Hi

A) entering data in an Excel column and using the data analysis tool

 mean = 20.0667 , varience = 180.2095,  standard deviation = 13.4242

B) z = (36-49) /6  and z = (78-49)/ 6

Hi

Using the standard slope-intercept form for an equation of a line y = mx + b

  where m is the slope and b the y-intercept.  

y = A+B(x-3)

y =  Bx - 3B + A   | ⊥ to y = 2x, therefore it's slope will be m = -1/2

  B = -1/2

y = (-1/2)x +3/2 + A  |using ordered pair pt(5,15) to solve for A

15 = -5/2 + 3/2 + A

16 = A



CHECKING our Answer

 y = 16 -(1/2)(x-3)

15 = 16 -(1/2)(5-3)

 15 = 16 - 1

Hi

if h=0 what is the answer to h=-16t^2+625

-16t^2 + 625 = 0  |multiplying thru by -1

 16t^2 - 625 = 0

    16t^2 = 625

    t^2 = 625/16

    t = ± 25/4

Hi

 S = r*t or  D/r = t

Question states***

 D/1.6kmph + D/2.4kmph = 11hrs  |multiplying thru by 4.8

 3D + 2D = 11*4.8

    5D = 52.8 

     D = 10.56 km

Hi

See the repost with the rates given.

will address that question.

Hi

Note using < for angle does not work in the translation for this site.

|ac| has another meaning than for side lengths of triangles,

might recommend just using  'ac'

In a triangle abc,|ac|=16cm,|bc|=10cm, ∠bac=30 degrees. If ∠abc = 90 degrees, find |ab|

 ac is across from the right angle and therefore length 16cm is the hypotenuse

Pythagorean Theorem applies:  ac = sqrt(16cm^2 - 10cm^2) = 12.49cm

  

Hi

2x-y = 5  OR y = 2x - 5  |good work!

2x+y=3  OR   y = -2x + 3 |note subtracting 2x from both sides of the equation

Yes!! solving for y, the coefficient of x is the slope

to be parallel, line must have same slope

to be ⊥, lines must have slopes that are negative 'reciprocals' of one another

Neither is the case, therefore the lines are neither parallel or perpendicular.

However, Yes!, they do intersect at Pt (2,-1)...have that point in common

Hi

The sum of two integers is 30

Let x and (30-x) represent the smaller and larger number respectively

Question states***

 2(30-x) = 5x -10

solving for x

  60 - 2x = 5x-10

     70 = 7x

      x = 10, the smaller number.  The larger number is 20.   (30-10)



CHECKING our Answer***

 40  = 50 - 10

Hi

invested a total sum of $25,000 om two accounts

 x  and ($25,000-x) would represent the individual amounts in these two accounts

Hi

simplify the expression. 16 + (x + 4)  =  x + 20

simplify the expression. (8 * b) * 4   =  32b

the sum of a number and 16 is 31. 

   x + 16 = 31  |subtracting 16 from both sides of equation

      x = 15    | x is equal to 15

the difference of 22 and a number is 8.

  22 - y = 8  |subtracting 8 and adding y to both sides of equation

     14 = y   | y is equal to 14

Note: when solving, we must isolate the variable on one side of the equation,

so as, we can 'read' the solution

Hi

Using the point-slope formula,  to find slope

(7,10) and 

 (4,2) m = 8/3, the slope of the line containg these points

Using the standard slope-intercept form for an equation of a line y = mx + b

  where m is the slope and b the y-intercept.  

 y = (8/3)x + b  |using ordered pair Pt(4,2) to solve for b

 2 = 32/3 + b

 -26/3 = b

 y = (8/3)x -20/3

 Pt(5,5) is the point of intersection of these lines according to the graph

CHECKING our Answer: 

x = (8/3)x -20/3, 3x = 8x - 20, 20 = 5x, x = 5 and y = 5  (y = x)

 

