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Janaisa Harris, BA (Mathematics) |
Mathematics
Review Board Member
Ms. Janaisa Harris, an experienced educator, has devoted 4 years to teaching high school math and 6 years to tutoring. She holds a bachelor's degree in Mathematics (Secondary Education, and Teaching) from the University of North Carolina at Greensboro and is currently employed at Wilson County School (NC) as a mathematics teacher. She is now broadening her educational impact by engaging in curriculum mapping for her county. This endeavor enriches her understanding of educational strategies and their implementation. With a strong commitment to quality education, she actively participates in the review process of educational quizzes, ensuring accuracy and relevance to the curriculum.
, BA (Mathematics)
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Quizzes Created: 1 | Total Attempts: 13,917
Questions: 10 | Viewed: 13,946

1.

### What is the solution to x + 5 = 12?

Explanation:
The solution to the equation x + 5 = 12 is:
Subtract 5 from both sides to isolate x:
x + 5 - 5 = 12 - 5
x = 7
So, x = 7.
2.

### How do you simplify 3x + 2x?

Explanation:
Combine like terms: Both terms have the same variable x, so you can add their coefficients (3 and 2).
Add the coefficients: 3 + 2 = 5.
Rewrite the expression: 5x.
So, 3x + 2x simplifies to 5x.
3.

### What is the product of (x - 3)(x + 3)?

Explanation:
To find the product of (x - 3)(x + 3), you can use a special algebraic formula called the difference of squares. The difference of squares formula states that:
(a - b)(a + b) = a^2 - b^2
In this expression, "a" is x, and "b" is 3. So when you apply the formula:
(x - 3)(x + 3) becomes x^2 - 3^2.
Next, calculate the square of 3:
3^2 = 9.
So, the expression simplifies to:
x^2 - 9.
Therefore, the product of (x - 3)(x + 3) is x^2 - 9.
4.

### What is the result of (2x)^2?

Explanation:
To calculate the result of (2x)^2, you need to square both the coefficient (2) and the variable (x):
First, square the coefficient 2:
2^2 = 4.
Then, square the variable x:
x^2 = x^2.
Combine the results:
4x^2.
So, when you square (2x), the result is 4x^2.
5.

### Which expression is equivalent to 4(x + 2)?

Explanation:
The expression that is equivalent to 4(x + 2) is 4x + 8.
This is found by distributing the 4 to both terms inside the parentheses:
4(x + 2) = 4 * x + 4 * 2 = 4x + 8.
6.

### What is the value of x if 3x - 2 = 7?

Explanation:
To find the value of x in the equation 3x - 2 = 7, follow these steps:
Add 2 to both sides of the equation to isolate the term with x:
3x - 2 + 2 = 7 + 2
This simplifies to:
3x = 9
Divide both sides by 3 to solve for x:
3x / 3 = 9 / 3
This simplifies to:
x = 3
So, the value of x is 3.
7.

### Solve for x: 2x/3 = 8

Explanation:
To solve for x in the equation 2x/3 = 8:
Multiply both sides by 3:
2x = 8 * 3
2x = 24
Divide both sides by 2:
x = 24 / 2
x = 12
So, x = 12.
8.

### What is the quadratic formula?

Explanation:
The quadratic formula (-b±sqrt(b^2-4ac))/2a is derived from rearranging the standard form of a quadratic equation ax^2 + bx + c = 0. It provides a systematic method for finding the roots of any quadratic equation, crucial for solving quadratic equations where factors are not easily apparent.
9.

### If y varies directly with x, and y = 6 when x = 2, what is y when x = 3?

Explanation:
If y varies directly with x, the relationship can be written as:
y = kx
where k is the constant of proportionality.
Given that y = 6 when x = 2, you can find k:
6 = k(2)
k = 6/2 = 3
Now that you know k = 3, you can find y when x = 3:
y = 3(3) = 9
So, y = 9 when x = 3.
10.

### What is the simplified form of (x^2 - 4)/(x - 2)?

Explanation:
To simplify the expression (x^2 - 4)/(x - 2):
Factor the numerator. The expression x^2 - 4 is a difference of squares, which can be factored as (x - 2)(x + 2).
The expression now looks like this: (x - 2)(x + 2)/(x - 2).
Since (x - 2) appears in both the numerator and the denominator, you can cancel it out, leaving you with just x + 2.
So, the simplified form of (x^2 - 4)/(x - 2) is x + 2, with the condition that x ≠ 2, because division by zero is undefined.

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