Choice C is correct. The solution to the system of two equations corresponds to the point where the graphs of the equations intersect. The graphs of the linear equation and the nonlinear equation shown intersect at the point (4, 5). Thus, the solution to the system is (4, 5).

Choice A is incorrect and may result from conceptual or calculation errors.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.

As you notice in question, it is written (x, y) so we need to put the value of x first then y. Whenever you see a crossed line in a graph, focus on the intersected point.

Choice B is correct. It’s given that the film club has 90 members on the first day
of a semester, and 10 new members join the film club each day after the first day
of the semester. This means that after 4 days, 4 x 10, or 40, new members will
have joined the club. Adding 40 members to the original 90 club members yields
130 members. Thus, the film club will have 130 total members 4 days after the
first day of the semester.

Choice A is incorrect. This is the number of members that will have joined the film club 4 days after the first day of the semester if 100 new members, not 10, join the film club each day.

Choice C is incorrect. This is the number of members the film club will have 4 days after the first day of the semester if 1 new member, not 10, joins the film club each day.

Choice D is incorrect. This is the number of members the film club has on the first day of the semester.

It is a simple multiply and addition equation, work on your speed of calculation by practicing more and more.

Choice D is correct. The y-intercept of a graph is the point where the graph intersects the y-axis. The graph of a function f shown intersects the y-axis at the point (0, 8). Therefore, the y-intercept of the graph of f is (0, 8).

Choice A is incorrect. This is the point where the x-axis, not the graph of f, intersects the y-axis.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Basically, it is just asking for a positive y-axis and the part that is intercepted.

Choice B is correct. The second equation in the given system is r = 3. Substituting 3 for r in the first equation in the given system yields s + 7(3)=27, or s + 21 = 27. Subtracting 21 from both sides of this equation yields s = 6. Therefore, the solution (r, s) to the given system of equations is (3, 6).

Choice A is incorrect. This is the solution (s, r), not (r, s), to the given system of equations.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.

When digits have plus or minus signs then interchanging digits from one side of equal to another side of equal will always change the sign to opposite. Second, we have already given the value of r = 3. So, option A and option D are out of the equation.

Choice B is correct. The given values show that as x increases, f (x) also increases, which means that f is an increasing function. Furthermore, f (x) increases at a constant rate of 1 for each increase of x by 1. A function with a constant rate of change is linear. Thus, the function f can be described as an
increasing linear function.

Choice A is incorrect. For a decreasing linear function, as x increases, f (x) decreases rather than increases.

Choice C is incorrect. For a decreasing exponential function, for each increase of x by 1, f (x) decreases by a fixed percentage rather than increases at a constant rate.

Choice D is incorrect. For an increasing exponential function, for each increase of x by 1, f (x) increases by a fixed percentage rather than at a constant rate.

It is increasing, because that is how integers work. The linear is increasing here: -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5…

Choice B: The correct answer is 9. It’s given that the customer spent $27 to purchase oranges at $3 per pound. Therefore, the number of pounds of oranges the customer purchased is $27 (1 pound / $3) , or 9 pounds.

Choice A is incorrect because we do not add values here.

Choice C is incorrect because we do not subtract values here.

Choice D is incorrect because we do not multiply values here.

The key points, you need to follow are: we have an overall cost of $27, we have a per pound cost which is $3 and it is asking how many pounds. This informs us to divide.

Choice B: The correct answer is 10. It’s given that the cost for the entire purchase was $27 after a coupon was used for $63 off the entire purchase. Adding the amount of the coupon to the purchase price yields 27+63=90. Thus, the cost for the entire purchase before using the coupon was $90. It’s given that Nasir bought 9 storage bins. The original price for 1 storage bin can be found by dividing the total cost by 9. Therefore, the original price, in dollars, for 1 storage bin is 90/9, or 10.

Choice A is incorrect because we do not add values here.

Choice C is incorrect because we do not subtract values here.

Choice D is incorrect because we do not add and subtract values here.

Asking for one storage price and buying 9 bins, he paid $27 but he used a coupon with a $63 discount for calculation, we need the original price, as it is stated at the end of the question. So, $27 + $63 and then divide them the same way we did question 6th.

Choice A is correct. An equation that defines a linear function f can be written in the form f(x) = mx + b, where m and b are constants. It’s given in the table that when x = 0, f(x) = 29. Substituting 0 for x and 29 for f(x) in equation f(x) = mx + b yields 29 = m(0) + b, or 29 = b. Substituting 29 for b in the
equation f(x) = mx + b yields f(x) = mx + 29. It’s also given in the table that when x = 1, f(x) = 32. Substituting 1 for x and 32 for f(x) in the equation f(x) = mx + 29 yields 32 = m(1) + 29, or 32 = m + 29. Subtracting 29 from both sides of this equation yields 3 = m. Substituting 3 for m in the equation
f(x) = mx + 29 yields f(x) = 3x + 29.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.

It is simply asking you the difference between each f(x). It is 32 – 29 = 3. The most important thing that helps you find the right option is the value of difference. If it is not optional then in place of 29, you can also use 32 or 35.

