Math: Are You Able To Solve The Equation Question? Quiz

The down payment is calculated by multiplying the list price of the home by the percentage being put down. In this case, 15% of $140,000 is $21,000. Therefore, the down payment is $21,000.

The original function y = x^2 represents a parabola that opens upwards. When the function is changed to y = x^2 - 2, the entire graph is shifted downwards by 2 units. This means that every point on the graph is moved 2 units lower on the y-axis. Therefore, the correct answer is B. It was shifted down 2 spaces.

The original function is y = x^2 - 2. Shifting the graph up 6 units means adding 6 to the function. Therefore, the new function will be y = x^2 - 2 + 6, which simplifies to y = x^2 + 4.

Having a credit card allows individuals to spend more money at once, which can lead to overspending and accumulating debt. This can be seen as a disadvantage rather than an advantage of having a credit card.

To find the percentage of yearly salary spent on rent, divide the monthly rent by the annual salary and multiply by 100. In this case, $700 divided by $40,000 equals 0.0175. Multiplying by 100 gives 1.75%. Therefore, the correct answer is 21%.

Based on the given options, the correct answer is "This is a quadratic function." A quadratic function is a polynomial function of degree 2, which means it can be written in the form f(x) = ax^2 + bx + c. Since the question does not provide any specific equation or context, we can assume that the given function can be represented by a quadratic equation.

The equation y = 3x + 1 best describes the relationship between x and y because it is the only equation that satisfies all four given points (-4,-11), (-1,-2), (2,7), and (5,16).

The correct answer is "It’s been vertically stretched (narrower) by a factor of 3." When the coefficient in front of the x^2 term is increased, the graph of the function is vertically stretched. In this case, the coefficient has been changed from 1 to 3, which means the graph has been stretched vertically by a factor of 3. This makes the graph narrower and taller compared to the original function.

The domain in a set of data refers to all possible x values. It represents the set of input values or independent variables in a function or relationship. In other words, it is the range of values that the variable can take on.

The correct answer is the graph that shows a line with a slope of 1/2 and a y-intercept of 4. This means that the line starts at the point (0, 4) and for every increase of 2 in the x-coordinate, the y-coordinate increases by 1. The line will have a positive slope and will be slanting upwards from left to right.

If the slope of the graph of y = 4x + 8 is changed to 5, it means that the line becomes steeper. The slope represents the rate of change of y with respect to x, so a higher slope means that for every increase in x, there is a larger increase in y. Therefore, the graph will become steeper and the slope increases.

The equation c = 0.75t represents the total cost of t tickets on a bus. Looking at the table in option B, we can see that as the value of t increases by 1, the value of c also increases by 0.75. This fits the equation c = 0.75t, making option B the correct answer.

Tommy earned $450 last week and 15% of that is taken out for taxes. To calculate the amount taken out for taxes, we can multiply $450 by 15% (or 0.15). This gives us $67.50. To find Tommy's paycheck, we subtract the amount taken out for taxes from his total earnings: $450 - $67.50 = $382.50. Therefore, Tommy's paycheck is $382.50.

When the y-intercept of the equation y = 4x + 8 is changed to -3, it means that the point where the line intersects the y-axis has shifted downwards from 8 to -3. This results in a decrease in the y-intercept value. The slope of the line remains the same at 4, as it is not stated that the slope has changed. Therefore, the correct answer is that the y-intercept decreases.

The correct answer is (3,5) because when we substitute x = 3 into both equations, we get y = 3 + 2 = 5 and y = 2(3) - 1 = 5. Therefore, the point (3,5) satisfies both equations and is the solution to the system of equations.

The range in a set of data refers to all possible y values. It represents the difference between the highest and lowest values in the data set and provides information about the spread or variability of the data. It is calculated by subtracting the lowest value from the highest value in the data set.

The zeros of a quadratic equation are the values of x that make y equal to zero. To find the zeros of the equation y = x^2 - 5x + 6, we need to set y equal to zero and solve for x. By factoring the equation, we can rewrite it as (x - 2)(x - 3) = 0. Setting each factor equal to zero, we find that x = 2 and x = 3. Therefore, the zeros of the equation are 2 and 3.

To solve the system of equations, we can use the substitution method. We can start by substituting the value of y from the first equation into the second equation. By substituting -3 - x for y, the second equation becomes 2x - (-3 - x) = -3. Simplifying this equation gives us 2x + 3 + x = -3. Combining like terms, we get 3x + 3 = -3. Subtracting 3 from both sides, we have 3x = -6. Dividing both sides by 3, we find that x = -2. Substituting this value back into the first equation, we can solve for y. Plugging in -2 for x, the first equation becomes y = -3 - (-2), which simplifies to y = -1. Therefore, the solution to the system of equations is (-2, -1).