Use the figure below to answer questions 10-11.

Mathematics

1 answer:

Anton [14]4 years ago

5 0

The two marked angles are complementary angles. This means that the angles are equal.

Hence, X + 1 = 2X - 3.

By rearranging, X = 4.

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Find the student’s error in solving the following inequality.

Mars2501 [29]

Answer:

The correct option is:

The student should have switched the direction of the inequality sign to get –5> x for a final answer

Step-by-step explanation:

The students has made a mistake in the 3rd step.

We know that when we multiply or divide any negative number on both sides of the inequality, the sign of inequality reverse its direction.

In step 3 the student divided 25 by -5 but did not switch direction of the inequality sign.

Therefore the correct option is: The student should have switched the direction of the inequality sign to get –5> x for a final answer

5 0

3 years ago

The following statement is either true (in all cases) or false (for at least one example). If false, construct a specific e

matrenka [14]

Answer:

False, counterexample below

Step-by-step explanation:

Denote the unit vectors of R^3 by $e_1=(1,0,0), e_2=(0,1,0), e_3=(0,0,1)$ . Now consider $v_1=e_1, v_2=2e_1$ and $v_3=e_3$ . We have that $v_1, v_2,v_3 \in \mathbb{R}^3$ . Also, the vector $v_3$ is not a linear combination of $v_1, v_2$ because any linear combination of these two vectors will have third coordinate zero, but v_3 has third coordinate 1 so they can't be equal.

However, the set $\{v_1, v_2,v_3\}$ is not linearly independent, because $2v_1-v_2+0v_3=0$ is a non-trivial linear combination of these vectors that equals zero.