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Rus_ich [418]
3 years ago
15

At what point is the following function continuous?

Mathematics
1 answer:
liubo4ka [24]3 years ago
4 0

Check the picture below.

something worth noticing           \bf \cfrac{x^2-x-6}{x-3}\implies \cfrac{(\underline{x-3})(x+2)}{\underline{x-3}}\implies x+2

so, we're really graphing x+2, with a hole at x = 3, however, when x = 3, we know that f(x) = 5, but but but, when x = 3, x+2 = 5, so we end up with a continuous line all the way, x ∈ ℝ, because the "hole" from the first subfunction, gets closed off by the second subfunction in the piece-wise.

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Unknown angle problems (with algebra)
lubasha [3.4K]
Answer: x = 20 degree
3x = 3×20 which is 60 degree
And the other one is 100 degree
Add all the number 100+60+20 degree is 180 degree
7 0
3 years ago
What is the result of subtracting the second equation from the first?
gtnhenbr [62]
This is the answer with explanation

4 0
2 years ago
A group of friends wants to go to the amusement park. They have $116 to spend on parking and admission. Parking is $10.25, and t
Alexus [3.1K]

Answer:

2 people

Step-by-step explanation:

no. of people = x

total parking costs = 10.25x

total tickets cost = 35.25x

total = 10.25x + 35.25x

suppose 3 people go, then the total cost will be

10.25(3) + 35.25(3) = 136.5 and this is greater than 116

Suppose 2 people go then the cost will be

10.25(2) + 35.25(2) = 91 which is less than 116

so only 2 people can go.

7 0
1 year ago
To two decimal places, find the value of k that will make the function f(x) continuous everywhere. f of x equals the quantity 3x
Fiesta28 [93]

Given function is

f(x)=\left\{\begin{matrix}3x+k & x\leq -4 \\ kx^2-5 & x> -4\end{matrix}\right.

now we need to find the value of k such that function f(x) continuous everywhere.

We know that any function f(x) is continuous at point x=a if left hand limit and right hand limits at the point x=a are equal.

So we just need to find both left and right hand limits then set equal to each other to find the value of k

To find the left hand limit (LHD) we plug x=-4 into 3x+k

so LHD= 3(-4)+k

To find the Right hand limit (RHD) we plug x=-4 into

kx^2-5

so RHD= k(-4)^2-5

Now set both equal

k(-4)^2-5=3(-4)+k

16k-5=-12+k

16k-k=-12+5

15k=-7

k=-\frac{7}{15}

k=-0.47

<u>Hence final answer is -0.47.</u>




7 0
3 years ago
De un grupo de 60 personas, la tercera parte finalizó la escuela primaria solamente, y las ⅖ partes completaron la secundaria. E
notka56 [123]

Answer:

36 personas

Step-by-step explanation:

las 2/5 partes q completaron secundaria tambien finalizaron primaria

con lo cual el tercio que estudio primaria esta dentro del grupo de personas que estudiaron

60*2/5 = 24  

24 personas estudiaron

60-24=36

4 0
3 years ago
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