If  is one odd number, then the next odd number is . If their product is 143, then the following equation is true.

Distribute into the parenthesis.

Subtract 143 from both sides.

This can be solved by factoring, or by the quadratic equation. We will use the latter.

We are told that both integers are positive, so .

The other integer is .

Know that the general rule for an arithmetic sequence is

,

where  represents the first number in the sequence,  is the common difference between consecutive numbers, and  is the -th number in the sequence.  

In our problem, .

Each time we move up from one number to the next, the sequence increases by 3.  Therefore, . 

The rule for this sequence is therefore .

The first term for the sequence is where . Thus,

So the first term is 4.  Repeat the same thing for the second , third , fourth , and fifth  terms.

We see that the first five terms in the sequence are

When finding consecutive numbers assign the first number a variable.

If the first number is assigned the letter n, then the second number that is consecutive must be  and the third number must be .

Write it out as an equation and it should look like:

Simplify the equation then,

If  then 

And 

So the answer is 

Let the first number be .

If  is an odd number, the next odd numbers will be:

, , , and 

The fourth highest number would then be:

Set up an equation where the sum of all these numbers add up to .

Simplify this equation.

Subtract 20 from both sides.

Simplify both sides.

Divide by five on both sides.

Corresponding to the five numbers, the set of five consecutive numbers that add up to  are: 

The fourth largest number would be .

The TRUE statement:

"The lines intersect and are perpendicular." This is true because the slopes of the two lines are opposite-reciprocals of each other.

The FALSE statements:

"The lines intersect at the point ." The lines actually intersect at the point . Neither line touches the point , as their y-intercepts are given in their respective equations as and .

"The slopes of the two lines are identical." This is not true because the slope of Line 1 is  whereas the slope of Line 2 is .

"The lines do not intersect." The lines would need to be parallel (i.e., have the same slope) for this to be the case, but the lines do not have the same slope.

"The lines intersect only once because they are parallel." Parallel lines never intersect, so this statement cannot be made of any set of two lines.

For lines to be perpendicular, the slopes need to be negative reciprocals of each other.  For the line , the slope is 1.  For a line to be perpendicular to it, it will need to have a slope of .  Since the line  has a slope of -1, the lines are perpendicular to each other.

Perpendicular lines have slopes that are negative reciprocals of each other. If you convert the given line to the  form, you get 

which indicates a slope of . Thus, the slope of the perpendicular line must be , which is the negative reciprocal of . The only line with a slope of  is 

.

The line  is a vertical line.  Therefore, a perpendicular line is going to be horizontal and have a slope of zero.  

The equation  is such a line.  

The lines  and  are both vertical lines, while the lines  and  have slopes of  and , respectively.

Perpendicular lines have slopes that are negative reciprocals of one another. Since all of these lines are in the format, it is easy to determine their slopes, or .

The slope of the original line is , so any line that is perpendicular to it must have a slope of .

The only line with a slope of is .