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Let's say that y=mx+b, m=slope, b=y-intercept

y=-6x+b
We can solve for b using given coordinates on the line (-3,5)
5=-6*(-3)+b
b=-13
 

Therefore, the equation would be y=-6x-13.

Hope this helped!

Since  AB  = AD, then angle ABD   = angle ADB   

Let them  be  = x

So  angle BAD  = 180 - 2x  = angle   CAE

And angle CDE  is vertical to angle ADB..so it too   = x

And since CD  = CE, then angle  CDE  = angle CED  = x   

So....angle CEA   =  angle CED   =   x

So....angle  ACE  =  180  - angle  CAE  - angle   CEA   

So  ...angle ACE  =  180 - (180 - 2x) - x  =   2x - x  =  x

But this is the same measure as angle  CEA

Therefore, in triangle AEC, angle ACE = angle CEA

Therefore...it is isosceles

done

Mia can only shoot at  Ducks 2-9, since there is no duck to the left of Duck 1 or to the right of Duck 10.

Therefore, the equation will be (9-2+1) ! which is 40320 ways.

Hope this helped!

At least 6  heads means

6 heads  =  C(10,6) (,5)^10

7 heads = C(10, 7) (.5)^10

8 heads   = C(10,8)(.5)^10

9 heads  = C(10,9) (,5)^10

10 heads = (.5)^10

So....the total probability is

(.5)^10  [  C(10,6) +C(10,7) + C(10,8) + C(10,9)  + 1  ]     ≈ .3769  ≈  37.69%

First, let's define slope-intercept form: it's the form that's usually taught first in math with coordinates(at least in my experience):

y = mx + b, where m is the slope, and b is the y-intercept.

The problem already gives us a slope of -2, so we can already write part of our desired equation:

y = -2x + b

Next, the problem gives us a point of (-1, 8). Here, we can plug the point into the equation, with the respective x and y values, giving us:

8 = -2 * (-1) + b

This simplifies to

8 = 2 + b, or 

b = 6

Finally, we have our desired equation, which is y = -2x + 6!(not factorial)

perimeter of a rhombus is 68 one diagonal is 16 what is the lenth of the secound diagonal

Diagonal    D = {sqrt [(68/4)² - (16/2)²]} * 2 = 30  

Ok let's take a look at the first statement the problem gives us, which is that h(x) = f(x) * g(x). Since we know the constant terms of both of these terms, which are -4 and 3 respectively, that should hint at something already. Remember, the definition of the constant term is basically the term of an equation with no x coefficient(more or less). What that implies here is that these equations have some random preceding x terms, with the rightmost terms being -4 and 3 respectively. Remember, the question doesn't ask us to find these two equations explicitly. That's because we don't have to. It only asks us the value of g(0). Lucky for us, if f(x) = x^2 + x + 1, then when you have f(0), that causes all of the x's to become obsolete, leaving only the constant terms(remember plugging in the 0 for the x's?). That means since h(x) = f(x) * g(x), you can just ignore all the leading terms with x's, and rewrite it as: 3 = -4 * x  with x being the constant term of g(x). That gives us the constant term of g(x) which is -3/4

someone please help me

The vertex  is at  ( 2,-4)

And the  point  (4, 12)  is on the graph

We  have  the  form

4p ( y - k)  = (x - h)^2      where   (h,k) is the vertex  and (x, y) is a point on the parabola

So we have

4p (12 - - 4) = ( 4 - 2)^2      simplify

4p (16)  = 2^2

64p  = 4

p  =  4/64  =  1/16

We can rewrite  this as

4 (1/16) ( y + 4)  =  ( x - 2)^2

 (1/4) ( y + 4) = (x - 2)^2       multiply  both sides by 4

y + 4  = 4(x - 2)^2     simplify

y  = 4 (x^2 - 4x + 4)  - 4

y = 4x^2 - 16x + 16 - 4

y = 4x^2 - 16x  + 12

To find the roots....let  y  = 0

4x^2 - 16x + 12  = 0               divide through by 4

x^2  - 4x  + 3   =  0       factor

(x - 3) (x - 1)  =  0

Setting both factors to  0   and solving for  x  produces  the roots  x  = 3   and  x  = 1

So

m  = 3    and  n  =  1

So

m - n  =   2

I still need help :( The other post was not answered. Thanks for replying.

Rewrite the quadratic equation as a(x-h)^2+k, where h and k are parts of the vertex.

y=a(x-2)^2-4

Since (4,12) is a point on the parabola, we can substitute these values in the equation.

12=a(4-2)^2-4, 12=4a-4, 4a=16, a=4

Now, the equation is complete: \(y=4(x-2)^2-4, y=4x^2-16x+12\)

We then plug y=0, to get x=3, x=1.

Thus, m-n=3-1=2.

10! / [6!*4!*2^10] + 10! / [7!*3!*2^10] + 10! / [8!*2!*2^10] + 10! / [9!*1!*2^10] + 10! / [10!*2^10] =193 / 512 =37.6953125%

The same question was posted here: https://web2.0calc.com/questions/geometry-help-thanks_1

Hope this helped!

they are both wrong 

a was 2.51cm and b is wrong too

Each coin has two sides, heads or tails, so the total number of possible outcomes is \(2^{10}=1024\).

The number of ways of getting heads is 10 C 6   *   10  C  7   + 10   C  8  +  10 C  9   + 10  C  10=210+120+45+10+1=386 ways.

193/512  but I might be worng

so all we need to prove is that angle aec = angle ace but how?

Sorry....I didn't mean to repeat tertre's answer verbatim   !!!!!

If the perimeter is 68.....one side  =  68 / 4   =  17

1/2 of the  known diagonal length  =  8

So  ...using the Pythagorean Theorem 1/2  the length of the other diagonal  = sqrt (17^2 - 8^2)  = sqrt (289 - 64) = sqrt (225) = 15

So....the length of the other diagonal  =  2 * 15  =  30

Since all four sides in a rhombus are equal, each side should be equal to \(\frac{68}{4}=17.\)

The key idea in this problem is that the two diagonals in the rhombus are perpendicular to each other, and most importantly, the diagonals bisect each other...

We have a right triangle, with one leg as eight(8) units and the hypotenuse has length seventeen(17) units.

By the Pythagorean theorem, the other side length has length fifteen(15) units.

Thus, the second diagonal has length \(2*15=30\) units.

  A         9                B

                              12

         D          4       C

Let A  = (0,0)

Let B= (9,0)

Let C = ( 9, -12)

Let D = (5, -12)

We know  three sides......we  just need to find AD  =  sqrt [ ( 0 - 5)^2 + ( -12 - 0)^2 ] =

sqrt [ (-5)^2  + (-12)^2 ]  =

sqrt [ 25  + 144 ] =

sqrt [ 169]  =

13

So.....the perimeter is    9 + 12 + 4 + 13   =   38 cm

Math is art.

Thanks Dragan,

That ties in with my finding but .... 

Mmm we are still looking for a proper explanation of why it must be a 30,60 90 triangles.

Circumference of circle = pi * d

                                      = pi 80   =    251.33 cm

B.      11 m    x     (100 cm/m)    /   (251.33 cm / rotation)  =   4.38 rotations ~~ 4 rotations