2

This matrix reads your solution.

x = 6

y = -3

z = 2

What is the quotient and the remainder of (4x^3 - 2x^2 + 1) / ( -x + 2 )?'

\(\frac{(-4x^3 + 2x^2 - 1) }{( x - 2 )}\\ -4*2^3+2*2^2-1=-4*8+8-1=-25\\ \mbox{so using remainder theorem the remainder will be -25}\\ =\frac{(-4x^3 + 2x^2 +24)-25 }{( x - 2 )}\\ =\frac{2[-2x^3 + x^2 +12]-25 }{( x - 2 )}\\ =\frac{2[(x-2)(-2x^2-3x-6]-25 }{( x - 2 )}\\ =\frac{2[(x-2)(-2x^2-3x-6] }{( x - 2 )}+\frac{-25 }{( x - 2 )}\\ =2[-2x^2-3x-6] +\frac{-25 }{( x - 2 )}\\ \mbox{so the answer is}\\ -4x^2-6x-12\;\;remainder \;\;-25 \)

Mind you, this was a very weird way to do it - normally you would just use algebraic division and you'd get to the answer more simply :))