Card 0 of 490
Consider the equation
Which of the following is true?
Multiply both sides by LCD :
or
There are two solutions of unlike sign.
Compare your answer with the correct one above
A sequence of numbers is: 2, 5, 8, 11. Assuming it follows the same pattern, what would be the value of the 20th number?
This goes up at a constant number between values, making it an arthmetic sequence. The first number is 2, with a difference of 3. Plugging this into the arithmetic equation you get An = 2 + 3 (n – 1). Plugging in 20 for n, you get a value of 59.
Compare your answer with the correct one above
The first four numbers of a sequence are 5, 10, 20, 40. Assuming the pattern continues, what is the 6th term of the sequence?
Looking at the sequence you can see that it doubles each term, making it a geometric sequence. Since it doubles r = 2 and the first term is 5. Plugging this into the geometric equation you get An = 5(2)n–1. Setting n = 6, you get 160 as the 6th term.
Compare your answer with the correct one above
Given f(x) = x2 – 9. What are the zeroes of the function?
The zeroes of the equation are where f(x) = 0 (aka x-intercepts). Setting the equation equal to zero you get x2 = 9. Since a square makes a negative number positive, x can be equal to 3 or –3.
Compare your answer with the correct one above
Give the lines y = 0.5x+3 and y=3x-2. What is the y value of the point of intersection?
In order to solve for the x value you set both equations equal to each other (0.5x+3=3x-2). This gives you the x value for the point of intersection at x=2. Plugging x=2 into either equation gives you y=4.
Compare your answer with the correct one above
Find the solution to the following equation if x = 3:
y = (4x2 - 2)/(9 - x2)
Substituting 3 in for x, you will get 0 in the denominator of the fraction. It is not possible to have 0 be the denominator for a fraction so there is no possible solution to this equation.
Compare your answer with the correct one above
I. x = 0
II. x = –1
III. x = 1
Compare your answer with the correct one above
Compare your answer with the correct one above
A fraction is considered undefined when the denominator equals 0. Set the denominator equal to zero and solve for the variable.
Compare your answer with the correct one above
Consider the equation
Which of the following is true?
Multiply the equation on both sides by LCM :
or
Substitution confirms that these are the solutions.
There are two solutions of unlike sign.
Compare your answer with the correct one above
All of the following equations have no solution except for which one?
Since all of the equations have the same symbols save for one number, the problem is essentially as follows:
For what value of does the equation
have a solution set other than the empty set?
We can simplify as follows:
If and
are not equivalent expressions, the solution set is the empty set. If
and
are equivalent expressions, the solution set is the set of all real numbers; this happens if and only if:
Therefore, the only equation among the given choices whose solution set is not the empty set is the equation
which is the correct choice.
Compare your answer with the correct one above
Which of the following equations has no solution?
The problem is basically asking for what value of the equation
has no solution.
We can simplify as folllows:
Since the absolute value of a number must be nonnegative, regardless of the value of , this equation can never have a solution. Therefore, the correct response is that none of the given equations has a solution.
Compare your answer with the correct one above
Which of the following equations has no real solutions?
We can examine each individually.
This equation has a solution.
This equation has a solution.
This equation has a solution.
This equation has no solution, since a fourth root of a number must be nonnegative.
The correct choice is .
Compare your answer with the correct one above
Solve .
By definition, the absolute value of an expression can never be less than 0. Therefore, there are no solutions to the above expression.
Compare your answer with the correct one above
Compare your answer with the correct one above
In the equation below, ,
, and
are non-zero numbers. What is the value of
in terms of
and
?
Compare your answer with the correct one above
Compare your answer with the correct one above
If 6_x_ = 42 and xk = 2, what is the value of k?
Solve the first equation for x by dividing both sides of the equation by 6; the result is 7. Solve the second equation for k by dividing both sides of the equation by x, which we now know is 7. The result is 2/7.
Compare your answer with the correct one above
If 4_x_ + 5 = 13_x_ + 4 – x – 9, then x = ?
Start by combining like terms.
4_x_ + 5 = 13_x_ + 4 – x – 9
4_x_ + 5 = 12_x_ – 5
–8_x_ = –10
x = 5/4
Compare your answer with the correct one above
If 3 – 3_x_ < 20, which of the following could not be a value of x?
First we solve for x.
Subtracting 3 from both sides gives us –3_x_ < 17.
Dividing by –3 gives us x > –17/3.
–6 is less than –17/3.
Compare your answer with the correct one above