All Answers 355967 Answers

Nope, it is 4. Thank you for your help anyways and have a good weekend!

AC = BC   ....so....

3x + 7 =  4x +4

7- 4 =  4x  - 3x

3  = x 

AB = 2x  + 3  =  2(3) + 3  = 9

RV = TV = SV

6x - 10 = 3x + 8

x = 6   ==> SV = 6

Angle RVU = 180 - 2*30 

Using synthetic division

2  [  1    0       -1      k  ]

             2        4     6

    _________________

      1     2       3     k + 6

k + 6  = 0

k  =  -6

So

2 [   1     0      -1      -6   ]

              2       4       6

    ____________________

      1      2       3       0

The remaining polynomial  is

x^2  + 2x   +  3     =   0           complete  the square

x^2  + 2x   =  -3

x^2 + 2x   + 1  =  -3  + 1

(x + 1)^2  = -2    take both roots

x + 1  = sqrt (-2)          x   + 1  =  -sqrt (-2)

x =  -1 + sqrt ( 2) i       x =  -1  - sqrt (2) i         ⇒  the other two roots

Answer: 

by corresponding interior angles, angle DHF is congruent to angle BGH, and they both equal 59 degrees.

exterior angles of a triangle are always the sum of the other two interior angles, so the measure of angle E would be 59 - 16 = 43.

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

from 1 to 1000:

2^0, 2^1, ..., 2^9 (10 numbers)

3^0, 3^1, ..., 3^6 (7 numbers)

2^0 = 3^0 = 1 was counted twice, so 16 numbers from 1 to 1000

from 1/1000 to 1:

1/2^9, 1/2^8, ..., 1/2 (9 numbers)

1/3^6, 1/3^5, ..., 1/3 (6 numbers)

Therre are 15 numbers from 1/1000 to 1.

Overall, there are 31 numbers.

If you don't know Pick's Theorem, you could also do it this way:

shaded = (area of total region) - (area not shaded)

= \((4 \cdot 4) - (\frac{2 \cdot 3}{2} + \frac{1 \cdot 1}{2} + 1 + \frac{1 \cdot 2}{2} + \frac{1 \cdot 3}{2})\)

= \(16 - 7\)

= \(\boxed{9}\)

You could also find the area of the shaded region directly, which is just made out of squares and triangles.

\(\frac{2 \cdot 2}{2} + 2 + \frac{3 \cdot 1}{2} + 1 + \frac{2 \cdot 1}{2} + \frac{3 \cdot 1}{2}\)

= \(2 + 2 + \frac{3}{2} + 1 + 1 + \frac{3}{2}\)

= \(\boxed{9}\)

2^0, 2^1, 2^2, ..., 2^9 -> 10 numbers

3^0, 3^1, 3^2, ..., 3^6 -> 7 numbers

Total of 17 numbers

We can use Pick's rule for the area:

\(A=I+{\frac {p} {2}}-1\)

-Where I is the points inside the figure and p is the points on the perimeter.

There are 5 points inside and 10 on the perimeter.

A = 5 + 10/2 - 1

A = 5+5-1

A=9

Therefore the area is 9 square units.

Let b represent the number of burgers sold.

Let h represent the number of hot dogs sold.

Note that:

2.35b+1.10h = 294.20

b+h=172

b+h=172

h=172-b

Now solve the system of equations with substitution:

2.35b+1.10h = 294.20

2.35b+1.10(172-b) = 294.20

2.35b + 189.2 - 1.1b = 294.20

1.25b=105

b=84

b+h=172

84+h=172

h=88

Therefore there are 84 burgers and 88 hot dogs.

Solved! :)

(3/8) ( 32)  =  12 have  cats  which implies  that

x +  z + w  =  3        (1)

(1/2) (32)  = 16   have dogs  which  implies  that

x + z + y =  6      (2)

8 have some other pet  which implies  that

w + z +  y =  4

And  since  5  have  no pets  at all.....this implies  thsat

w + x + y + z  + 9 + 2 + 10  =  32 - 5 

w + x + y + z + 21  = 27               subtract 21  from both sides

w + x + y + z  =  6     (4)

Sub  (1)  into  (4)   and  we  get  that

y   + (x  + z + w)  =  6

y + 3  =  6

y = 3

And  

x + z  + y  =  6

x + z  + 3  =6

x  + z  = 6 - 3

x + z  = 3      (5)

And 

w + z + y =  4

w + z +  3  = 4

w + z = 4-3

w + z =  1    

So  subbing (5)    into (4)  we  get  that

w + x + y  + z =  6

w + (x + z) + y = 6

w  + 3 + 3   = 6

So w  = 0

And w  + z  =1   means z  =  1

And   x + z = 3     so    x + 1  = 3    so    x   = 2 

So

 w = 0

x  = 2

y = 3

z  = 1   =  the  number  that  own all three

Thanks for clearly explaining!

