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3 years ago

Where is the removable discontinuity of f(x)= x+5/x^2+3x-10 located?

Mathematics

2 answers:

Alex17521 [72]3 years ago

6 0

Answer:

x= -5

Step-by-step explanation:

we are given with the function:

$f(x)=\frac{x+5}{x^2+3x-10}$

We will factorize the denominator

$x^2+3x-10$

$x^2+5x-2x-10$

$x(x+5)-2(x+5)$

$(x-2)(x+5)$

Hence, We can see that (x+5) can be eliminated since, it can get cancelled with the numerator

Hence, the removable discontinuity is at (x+5) or x= -5

Removable discontinuity is that which can be eliminated from the function.

Doss [256]3 years ago

3 0

get the point of discontinuity we proceed as follows;
f(x)=x+5/x^2+3x-10
f(x)=4x+5x^2-10

this can be written is such a way that they have the same denominator, here we shall have:
f(x)=(4x^3-10x^2+5)/x^2
The denominator= x^2
The numerator=4x^3-10x^2+5

The discontinuity is at the point x=0

the removable discontinuity is the the point x=2

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3 years ago

To make the chocolate shake, Dona added 40 mL of chocolate syrup,

Vsevolod [243]

Answer:

0.225 L of milk, would be required if she uses 450 m L of water.

Step-by-step explanation:

Here, to make the shake, ingredients used by Dina are:

40 m L of chocolate syrup,

200 m L of milk, and 400 m L of water.

So, here Amount of water used = 2 x ( Amount of Milk used) ....... (1)

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5 0

3 years ago

Does anyone have the answers for all?

Shkiper50 [21]

Answer and Step-by-step explanation:

1-6

What you can do is plug in 6 and start by doing the first machine first, then the second. If this doesn't work, do the second machine, then the first machine.

The order that works is second machine, then first machine.

Second Machine:

y = $(6)^{2} -6$ = 36 - 6 = 30

Plug into first machine now.

First Machine:

y = $\sqrt{(30) - 5} = \sqrt{25} = 5$

We see that the result is 5.

b. If we were to do the order of second machine, then first machine, we will never get a negative result (or -5 for that matter), due to the fact that you can't algebraically square root a negative number.

However, if we were to do the order of first machine, second machine, we can get a negative number. To get -5, we plug in 6 for x in the first machine, getting an answer of 1. We plug this into the second machine, getting 1^2 - 6, which results in -5.

1-7. The absolute value of a value is the positive version of that value.

a. |54| = 54

b. $-|-7\frac{3}{5}|$ = $-7\frac{3}{5}$

c. |3| - |-1| = 3 - 1 = 2

d. |2.2 - 5.13| = |-2.93| = 2.93

1-8.

| |

| |

| || || || || |

(5 boxes on each side)

| |

| |

| || || || || || |

(6 boxes on each side)

b. The amount of squares on each side of the figure increases by 1.

c. There would be 1 square, because we know that the pattern is there is 2 squares added to the next figure, 1 at each end. If we go back a figure, we take away 2 squares.

1-9.

a. -42 - 17 = -59

b. 8 - (-9) = 8 + 9 = 17

c. 8(-9) = -72

d. -42 ÷ (-7) = 6

e. -2(-3)(-4) = 6(-4) = 24

f. -18 - 7 = -25

g. $(-5)^{2}$ = 25