Which of the graphed systems share the same solution set?

Mathematics

2 answers:

Darya [45]4 years ago

4 0

Answer:

The correct option is 1.

Step-by-step explanation:

In figure 1, both the lines are coincident. It means all the points lie on the line are solutions of the system.

It means the system has many solutions and the systems share the same solution set.

In figure 2, both the line are parallel and two parallel lines never intersect each other. If the system of equations represent two parallel line, then the system of equal has no solution.

Therefore the second system represent no solution.

In figure 3, both the line intersect each other at one point. It means the system of equations has no solution.

Therefore the third system represent one solution.

Therefore the correct option is 1.

TEA [102]4 years ago

3 0

It is the graph where the two lines intersect, when they intersect there is a point where they connect, and that is your answer

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Scalcet8 4. 2. 26. suppose that 2 ≤ f '(x) ≤ 4 for all values of x. what are the minimum and maximum possible values of f(4) − f

ziro4ka [17]

The minimum value of f(4) - f(1) is 6.

The maximum value of f(4) - f(1) is 12.

In the question, we are given that, 2 ≤ f'(x) ≤ 4 for all values of x.

Taking the given inequality as (i).

We are asked to find the minimum and maximum possible values of f(4) - f(1).

We multiply (i) by dx throughout, to get:

4dx ≤ f'(x)dx ≤ 5dx.

To find this, we integrate (i) in the definite interval [4, 1] with respect to dx, to get:

$\int_{1}^{4}2dx \leq \int_{1}^{4}f'(x)dx \leq \int_{1}^{4}4dx\\\Rightarrow [2x]_{1}^{4} \leq [f(x)]_{1}^{4} \leq [4x]_{1}^{4}\\\Rightarrow 2*4 - 2*1 \leq f(4)-f(1) \leq 4*4 - 4*1\\\Rightarrow 6 \leq f(4) -f(1) \leq 12$