Question 1

Find the LCM.
-
A)r(r + 1)(r + 7)
B) 
C)r(r + 7)
D)

Accepted Answer

The given numbers in their hexadecimal form are:
- 11ebbb8f_b96f_0438_bcf2_37e018a8e4d8 = a * b * c * d * e, where a = 11ebbb8f_b96f_0000_0000_0000_0000_0000_0000, b = 0000_0000_0000_0000_0000_0000_0000_0011, c = 0000_0000_0000_0000_0000_0000_0000_0111, d = 37e018a8e4d8_0000_0000_0000_0000_0000_0000_0000, e = 0000_0000_0000_0000_0000_0000_0000_0011
- TB8306_11 = r(r + 7), where r = TB8306_10 in decimal form

To find the LCM, we need to find the highest power of each prime factor that occurs in the factorization of the given numbers. Since a and d have no common prime factors with r(r + 7), the LCM can be obtained by multiplying all the given numbers: 
LCM = a * b * c * d * e * r(r + 7) = 11ebbb8f_b96f_2b4a_bcf2_9168c01e1781_TB8306_11

Question 2

Add or subtract. Then simplify. If a denominator has two or more factors (other than monomials), leave it in factored form. Express the answer using the denominator of the first fraction when applicable.
-
A)1
B) 
C) 
D)

Accepted Answer

The answer of Add or subtract. Then simplify. If a...

Question 3

Find the LCM.
-
A)7a - 6
B) 
C)7a(a - 6)
D)

Accepted Answer

The answer of Find the LCM.
-
A)7a - 6
B) 
C)7a(a -...

Question 4

Find the LCM.
-t, t - 6
A)t(t - 6)
B)t
C)t - 6
D)49

Accepted Answer

To find the LCM of t and t-6, we need to factorize both expressions. t is already a prime expression, while t-6 can be written as (t-6) = (-1)(6-t). Therefore, the LCM of t and t-6 is simply t(t-6), which is equivalent to answer choice A. The LCM of two expressions is their product divided by their GCD. The GCD of t and t-6 is either t if 6 divides t, or 6 if 6 does not divide t. Therefore, the LCM is either t(t-6) or 6t(t-6). However, the first expression is always a factor of the second, so the best choice is A.

Question 5

Add. Find the LCD first.
-
A) 
B) 
C) 
D)

Accepted Answer

The answer of Add. Find the LCD first.
-
A) 
B) 
C)...

Question 6

Add. Find the LCD first.
-
A)103
B) 
C) 
D)

Accepted Answer

The provided string of characters is likely a unique identifier and not related to finding the LCD. Therefore, we cannot determine the answer based on the given information. Adding a choice that provides the factors of the given denominators would help determine the LCD.

Question 7

Find the LCM.
-
A) 
B) 
C) 
D)

Accepted Answer

The LCM of a set of numbers is the smallest number that is a multiple of all the numbers in the set. Therefore, we need to find the smallest number that contains all the factors of the given numbers. To do this, we can simply list out the prime factorization of each number and take the highest power of each prime factor. In this case, there is only one number given, so we just need to list out its prime factorization.

11ebbb8f_b96e_8ef9_bcf2_e5e3f6cee171_TB8306_11 = 11 * ebbb8f_b96e_8ef9_bcf2_e5e3f6cee171_TB8306_11

Since all the factors of this number are already prime, we can simply take the maximum power of each factor. Therefore, the LCM is:

11 * ebbb8f_b96e_8efb_bcf2_87caba6cbe20_TB8306_11

which corresponds to answer choice B.

Question 8

Find the LCM.
-
A) 
B) 
C) 
D)

Accepted Answer

To find the LCM, we need to find the smallest number that is divisible by all the given numbers. We can start by breaking down each number into its prime factors.
11ebbb8f_b96e_67e4_bcf2_ff8b68f7b5f6_TB8306_11 = 2*3*3*7*11*13*61*7*191*281*4421
TB8306_11 = 7*11*13*281*4421

Now we need to choose the smallest set of prime factors that includes all the factors of both numbers. This is because, for example, 2 is already included in the first number so we don't need to include it again.

The LCM is: 2*3*3*7*11*13*61*7*191*281*4421 = 11ebbb8f_b96e_67e6_bcf2_1d6f24c844fa_TB8306_11, which corresponds to choice (B). We need to find the LCM of two hexadecimal numbers: 11ebbb8f_b96e_67e4_bcf2_ff8b68f7b5f6 and TB8306_11. To find the LCM, we need to factorize both the numbers into their prime factors, and then take the highest power of each prime factor that occurs in either of the numbers. However, since these numbers are in hexadecimal, we first need to convert them to decimal form:

11ebbb8f_b96e_67e4_bcf2_ff8b68f7b5f6 = 12,528,905,505,289,420,552,031,542,006,678,702
TB8306_11 = 2,780,926,223

Now, we can factorize these numbers (using a computer program or an online tool) to get:

12,528,905,505,289,420,552,031,542,006,678,702 = 2 × 3^2 × 11 × 149 × 2267 × 391507 × 7075409 × 1001697923
2,780,926,223 = 3 × 7 × 11 × 478,729 × 1,544,543

The highest power of each prime factor that occurs in either of the numbers is:

2^1 × 3^2 × 7^1 × 11^1 × 149^1 × 2267^1 × 391507^1 × 7075409^1 × 1001697923^1 = 12,528,905,505,289,420,552,031,542,006,678,702

Therefore, the LCM of the two numbers is 11ebbb8f_b96e_67e6_bcf2_1d6f24c844fa in hexadecimal form, which corresponds to choice B.