Distance  / rate  =  total time

So

time for first 15 miles +  time for last 60 miles =   2 hrs  ....so.....

15 /  r    +  (75 - 15)  / ( r + 10)  =  2         simplify

15 / r  +  60 / (r + 10)  =  2

15 ( r + 10)  + 60r

_______________   =  2

         r ( r + 10)

15r + 150 + 60r   =  2  r  ( r + 10)

75r  + 150  =  2 ( r^2 + 10r)

75r  + 150  =  2r^2  +  20r       rearrange  as

2r^2 - 55r - 150  = 0        factor  as

(2r + 5) ( r - 30)  = 0

The  second factor set to 0   gives us what we need

r   - 30   = 0

r = 30  (mph) =   the  rate during the  first 15 miles

Nothing too much  to do here but to find the height

The  height of the cone   =  sqrt (5^2  - 3^2)  = sqrt ( 25 - 9) = sqrt 16  =  4 cm

Volume (cone)  =  pi  * radius^2  * height  / 3   =

3.14 * 3^2 * 4   / 3   =

3.14 * 12  = 

37.68  cm^3

From  the top right vertex,  draw  a line parallel to  the  base......the length of  this line segment  inside the trapezoid = 24

So  this froms  a   7  - 24  - 25    right triangle   at  the top of the trapezoid

So....the perimeter   =

7  + 13  + 24  + 13  + 25  =  

82

  x + 1               x  +  1                 (x + 1)                        1                    1

_______  =     _________  =   _____________  =    _______  =    ______ 

x^3  - x             x ( x^2 - 1)        x ( x + 1) ( x - 1)       x ( x  -1)         x^2 - x

The  first parabola  has  the form

y =  a ( x - 3) ( x - 5)

Since  (2, -1)  is on the parabola   we can solve for a  thusly

-1  = a ( 2 - 3) ( 2 - 5)

-1 = a ( -1)(-3)

-1  = 3a

a = -1/3

Then the parabola  can be written  as

y =  -(1/3)(x - 3) ( x - 5)

y= -(1/3) (x^2 - 8x  + 15)      (1)

The second  parabola  has  the form

y = a (x - 1)(x - 4)

Since  the  y intercept =  2....then the pont (0, 2)  is on this graph....so

2 = a ( 0 - 1)( 0 -4)

2 = 4a

a  =  2/4  =  1/2

So this parabola  can be written as

y = (1/2) (x - 1) ( x - 4)

y= (1/2) ( x^2 - 5x + 4)      (2)

Set  (1)  = (2)

(-1/3) ( x^2 -8x + 15)  = (1/2)(x^2 - 5x + 4)        mutiply through  by  6

-2 ( x^2  - 8x + 15)  =  3(x^2 -5x  + 4)       simplify

-2x^2 + 16x  - 30  =  3x^2 - 15x + 12        rearrange  as

5x^2 -31x + 42  =  0        factor  as

(5x - 21) (x - 2)  =  0

Set  each  factor to 0  and solve  for  x

5x - 21 = 0                       x - 2  =  0

5x= 21

x= 21/5  = 4.2                  x  = 2

When x = 4.2   ....y =  (1/2) ( 4.2^2  -5(4.2) + 4)  =  .32

When x =2  we know  that y = -1

Here's a graph  :  https://www.desmos.com/calculator/9js5dz8aue

Thanks for your effort but it wasn't right. Also only the a, b, and c values that you found only work with the first two equations but not a+b+3c=19 because -5+1+3(11)=29 and not 19. 

                         B

                        62

                C                 D

Since BC =  DC,  then  angles  C and D  are equal......so either angle =  

(180  - 62)  /  2   =    118  /   2   =    59°

50 - 59   =  10 numbers

5, 15, 25, 35, 45  = 5  more

15  numbers

x =    180 -   (180 - 98)  -  85  =

98  -  85   = 

13°

(2x + 13) + 39  =  90

          2x + 52  =  90

                  2x  =  38

                    x  =  19

a = -5, b = 1, and c = 11, so abc = (-5)(1)(11) = -55.