Hi

*Note: 

P = .975  then z = 1.9599

1.9599 = (x - 500) / 100

195.99 = x-500

x = 695.99 Or 696 SAT score

Hi





log2x-log(x-7)=log3 

log2x-log(x-7)-log3=0

log(2x/3(x-7) = 0 



10 ^0 = 2x/3(x-7)

1 = 2x/3(x-7)

3(x-7)= 2x

3x - 21 = 2x

x = 21

Hi

(a^-2 + a) / a + 1



(1 + a^3) / a^2(a + 1) Multiplying numerator and denominator by a^2



(a^3 +1) / a^2(a + 1)



(a +1)(a^2 -a +1) / a^2(a + 1) factoring out (a+1) in the numerator



(a^2 -a +1) / a^2  Simplifying

Hi,

y = 3x^2 + 9x 

y intercept shen x = 0

(0,0) the y intercept

x-intercepts is when y = 0

0 = 3x^2 + 9x

0 = 3x(x+3)

x= 0

x = -3

x-intercepts (0,0) and (-3,0)

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

y = 3(x^2 + 3x)

y = 3[(x+ 3/2)^2 - 9/4]

y = 3(x + 3/2)^2 - 27/4

vertex Pt(-3/2,-27/4)

Range [-27/4,)

Hi,

Solving the equation

x – 5 + 6x = -2 + 7x

7x - 5 = 7x - 2

-5 ≠ -2  There is NO solution

Hi,

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

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

Line parallel to the following  

 x +6y=5   Solving for y to put into the slope-intercept form

y = -x/6 + 5/6  m = (-1/6)

New line parallel to this line has the same slope

y = -x/6 + b  Using ordered pair Pt(2,4) to solve for b

4 = -2/6 + b

4 + 1/3 =  13/3 = b

y = -x/6 + 13/3

Hi,

log3(x - 1) = 4

Using the following Property of Logarithms



3^4 = (x-1)

81 = x-1

82 = x



log3(x - 1) = log34   logarithm bases are equal in this example, therefore:

 (x-1) = 4

  x = 5

Hi,

Let x represent length of the shorter piece

then (21ft -x) would represent the lomger piece

Question states***

5x = 3(21ft-x) +1ft

solving for x

5x = 63ft - 3x + 1ft

8x = 64ft

x = 8 ft, the length of the shorter piece

Longer piece is 13ft  (21ft-8ft)

CHECKING our Answer***

5*8ft = 3*13ft + 1ft = 40ft

Hi,

(x+7)^2

(x+7)(x+7)

x^2 + 14x + 49 Note:SUM of the inner product(7x) and the outer product(7x) = 14x



Checking our answer

(x+7)(x+7)= x(x+7) + 7(x+7) = x^2 + 7x + 7x + 49 = x^2 +14x + 49

Hi,

(x+y)(x-y)

x^2 - y^2  Note:SUM of the inner product(x*y) and the outer product(-x*y) = 0

Hi

Let x represent the pounds of $8 per pound candy

Mixing the candy to create a mixture that cost 9$ per pound

8x + 10.50*4lb = 9*(x + 4lb)

solving for x

8x + 10.50*4lb = 9*x + 9*4lb

1.50*4lb = x

6lb = x, the amount of the pounds of $8 per pound candy

CHECKING our Answer

$8/lb*6lb + $10.50/lb*4lb = $48 + $42 = $90 = 9/lb*10lb

Hi,

Finding an equation of the line containing the given pair of points. 

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

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

(1/4, - 1/2) and (3/4, 6) Using the points to find the slope m 





m = (13/2)/(1/2) = 13

y = 13x + b  using Pt(3/4,6) to solve for b

6 = 39/4 + b

-15/4 = b

y = 13x - 15/4

Hi,

Let x represent the age of the youngest, (x + 3), the middle one and 3x the eldest

Question states

3x = x + (x+3) + 2

solving for x

x = 5, the age of the youngest

the eldest gradchild is 15

CHECKING our Answer

15 = 5 +8 + 2

Hi,

Let x represent May's age.  Then the mother's age would be represented by 4x

5 years ago, the mother was 7 times as old as May***

4x - 5 = 7(x-5)

solving for x

4x - 5 = 7x - 35

30 = 3x

10 = x, May's age NOW.  the mother is NOW 40  (4*10)

how old is each 2 years from now

May is 12 and the mother is 42

CHECKING OUR ANSWER

5 years ago, the mother was 7 times as old as May***

35 = 7*5

Hi,

Let x represent the number of years so that the man will be twice as old as his son.

