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   Suppose that a is inversely proportional to b.     

   If  a = -3  when  b = 8, find a when b = 6.     

   Express your answer as a fraction.     

   When b = 8 and a = –3 then ab = –24     

   When the values of a and b change inversely, the product will remain –24.     

   In other words, when b becomes 6, the product of a and b still equals –24.     

   a • b  =  –24       

   a • 6  =  –24     

        a  =  –24 / 6     

        a  =  – 4 / 1     

   .     

   Compute the smallest base-10 positive integer greater than 5     

   that is a palindrome when written in both base 2 and 4.     

        15     

        in base 2  =  1111     

        in base 4  =  33     

   _.     

   Select two points so that the distance between them is equal to 2 sqrt(5).     
   (0,3), (-20,15), (12,7), (3,4), (1,-8), (0,3), (4,4), (-5,8), (-10,-12)     

   Going to use Pythagoras' Theorem     

   c²  =  a² + b²     

   (2 sqrt(5))²  =  a² + b²     

   (4 • 5)  =  a² + b²     

   20  =  a² + b²     

   I can't make any of the provided pairs work.     

   However, take note that (0,3) is listed twice.     

   Why?  Let's assume there’s a typo.  What if     

   the second one were (10,3) instead.  When    

   we choose (10,3) & (12,7) we find precisely     

   what we want, the hypotenuse as follows:     

              c²  =  (7 – 3)² + (12 – 10)²       

              c²  =  4² + 2²  =  16 + 4     

              c²  =  20     

              c    =  sqrt(20)  =  2 sqrt(5)     

   _.     

   i need 2 square root numbers that equal the square root of 400     

   Every number is the square root of some number.     

   The square root of 400 is +20, so I suppose 4 and 16 will suffice.     

   _.     

   When given the volume of a sphere, how to I then find the radius of said sphere?     

   V_sphere  =  ⁴/₃ π r³       solve for r     

   _.     

   A person standing on level ground is 2,000 feet away from the foot of a 420-foot-tall building,     

   a shown in the zccompanying diagram, to the nearest degree, what is the value of x?     

   There is no accompanying diagram shown, but I think I can     

   tell what "X" means.  I'm guessing it's the angle of elevation.     

   If there was a diagram, the solution would be obvious.     

   tangent  =  opposite over adjacent     

   tan(x)  =  420 / 2000     

   tan(x)  =  0.21000     

   tan^–1(0.21000)  =  11.86^o     

   _.     

2 sqrt (x^2 + y^2))  = sqrt [ (x-12)^2 + y^2]

4 [ x^2 + y^2]  = [ x^2 - 24x + 144 + y^2]

4x^2 + 4y^2  = x^2 - 24x + 144 + y^2

3x^2 + 3y^2  = 144 - 24x

x^2 + y^2  = 48 - 8x

x^2 + 8x + y^2  = 48   ........complete the square on x

x^2 + 8x + 16 + y^2 = 48 + 16

(x + 4)^2 + y^2  = 64

The set of points lie on a circle with center (-4,0) and radius = 8

   A rectangular tennis court is 78 ft long and 36 ft wide and is surrounded by auniform pathway.     

   If the total area of the tennis court along with the pathway measures 3280 ft, find the width of the pathway.     

   Area of pathway equals  (2 • 78 • W)  +  (2 • 36 • W)  +  (4W² )              The 4W² are the four corners.     

   Area of pathway equals  3280 – (78)(36)  =  3280 – 2808  =  472     

   156W + 72W + 4W²  =  472     

    4W² + 228W – 472  =  0     

        W² + 57W – 118  =  0     

         (W + 59)(W – 2)  =  0     

                               W  =  –59  discard     

                               W  =  2     

   _.     

   The difference between two numbers is 36.     

   Four times the smaller is equal to 3 more than the larger.     

   What are the numbers?     

   L – S  =  36     —>     L  =  36 + S

   4S  =  L + 3                                        —>    4S  =  (36 + S) + 3     

                                                                       4S  =  36 + S + 3     

                                                                       3S  =  39     

                                                                         S  =  13     

                                                                         L  =  36 + S     

                                                                         L  =  36 + 13     

                                                                         L  =  49     

   .     

The answer is ab > cd > c/d + ac > cd + a/b  > a + b > ab.

like y = 3x - 7.

A point (x,y)(x, y)(x,y) is twice as far from (12,0) as from (0,0).

Step 1: Write distances

From (0,0)(0,0)(0,0):

x2+y2\sqrt{x^2 + y^2}x2+y2​

From (12,0)(12,0)(12,0):

(x−12)2+y2\sqrt{(x-12)^2 + y^2}(x−12)2+y2​

Step 2: Apply condition

(x−12)2+y2=2x2+y2\sqrt{(x-12)^2 + y^2} = 2\sqrt{x^2 + y^2}(x−12)2+y2​=2x2+y2​

Step 3: Square both sides

(x−12)2+y2=4(x2+y2)(x-12)^2 + y^2 = 4(x^2 + y^2)(x−12)2+y2=4(x2+y2)

Step 4: Expand

x2−24x+144+y2=4x2+4y2x^2 - 24x + 144 + y^2 = 4x^2 + 4y^2x2−24x+144+y2=4x2+4y2

Step 5: Simplify

−3x2−3y2−24x+144=0-3x^2 - 3y^2 - 24x + 144 = 0−3x2−3y2−24x+144=0

Divide by −3-3−3:

x2+y2+8x−48=0x^2 + y^2 + 8x - 48 = 0x2+y2+8x−48=0

Final Answer:

👉 x2+y2+8x−48=0x^2 + y^2 + 8x - 48 = 0x2+y2+8x−48=0

The answer is y = 3x - 7.

The answer is (0,3) and (4,4).

The answer is (-20,15), (0,4), and (-10,-12).

The answer is (3,4) and (-5,8).

The answer is (12,7) and (-10,-12).

The answer is (3,4) and (4,4).

   A semicircular pipe has a cross-sectional area of 14.1 cm squared. work out the radius of the pipe.     

   If it were a round pipe, the Area would be  π r²     

   Since it's a semicircle, the Area equals      ¹/₂ • π r²     

                                                            A  =  ¹/₂ • π r²     

                                                       14.1  =  ¹/₂ • (3.1416) r²     

                                                       28.2  =  (3.1416) r²     

                                                           r²  =  28.2 / 3.1416     

                                                           r²  =  8.9763     

                                                           r    =  2.996  call it   3     

   _.     

   The first two terms of a geometric sequence are 9 and 3. What is the fourth term of the sequence?     

   You can use r = ¹/₃ for the common ratio, and then the geometric sequence is 9, 3, 1, ¹/₃     

   _.     

   x2-2x-15     

   What's the question?     

   If you want it factored . . .  x² – 2x – 15  =  (x – 5)(x + 3)     

   _.