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-Dominant- [34]

4 years ago

12

A. addition property of equality

1 answer:

Masteriza [31]4 years ago

8 0

Division property of equality

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Which represents the inverse of the function

77julia77 [94]

H(x) = 1/4x would be the inverse

3 0

3 years ago

If I put 1500 into my savings account and 180 of interest at 4% simple interest how long was my money in my bank

stealth61 [152]

10,800 I think that's the answer

6 0

3 years ago

<img src="https://tex.z-dn.net/?f=f%28x%29%20-%20%5Cfrac%7Bx%5E%7B2%7D-4%20%7D%7Bx%5E%7B4%7D%20%2Bx%5E%7B3%7D%20-4x%5E%7B2%7D-4%

Llana [10]

a) The given function is

$f(x)=\frac{x^2-4}{x^4+x^3-4x^2-4}$

The domain refers to all values of x for which the function is defined.

The function is defined for

$x^4+x^3-4x^2-4\ne0$

This implies that;

$x\ne -2.69,x\ne 1.83$

b) The vertical asymptotes are x-values that makes the function undefined.

To find the vertical asymptote, equate the denominator to zero and solve for x.

$x^4+x^3-4x^2-4=0$

This implies that;

$x= -2.69,x=1.83$

c) The roots are the x-intercepts of the graph.

To find the roots, we equate the function to zero and solve for x.

$\frac{x^2-4}{x^4+x^3-4x^2-4}=0$

$\Rightarrow x^2-4=0$

$x^2=4$

$x=\pm \sqrt{4}$

$x=\pm2$

The roots are $x=-2,x=2$

d) The y-intercept is where the graph touches the y-axis.

To find the y-inter, we substitute;

$x=0$ into the function

$f(0)=\frac{0^2-4}{0^4+0^3-4(0)^2-4}$

$f(0)=\frac{-4}{-4}=1$

e) to find the horizontal asypmtote, we take limit to infinity

$lim_{x\to \infty}\frac{x^2-4}{x^4+x^3-4x^2-4}=0$

The horizontal asymtote is $y=0$

f) The greatest common divisor of both the numerator and the denominator is 1.

There is no common factor of the numerator and the denominator which is at least a linear factor.

Therefore the function has no holes.

g) The given function is a proper rational function.

There is no oblique asymptote.

See attachment for graph.

6 0

3 years ago

Write a linear equation that contains the ordered pair shown in the table below:

Amiraneli [1.4K]

Answer:

$y=2x-4$

Step-by-step explanation:

Let the equation of line is $y=mx+b$ , where $m$ is the slope of the line.

It passes through $(-5,-14),(-2,-8)\ and\ (1,-2)$ .

(<em>Slope of the line</em> joining $(x_1,y_1)\ and\ (x_2,y_2)=\frac{y_2-y_1}{x_2-x_1}$ )

Hence slope of the given line

$m=\frac{-8(-14)}{-2-(-5)}=\frac{-8+14}{-2+5}=\frac{6}{3}=2$

Equation of line is: $y=2x+b$

The line passes through $(1,-2)$

$-2=2\times 1+b\\b=-2-2\\b=-4$

Check if $(-5,-14)$ is on the line $y=2x-4$

$L.H.S.=-14\\R.H.S.=2\times (-5)-4=-10-4=-14\\L.H.S.=R.H.S.$

Hence line passes through $(5,-14)$ .

Check if $(-2,-8)$ is on the line $y=2x-4$

$L.H.S.=-8\\R.H.S.=2\times (-2)-4=-4-4=-8\\L.H.S.=R.H.S.$

Hence line passes through $(-2,-8)$ .

4 0

3 years ago

Explain how to find the product 3^5 x 3^2 using rules for exponents.

AlekseyPX

Step-by-step explanation:

$\because \: {a}^{m} \times {a}^{n} = {a}^{m + n} \\ \\ \therefore \: {3}^{5} \times {3}^{2} = {3}^{5 + 3} = {3}^{8} = 6,561 \\$

7 0

4 years ago