hectictar

The triangles are similar.

What is the value of  x  ?

Like the last problem, notice...

7 * 4  =  28

24 * 4  =  96

each side of the bigger triangle   =   4 * the corresponding side of the smaller triangle

25 * 4   =   6x + 28

100   =   6x + 28       Subtract  28  from both sides.

72   =   6x                 Divide both sides by  6 .

12   =   x

The triangles are similar:

What is the value of  x  ?

Notice that...

3 * 4  =  12

5 * 4  =  20

To make the bigger triangle, take each side of the smaller triangle and multiply it by  4  .

So...to find  x  ,  take the corresponding side on the smaller triangle and multiply it by  4 .

Since   △ABC ∼ △EFG ,    m∠C  =  m∠G  .

Since   m∠G  =  61°  ,   m∠C  =  61°

Now we know two of the angles in triangle  ABC  ....

m∠B  =  48°   and   m∠C  =  61°  .

How can we find the measure of the third angle, angle A ?

Remember that the sum of the angles in every triangle  =  180°

m∠A  +  m∠B  +  m∠C   =   180°      Plug in what we know....

m∠A  +   48°   +    61°    =   180°     Subtract  61°  and  48°  from both sides of the equation.

m∠A   =   180°  -  61°  -  48°

m∠A   =   71°

midpoint of  (4, -7)  and  (-3, 5)   =   \((\frac{{\color{red}4}+{\color{purple}-3}}{2},\frac{{\color{green}-7}+{\color{blue}5}}{2})\)   =   \((\frac12,\frac{-2}{2})\)   =   \((0.5,-1)\)

f(x)  =  3x + 2

We want to find the value of  x  that makes     f(x)    be  -4 . That is...

We want to find the value of  x  that makes  3x + 2  be  -4 .

We want to find the value of  x  that makes this equation true:

3x + 2  =  -4      Now let's solve this equation for  x .  Subtract  2  from both sides.

3x  =  -4 - 2

3x  =  -6          Divide both sides by  3 .

x  =  -2

y  =  (x - 2)^2 + 3

This parabola has its vertex at  (2, 3) . Rotating it  180°  about its vertex has the same effect as flipping it over the x-axis and then shifting it up  6  units. So our new parabola has the equation...

y  =  -[ (x - 2)^2 + 3 ] + 6

Now let's shift it  3  units to the left...

y  =  -[ (x - 2 + 3)^2 + 3 ] + 6

And  2  units down...

y  =  -[ (x - 2 + 3)^2 + 3 ] + 6 - 2          Then simplify.

y  =  -(x +1)^2 + 1

The zeros of this parabola are the  x  values when...

0  =  -(x +1)^2 + 1

(x +1)^2  =  1

x + 1   =   ±√1

x + 1  =  1          or         x + 1  =  -1

x  =  0                or         x  =  -2

And the sum of the zeros   =   0 + -2   =   -2

I think they represent the random sample.

Thanks! If you do need some help on that one don't hesitate to ask!

Or if you're unsure of it we can check your work.

a)  It will make a dotted line (or if the bike is not traveling straight, a dotted curve).

b)  It will travel the circumference of the wheel between each mark.

     The circumference of the wheel  =  2pi * 46 cm   =   92pi  cm

c)   1 km  =  1,000 m  =  100,000 cm

      100,000 / (92pi)   ≈   345.989

Depending on where the paint was on the wheel to begin with, there will be either 345 marks or 346 marks.

e + (-15)  =  15

e  -  15   =   15       Add  15  to both sides.

e   =   15 + 15

e   =   30