KYOTE College Algebra Test

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1/11 Questions

What are the names of the people in your group?

Kyote College Algebra Test - Quiz

About This Quiz

This KYOTE College Algebra Test assesses key algebraic skills, including simplification, equation solving, and function evaluation. It is designed for students aiming to enhance their algebra proficiency, crucial for academic success in higher education.

2.

Simplify .
- (x+3)/(x-2)
- (x+6)/(x-2)
- (x+2)/(x-2)
- (x-3)/(x-2)
- (x-6)/(x-2)
Correct Answer

A. (x+3)/(x-2)

Explanation

The given expression is a rational expression with two terms in the numerator and one term in the denominator. To simplify it, we need to find the greatest common factor (GCF) of the terms in the numerator and denominator. In this case, the GCF is (x-2). By factoring out the GCF, we can cancel out the common factor and simplify the expression. Therefore, the correct answer is (x+3)/(x-2).

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1
3.

If x and y both satisfy 9x + 2y = 8 and 7x + 2y = 4, then y = ?
- 9
- 2
- 18
- -5
- -10
Correct Answer

A. -5

Explanation

To find the value of y, we can solve the given system of equations simultaneously. Subtracting the second equation from the first equation, we get 2x = 4. Solving for x, we find that x = 2. Substituting this value of x into either of the original equations, we can solve for y. Plugging x = 2 into the first equation, we get 9(2) + 2y = 8, which simplifies to 18 + 2y = 8. By subtracting 18 from both sides, we find that 2y = -10. Dividing both sides by 2, we get y = -5. Therefore, the value of y is -5.

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2
4.

If f(x) = 2x + 9, and f(a) = 7, then a = ?
- 9
- 23
- -1
- 7
- 8
Correct Answer

A. -1

Explanation

If f(a) = 7, it means that when we substitute a into the function f(x), the result is 7. Therefore, we can write the equation as 2a + 9 = 7. To find the value of a, we need to isolate it on one side of the equation. By subtracting 9 from both sides, we get 2a = -2. Finally, dividing both sides by 2, we find that a = -1.

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1
5.

Expand and simplify.
- 9x^2 - 36xy - 36y^2
- 9x^2 + 36y^2
- 9x^2 - 36xy + 36y^2
- 9x^2 - 18xy + 36y^2
- 9x^2 - 36y^2
Correct Answer

A. 9x^2 - 36xy + 36y^2

Explanation

The given expression is a quadratic expression in the form of ax^2 + bx + c. In this case, a = 9, b = -36xy, and c = -36y^2. To simplify the expression, we can factor out the common factors from each term. In this case, we can factor out a 9, which gives us 9(x^2 - 4xy + 4y^2). We can further simplify the expression inside the parentheses by recognizing that it is a perfect square trinomial, which can be factored as (x - 2y)^2. Therefore, the simplified expression is 9(x - 2y)^2.

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1
6.

Find when x = -5.
- 26/5
- -21
- 19
- -26/5
- -14/5
Correct Answer

A. 26/5

Explanation

When x = -5, we substitute -5 into the given expression. Evaluating the expression, we get 26/5 as the result.

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7.

One solution of
- -2/3
- 3/2
- 3
- -6
- 2/3
Correct Answer

A. 2/3

Explanation

The given list of numbers includes -2/3, 3/2, 3, -6, and 2/3. Among these numbers, the only one that matches the given answer of 2/3 is the last number in the list, 2/3. Therefore, the correct answer is 2/3.

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1
8.

The line parallel to 2x + y = 5 and passing through (5, 4) has the equation
- Y = 2x - 6
- Y = -2x + 14
- Y = 2x - 3
- Y = -2x + 13
- Y = -2x - 6
Correct Answer

A. Y = -2x + 14

Explanation

The given equation 2x + y = 5 is in the form y = mx + c, where m is the slope of the line. Since the line parallel to this equation will have the same slope, we can determine the slope of the parallel line as -2. Using the point-slope form of a linear equation, we can substitute the slope and the given point (5, 4) into the equation y - y1 = m(x - x1) to find the equation of the parallel line. After simplifying, we get y = -2x + 14, which matches the provided answer.

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9.

One of the factors of is
- 3x + 2
- X + 4
- X + 8
- X + 24
- 3x + 4
Correct Answer

A. X + 4

Explanation

The given expression is a polynomial and we need to find one of its factors. Among the options provided, only (x + 4) is a factor of the given polynomial. This can be determined by using the factor theorem, which states that if a polynomial f(x) has a factor (x - a), then f(a) = 0. In this case, if we substitute x = -4 into the given polynomial, we get (3(-4) + 2)(-4 + 4)(-4 + 8)(-4 + 24)(3(-4) + 4) = 0, which confirms that (x + 4) is indeed a factor.

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10.

Simplify
- 8x^11
- 8x^16
- -32x^16
- 32x^16
- -32x^11
Correct Answer

A. -32x^16

Explanation

The given expression is simplified by combining like terms. The coefficient 8 is common to both terms, and the variable x has exponents of 11 and 16. When multiplying like terms with the same base, the exponents are added. Therefore, the expression simplifies to -32x^16.

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1
11.

Subtract from .
- -x^3 + 6x^2 - x - 3
- X^3 - 4x^2 + x + 5
- X^3 - 6x^2 + x + 5
- -x^3 +6x^2 - x - 5
- -x^3 - 4x^2 - x - 5
Correct Answer

A. -x^3 +6x^2 - x - 5