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Anastasy [175]
3 years ago
8

Explain why f(x) = x2+4/x2-x-2 is not continuous at x = 2.

Mathematics
2 answers:
emmasim [6.3K]3 years ago
7 0

Answer:

Step-by-step explanation:

We have given a function :

f(x) = (x²+4)/(x²-x-2)

We have to explain why the function is not continuous at x = 2.

Simplify the denominator of the function.

x²-x-2 = x²+x-2x-2

x²-x-2 = (x+1)(x-2)

Putting this simplification of denominator in above function we get,

f(x) =  (x²+4)/(x+1)(x-2)

The domain is the all possible values of x in for which the function is defined.

when we put x=2, the denominator is zero and function is undifined.

So, the function is not  continuous at x = 2.

Choice a  is correct.

xxTIMURxx [149]3 years ago
6 0

Answer: Option a.

Step-by-step explanation:

 Make the denominator equal to zero and solve for x:

Factor the quadratic equation. Find two number whose sum is -1 and whose product is -2. Then:

x^{2}-x-2=0\\(x-2)(x+1)=0\\x=2\\x=-1

Then, as you can see the value x=2 makes the denominator equal to zero and the division by zero does not exist. Therefore you can conclude that the function shown in the problem is not defined at x=2

The answer is the option a.

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Identify the two triangle congruence criteria that do NOT guarantee congruence. Explain why they do not guarantee congruence, an
Mashcka [7]

Answer: Hello mate!

there are two congruence criteria that do not guarantee congruence:

AAA ( or 3 angles)

two triangles can have the same 3 angles, but different size, then they are not congruent; an example of this is:

take the triangle rectangle of both cathetus = 1 and hypotenuse = √2, where the angles are 90°, 45° and 45°

and now take the triangle rectangle with both cathetus = 2 and hypotenuse = √8, this triangle also has the angles 90°, 45°, and 45°, so this two triangles succeed the AAA criteria, but are not congruent.

SSA (side-side-angle)

If two triangles satisfy the SSA  criteria and the corresponding angles are acute and the length of the side opposite to the angle is greater than the length of the adjacent side multiplied by the sine of the angle (but less than the length of the adjacent side), then the two triangles are not necessarily congruent.

This is kinda harder to illustrate;  

think on a triangle rectangle where you have the measure of both cathetus and one of the angles different from 90° as the SSA data.

and now think on another triangle that has the same adjacent cathetus and angle, and where the other cathetus is rotated (in a sense where 90° is decreasing) to the point where its tip intercepts the hypotenuse of the first triangle.

Those two triangles meet the SSA criteria but are not congruent.

7 0
3 years ago
Jim's monthly salary is $1,079.40. His monthly job hours are 140. What is his hourly rate of pay?
alex41 [277]

I'm guessing 7.71

Step-by-step explanation:

1,079.40/140

3 0
2 years ago
00:00
vaieri [72.5K]

Answer:

(D)What did Micah eat for lunch yesterday?

Step-by-step explanation:

A statistical question is a question for which the expected response varies. That is, we do not expect to get a single answer. Out of the given options,

Option D is not a valid statistical question as the response to the question will always be the same for a particular day,

If Micah ate cheesecakes for lunch yesterday, asking repeated times will not change the response.

6 0
3 years ago
The Scott family is trying to save as much money as possible. One way to cut back on the money they spend is by finding deals wh
avanturin [10]

Answer:

Unit price of strawberries at Grocery Mart is $ 1.495 or 150 pennies

Unit price of strawberries at Baldwin Hills Market is $ 1.33 or 133 pennies.

Step-by-step explanation:

1 dollar = 100 pennies

Given:

Cost of 2 pounds of strawberries at Grocery Mart = $ 2.99

Cost of 3 pounds of strawberries at Baldwin Hills Market = $3.99

∵ Cost of 2 pounds of strawberries at Grocery Mart = $ 2.99

∴ Cost of 1 pound of strawberries at Grocery Mart = \frac{2.99}{2}=\$1.495=1.495\times 100\approx 150\textrm{ pennies}

∵ Cost of 3 pounds of strawberries at Baldwin Hills Market = $3.99

Cost of 1 pound of strawberries at Baldwin Hills Market = \frac{3.99}{3}=\$1.33= 1.33\times 100 = 133\textrm{ pennies}

Therefore, the unit price of strawberries at each grocery store is the cost of 1 pound of strawberries. So, unit rate at Grocery Mart is 150 pennies and at Baldwin Hills Market is 133 pennies.

7 0
3 years ago
I need help. once again. bahahaha
katrin [286]

Answer:

letters d. and e.

5 0
3 years ago
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