Now, the man is 32 years old while his son is 8 years old

32 + x = 2(8 + x)

solving for x

32 + x = 16 + 2x

16 = x, the number of years from now that the man will be twice as old as his son

CHECKING our Answer

32 + 16 = 2(8 + 16)= 2*24 = 48

Hi,

Let x be ben's age now and y represent larry's age now.

y - 3 =2(x -3)=2x - 6  3 years ago, larry was twice as old as ben

y + 3 =(3/2)(x + 3)=(3/2)x + (9/2) three years from now he will be 1 1/2 times as old as ben

y - 3 =2x - 6

y + 3 =(3/2)x + (9/2)

Solving for x by eliminating y

y - 3 =2x - 6

-y - 3 =-(3/2)x - (9/2) subtracting second equation from the first

-6 = x/2 - 21/2

9/2 = x/2

9 = x, ben's age now.

Substituting for x to solve for y, larry's age now

y - 3 = 2x - 6

y = 2x -3

y =2*9 - 3 = 15, larry's age now



checking our answer

3 years ago, larry was twice as old as ben

12 = 2*6

Hi,

in four years, cindy's age will be the same as tina's age now

Let x represent tina's age now, than cindy's is (x-4)

tina is an always will be 4 years older than cindy.

x = 2(x-4) in two years

x = 2x - 8

8 = x, tina's age in two years, tina is now 6 and cindy is 2  (6-4)

the age of cindy in 3 years is 2 + 3 = 5

Hi

Finding the x-intercepts for the graph of the equation 

y=x^2-3x-4 (y=0 when the graph crosses the x-axis)

0 = x^2-3x-4

solving by factoring

(x-4)(x+1)=0 Note:SUM of the inner product(-4x) and the outer product(1*x) = -3x

(x-4)=0

x=4

(x+1)=0

x = -1 

Hi,

solving

x^2+6x-4=0

Using the Quadratic formula

 

 

 



 

Hi,

factoring

21-10a+a^2

a^2-10a + 21

factoring

(a-7)(a-3)Note:SUM of the inner product(-7a) and the outer product(-3a) = -10a

Hi,

solving 

c^2+3c-54=0 

factoring

(c+9)(c-6)=0 Note:SUM of the inner product(9c) and the outer product(-6c) = 3c

(c+9)=0

c = -9

(c-6)=0

c = 6

Hi

solving

a^2-6a-27=0

factoring

(a-9)(a+3)= 0 Note:SUM of the inner product(-9a) and the outer product(3a) = -6a

(a-9)=0

a = 9

(a+3)= a = -3

Hi

*Note: 



z = 18/5 = 3.6

P(z ≥ 3.6) = 1 - .9998 =.00016

Hi,

solve









x(x+9) = 10^1

x^2 + 9x = 10

x^2 + 9x - 10 = 0

factoring

(x+ 10)(x-1)=0

(x+10) = 0  

x = -10 This is an Extraneous solution

(x-1)= 0

x = 1

Hi

Use the Quadratic Formula to solve

x^2 – 2x – 11 = 0 









x = 4.464

x = -2.464

Hi,

Let x represent the score on the forth test

(71 + 83 + 96 + x)/4 ≥ 85

(71 + 83 + 96 + x) ≥ 340

250 + x ≥ 340

x ≥ 90

he must score a least a 90 on his fourth test

Hi,

*Note: Formula for the test statistic is 

In this case n = 10

Entering the Data into an Excel worksheet column and applying the Data Analysis tool

found  and  for this sampling.

 = -3.8/2.328 = -1.632

P(t < -1.632) can be found using the NORMSDIST(-1.632)function in Excel

or by looking at an usual standard normal table.

P(t < -1.632) = .05134 or 5.1%

The test results show that this sampling is in the low range of normal hearing

Hi,

*Note: Formula for the test statistic is 

In this case n = 5

Entering the Data into an Excel worksheet column and applying the Data Analysis tool

found  and  for this sampling.

 = -.02/.086 = -.2326

P(t < -.2326) = .4080 Or 40.80%

The test results would show that this sampling is well within the average

of mu = .4sec

Hi,

 x2 + 144 = 0

x^2 = -144



x = ± 12i

Answer b. would be the proper selection

Hi,

factoring quadratic expression

–8x2 + 32

-8(x^2 - 4)

-8(x+2)(x-2) Note:SUM of the inner product(2x) and the outer product(-2x) = 0