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bezimeni [28]
3 years ago
11

Which undefined term can contain parallel lines?

Mathematics
1 answer:
White raven [17]3 years ago
7 0
Coplanor lines that never intersect 
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Let g' be the group of real matricies of the form [1 x 0 1]. Is the map that sends x to this matrix an isomorphism?
aliina [53]

Yes. Conceptually, all the matrices in the group have the same structure, except for the variable component x. So, each matrix is identified by its top-right coefficient, since the other three entries remain constant.

However, let's prove in a more formal way that

\phi:\ \mathbb{R} \to G,\quad \phi(x) = \left[\begin{array}{cc}1&x\\0&1\end{array}\right]

is an isomorphism.

First of all, it is injective: suppose x \neq y. Then, you trivially have \phi(x) \neq \phi(y), because they are two different matrices:

\phi(x) = \left[\begin{array}{cc}1&x\\0&1\end{array}\right],\quad \phi(y) = \left[\begin{array}{cc}1&y\\0&1\end{array}\right]

Secondly, it is trivially surjective: the matrix

\phi(x) = \left[\begin{array}{cc}1&x\\0&1\end{array}\right]

is clearly the image of the real number x.

Finally, \phi and its inverse are both homomorphisms: if we consider the usual product between matrices to be the operation for the group G and the real numbers to be an additive group, we have

\phi (x+y) = \left[\begin{array}{cc}1&x+y\\0&1\end{array}\right] = \left[\begin{array}{cc}1&x\\0&1\end{array}\right] \cdot \left[\begin{array}{cc}1&y\\0&1\end{array}\right] = \phi(x) \cdot \phi(y)

8 0
3 years ago
16. Find the measures of ∠1 and ∠2 in the kite at right. (That rhymed!)
nikdorinn [45]
<2 = 90 - 67 = 23
<1 = 90

5 0
3 years ago
2 1 point
mafiozo [28]

Answer:

  • The graph has a minimum.
  • The graph has a y-intercept at (0, -3).
  • The solutions ... are -1 and 3.
  • The vertex is located at (1, -4).
  • In the equation, 'a' would be positive.

Step-by-step explanation:

When the graph has a low point, it has a minimum. 'a' is positive in that case. The coordinates of that low point are (1, -4). That point is the vertex.

The graph crosses the y-axis at y = -3, so the y-intercept is (0, -3).

The graph crosses the x-axis at (-1, 0) and (3, 0). These points represent the solution to the equation y = 0.

  • The graph has a minimum.
  • The graph has a y-intercept at (0, -3).
  • The solutions ... are -1 and 3.
  • The vertex is located at (1, -4).
  • In the equation, 'a' would be positive.
5 0
3 years ago
A survey is being planned to determine the mean amount of time corporation executives watch television. a pilot survey indicated
Natali [406]
Missing question: How many executives should be surveyed?

Solution:
Mean = 13 hours
SD = 3 hours
Confidence level = 95%

Mean viewing time within a quarter of an hour = 0.25 = 1.96*3/sqrt (N)

Where N = Sample population

N = {(1.96*3)/0.25}^2 = 553.19 ≈ 554

Therefore, 554 executives should be surveyed to yield such results.
5 0
3 years ago
Tom went to the supermarket and could not spend more than $30.00. He spent $9 on dairy
valina [46]

Answer:

it will be c

Step-by-step explanation:

6 0
3 years ago
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