1.### If the set of numbers 3, -12, 48, -192 form a geometric sequence, what is the common ratio between any two consecutive terms?

Answer:
-4

Explanation:

The common ratio between any two consecutive terms in a geometric sequence is found by dividing one term by the previous term. In this case, dividing -12 by 3 gives us -4. Therefore, -4 is the common ratio between any two consecutive terms in the given sequence.

2.### What is the next term in the arithmetic sequence: 2, 13/4, 9/2, 23/4

Answer:
7

Explanation:

The given arithmetic sequence starts with 2 and increases by 5/4 each time. To find the next term, we add 5/4 to the previous term 23/4, which gives us 28/4 or 7. Therefore, the next term in the sequence is 7.

3.### Which of the following is NOT an example of a harmonic sequence?

Answer:
4, 0, -4, -2

Explanation:

The option "4, 0, -4, -2" is not a harmonic sequence because harmonic sequences consist of the reciprocals of an arithmetic sequence's terms, and no term in a harmonic sequence can be zero, as division by zero is undefined. This option also does not follow a pattern of reciprocals from any arithmetic sequence, distinguishing it from a true harmonic progression.

4.### What is the sum of all even integers from 21 to 51?

Answer:
540

Explanation:

The sum of all even integers from 21 to 51 can be calculated by finding the average of the first and last even numbers in the range (22 and 50) and multiplying it by the number of terms. Calculating the number of terms = (50 - 22) / 2 + 1 = 15. The average of 22 and 50 is 36, so multiplying it by 15 gives us a sum of 540.

5.### What quotient shall be obtained when (x+9) divides (x2 – 81)?

Answer:
X-9

Explanation:

When (x+9) divides (x^2 - 81), it means that (x^2 - 81) can be expressed as a product of (x+9) and another factor. To find this factor, we can use the method of polynomial long division. By dividing (x^2 - 81) by (x+9), we get a quotient of (x-9). Therefore, the correct answer is X-9.

6.### Which of the following is (3a + 1) a factor of?

Answer:
6a^{2} + 5a + 1

Explanation:

(6a^2 + 5a + 1) is divisible by (3a + 1), because when we divide it by (3a + 1), we get no remainder:

(6a^2 + 5a + 1) ÷ (3a + 1) 2(3a^2 + 3a) + 1 = (2 * 3a^2) + (2 * 3a) + 1

When we divide the first two terms, we get a quotient of (2 * 3a^2) + (2 * 3a), which is the same as (3a^2 + 3a) multiplied by 2. Therefore, (3a + 1) is a factor of (6a^2 + 5a + 1).

(6a^2 + 5a + 1) ÷ (3a + 1) 2(3a^2 + 3a) + 1 = (2 * 3a^2) + (2 * 3a) + 1

When we divide the first two terms, we get a quotient of (2 * 3a^2) + (2 * 3a), which is the same as (3a^2 + 3a) multiplied by 2. Therefore, (3a + 1) is a factor of (6a^2 + 5a + 1).

7.### What is the value of K if the expression (- 5x3 + 4x2 – 3x + K) is divided by (x-1), and obtains a remainder of 10?

Answer:
14

Explanation:

When a polynomial is divided by a linear expression, the remainder is obtained by substituting the value of the variable in the linear expression. In this case, when the expression (-5x^3 + 4x^2 - 3x + K) is divided by (x-1) and obtains a remainder of 10, it means that when x=1, the expression equals 10. Substituting x=1 into the expression, we get (-5(1)^3 + 4(1)^2 - 3(1) + K) = 10. Simplifying this equation gives us K=14. Therefore, the value of K is 14.

8.### Jace will evaluate a 7th-degree polynomial in m, whose value is 5 through synthetic division. How many coefficients of m shall be written in the first row of the synthetic division procedure?

Answer:
8

Explanation:

In synthetic division, the number of coefficients written in the first row is equal to the degree of the polynomial plus one. Since the polynomial in this question is a 7th-degree polynomial, there will be 8 coefficients written in the first row of the synthetic division procedure.

9.### What is the value of P(-2) in the expression: P(x) = 7x4 – 5x3 + 2x2 – 3?

Answer:
157

Explanation:

To find the value of P(-2), we substitute -2 for x in the expression P(x). Plugging in -2, we get P(-2) = 7(-2)^4 - 5(-2)^3 + 2(-2)^2 - 3. Simplifying this expression, we get P(-2) = 7(16) + 5(8) + 2(4) - 3 = 112 + 40 + 8 - 3 = 157. Therefore, the value of P(-2) is 157.

10.### Which of the following polynomial equation with roots -1, 1, and 4?

Answer:
P(x) = x^{3} – 4x^{2} – x + 4

Explanation:

The given polynomial equation has roots -1, 1, and 4. To find the correct equation, we need to check which equation gives us these roots when plugged in. By substituting -1, 1, and 4 into each equation, we find that only P(x) = x3 – 4x2 – x + 4 gives us the desired roots. Therefore, P(x) = x3 – 4x2 – x + 4 is the correct equation.

11.### What are the roots of the quadratic equation b2 – 5b – 36 = 0?

