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maksim [4K]
2 years ago
14

Name two monomials with a quotient of 12

Mathematics
1 answer:
photoshop1234 [79]2 years ago
7 0
36 and 3 are two monomials with a quotient of 12. How? Well, we can first off start by defining what a monomial is. A monomial is any whole number or variable term in an algebraic expression. 36 and 3 are both monomials because they are constants (in other words, numbers without any variables). 36 and 3 can be divided to result in 12. If you need to better understand, let me know and I will gladly assist you.
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The Johnson twins were born five years after their older sister. This​ year, the product of the three​ siblings' ages is exactly
Mamont248 [21]

Answer:

13 years.

Step-by-step explanation:

Suppose, today, the Johnson twins' age is x years. Then the age of their elder sister will be (x + 5) years old. It is given that product of the three​ siblings' ages is exactly 2998 more than the sum of their ages. Therefore:

x + x + x + 5 + 2998 = (x)(x)(x + 5).

3x + 3003 = x^3 + 5x^2.

x^3 + 5x^2 - 3x - 3003 = 0.

To solve the question, factor theorem will be used. It states if any number c satisfies the equation f(c) = 0, then c is the factor of f(x). By observation, it can be seen that x = 13 can be a possible candidate for the factor of f(x). To verify, check f(13).

f(13) = 13^3 + 5(13^2) - 3(13) - 3003 = 2197 + 845 - 39 - 3003 = 0.

Since f(13) = 0, therefore x = 13 is the factor of f(x).

Now applying synthetic division:

Column 1       2       3       4            5

     13    |         1       5      -3        -3003  (Row 1)

______|______<u>  _13__234___3003</u>   (Row 2)

            |         1       18      231          0    (Row 3)

The method requires to write the coefficients of all the powers in the Row 1 on the right hand side of the table. Put the factor x = 13 on the left hand side of the table (Row 1 Column 1). The first step involves the second column elements to be added. Since there is only 1, thus there will be 1 below the line. Next step involves multiplying 1 with the factor (which is 13) and this will be the element for row 2 column 3. The add the elements of the column 3. The answer comes out to be -3. Repeat the above steps for the columns 4 and 5. The sum of the column 5 (the last column) should be 0, which is the case. The elements of the last row are actually the coefficients of the quadratic equation which is resultant from dividing f(x) by (x - 13). Thus:

x^2 + 18x + 231 = 0.

Using completing the square:

x^2 + 18 = -231.

(x)^2 + 2*(x)*(9) + (9)^2 = -231 + (9)^2.

(x + 9)^2 = -231 + 81.

(x + 9)^2 = -150.

Taking square root on both sides shows that rest of the 2 answers of this polynomial will be complex roots since square root of -150 does not exist in real numbers. Therefore, since the age is a real quantity and not a complex quantity, the age of the twins is 13 years!!!

8 0
3 years ago
The function g(x) = 8(4)x is reflected across the x - axis to creat f(x). What is the equation for f(x)
Nikolay [14]

The function g(x) = 8(4)x is reflected across the x - axis to creat f(x). What is the equation for f(x)

4 0
3 years ago
Haha please help i don't know what I'm doing
tresset_1 [31]

Answer:

(5x+1)(x+7)

Step-by-step explanation:

4x^2+26x+6+x^2+10x

5x^2+36x+7

(5x+1)(x+7)

Prove

5x*x + 5x*7 + 1*x + 1*7

= 5x^2 + 35x + x + 7

= 5x^2 + 36x + 7

4 0
2 years ago
lumangbayan elem school has 1485 students. about 80% of them attended the school orientation. how many students did not attend?
Allushta [10]

Answer:

20% did not attend

Step-by-step explanation:

sorry if wrong

5 0
3 years ago
Suppose △JMN≅△KQR . Which congruency statements are true?
dlinn [17]
The  first , second and fourth choices are correct.

4 0
3 years ago
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