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3 years ago

Find the equation in standard form of the line passing through the points (2,-3) and (4,2)

Mathematics

1 answer:

Sonja [21]3 years ago

5 0

The equation of the line passing through the points $(x_1,y_1)$ and $(x_2,y_2)$ is

$\frac{x-x_1}{y-y_1} =\frac{x_2-x_1}{y_2-y_1}$ . Here $\frac{y_1-y_1}{x_2-x_1}$ is the slope of the line.

Substituting numerical values,

$\frac{x-2}{y+3} =\frac{4-2}{2+3} \\ \frac{x-2}{y+3} =\frac{2}{5} \\ 5x-10=2y+6\\ 5x-2y-16=0$

The equation of the line in standard form is $5x-2y-16=0$ .

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Let E = {(x, y) e R2|xy > 0}. Determine whether E is a subspace of R2 . X3

gayaneshka [121]

Answer:

E is not a subspace of $\mathbb{R}^2$

Step-by-step explanation:

E is not a subspace of $\mathbb{R}^2$

In order to see this, we must find two points (a,b), (c,d) in E such that (a,b) + (c,d) is not in E.

Consider

(a,b) = (1,1)

(c,d) = (-1,-1)

It is easy to see that both (a,b) and (c,d) are in E since 1*1>0 and (1-)*(-1)>0.

But (a,b) + (c,d) = (1-1, 1-1) = (0,0)

and (0,0) is not in E.

By the way, it can be proved that in any vector space all sub spaces must have the vector zero.

5 0

3 years ago

Find the midpoint of the segment with the given endpoints. <br> 4 and 11<br>

brilliants [131]

Hey there!!

How do we find the midpoint?

We take the average , the average is =

Sum of the observations / total number of observations

The end points are given as 4 and 11

Sum = 11 + 4

Number of observations = 2

= 15 / 2

= 7.5 is the midpoint

4 0

3 years ago

Read 2 more answers

Mr.Brown has a gate that measures 65 ft by 72 ft. He needs to reinforce the gate by placing a strip of wood on the diagonal of t

Daniel [21]

Answer: 97ft

Step-by-step explanation:

Pythagore

Strip^2 = 65^2 + 72^2 = 9409

Strip = squareroot 9409 = 97 ft

7 0

3 years ago

The figure shows a circle with center P and inscribed isosceles Triangle ABC. If AC has the same length as the radius of the cir

Ksenya-84 [330]

Answer:

<ABC = $30^{0}$ (The central angle of a circle is twice any inscribed angle subtended by the same arc).

Step-by-step explanation:

From the diagram, ABC is an inscribed isosceles triangle. But the radius of the circle equals the length AC.

Join P to A and C to form an equilateral triangle. An equilateral triangle has equal sides and angles. So, the value of each interior angle of the equilateral triangle is;

Sum of angle in a triangle = $180^{0}$

So that each interior angle = $\frac{180^{0} }{3}$

= $60^{0}$

The value of each interior angle of the triangle is $60^{0}$ . Thus, <APC = $60^{0}$ .

⇒ <ABC = $30^{0}$ (The central angle of a circle is twice any inscribed angle subtended by the same arc.)

7 0

3 years ago

The following figure is a rhombus. Find the value of m. Then, use that value to find the measure of VW

maxonik [38]

Answer:

$m=8$

The length of VW = 36 units.

Step-by-step explanation:

We know that a rhombus is a quadrilateral with four sides. All four sides have the same length.

From the diagram, it is clear that

The length of VW= 6m-12

The length of WX = 4m+4

As all the four sides of the rhombus have equal length.

So we can observe

$VW=WX$

$6m-12 = 4m+4$

Add 12 to both sides

$6m-12+12=4m+4+12$

$6m=4m+16$

$2m=16$

Divide both sides by 2

$\frac{2m}{2}=\frac{16}{2}$

$m=8$

The length of VW= 6m-12

= 6(8)-12 ∵ $m=8$

= 48-12

= 36

Thereofore, the length of VW = 36 units.

3 0

2 years ago