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3 years ago

What are the discontinuities of the function f(x) = the quantity x squared minus 16 over the quantity 4x plus 24?

Mathematics

2 answers:

Kay [80]3 years ago

8 0

Answer with Step-by-step explanation:

we are given a function:

$f(x)=\dfrac{x^2-16}{4x+24}$

We have to find the point of discontinuity of the function.

As we can clearly see that the function is not well defined if the denominator is zero.

So, the point of discontinuity is that value of x where denominator is zero

i.e. x such that 4x+24=0

4x= -24

x= -6

Hence, function is discontinuous at x= -6

and is continuous at all x ≠ -6

Ivanshal [37]3 years ago

3 0

The first thing we should do is write the function:
(x ^ 2-16) / (4x + 24)
This function represents a discontinuity in the x that make the denominator zero.
We have then
4x + 24 = 0
x = -24 / 4 = -6
answer
the discontinuities of the function f (x) is x ≠ - 6

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Which graph represents a non-proportional relationship?

Semmy [17]

Answer:

because look at y intercept

Step-by-step explanation:

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3 years ago

A company has an inventory of books that is decreasing at a constant rate. After selling the book for 4 days, they have 8.840 bo

lbvjy [14]

Answer:

The linear equation is:

$B(d) = 9500 - 165d$

Step-by-step explanation:

Linear function:

A linear function has the following format:

$y = mx + b$

In which m is the slope(how much y changes when x changes by 1) and b is the y-intercept(value of y when x = 0).

A company has an inventory of books that is decreasing at a constant rate. Write a linear equation for B in terms of d.

This means that the situation is modeled by a linear function in the following format:

$B(d) = B(0) + md$

After selling the book for 4 days, they have 8.840 books in stock and after selling it for 10 days they have 7,850 books in stock.

This means that B(4) = 8840, B(10) = 7850

Finding the slope:

The slope, having two points, is given by the change in the output(in this case B) divided by the change in the input(in this case d).

We have the points

(4,8840) -> When d = 4, B = 8840

(10,7850) -> When d = 10, B = 7850

Change in B: 7850 - 8840 = -990

Change in d: 10 - 4 = 6

Slope: $m = \frac{-990}{6} = -165$

$B(d) = B(0) - 165d$

(10,7850) -> When d = 10, B = 7850

We use this to find B(0). So

$B(d) = B(0) - 165d$

$7850 = B(0) - 165*10$

$B(0) = 9500$

The linear equation is:

$B(d) = 9500 - 165d$

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3 years ago

Donna sells beaded necklaces. Each large necklace sells for $5.20 and each small necklace sells for $4.90. How much will she ear

stiv31 [10]

Answer:

$32.6

Step-by-step explanation:

$5.20 x 3 = $15.6

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$19.6 + $15.6 = $35.2

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3 years ago

Read 2 more answers

Which set of orderd pairs is a function A.( -6, -4 ), (-4, -2) , ( 0, 0 ), (-4, 2 ) ,( -6, 4) B. ( -2 , 1 ) , (-4, 2) , ( 0, 3)

Oxana [17]

Answer:

The answer is D

Step-by-step explanation:

To be a function, you cannot have the same x values.

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4 years ago

Use Lagrange multipliers to find the maximum and minimum values of f(x,y)=x+4y subject to the constraint x2+y2=9, if such values

Vesnalui [34]

The Lagrangian is

$L(x,y,\lambda)=x+4y+\lambda(x^2+y^2-9)$

with critical points where the partial derivatives vanish.

$L_x=1+2\lambda x=0\implies x=-\dfrac1{2\lambda}$

$L_y=4+2\lambda y=0\implies y=-\dfrac2\lambda$

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Substitute $x,y$ into the last equation and solve for $\lambda$ :

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Then we get two critical points,

$(x,y)=\left(-\dfrac3{\sqrt{17}},-\dfrac{12}{\sqrt{17}}\right)\text{ and }(x,y)=\left(\dfrac3{\sqrt{17}},\dfrac{12}{\sqrt{17}}\right)$

We get an absolute maximum of $3\sqrt{17}\approx12.369$ at the second point, and an absolute minimum of $-3\sqrt{17}\approx-12.369$ at the first point.

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3 years ago