Archive for December, 2014

Problem 452

Simplify the expression. Write answer with positive exponents.

\frac{3^{-10}}{3^{-6}}

 

Solution

 

We can write it as

3^{-10}*3^{6}

When base are same then power will be add

So 3^{-10+6} = 3^{-4}

 

Problem 451

Factor completely.


x^{2} + 5x – 36

 

Solution:-

 

Do factor

x^{2} + 9x – 4x – 36

X(x+9)-4(x+9)

(x+9)(x-4)

 

Problem 450

Solve the equation.

\left | 4s+7 \right |=\left | s+9 \right |

 

Solution:-

 

When we remove mod sign then value become positive but here both sides  have mod so one time we take any one side positive and second time we take negative so here

First take positive we get

4s+7=s+9

4s-s=9-7

3s=2

S=\frac{3}{2}

Now take negative

-(4s+7)=s+9

-4s-7=s+9

-4s-s=9+7

-5s=16

S= – \frac{16}{5}

 

Problem 449

Evaluate the expression, given x = -2, y = 3, and a = -4.

-6(x + 4) + 5a^{2}

 

Solution

 

Put all values

-6(-2+4) +5 (-4)^{2}

= 12-24+5(16)

= -12+80

=68

 

Problem  448

Evaluate the expression, given x = -2, y = 3, and a = -4.


2a – 7y – 4x

 

Solution

 

Put all values

2(-4)-7(3)-4(-2)

= -8-21+8

= -21

 

problem 447

Solve the equation.


20t + 1 = 11t + 7

 

Solution:-

 

20t-11t=7-1

9t=6

T=\frac{6}{9}=\frac{2}{3}

 

Problem 446

Solve the equation for x.

x = (6x – 2)(2k + 1)

 

Soluiton:-

 

X=6x(2k+1)-2(2k+1)

X=12xk+6x-4k-2

x-12xk-6x=-4k-2

x(1-12k-6)= -4k-2

x(-12k-5)= -4k-2

x=\frac{(-4k-2) }{(-12k-5)} 

x=\frac{(4k+2) }{(12k+5)} 

 

Problem 445

Find expressions for the Revenue, Cost, and Profit from selling x thousand items.


Item Price Fixed Cost Variable Cost
$5.00 $58,684 3698x

 

Solution:

 

Revenue=5000x (5 dollar per item * 1000x)

Cost=58684+3698x (fixed cost+variable cost)

Profit=5000x-58684-3698x (revenue profit)

Profit= 1302x-58684

 

Problem 444

Use factoring to solve the equation.

5m^{2} – 14m = 0

 

Solution:-

 

Take m common

M(5m-14)=0

So    m=0    or    5m-14=0

M=0         or      m=\frac{14}{5}

 

Problem 443

Find the reciprocal of (\frac{-1}{5})(15)

 

Solution

 

Reciprocal means multiply the given value by other value then answer become 1

So in this question

\frac{-15}{5}

If we multiply it by \frac{-5}{15} then value become 1