Choice B is correct. In similar triangles, corresponding angles are congruent. It’s given that right triangles PQR and STU are similar, where angle P corresponds to angle S. It follows that angle P is congruent to angle S. In the triangles shown, angle R and angle U are both marked as right angles, so angle R and angle U are corresponding angles. It follows that angle Q and angle T are corresponding
angles, and thus, angle Q is congruent to angle T . It’s given that the measure of angle Q is 18 degrees, so the measure of angle T is also 18 degrees. Angle U is a right angle, so the measure of angle U is 90 degrees. The sum of the measures of the interior angles of a triangle is 180 degrees. Thus, the sum of the measures of the interior angles of triangle STU is 180 degrees. Let’s represent the measure, in degrees, of the angle S. It follows that s + 18 + 90 = 180, or s + 108 = 180. Subtracting 108 from both
sides of this equation yields s = 72. Therefore, if the measure of angle Q is 18 degrees, then the measure of angle S is 72 degrees.

Choice A is incorrect. This is the measure of angle T.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect. This is the sum of the measures of angle S and angle U.

Always remember, the straight verticle line is 90 degrees and the straight horizontal line is 180 degrees. So, STU = 180 degrees. As the question suggested both both triangles are the same. Q = T. Now, put the value s + 18 + 90 = 180.

Choice D is correct. The data points suggest that as the variable x increases, the variable y decreases, which implies that an appropriate linear model for the data has a negative slope. The data points also show that when x is close to 0, y is greater than 9. Therefore, the y-intercept of the graph of an appropriate linear model has a y-coordinate greater than 9. The graph of an equation of the form
y = a + bx, where a and b are constants, has a y-intercept with a y-coordinate of a and has a slope of b. Of the given choices, only choice D represents a graph that has a negative slope, -0.9, and a y-intercept with a y-coordinate greater than 9, 9.4.

Choice A is incorrect. The graph of this equation has a positive slope, not a negative slope, and a y-intercept with a y-coordinate less than 1, not greater than 9.

Choice B is incorrect. The graph of this equation has a y-intercept with a y-coordinate less than 1, not greater than 9.

Choice C is incorrect. The graph of this equation has a positive slope, not a negative slope.

You don’t need to find the exact measure, they easily describe it for you. Notice all the options, you will find the same digits but the position and signs are different. They asked for the relation between two variables, so we need to find something that has somewhat connection. If you notice, you will find “9y, 1x” has an intercept and similarly “1y, 9x” has one too.

Choice D:

Choice A is incorrect and may result from conceptual or calculation errors.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

The question gives us a hint again. The value of h(x) is h(2), which means we know x is 2. Now, just solve the equation.

Choice A:

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.

In simple words, if you see a question like this, just remember one thing the sloppy angle is half of the multiplication of horizontal and vertical vertex (line). Look 5 x 3 = 15, now half of it is 7.5 or 15/2.

Choice B is correct. It’s given that the graph models the number of active projects a company was working on x months after the end of November 2012. Therefore, the value of x that corresponds to the end of November 2012 is 0. The point at which x = 0 is the y-intercept of the graph. It follows that the y-intercept of the graph shown is the point (0, 5). Therefore, according to the model, the predicted
number of active projects the company was working on at the end of November 2012 is 5.

Choice A is incorrect. This is the value of x that corresponds to the end of November 2012, not the predicted number of active projects the company was working on at the end of November 2012.

Choice C is incorrect. This is the predicted number of active projects the company was working on 2 months after the end of November 2012.

Choice D is incorrect. This is the predicted number of active projects the company was working on 4 months after the end of November 2012.

Don’t beat yourself up! This sign means (≤) less or equal than which means 0 ≤ x ≤ 6. We need to find the x value, according to the sign, we need a digit that is less than or equal to 6 but 0 is also less than x. So, the options make it easy for you, 5 is that value. Take a look at the options.

Choice D is correct. It’s given that the graph of the rational function f is shown, where y = f(x) and x ≥ 0. The graph shown passes through the point (3, 3). It follows that when the value of x is 3, the value of f(x) is 3. When the value of f(x) is 3, the value of f(x) + 5 is 3 + 5, or 8. Therefore, the graph of y = f(x) + 5 passes through the point (3, 8). Of the given choices, choice D is the only graph that passes through the point (3,8) and is, therefore, the graph of y = f(x) + 5.

Choice A is incorrect. This is the graph of y = f(x) – 5, rather than y = f(x) + 5.

Choice B is incorrect. This is the graph of y = f(x)/5, rather than y = f(x) + 5.

Choice C is incorrect and may result from conceptual or calculation errors.

In simple words, it says (x ≥ 0), x is bigger or equal to 0 then the value of y = f(x) + 5. If we add 5 to the f(x), it should become y. So according to the graph from the value of x, you will see a gap of 1. If we pick 3 and add 5 to it, it will become 8. Check in option D (between 2 and 4 of the x-axis and 8 of the y-axis), and you will notice an intercept. [But if we use something else except 3, it won’t intercept.]

