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We can let the quotient be a. Then pa + 18x = 1. We must have that p is divisible by 18, so p=1,2,3,6,9,18. However, the only primes are 2 and 3, so we have sum(p) = 5.

This would mean that $9m \equiv 1 \pmod m.$ Therefore, $0 \equiv 1 \pmod m,$ so $m = 1.$ But, if we plug this in to $2m \equiv 1 \pmod m,$ we get 2 = 1 mod 1 which is obviously true. Therefore, there is no solution.

suppose that 15 inches of wire costs 60 cents at the same rate how much (in cents ) will 47 inches of wire costs ?     

First find the cost of the wire in cents per inch 

When you see "per" in a proposition it always means divide                    60 ¢ 

                                                                                                                ––––  =  4 ¢/in  

                                                                                                                15 in  

Now multiply the cost in ¢/in times 47 in                                                   4 ¢/n • 47 in  =  188 ¢  or  $1.88  

_.

The area of the octagon is the area of the original square minus the area of the four triangles.  

Area of the original square                                   20 • 20  =  400 

                                                                               1  

Area of one triangle                                              ––– • 4 • 4  =  8  

                                                                               2  

Area of all four triangles                                         4 • 8  =  32  

Area of octagon (square minus triangles)              400 – 32  =  368  

_.

An equilateral triangle of side length 6 is rotated about an altitude to form a cone. What is the volume of the cone?

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Cone radius         r = 3 

Slant height         h_s = 6               ( Height  h = √27 )

Cone volume         V = 1/3 * pi * r² * sqrt(h_s² - r²)    ==>  V = 48.97258284 u³

                                         or

                              V = r² * pi * h / 3        ===> V = 48.97258284 u³

I mean this one

For what values of  x is \(2x^2+8x\leq -6\) ? Express your answer in interval notation.

Hello Guest!

\(2x^2+8x+6\le0\\ x^2+4x+3=0\)

         p        q

\(x=-\frac{p}{2}\pm \sqrt{(\frac{p}{2})^2-q}\\ x=-2\pm\sqrt{4-3}\)

\(x_1=-1\\ x_2=-3\)

\(For\ {\color{blue}-3\le x\le -1} \ is \ \color{blue}-2x^2+8x\leq -6. \)

  !

12 km for 1/2 hr = 6km

10 perimeters = 6 km

1 perimeter = 600 meters

 2w + 2w + w + w= 6w      = 600 m

       So w = 100 m    L= 2w = 200 m

100 m  x  200 m = 2 0 000 m²

Lateral surface area = 2pi r * h

28 pi =   2pi * r * h

28  pi  = 2pi * r * h

28/2  = r * h

14/r =  h

Volume =  pi* r^2 * h

24pi =  pi * r^2  [ 14/r]

24   = r  * 14

(24/14)  = r

(12/7) (inches) = r

https://web2.0calc.com/questions/a-288-degree-circular-sector#r3

This link may help you.

$3.50

Open the small end to make a rectangle of dimension 40 x 32

From P to Q is hypotenuse of right triangle with leg lengths of 16 and 24

   Via Pythagorean theorem : path = 28.84 cm

Thank you so so so so so so so so much! You're amazing CPhill. A true life saver. Thanks again!!!!

Notice if the  center is on the  x axis...it must have the coordinates of  (a, 0)

Because the  distance  from each point to  the  center is the  same we  can solve for a  thusly :

(a-0)^2  + (0 - 4)^2   =  ( a -1)^2  + ( 0 -3)^2    simplify

a^2  + 16 = a^2  -2a + 1  + 9     subtract a^2  from both sides

16  = -2a + 10

16 - 10  = -2a

6 = -2a

6/-2 =  a

-3  = a

Coordinates of center=  (-3,0)

Radius =  sqrt [ (-3 - 0)^2   + (4 - 0)^2  ]  =  sqrt [ 9 + 16 ] =  sqrt 25  =  5

Here's a graph :   https://www.desmos.com/calculator/cu9ityz6lb

See my answer, here  :

https://web2.0calc.com/questions/help-i-don-t-know-what-to-do

Sum  = 11/12

Product  =1/6 =  2/12

a*b =  2/12      (1)

a + b =  11/12      b = 11/12 - a     (2) 

Sub (2)  into (1)

a ( 11/12 - a)  = 2/12     

(11/12)a  - a^2  = 2/12       multiply through by 12 and rearrange  as

12a^2 - 11a + 2a  =   0       factor

(4a - 1 )  ( 3a  - 2)  = 0          set each factor to 0  and solve  for  a

4a - 1  =  0                3a - 2   = 0

4a  = 1                       3a  =  2

a = 1/4                         a  = 2/3

Lesser of two  fractions is   1/4

Thank you so much!

3x^2  - 8x    -2          factor out the 3

3 (x^2  - (8/3)x   - (2/3)  )

Take (1/2)  of 8/3 = 4/3...square this =  16/9....add and subtract  this inside the parentheses

3 ( x^2  - (8/3)x  + 16/9  - (2/3)  - 16/9)    factor the  first three terms, simplify the rest

3 [ ( x - 4/3)^2  -  22/9 ]       distribute the 3

3 ( x - 4/3)^2  - 22/3

a = 3      h = 4/3    k =   -22/3

a  +  h  +  k   =

3 + 4/3 - 22/3  =

3 - 18/3   = 

3  - 6   =

-3

thxx

a^2/b  = 1

b^2/c  = 2

c^2/a  = 4

a^2 = b    →   a^4  = b^2

b^2/c →  a^4/c  = 2  →  a^4 = 2c  →  a^4/2  = c  →  a^8/4  = c^2

c^2/a →  (a^8 /4 ) ( 1/a)  =  4

a^7  =  16

a  =  16^(1/7)  =  ⁷√16

C(4,2) ( x)^2 (y)^2     =   6x^2y^2

C(4,2)   ( x)^2  ( 3y)^2  =  6x^2 * 9y^2  =  54x^2y^2

(6 + 54) x^2 y ^2  = 

60 x^2y^2

(1) ( 9 + 3/2 ) - (3(1)  - 2(1)) ( 1 + 1)  =

( 21/2) - ( 3 - 2) (2)  =

(21/2) -  (1) (2)  =

21/2   -  2  = 

21/2  -  4/2   =

17/2

C =  180  - 102  - 28  =  50°

x / sin 50° =  a / sin 102°

x /sin 50°  = 160 / sin 102°

x =  160 sin 50° / sin 102°  ≈  125.3

6 are red

2 are white

2 are blue

a)  P (white or red)  = 2/10  + 6/10  =  8/10   = 4/5

b) P (not red)  =  1  - P(red)  =   1  -  6/10  =   4/10  =  2/5

c) P (blue or red)  = (2/10  + (6/10)  = 8/10 =  4/5

d) P (white)  = 2/10  =  1/5