to find the vertical asymptote, you have to put the rational function in the simplest form, which means to cancel any common factor between the numerator and denominator. here we don't have anything to cancel. then take the denominator and equal it to 0. x-3=0 ,x=3

to find the horizontal asymptote, in this situation, the degree of the numerator and denominator are the same which is 1. therefore, y=the coefficient of the numerator ÷ the coefficient of the denominator. y=6÷1 ,y=6

7 0

3 years ago

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What is the factored form of x^12y^18+1

Black_prince [1.1K]

Answer: The required factored form of the given expression is

$(x^4y^6+1)(x^8y^{12}-x^4y^6+1).$

Step-by-step explanation: We are given to find the factored form of the following algebraic expression:

$E=x^{12}y^{18}+1.$

We will be using the following formula:

$a^3+b^3=(a+b)(a^2+ab+b^2).$

Now, we have

$E\\\\=x^{12}y^{18}+1\\\\=(x^4y^6)^3+1^3\\\\=(x^4y^6+1)\{(x^4y^6)^2-x^4y^6\times1+1^2\}\\\\=(x^4y^6+1)(x^8y^{12}-x^4y^6+1).$

Thus, the required factored form of the given expression is

$(x^4y^6+1)(x^8y^{12}-x^4y^6+1).$

4 0

3 years ago

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Please help me fill in the blanks :)

guapka [62]

Answer:

Absolute value is the distance from numbers on a number line. The absolute value of -7 is 7 b/c it is 7 units from 0. The absolute value of 5 is 5 b/c it is 5 units from 0.

A negative number is a number that is negative. On a horizontal number line negative numbers are to the left.

A positive number is a number that is positive. On a horizontal number line positive numbers are to the right.

I don't understand the last paragraph though. Hope this helped :D

Step-by-step explanation:

4 0

3 years ago

What is 4 2/7 ⋅ 2 1/5 ?

Vikki [24]

Answer: 9 and 3/7

Step-by-step explanation: To multiply a mixed number by a mixed number, we first want to write each mixed number as an improper fraction.

We can write a mixed number as an improper fraction by multiplying the denominator by the whole number and adding the numerator.

We can change $4\frac{2}{7}$ to the improper fraction 30/7.

We can also change $2\frac{1}{5}$ to the improper fraction 11/5.

Now, we are simply multiplying fractions. To multiply fractions, we multiply across the numerators and multiply across the denominators. When we multiply these fractions, we will end up with the fraction 330/35. Since 330/35 is not in lowest terms, we need to divide both the numerator and denominator by the greatest common factor of 330 and 35 which is 5 and we will get the improper fraction 66/7.

Notice however that 66/7 can be changed into a mixed number by dividing the denominator which is 7 into the numerator which is 66.

66 divided by 7 equals 9 with a remainder of 3 so we can write 66/7 as the mixed number 9 and 3/7.

Therefore, 4 and 2/7 × 2 and 1/5 = 9 and 3/7

3 0

4 years ago

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Order the numbers from least to greatest. -0.25,1/4,-1/3,0.3​

Order the numbers from least to greatest. -0.25,1/4,-1/3,0.3