Answer:
(9,-4)

Explanation:

To find the roots of the quadratic equation b^2 - 5b - 36 = 0, we can use the quadratic formula. The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the roots can be found using the formula:

x = (-b ± √(b^2 - 4ac)) / 2a

In this case, our equation is b^2 - 5b - 36 = 0. So, we have:

a = 1 b = -5 c = -36

Plugging these values into the quadratic formula, we get:

b = [5 ± √((-5)^2 - 4(1)(-36))] / 2(1) b = [5 ± √(25 + 144)] / 2 b = [5 ± √169] / 2 b = [5 ± 13] / 2

Now, we have two possible roots:

b = (5 + 13) / 2 = 18 / 2 = 9

b = (5 - 13) / 2 = -8 / 2 = -4

Therefore, the roots of the quadratic equation b^2 - 5b - 36 = 0 are 9 and -4.

x = (-b ± √(b^2 - 4ac)) / 2a

In this case, our equation is b^2 - 5b - 36 = 0. So, we have:

a = 1 b = -5 c = -36

Plugging these values into the quadratic formula, we get:

b = [5 ± √((-5)^2 - 4(1)(-36))] / 2(1) b = [5 ± √(25 + 144)] / 2 b = [5 ± √169] / 2 b = [5 ± 13] / 2

Now, we have two possible roots:

b = (5 + 13) / 2 = 18 / 2 = 9

b = (5 - 13) / 2 = -8 / 2 = -4

Therefore, the roots of the quadratic equation b^2 - 5b - 36 = 0 are 9 and -4.

12.### A square with a side of 12 cm and a rectangle with a width of 8 cm have the same area. What is the length of the rectangle?

Answer:
18 CM

Explanation:

The area of a square is calculated by multiplying the length of one side by itself. In this case, the side of the square is given as 12 cm, so the area of the square is 12 cm * 12 cm = 144 cm^2. The area of a rectangle is calculated by multiplying its length by its width. Since the rectangle and the square have the same area, we can set up the equation 144 cm^2 = length of rectangle * 8 cm. Solving for the length of the rectangle, we find that it is 18 cm.

13.### In square FATE, the measure of angle F is 4x + 30. What is the value of x?

Answer:
15 degrees

Explanation:

The measure of angle F in square FATE is given as 4x + 30. To find the value of x, we can equate this expression to the given answer choices and solve for x. By substituting 15 degrees for x in the expression 4x + 30, we get 4(15) + 30 = 60 + 30 = 90 degrees. Since 90 degrees is not one of the answer choices, we can conclude that the given answer of 15 degrees is incorrect. Therefore, the correct answer cannot be determined from the information provided.

14.### What is the sum of the first 8 terms of an arithmetic sequence whose first term is 37 and the common difference is -4?

Answer:
184

Explanation:

The sum of the first 8 terms of an arithmetic sequence can be found using the formula: Sn = (n/2)(2a + (n-1)d), where Sn is the sum of the terms, n is the number of terms, a is the first term, and d is the common difference. Plugging in the given values, we get Sn = (8/2)(2(37) + (8-1)(-4)) = 4(74 + 7(-4)) = 4(74-28) = 4(46) = 184. Therefore, the correct answer is 184.

15.### The polynomial function P(x) = xn is true when,

Answer:
N is an non-negative number

Explanation:

The given polynomial function P(x) = xn is true when N is a non-negative number because the exponent, represented by N, must be a non-negative integer or zero. This is because raising a number to a negative exponent or a non-integer exponent would result in a non-polynomial function. Therefore, the given polynomial function is only true when N is a non-negative number.

16.### What is the leading term in a polynomial function P(x) = 5 + 7x4 – 3x + 2x5?

Answer:
5

17.### The computation for profit in a textile store is presented by the mathematical model
P(x) = 3x2 + 6x – 120,000 where x is the number of meters being sold. What is the computed profit if the number of meters being sold is 250?

Answer:
69000.00

Explanation:

To find the computed profit when 250 meters are being sold, we can substitute the value of x = 250 into the given mathematical model:

P(x) = 3x^2 + 6x - 120,000

So,

P(250) = 3(250)^2 + 6(250) - 120,000

Now, let's compute:

P(250) = 3(62500) + 1500 - 120,000 = 187500 + 1500 - 120,000 = 189000 - 120,000 = 69,000

Therefore, the computed profit when 250 meters are being sold is $69,000.

P(x) = 3x^2 + 6x - 120,000

So,

P(250) = 3(250)^2 + 6(250) - 120,000

Now, let's compute:

P(250) = 3(62500) + 1500 - 120,000 = 187500 + 1500 - 120,000 = 189000 - 120,000 = 69,000

Therefore, the computed profit when 250 meters are being sold is $69,000.

18.### Which of the following function will cross the x-axis thrice?

Answer:
P(x) = (2x^{2} – 5x + 2) (x+3)

Explanation:

The function P(x) = (2x^2 - 5x + 2) (x+3) will cross the x-axis thrice because it is a quadratic function with a leading coefficient of 2, which means it opens upwards. The quadratic factor (2x^2 - 5x + 2) will have two x-intercepts, and the linear factor (x+3) will have one x-intercept. When multiplied together, these factors will result in a function that crosses the x-axis three times.

19.### Which of the following mathematical models is used to determine the distance between two points whose coordinates are (x1, y1) and (x2, y2)?

Answer:
D.

Explanation:

The correct answer is D. The distance between two points whose coordinates are (x1, y1) and (x2, y2) can be determined using the mathematical model known as the distance formula. This formula is derived from the Pythagorean theorem and states that the distance between two points in a Cartesian plane is equal to the square root of the sum of the squares of the differences between their x-coordinates and y-coordinates.

20.### What is the expansion of (2x – 3)3?

Answer:
8x^{3} – 36x^{2} + 54x – 27

Explanation:

The given expression is (2x – 3)3. To expand this expression, we use the binomial expansion formula, which states that (a + b)n = an + (nC1)a(n-1)b + (nC2)a(n-2)b2 + ... + (nCn-1)ab(n-1) + bn, where nCk represents the binomial coefficient. In this case, a = 2x and b = -3, and n = 3. Expanding the expression using the formula, we get 8x3 – 36x2 + 54x – 27. Therefore, the correct answer is 8x3 – 36x2 + 54x – 27.

×

Wait!

Here's an interesting quiz for you.