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3 years ago

In the diagram provided, line I is parallel to line m. Select which of the following statements could be used to prove that

Mathematics

1 answer:

atroni [7]3 years ago

8 0

<h3>Answer: There is only one answer and it is choice B</h3><h3>Angle 1 and angle 4 are alternate interior angles</h3>

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Explanation

A. This is false because it should be angle 4 + angle 5 = 180 without the angle 6. Adding on angle 6 results in some angle larger than 180. Note how angle 5 = (angle 3)+(angle 6).
B. This is true and useful to showing that the three angles of a triangle add to 180 degrees. This is because you'll use the fact that angles 4, 5 and 6 combine to 180 degrees.
C. While this is a true statement by the exterior angle theorem, it is not useful to the proof. It is better to state that angle 2 and angle 6 are congruent because they are alternate interior angles.
D. Like choice C, it is true but not useful. It's better to say that angle 1 is congruent to angle 4. See choice B above.

Note how it's not enough for a statement to be true. It also needs to be relevant or useful to the context at hand. A more simpler example of this could be stating that x+x = 2x.

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Which expression is equivalent to *picture attached*

DiKsa [7]

Answer:

The correct option is;

$4 \left (\dfrac{50 (50+1) (2\times 50+1)}{6} \right ) +3 \left (\dfrac{50(51) }{2} \right )$

Step-by-step explanation:

The given expression is presented as follows;

$\sum\limits _{n = 1}^{50}n\times \left (4\cdot n + 3 \right )$

Which can be expanded into the following form;

$\sum\limits _{n = 1}^{50} \left (4\cdot n^2 + 3 \cdot n\right ) = 4 \times \sum\limits _{n = 1}^{50} \left n^2 + 3 \times\sum\limits _{n = 1}^{50} n$

From which we have;

$\sum\limits _{k = 1}^{n} \left k^2 = \dfrac{n \times (n+1) \times(2n+1)}{6}$

$\sum\limits _{k = 1}^{n} \left k = \dfrac{n \times (n+1) }{2}$

Therefore, substituting the value of n = 50 we have;

$\sum\limits _{n = 1}^{50} \left k^2 = \dfrac{50 \times (50+1) \times(2\cdot 50+1)}{6}$

$\sum\limits _{k = 1}^{50} \left k = \dfrac{50 \times (50+1) }{2}$

Which gives;

$4 \times \sum\limits _{n = 1}^{50} \left n^2 = 4 \times \dfrac{n \times (n+1) \times(2n+1)}{6} = 4 \times \dfrac{50 \times (50+1) \times(2 \times 50+1)}{6}$

$3 \times\sum\limits _{n = 1}^{50} n = 3 \times \dfrac{n \times (n+1) }{2} = 3 \times \dfrac{50 \times (51) }{2}$

$\sum\limits _{n = 1}^{50}n\times \left (4\cdot n + 3 \right ) = 4 \times \dfrac{50 \times (50+1) \times(2\times 50+1)}{6} +3 \times \dfrac{50 \times (51) }{2}$

Therefore, we have;

$4 \left (\dfrac{50 (50+1) (2\times 50+1)}{6} \right ) +3 \left (\dfrac{50(51) }{2} \right )$ .

4 0

3 years ago

URGENT!!!! PLEASE!!!! HELP!!!!!

n200080 [17]

Answer:

Raul's claims are not correct

The equation of the graph is $y=\frac{10}{15}x$

Step-by-step explanation:

Part a)

we know that

The fact that the data form a straight line does not imply that it is a proportional relationship. In order for it to be a proportional relationship, in addition to the fact that a straight line must be formed, it must pass through the origin.

In this problem the graph shows a proportional relationship because the data forms a straight line and passes through the origin (0,0)

therefore

The claim that the graph shows a proportional relationship because the data forms a straight line is not correct

Part B)

<u>Find the slope of the straight line</u>

Let

$A(0,0),B(15,10)$

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

substitute the values

$m=\frac{10-0}{15-0}$

$m=\frac{10}{15}=0.67\frac{pages}{minute}$

therefore

The claim that he reads 1.5 pages per minute is not correct

Part C)

The equation of the graph is equal to

$y=\frac{10}{15}x$

7 0

4 years ago

Solve for all values of x by factoring. x^2-1=0

SashulF [63]

Answer:

x = 1

Step-by-step explanation:

The reason the answer is one because, 1^2 = 1

and 1 - 1 = 0

3 0

4 years ago

How to solve linear equations

Harman [31]

There are many methods to solve linear equations, such as:

1. Equating method: Let's take two simultaneous linear equations x+y=5 and x-y=1.

x+ y=5 can be written as x = 5-y.........(1)

In the same way,

x-y=1 or, x = 1+y.............(2)

Here, we equate the two equations and get the value of unknowns.

2. Substituting method: Again, take the equations x+y=5 and x-y=1.

x+y=5

or, x=5-y.........(1)

x-y=1............(2)

Substituting equation (1) in (2),

(5-y) - y=1

or, 5-2 y = 1

or, y = 2.

This is called substitution method.

3. Formula method: simultaneous linear equations can also be solved by formula.

If there are two equations: ax+by +c=0 and d x+e y+f=0 then the solution of such equation would be:

x = (bf - e c)/( a e - db), y = (a f-dc)/(db - a e).

For example,

2 x+ 3 y = 10 or, 2 x +3 y-10=0..................(1)

x+y=-44 or, x+y+44=0..................(2)

Comparing equation (1) and (2) with ax+by+c = 0 and dx+ey+f=0, a=2, b=3, c=-10, d =1, e=1, f=44.

Using formula,

x= -142 and y = 98.

4. Graphical method

5. Elimination method

6. Matrix method

8 0

4 years ago

What are the coordinates of point A?<br><br> (8, –6)<br> (–6, 8)<br> (–5, 7)<br> (7, –5)

Ratling [72]

Answer:

(7, - 5 )

Step-by-step explanation:

A is positioned at (7, - 5 )

5 0

3 years ago