geno3141

What is the height of the bar that represents ages 31-45?

What is the height of the bar that represents ages 46-60?

Find the answers to the above two questions and add them together for the final answer.

A cube is the square-based prism with maximum volume. What are the dimensions of a cube whose total surface area is 150 cm²?

To find the mean, add all the numbers together and divide by the number of numbers.

Which one represents adding the numbers together and dividing by the number of numbers?

log_b343  =  -3/2

In exponential notation:  b^-3/2  =  343

Since 343  =  7³    --->   b^-3/2  =  7³

                           --->   b^3/2  =  7^-3                                   Take the -1 power of both sides.

                           --->   b^3/2  =  (1/7)³                              Rewriting 7^-3  

                           --->     b³  =  [ ( 1/7)³ ]²                  Squaring both sides

                           --->     b³  =  ( 1/7)⁶                       Power to a power  -->  multiply exponents

                           --->     b    =  [ ( 1/7)⁶ ]^1/3                  Take the cube root of both sides

                           --->     b    =  (1/7)²                          Power to a power  -->  multiply exponents

                           --->     b    =  1/49                          Simplify

To emphasize what Melody did:

The equation:  |3x| + |4y|  =  12

Can be split into 4 separate equations; 2 for the  |3x| = ± 3x  and  2 for the  |4y| = ± 4y :

--->                 3x + 4y  =  12       --->   y  =  (12 - 3x)/4

                      -3x + 4y  =  12       --->   y  =  (12 + 3x)/4

                       3x - 4y  =  12       --->   y  =  (12 - 3x)/-4

                      -3x - 4y  =  12        --->   y  =  (12 + 3x)/-4  

Graphing these individually will give you the parallelogram that Melody got.

√[ 4 + √(16 + 16a) ]  +  √[ 1 + √(1 + a) ]  =  6

     √[ 4 + √(16 + 16a) ]      +  √[ 1 + √(1 + a) ]  =  6 

=>  √[ 4 + √[16(1 + a) ] ]     +  √[ 1 + √(1 + a) ]  =  6

=>  √[ 4 + √16·√(1 + a)  ]    +  √[ 1 + √(1 + a) ]  =  6

=>  √[ 4 + 4·√(1 + a)  ]        +  √[ 1 + √(1 + a) ]  =  6

=>  √[ 4(1 + √(1 + a) )  ]      +  √[ 1 + √(1 + a) ]  =  6

=>  √4·√[ 1 + √(1 + a) ]        +  √[ 1 + √(1 + a) ]  =  6

=>  2√[ 1 + √(1 + a) ]          +    √[ 1 + √(1 + a) ]  =  6

=>  3√[ 1 + √(1 + a) ]  =  6

=>  √[ 1 + √(1 + a) ]  =  2       (divide both sides by 3)

=>   1 + √(1 + a)  =  4             (square both sides)

=>    √(1 + a)  =  3                   (subtract 3 from both sides)

=>  1 + a  =  9                          (square both sides)

=>     a  =  8

log_1/39  =  x     --->   (1/3)^x  =  9     --->     (3^-1)^x  =  3²     --->     3^-x  =  3²

     --->     -x  =  2     --->     x  =  -2

|x - 4| - 10  =  2

Add 10 to both sides:  |x - 4|  =  12

So, either                       x - 4  =  -12         or         x - 4 = 12

                                            x  =  -8           or              x  =  16

Those are the two possible values of x; the product of these two numbers will be your answer. 

csc²(x) · sec(x) / sec²(x)  +  csc²(x)

=  csc²(x) · [ sec(x) / sec²(x) ]  +  csc²(x)                           

=  csc²(x) · [ 1 /sec(x) ]  +  csc²(x)                        <---   simplify:  sec(x) / sec²(x)

=  csc²(x) · ( cos(x) )  +  csc²(x)                            <---    cos(x)  =  1 / sec(x)

=  csc²(x) · [ cos(x) + 1 ]                                        <---    factor

=  [ 1 / sin²(x) ] · [ cos(x) + 1 ]                              <---    csc²(x)  =  1 / sin²(x)

=  [ cos(x) + 1 ] / sin²(x)

=  [ cos(x) + 1 ] / [ 1 - cos²(x) ]                             <---    sin²(x)  =  1 - cos²(x)

=  [ cos(x) + 1 ] / [ ( 1 - cos(x) )·( 1 - cos(x) ) ]      <---    factor

=  1 / [ 1 - cos(x) ]                 <--- provided that sec²(x) ≠ 0, cos(x) ≠ 0

The second part was just answered.

First part:  √(10p)·√(5p²)·√(6p⁴)  =  √(10p·5p²·6p⁴)  =  √(300p⁷)  =  √(100p⁶)√(3p)  =  10p³√(3p)

(x - 5x + 12)² + 1  =  -|x|   ---> is equivalent to --->    (x - 5x + 12)² + 1 + |x|  =  0  

 (x - 5x + 12)² can never be less than 0; similarly |x| can never be less than 0; whatever the sum of these two are, when you add another +1, you must get a number which is greater than 0.

Therefore, there can be no real solutions.