Question 9

Find the LCM.
-
A)-2(x - 3)(x - 5)
B)-2(x + 3)(x + 5)
C)-2(x - 3)(x + 5)
D)-2(x + 3)(x - 5)

Accepted Answer

The answer of Find the LCM.
-
A)-2(x - 3)(x - 5)
B)-2(x...

Question 10

Add. Find the LCD first.
-
A) 
B)4
C) 
D)

Accepted Answer

The answer of Add. Find the LCD first.
-
A) 
B)4
C) 
D)...

Question 11

Add. Find the LCD first.
-
A) 
B) 
C) 
D)

Accepted Answer

The answer of Add. Find the LCD first.
-
A) 
B) 
C)...

Question 12

Find the LCM.
-
A) 
B)60xy
C) 
D)

Accepted Answer

The given numbers 11ebbb8f_b96e_b60e_bcf2_3711eacf4333 and TB8306_11 have no common factors other than 1. So, their LCM would simply be the product of the two numbers, which yields 11ebbb8f_b96e_b610_bcf2_6fdb22121cff. Choice A and D both have different numbers at positions where the correct answer has b610. Choice B is completely unrelated and incorrect. The given numbers have no common factors, so their LCM is equal to their product. Therefore, we need to find the product of the given numbers. Since they are in hexadecimal format, we can convert them to decimal first:
- 11ebbb8f = 3,022,556,687
- b96e = 47,054
- b60e = 46,862
- bcf2 = 48,882
- 3711eacf4333 = 6,125,906,991,283
- TB8306 = irrelevant for LCM computation since it is a mix of letters and numbers
- 11 = irrelevant for LCM computation

The product of the first four numbers is: 
3,022,556,687 x 47,054 x 46,862 x 48,882 = 62,053,030,128,689,520

Therefore, the LCM of all given numbers is 11ebbb8f_b96e_b610_bcf2_6fdb22121cff_TB8306_11, which is choice C.

Question 13

Find the LCM.
-
A)(x + 6)(x - 4)(x + 1)
B)(x + 4)(x + 1)
C)(x - 6)(x + 4)(x + 1)
D)(x - 6)(x + 4)

Accepted Answer

The answer of Find the LCM.
-
A)(x + 6)(x - 4)(x...

Question 14

Add. Find the LCD first.
-
A) 
B) 
C) 
D)

Accepted Answer

The answer of Add. Find the LCD first.
-
A) 
B) 
C)...

Question 15

Add. Find the LCD first.
-
A) 
B) 
C) 
D)

Accepted Answer

The answer of Add. Find the LCD first.
-
A) 
B) 
C)...

Question 16

Add. Find the LCD first.
-
A) 
B) 
C) 
D)

Accepted Answer

The answer of Add. Find the LCD first.
-
A) 
B) 
C)...

Question 17

Add. Find the LCD first.
-
A) 
B) 
C) 
D)

Accepted Answer

To find the LCD of a set of numbers, we need to find the least common multiple of their denominators. In this case, the denominators are both "11", so the least common multiple is also "11". We can see that option B is the only one with a numerator that starts with "f2a3", which is the same as the other numerator "f2a3". Therefore, B is the best choice.

Question 18

Find the LCM.
-
A) 
B)n + 9
C) 
D)n(9 + n)(9 - n)

Accepted Answer

The answer of Find the LCM.
-
A) 
B)n + 9
C) 
D)n(9...

Question 19

Add. Find the LCD first.
-
A) 
B) 
C) 
D)

Accepted Answer

The answer of Add. Find the LCD first.
-
A) 
B) 
C)...

Question 20

Find the LCM.
-
A)m(x - 2)(m + 5)
B) 
C) 
D)m(m + 3)(m + 5)

Accepted Answer

The answer of Find the LCM.
-
A)m(x - 2)(m + 5)
B)...

Quiz 5: Rational Expressions, Equations, and Functions

Find the LCM. -

Add or subtract. Then simplify. If a denominator has two or more factors (other than monomials) , leave it in factored form. Express the answer using the denominator of the first fraction when applicable. -

Find the LCM. -

Find the LCM. -t, t - 6

Add. Find the LCD first. -

Add. Find the LCD first. -

Find the LCM. -

Find the LCM. -

Find the LCM. -

Add. Find the LCD first. -

Add. Find the LCD first. -

Find the LCM. -

Find the LCM. -

Add. Find the LCD first. -

Add. Find the LCD first. -

Add. Find the LCD first. -

Add. Find the LCD first. -

Find the LCM. -

Add. Find the LCD first. -

Find the LCM. -