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3 years ago

Solve the following equation for X: 2x - 8 = -2

Mathematics

1 answer:

Morgarella [4.7K]3 years ago

7 0

Answer:

x = 3

Step-by-step explanation:

2x - 8 = -2

+8 +8

2x = 6

2 2

x = 3

If you want to check your solution then you add 3 to x. Once its added 2 x 3 equals 6 - 8 = - 2

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Let P and Q be polynomials with positive coefficients. Consider the limit below. lim x→[infinity] P(x) Q(x) (a) Find the limit i

jenyasd209 [6]

Answer:

If the limit that you want to find is $\lim_{x\to \infty}\dfrac{P(x)}{Q(x)}$ then you can use the following proof.

Step-by-step explanation:

Let $P(x)=a_{n}x^{n}+a_{n-1}x^{n-1}+\cdots+a_{1}x+a_{0}$ and $Q(x)=b_{m}x^{m}+b_{m-1}x^{n-1}+\cdots+b_{1}x+b_{0}$ be the given polinomials. Then

$\dfrac{P(x)}{Q(x)}=\dfrac{x^{n}(a_{n}+a_{n-1}x^{-1}+a_{n-2}x^{-2}+\cdots +a_{2}x^{-(n-2)}+a_{1}x^{-(n-1)}+a_{0}x^{-n})}{x^{m}(b_{m}+b_{m-1}x^{-1}+b_{n-2}x^{-2}+\cdots+b_{2}x^{-(m-2)}+b_{1}x^{-(m-1)}+b_{0}x^{-m})}=x^{n-m}\dfrac{a_{n}+a_{n-1}x^{-1}+a_{n-2}x^{-2}+\cdots +a_{2}x^{-(n-2)}+a_{1}x^{-(n-1)})+a_{0}x^{-n}}{b_{m}+b_{m-1}x^{-1}+b_{n-2}x^{-2}+\cdots+b_{2}x^{-(m-2)}+b_{1}x^{-(m-1)}+b_{0}x^{-m}}$

Observe that

$\lim_{x\to \infty}\dfrac{a_{n}+a_{n-1}x^{-1}+a_{n-2}x^{-2}+\cdots +a_{2}x^{-(n-2)}+a_{1}x^{-(n-1)})+a_{0}x^{-n}}{b_{m}+b_{m-1}x^{-1}+b_{n-2}x^{-2}+\cdots+b_{2}x^{-(m-2)}+b_{1}x^{-(m-1)}+b_{0}x^{-m}}=\dfrac{a_{n}}{b_{m}}$

and

$\lim_{x\to \infty} x^{n-m}=\begin{cases}0& \text{if}\,\, nm\end{cases}$

Then

$\lim_{x\to \infty}=\lim_{x\to \infty}x^{n-m}\dfrac{a_{n}+a_{n-1}x^{-1}+a_{n-2}x^{-2}+\cdots +a_{2}x^{-(n-2)}+a_{1}x^{-(n-1)}+a_{0}x^{-n}}{b_{m}+b_{m-1}x^{-1}+b_{n-2}x^{-2}+\cdots+b_{2}x^{-(m-2)}+b_{1}x^{-(m-1)}+b_{0}x^{-m}}=\begin{cases}0 & \text{if}\,\, nm \end{cases}$

3 0

3 years ago

Write the equation of a line with a slope of −2 and a y-intercept of 5

Aleonysh [2.5K]

Y or f(x) = -2x+5

the slope goes with the variable (x) and when the value of x is entered it makes a line, and the y-intercept is next to show where the point is on the y - line

8 0

3 years ago

A square in the board below and a letter in the word ATTENTION is chosen at

kolezko [41]

Answer:

4 /15

Step-by-step explanation:

From the number cube :

Count of Numbers greater than 4 = 16

Sample space of number cube = 20

P(number greater than 4) = 16 / 20 = 4/5

Word : ATTENTION

Count of letters in attention = 9

Count of T's in attention = 3

P(choosing T) = 3 / 9 = 1/3

P(greater than 4, then T) = 4/5 * 1/3 = 4 /15

5 0

2 years ago

Which of the following equations have the correct notation? Check all that apply. (Btw, most of my questions are from Apex learn

Llana [10]

The best and most correct answer among the choices provided by the question is the third choice.

The notation "AB (with line over) =4" is the equation that has the most correct notation.
I hope my answer has come to your help. God bless and have a nice day ahead!

3 0

3 years ago

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What is the expression equivalent to xy ^ 2/9

DochEvi [55]

Answer:

hi someone help me too

Step-by-step explanation:

6 0

3 years ago