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Serjik [45]
3 years ago
9

Explain why f(x) = x^2+4x+3/x^2-x-2 is not continuous at x = -1.

Mathematics
1 answer:
liberstina [14]3 years ago
3 0

Answer:

The value of x = -1 makes the denominator of the function equal to zero. That is why this value is not included in the domain of f(x)

Step-by-step explanation:

We have the following expression

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

Since the division between zero is not defined then the function f(x) can not include the values of x that make the denominator of the function zero.

Now we search that values of x make 0 the denominator factoring the polynomial x^2-x-2

We need two numbers that when adding them get as a result -1 and when multiplying those numbers, obtain -2 as a result.

These numbers are -2 and 1

Then the factors are:

(x-2) (x + 1)

We do the same with the numerator

x^2+4x+3

We need two numbers that when adding them get as a result 4 and when multiplying those numbers, obtain 3 as a result.

These numbers are 3 and 1

Then the factors are:

(x+3)(x + 1)

Therefore

f(x) = \frac{(x+3)(x+1)}{(x-2)(x+1)}

Note that \frac{(x+1)}{(x+1)}=1 only if x \neq -1

So since x = -1 is not included in the domain the function has a discontinuity in x = -1

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umka21 [38]

Answer:

m= 4

Step-by-step explanation:

3m +2n= 16 -----(1)

m -2n= 0 -----(2)

From (2):

m= 2n -----(3) (+2n on both sides)

subst. (3) into (1):

3(2n) +2n= 16

6n +2n= 16

8n= 16 (simplify)

n= 16 ÷8

n= 2

subst. n=2 into (3):

m= 2(2)

m= 4

7 0
3 years ago
Three more than twice a number is less than negative thirteen. Solve the inequality for the unknown number.
Goshia [24]

Answer:

Step-by-step explanation:

The number = x

Three more than the number = x + 3

twice the number = 2x

which means:

           

          2x + 3 < -13

          2x + 3 -3 < -13 -3                 (subtract 3 from both sides)

          2x < -16

          2x/2 < -16/2                       (divide 2 from both sides)

          x < -8

4 0
1 year ago
Calvin types 4 pages in 1/5 hour. The average page contains 250 words. What is Calvin's approximate typing speed in words per mi
RoseWind [281]

Answer:

83 1/3 words per minute

or approximately 83 words per minute

Step-by-step explanation:

4 pages * 250 words/ page = 1000 words

1/5 hour * 60 minutes/ 1 hour = 12 minutes

1000 words / 12 minutes = 83.333333333.... words per minute

83 1/3 words per minute


7 0
3 years ago
To make rice, you mix 1.5 cups of water for every 1 cup of dry rice. This will make 2 servings. How many cups of dry rice and ho
dalvyx [7]

Answer:

7.5 cups of water

5 cups of dry rice

Step-by-step explanation:

In total 1.5 water and 1 cup rice will equal 2 servings. If you are serving 10 people, you need to multiply each by 5.

6 0
3 years ago
Write an equation of the line that passes through the given points.
garik1379 [7]

Answer:

y=-2x+1

Step-by-step explanation:

to find the slope use the formula (y2-y1)/(x2-x1)

-5-3= -8

3-(-1) = 4

-8/4 = -2

8 0
3 years ago
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