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2 years ago

Solve the equation.

Mathematics

1 answer:

Readme [11.4K]2 years ago

8 0

Answer:

= 14/3

Step-by-step explanation:

add 3 to both sides of the equation

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What is the slope of the function?

d1i1m1o1n [39]

Answer: -6

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

"m divided by 3" is the same as

KonstantinChe [14]

M/3
OR
the quotient of a number, m, and 3

hope this helps :)

6 0

2 years ago

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The amount Lin's sister earns at her part-time job is proportional to the number

gulaghasi [49]

Answer:

$y = 9.6x$

Yes, y is a function of x.

$x = \frac{5}{48} y$

Step-by-step explanation:

For a proportional relation, the equation is given by:

$y = kx$

where k is the unit rate of change.

We were told that, Lin's sister earns $9.6 per hour.

This means k=9.6.

We substitute to get:

$y = 9.6x$

We could rewrite this as

$y(x) = 9.6x$

Yes, y is a function of x.

To obtain an equation describing x as a function of y, we solve for x to get:

$x = \frac{1}{9.6} y$

6 0

2 years ago

Given the functionf ( x ) = x^2 + 7 x + 10/ x^2 + 9 x + 20

vladimir1956 [14]

<em>x = -4 is a vertical asymptote for the function.</em>

<h2>Explanation:</h2>

The graph of $y=f(x)$ is a vertical has an asymptote at $x=a$ if at least one of the following statements is true:

$1) \ \underset{x\rightarrow a^{-}}{lim}f(x)=\infty\\ \\ 2) \ \underset{x\rightarrow a^{-}}{lim}f(x)=-\infty \\ \\ 3) \ \underset{x\rightarrow a^{+}}{lim}f(x)=\infty \\ \\ 4) \ \underset{x\rightarrow a^{+}}{lim}f(x)=\infty$

The function is:

$f(x)=\frac{x^2+7x+10}{x^2+9x+20}$

First of all, let't factor out:

$f(x)=\frac{x^2+5x+2x+10}{x^2+5x+4x+20} \\ \\ f(x)=\frac{x(x+5)+2(x+5)}{x(x+5)+4(x+5)} \\ \\ f(x)=\frac{(x+5)(x+2)}{(x+5)(x+4)} \\ \\ f(x)=\frac{(x+2)}{(x+4)}, \ x\neq 5$

From here:

$\bullet \ When \ x \ approaches \ -4 \ on \ the \ right: \\ \\ \underset{x\rightarrow -4^{+}}{lim}\frac{(x+2)}{(x+4)}=? \\ \\ \underset{x\rightarrow -4^{+}}{lim}\frac{(-4^{+}+2)}{(-4^{+}+4)} \\ \\ \\ The \ numerator \ is \ negative \ and \ the \ denominator \\ is \ a \ small \ positive \ number. \ So: \\ \\ \underset{x\rightarrow -4^{+}}{lim}\frac{(x+2)}{(x+4)}=-\infty$

$\bullet \ When \ x \ approaches \ -4 \ on \ the \ left: \\ \\ \underset{x\rightarrow -4^{-}}{lim}\frac{(x+2)}{(x+4)}=? \\ \\ \underset{x\rightarrow -4^{-}}{lim}\frac{(-4^{-}+2)}{(-4^{-}+4)} \\ \\ \\ The \ numerator \ is \ a \ negative \ and \ the \ denominator \\ is \ a \ small \ negative \ number \ too. \ So: \\ \\ \underset{x\rightarrow -4^{-}}{lim}\frac{(x+2)}{(x+4)}=+\infty$