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4 years ago

What is the discontinuity and zero of the function f(x) = the quantity of 2 x squared plus 5 x minus 12, all over x plus 4 ?

2 answers:

6 0

Remmber you can't divide by 0
if you can canel out something from both that is a hole

exampe if you had y=[(x-2)(x+3)]/(x-2), then the equation is y=x+3 with a hole at x=2 (since x=2 to make x-2=0 true)

so

$\frac{2x^2+5x-12}{x+4}= \frac{(x+4)(2x-3)}{x+4}=2x-3$
y=2x-3 is theh graph
zero at y=0 or x=3/2
(1.5,0) is the zero
set factored out thing to zero
x+4=0
x=-4
at x=-4
input into later one
y=2x-3
y=2(-4)-3
y=-8-3
y=-11
hole at (-4,-11)
the hole is at (-4,-11)
zero at (3/2,0)

FinnZ [79.3K]4 years ago

3 0

Answer:

A. Discontinuity at (−4, −11), zero at (three halves , 0)

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Which is the equation of a hyperbola with directrices at x = ±2 and foci at (5, 0) and (−5, 0)? y squared over 40 minus x square

N76 [4]

The equation of the hyperbola with directrices at x = ±2 and foci at (5, 0) and (−5, 0) is $\frac{x^2}{10} + \frac{y^2}{15} = 1$

<h3>How to determine the equation of the hyperbola?</h3>

The given parameters are:

Directrices at x = ±2
Foci at (5, 0) and (−5, 0)

The foci of a hyperbola are represented as:

Foci = (k ± c, h)

The center is:

Center = (h,k)

And the directrix is:

Directrix, x = h ± a²/c

By comparison, we have:

k ± c = ±5

h = 0

h ± a²/c = ±2

Substitute h = 0 in h ± a²/c = ±2

0 ± a²/c = ±2

This gives

a²/c = 2

Multiply both sides by c

a² = 2c

k ± c = ±5 means that:

k ± c = 0 ± 5

By comparison, we have:

k = 0 and c = 5

Substitute c = 5 in a² = 2c

a² = 2 * 5

a² = 10

Next, we calculate b using:

b² = c² - a²

This gives

b² = 5² - 10

Evaluate

b² = 15

The hyperbola is represented as:

$\frac{(x - k)^2}{a^2} + \frac{(y - h)^2}{b^2} = 1$

So, we have:

$\frac{(x - 0)^2}{10} + \frac{(y - 0)^2}{15} = 1$

Evaluate

$\frac{x^2}{10} + \frac{y^2}{15} = 1$

Hence, the equation of the hyperbola is $\frac{x^2}{10} + \frac{y^2}{15} = 1$

Read more about hyperbola at:

brainly.com/question/3405939

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2 years ago

What two consecutive whole numbers lie between the square root of 55?

Kamila [148]

$\boxed{7 \ \textless \ \sqrt{55} \ \textless \ 8}\\\\because\ 7^2=49 \ \textless \ 55\ and\ 8^2=64 \ \textgreater \ 55$

6 0

3 years ago

Read 2 more answers

How do I make this as simplest form <br>qns: 5 2/3 + 3 1/10 <br>pls answer<br>the prod. is 8 23/30

umka2103 [35]

Answer:

That is the final product

Step-by-step explanation:

According to all sites I used, they all said that was in the simplest form and cannot be simplified lower than that.

3 0

3 years ago

The time needed to complete a final examination in a particular college course is normally distributed with a mean of 80 minutes

mixer [17]

Answer:

0.02275

Step-by-step explanation:

We have been given that the time needed to complete a final examination in a particular college course is normally distributed with a mean of 80 minutes and a standard deviation of 10 minutes. We are asked to find the probability of completing the exam in one hour or less.

We know that 1 hour equals 60 minutes. First of all, we will find the z-score corresponding to 60 minutes.

$z=\frac{x-\mu}{\sigma}$