Hi

y = 12x^3-12x

Finding the zeros of the function

  12x^3 - 12x = 0

  12x(x^2 - 1) = 0

  12x(x+1)(x-1)= 0



  12x = 0   x = 0

  (x+1)=0   x = -1

  (x-1)= 0  x = 1

Hi

D = r*t  or t = D/r

 t =  23.5mi/80mph = .29375 hours  or 17.625min

Hi

Note: the product of reciprocals = 1

the reciprocal of 1/9 is 9/1 (or 9) as 

Hi

    |multiplyig each term by 12h so as all denominators = 1



   75h + 48 = 240h

       48 = 165h

       48/165 = h

         .2909 = h

Hi

21 questions wrong out of 80, then 59 were answered correctly

Percentage wise 59/80*100 = 73.75% were answered correctly

Hi

Using the quadratic formula to solve the equation.



 x^2 - 3x + 7 = 0







The solution set is , 

Hi



Using the vertex form of a parabola,  where(h,k) is the vertex

 |1/4 = a > 0, parabola opens upward

 Vertex is Pt(-1,5)is minimum point and the Line of symmetry is x = -1

f(x) = 5 is the minimum value for the function

Hi







Note:  (-1/4)^5 = -1/1024

   

Hi

Hi

Let x represent the number

Write as we Read***

 3x + 2x > 125

    5x > 125

     x > 25   |x being ALL real numberx greater than 25

Hi

A = L*W = s*s for a square where s is the length of each side

Question states***

  s^2 = 45 cm^2

  s =   Tossing out negative solution for length

    s =  

    s =  

|not uncommon for answers to be given in simplest radical form



Note: 3 *  = 6.7082 = sqrt(45)}}} 

Hi, have plotted respective images with a larger circle.

The idea being if one were to fold along line referenced, points would 'match' up

Hope this helps

image of A(-2, 3)

i) x-axis  (-2,-3)

ii) y-axis  (2,3)



image of A(-2, 3)

iii) y = x  (3,-2)

iv) y = -x  (-3,2)



image of A(-2, 3)

v)  x = 1  (4,3)

vi) y = -2 (-2,-7)



image of A(-2, 3)

vii) y = -x + 5  (2,7)

Hi

Solving by elimination method

0.05x+0.25y=66

0.15x+0.05y=72 



-.15x -.75y = -198   |mulitplying 1st equation by -3 to eliminate x  

0.15x +.05y =   72 

      -.70y = -126

          y = 126/.70

          y = 180

0.05x + 0.25y=66

          x = (66-45)/.05

          x = 420



CHECKING our Answer

0.15*420 + 0.05*180 = 63 + 9 =  72 



 

Hi

Let x represent the speed of the plane

Questions states***   (D = r*t  OR r = D/t

  x + 30 =  D/5

  x - 30 =  D/7

 2x = (12/35) D

  x = (6/35)D

 

  x + 30 =  D /5

(6/35)D + 30 =  D/5

       30 = (1/35)D

      30*35 = D

      1050mi  = D

              x = (6/35)1050 = 180mph



CHECKING our Answer

  150 = 1050/7

Hi

y = 5x-2  is a function describing ordered pairs that form a line when graphed

the standard slope-intercept form for an equation of a line is: y = mx + b 

 where m is the slope and b the y-intercept.  

y = 5x-2 is a line with slope m = 5 and the y-intercept is Pt(0,-2)

 m = (5/1)as y increases/decreases by 5, x increases/decreases by 1

Note: Plotting Pt(0,-2) and using slope to find at least one more point,

joining these points with a line completes the graphing

Hi

Ax + 3y = -3   |using ordered pair Pt(2,-5) to solve for A. (x= 2 and y= -5 )

A*2 + 3(-5) = -3 

 A*2 -15  = -3  

  2A = 12

   A = 6

Hi

Let x represent how miles can the boat travel on 60 gallons of gas

Question Sets Up the Proportion

   | cross multiplying to solve for x

  15x = 60gal*66mi

    x = 60*66/15gal

    x = 264mi



CHECKING our Answer

  4 times the gas, four times the miles that can be driven!

Hi

solving

x/2 + x/3= 3/4    |multiplying each term by 12



 6x + 4x = 9

    10x = 9

      x = 9/10

Hi

Let x represent the number

Write as we Read***

 x/2 + x/3 + x/4 = x + 12  

solving for x         

 6x +4x + 3x = 12x + 144      |multiplying each term by 12

           x = 144



CHECKING our Answer

 72 + 48 + 36 = 156 = 144 + 12

Hi