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Vinil7 [7]
3 years ago
9

On a number line: What does a closed circle mean and what does an open circle mean?

Mathematics
1 answer:
MArishka [77]3 years ago
4 0
A closed circle means greater than or equal to and less than or equal to.
An open circle is greater than or less than.
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On what interval is the functioning decreasing m(x)=4x^3-5x^2-7x?
Verdich [7]
M(x) = 4x^3 - 5x^2 - 7x
Let us first find the zeros of the function.
That is when it is equal to zero.

m(x) = 4x^3 - 5x^2 - 7x  = 0
x(4x^2 - 5x - 7) = 0.  Therefore x = 0 or 4x^2 - 5x - 7 = 0.
Using a quadratic function calculator to solve 4x^2 - 5x - 7
x = 2.09, -0.84
Therefore the zeros are x =-0.84, 0, 2.09 for the function m(x).

The intervals observed are imagining  that the zeros are on the number line:
x<-0.84,    -0.84<x<0,  0<x<2.09,  x>2.09.

For each of this range we would test the function with a number that falls in the range.

The function is decreasing in the interval where it is less than 0.
For x<-0.84, let us test x = -1, m(x) = 4x^3 - 5x^2 - 7x = 4(-1)^3 - 5(-1)^2 - 7(-1) = -4 -5 +7 = -2,    -2 < 0, so it is decreasing here.

For  -0.84<x<0, let us test x = -0.5, m(x) = 4x^3 - 5x^2 - 7x = 4(-0.5)^3 - 5(-0.5)^2 - 7(-0.5) = -0.5 -1.25 +3.5 = 1.75,  1.75 >0. It is not decreasing.


For  0<x<2.09, let us test x = 1, m(x) = 4x^3 - 5x^2 - 7x = 4(1)^3 - 5(1)^2 - 7(1) = 4 -5 -7 = -8,  -8 <0. It is decreasing.

For  x>2.09, let us test x = 3, m(x) = 4x^3 - 5x^2 - 7x = 4(3)^3 - 5(3)^2 - 7(3) = 108 -45 -21 = 42,  42 >0. It is not decreasing.

So the function is decreasing in the intervals:

x < -0.84,  & 0<x<2.09.

4 0
3 years ago
PLEASE HELP WILL GIVE BRAINLIST.<br> What is the slope of the line in the graph?
inn [45]

Answer:

x-1

Step-by-step explanation:

4 0
3 years ago
PLEASE HELP !!!!! 2 - 19 = 2?<br> BTW BTS OUTSOLD AND PAVED THE WAY !!!!!!!!!!
Ede4ka [16]

Answer:

its not true the answer is -17 i dont know if thats what your looking for

Step-by-step explanation:

5 0
2 years ago
Read 2 more answers
Verify the pythagorean identity 1 + c o t ^2 θ = c s c ^2 θ
Grace [21]

Answer: The identity is verified. See the explanation.

Step-by-step explanation:

You must keep on mind the following identities:

csc\theta=\frac{cos\theta}{sin\theta}\\\\csc\theta=\frac{1}{sin\theta}\\\\sin^2\theta+cos^2\theta=1

Therefore, by substitution, you can rewrite the identity as shown below:

1+cot^2\theta=csc^2\theta\\\\1+\frac{cos^2\theta}{sin^2\theta}=csc^2\theta

Simpliying, you obtain:

\frac{sin^2\theta+cos^2\theta}{sin^2\theta}=csc^2\theta\\\\\frac{1}{sin^2\theta}=csc^2\theta\\\\csc^2\theta=csc^2\theta

The identity is verified.

6 0
3 years ago
Jonas wants to serve serve 48 people one cup of tea each. How many gallons of tea must he prepare?
Aleks04 [339]

Answer:

3 gallons

Step-by-step explanation:

1 gallon=16 cups

48÷16=3

3 gallons makes 48 cups

6 0
3 years ago
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