Ultimate High School Math Quiz

Explanation
The slope of a line can be found using the formula (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are any two points on the line. In this case, using the points (-2, 3) and (10, -9), we can calculate the slope as (-9 - 3) / (10 - (-2)) = -12 / 12 = -1. Therefore, the slope of the line that passes through (-2, 3) and (10, -9) is -1.

Explanation
The greatest common factor (GCF) of two numbers is the largest number that divides both of them without leaving a remainder. In this case, the GCF of 55 and 65 is 5 because 5 is the largest number that can divide both 55 and 65 without leaving a remainder.

Explanation
The y-intercept of a linear equation represents the point where the line intersects the y-axis. To find the y-intercept, we set x = 0 and solve for y. In this equation, when x = 0, we have 3(0) + y = 6, which simplifies to y = 6. Therefore, the y-intercept is (0, 6).

Explanation
To solve the inequality 6 - 4x > 38, we need to isolate the variable x. Subtracting 6 from both sides gives -4x > 32. Dividing both sides by -4, we get x < -8. This means that any value of x that is less than -8 will make the inequality true.

Explanation
To find the exponential form of (3^6)(3^5), we can use the rule of exponents that states when multiplying numbers with the same base, you add the exponents. In this case, the base is 3. So, when we multiply (3^6)(3^5), we add the exponents 6 and 5, resulting in 3^(6+5) which simplifies to 3^11. Therefore, the correct answer is 3^11.

Explanation
To find the product of (2x^3)(7x^2), we multiply the coefficients (2 and 7) together to get 14. Then, we multiply the variables (x^3 and x^2) together to get x^(3+2) = x^5. Therefore, the correct answer is 14x^5.

Explanation
The x-intercept of a linear equation represents the point where the line crosses the x-axis. To find the x-intercept, we set y=0 and solve for x. In the equation x + y = 16, when y=0, we get x + 0 = 16, which simplifies to x = 16. Therefore, the x-intercept is at the point (16, 0).

Explanation
The y-intercept of a function is the value of the function when x is equal to 0. In this case, when x is equal to 0, f(x) = 0^2 - 16 = -16. Therefore, the y-intercept of f(x) = x^2 - 16 is -16.

Explanation
The inequality -3x + 6 > 16 can be solved by subtracting 6 from both sides to get -3x > 10. Then, dividing both sides by -3 (and reversing the inequality sign because of dividing by a negative number) gives x < -10/3.

Explanation
The reciprocal of a fraction is obtained by flipping the numerator and denominator. In this case, the reciprocal of 4/3 is 3/4. However, none of the given options match this answer, so it seems that the question may be incomplete or not readable.

Explanation
In the equation 3^2 = 9, the number 3 is referred to as the "base". The base is the number that is being raised to a power or exponent. In this case, 3 is being raised to the power of 2, resulting in 9.

Explanation
The given expression x^2 - 4x can be factored as x(x - 4). This can be done by finding the common factor of x in both terms and factoring it out. The remaining factor is (x - 4), which represents the other term in the factored form.

Explanation
A graph that does not make a straight line is called non-linear. This means that the data points on the graph do not follow a linear pattern or relationship. Instead, the graph may curve, bend, or take on other shapes. Non-linear graphs are commonly seen in situations where the relationship between variables is more complex and cannot be represented by a simple straight line.

Explanation
The base in the octal system of numeration is 8. In the octal system, numbers are represented using only 8 digits, from 0 to 7. This means that each place value in an octal number represents a power of 8. For example, the octal number 10 represents 1 * 8^1 + 0 * 8^0, which is equal to 8. Therefore, the correct answer is 8.

Explanation
Like terms are terms that have the same variables raised to the same power. They can be added or subtracted from each other because they represent the same quantity. Unlike terms have different variables or different powers, so they cannot be combined algebraically. Constants are numbers without variables and cannot be added to or subtracted from variables. Any variable terms refer to any terms that have variables, regardless of whether they are like terms or not. Therefore, the correct answer is "Like Terms" as they are the only terms that can be added together.