Choice B is correct. It’s given that at a particular track meet, the ratio of coaches to athletes is 1 to 26. If one number in a ratio is multiplied by a value, the other number must be multiplied by the same value in order to maintain the same ratio. If there are x coaches at the track meet, multiplying both numbers in the ratio by x yields 1(x) to 26(x), or x to 26x. Therefore, the expression 26x represents the
number of athletes at the track meet.

Choice A is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.

To find out any value from a ratio, we must multiply both sides with the same value, the value is unknown and mentioned as x. According to the question, coached to athletes (1 to 26), so 1 coach for 26 athletes. If there are x coaches then how many athletes? 1 x :26 x = x:26x, the question only ask for athletes = 26x.

Choice D is correct. A point (x, y) is a solution to a system of inequalities in the xy-plane if substituting the x-coordinate and the y-coordinate of the point for x and y, respectively, in each inequality makes both of the inequalities true. Substituting the x-coordinate and the y-coordinate of choice D, 14 and 0, for x and y, respectively, in the first inequality in the given system, y ≤ x + 7, yields 0 ≤ 14 + 7, or 0 ≤ 21, which is true. Substituting 14 for x and 0 for y in the second inequality in the given system, y ≥ -2x – 1, yields 0 ≥ -2(14) -1, or 0 ≥ -29, which is true. Therefore, the point (14, 0) is a solution to the given system of inequalities in the xy-plane.

Choice A is incorrect. Substituting -14 for x and 0 for y in the inequality y ≤ x + 7 yields 0 ≤ -14 + 7, or 0 ≤ -7, which is not true.

Choice B is incorrect. Substituting 0 for x and -14 for y in the inequality y ≥ -2x – 1, yields -14 ≥ -2(0) -1, or -14 ≥ -1, which is not true.

Choice C is incorrect. Substituting 0 for x and 14 for y in the inequality y ≤ x + 7 yields 14 ≤ 0 + 7, or 14 ≤ 7, which is not true.

Develop fast analytical skills by practicing more. Here the key is to be able to understand the chart quickly.

Choice C:

Choice A is incorrect and may result from conceptual or calculation errors.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.

A simple yet strange method in math that you can use by doing addition, subtraction, multiplication, and division of any number into the given equation. For example, here, we remove the root from both sides. The second thing is when we change sides the minus or plus sign changes to its opposite also. For example, 3x + 34 goes to the left side and becomes -3x – 34.

Choice D

Choice A is incorrect and may result from conceptual or calculation errors.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

(hx + k) (x + j), you can multiply every value to one another like ‘hx to x,’ ‘hx to j,’ ‘k to x,’ and ‘k to j.’ Did you notice ‘kj’ which is my name? Using it might get you more marks. There is another one but use this one, it is easy. The second way is to take a common value out of it ‘hx² + hxj + kx + kj.’ If you notice the x in the middle values is common, so put it out and put ‘hj + k’ inside the bracket. You will surely get more marks, not cause of using my name, but because it is the 18th question. The higher the question rank, the more marks you will get.

Choice C:

Choice A is incorrect. This is the value of a, not x.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.

If you thinking of using the formula of (a² – 2ab + b²), you cannot. The first reason is 2x², for it to be a² both values should have a square, but here 2 does not have a square. The second is you cannot get 21x if you calculate it as 2ab.

Choice C:

Choice A is incorrect. This is the length, in inches, of each of the congruent sides of the triangle, not the perimeter, in inches, of the triangle.

Choice B is incorrect. This is the sum of the lengths, in inches, of the congruent sides of the triangle, not the perimeter, in inches, of the triangle.

Choice D is incorrect and may result from conceptual or calculation errors.

If you understood the 12th question from above, that question was the base of this one. Remember, we multiply and then divide by 2. We are doing the same thing here by using the Pythagorean theorem. Have you also noticed dividing both sides with the same value?

Choice D:

Choice A is incorrect. If the equation of a parabola with a vertex at (9, -14) is written in the form of the given equation, where a, b, and c are constants and a + b + c = -23, then the value of a will be negative, which means the parabola will open downward, not upward, and will intersect the x-axis at zero points, not two points.

Choice B is incorrect. If the equation of a parabola with a vertex at (9, -14) is written in the form of the given equation, where a, b, and c are constants and a + b + c = -19, then the value of a will be negative, which means the parabola will open downward, not upward, and will intersect the x-axis at zero points, not two points.

Choice C is incorrect. If the equation of a parabola with a vertex at (9, -14) is written in the form of the given equation, where a, b, and c are constants and a + b + c = -14, then the value of a will be 0, which is inconsistent with the equation of a parabola.

Remember the formula, (a – b)² = Either you can write (a – b) (a – b) or (a² – 2ab + b²).

Choice A:

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.

To understand it well, keep in mind a few things: When one digit moves from one side to another, it changes its sign from ‘positive to negative’ or ‘negative to positive.’ The second thing is that when a division value moves from one place to another, it goes from ‘up to down’ or ‘down to up’ and then multiplies.
For example: (a) (13/7) = 65/7
65/7 x 7/13
65 x 7 / 7 x 13
450 / 91 = 5 answer.