All Answers 355967 Answers

3a  +  4b  = 7       multiply through by 2   

6a  + 8b =   7    

Tthe  second rearranges as

6a  + 8b =  k

The  system will have infinite solutions  when the  two equations are  exactly the same

So...k = 7

thank you!!

by vertical angles, angle e is 49 degrees.

angle f shares a straight angle with the 49 degree angle, so angle f is 180 - 49 = 131 degrees.

similarily, angle d shares a straight angle with the right angle, so angle d is simply 180 - 90 = 90 degrees.

hope this helped! please let me know if you are confused about anything i did :)

Possible  4 digit numbers =   5 * 5 * 4 * 3  =   300

Possible 3 digit numbers  =  4 * 5 * 5  =   100

Total problems = 300 * 100  =   30,000

14)

arc length =  2pi * radius * (210 / 360)  =  2 pi * 9 * (7/12)  =  10.5 pi ft  ≈  33 ft

16 )   a)   b)     PNQ  and PQO   are inscribed angles  subtending arc PQ.....their measures are half of this arc = 40°

18 )   We  have a right triangle with a hypotenuse of 12.5   one leg = 7.5  and the  other leg  = 2x

So

2?  =sqrt ( 12.5^2  - 7.5^2)  =  sqrt (100)  = 10 

2?  = 10

?  = 10 / 2  =  5

We  have  the form   y = ax^2  + bx  + c

The  x coordinate of the  vertex  occurs  at  - b / (2a)  =  -8/ ( 2 *-2)  =  -8 / -4  = 2

To find the y coordinate...put x  back into  the function

y= -2(2)^2  + 8(2)  -15  =    -8  + 16  - 15 =  -7

x coordinate =   - b/2a =  -  8/-4 =  2

   sub into equation to find y   coordinate     -2(2^2) + 8 (2) - 15 = -7                (2, -7)

y  =  -2x² + 8x - 15

Move the '-15' term to the other side by adding 15 to both sides:

     y + 15  =  -2x² + 8x

Factor out the '-2' term:

     y + 15  =  -2(x² - 4x)

Complete the square of x² - 4x     --->     x² - 4x + 4

Notice that the '4' will be on the inside of the factor, so really, it is a '-8':

     y = 15 - 8  =  -2(x² - 4x + 4)

Finishing:

     y + 7  =  -2(x - 2)²

The vertex occurs at (2, -7)

Hi guest!

Knowing that a triangle sums up to 180, you can just set all the equations to 180 which will be:

(9x-11)+80+57=180

solving for x, it will be 6

Complete the square on y = -2x^2 + 8x -15.

Then y = -2(x - 4)^2 + 17, so the vertex is (4,17).

You can either write them out which and count them up, which takes 20 seconds, or use your brain and realise that it's only 5 and 15, fo your answers is 2, both of which take less time to do than ask on this forum and waste people's time.

Hi Valencia!

im not sure If Im correct but heres my thoughts:

since it is a  equalateral rectangle, the all the sides are equal to its corresponding side, meaning the length= the other length and the width= the other width of the rectangle.

Now knowing this,you can split the triangle and rectangle by drawing a line between and the line value is 24, since mentioned above, length=length.

We have figured out all the sides of the rectangle and now only need to find the other small side of the triangle. 

Using pythagroean theorum, a^2+b^2=c^2, you can set the unknown part of the triangle to a^2.

plugging in the values: a^2+24^2=25^2, you can further simplify and get a as 7

Now that we have all the values, you can just add all the sides  EXCLUDING  the 24 of the imaginary length in the rectangle since we only needed that to find the other side of the triangle.coming to 13+24+13+7+25= 82, which is the perimeter 

hope this helped,

thanks!!

See my answer, Jenny, under your original post....not too sure about it, though  !!!

Here's  my best attempt

Mathematical expectation = 

Winnings * probability of winning -  cost to play

5(.08)  +  6(.26)  + 7(.34)  + 9(.20) + 12(.12)  -  8  =  -21/30  = -0.42  teeth

Daniel has been saving part of his allowance in a bag every month. The bag contains 2 dollar notes and 10 dollar notes and had a total value of 2148 dollar. 18 pieces of 10 dollar notes were exchanged for 2 dollar notes of the same value. IN THE END The number of 10 dollar noted was the same as 2 dollar notes. How many 2 dollar notes were there at first?

Let x be the initial number of 2s and y be the initial number of tens.

2x+10y=2148

18 tens is equal to 90 twos.

now if I reduce y by 18 I get y-18

and tht means I will then have  x+90   twos.

I am told these must be the same so     y-18=x+90

I am going to let you figure it out from there.

Oops small mistake...corrected  !!!

No prob .....

You are still being careless, and not putting in the time required to even copy the question properly.

You left out important information.

The  vertex  is at  (-1, -2)

We have the form

y = a ( x - - 1)^2  - 2

y =  a ( x + 1)^2  - 2

And  the point  0,-1)  is on the graph...so we  can find a

-1  = a ( 0 + 1)^2  - 2

-1 + 2  =  a

1 = a

So  we havr

y = 1 ( x + 1)^2  -  2

y = x^2  + 2x  + 1  - 2

y = x^2  + 2x  - 1

a = 1   b = 2    c = -1

a + b + c =  1 + 2  - 1    =  2

Its 2 then right? Because 1-4=-3 and -3+5=2.

The vertex  is  (2,1)

And  we have  the form

y = a(x - h)^2  +  k             where  ( h, k)  is  the vertex

And  the point  (0, 5)  is  on the graph....so...

5 = a (  0 - 2)^2 + 1

5 - 1  =  4a

4 = 4a

a = 1

So  we have

y= 1( x - 2)^2  + 1

y = x^2  -  4x  +  4 + 1

y = x^2  - 4x  +  5

a = 1  b  =  -4   c  = 5

a + b + c  =    1  - 4  + 5  =    2

Thanks!

thank you!  i understand better now 

Daniel has been saving part of his allowance in a bag every month. The bag contains 2 dollar notes and 10 dollar notes and had a total value of 2148 dollar. 18 pieces of 10 dollar notes were exchanged for 2 dollar notes of the same value. The number of 10 dollar noted was the same as 2 dollar notes. How many 2 dollar notes were there at first?