1. What is the excluded value for the rational expression x^2 - 4/3x - 6?
A: ?
2. The trinomial x ^2 - 6x + c is a perfect-square trinomial. What is the value of c?
A: 9
3. Find the positive solution of the equation x^2 + 5x - 4 = 0. Round your answer to the nearest tenth.
A: ?
4. What is the value of 4^0 - (2^-3)?
A: -7?
5. Identify the excluded value of y = x - 4/x - 2.
A: x = 2
6. Which of the following is equivalent to (2x^5y^2/ 8x)^-2?
a. 16/x^8y^4
b. x^8/16y^4
c. 4/x^4y^2
d. x^5/16
A: ?
#1 you cannot divide by zero. So, when the denominator is zero, that value of x must be excluded. So, what is x when 3x-6=0?
#2 ok
#3 use the quadratic formula for this one.
#4 Nope.
4^0 = 1
2^-3 = 1/2^3 = 1/8
So, 1 - 1/8 = 7/8
You calculated 4^0 - 2^3
#5 correct. So why did you have trouble with #1?
#6 since a^-n = 1/a^n, and 1/(a/b) = b/a,
(2x^5y^2/ 8x)^-2
= (x^4y^2/4)^-2
= 1/(x^4y^2/4)^2
= (4/(x^4y^2))^2
= 16/(x^8y^4)
1. x = 2?
3. 0.70 = 1 (rounded to the nearest tenth)?
#1 ok
#3 .701 = 0.7 to the nearest tenth. Your rounding doesn't have any tenths!
1. To find the excluded value for a rational expression, we need to identify any values of the variable that would make the expression undefined. In this case, the expression is x^2 - 4/3x - 6. The expression would be undefined if the denominator becomes zero, since division by zero is undefined. Therefore, we need to find the values of x that make the denominator equal to zero. The denominator in this case is 3x. Setting it equal to zero, we have:
3x = 0
Solving for x, we find that x = 0. Therefore, the excluded value for the rational expression is x = 0.
2. A perfect-square trinomial can be expressed as the square of a binomial. In this case, the trinomial given is x^2 - 6x + c. To determine the value of c that makes it a perfect-square trinomial, we need to take the coefficient of the linear term (-6x in this case), divide it by 2, and square the result. The result will be the value of c that makes the trinomial a perfect square.
For this trinomial, (-6/2)^2 = 9. Therefore, the value of c that makes the trinomial x^2 - 6x + c a perfect square is 9.
3. To find the positive solution of the equation x^2 + 5x - 4 = 0, we can use the quadratic formula. The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac))/2a
In this case, a = 1, b = 5, and c = -4. Plugging these values into the quadratic formula, we have:
x = (-(5) ± √((5)^2 - 4(1)(-4)))/2(1)
Simplifying further, we have:
x = (-5 ± √(25 + 16))/2
x = (-5 ± √41)/2
To find the positive solution, we take the positive square root:
x = (-5 + √41)/2
Rounding this value to the nearest tenth, we have the positive solution of the equation as approximately 0.8.
4. To evaluate the expression 4^0 - (2^-3), we can start by simplifying each term separately.
4^0 is equal to 1, because any number raised to the power of 0 is defined as 1.
2^-3 is equal to 1/2^3, which simplifies to 1/8.
Therefore, the expression becomes 1 - 1/8.
To subtract fractions, we need to have a common denominator. In this case, the common denominator is 8, so we have:
1 - 1/8 = 8/8 - 1/8 = 7/8
Therefore, the value of 4^0 - (2^-3) is 7/8.
5. To identify the excluded value of the rational expression y = (x - 4)/(x - 2), we need to find any values of x that make the denominator equal to zero. In this case, the denominator is x - 2. Setting it equal to zero, we have:
x - 2 = 0
Solving for x, we find that x = 2. Therefore, the excluded value for the expression is x = 2.
6. To determine which expression is equivalent to (2x^5y^2/ 8x)^-2, we can simplify the expression by cancelling out common factors in the numerator and denominator.
The expression (2x^5y^2/ 8x)^-2 can be simplified as follows:
= (2x^5y^2)^-2 / (8x)^-2
= (1/(2x^5y^2)^2) / (1/(8x)^2)
= (1/(4x^10y^4)) / (1/(64x^2))
= (1/(4x^10y^4)) * (64x^2/1)
= 64x^2 / (4x^10y^4)
= 16x^2 / (x^10y^4)
= 16/x^8y^4
Therefore, the equivalent expression is 16/x^8y^4, so the correct option is a. 16/x^8y^4.