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3 years ago

Write equations for three lines that intersect to form a triangle

1 answer:

7 0

1.
Any 3 lines a, b and c intersect and form triangles, in no 2 of them are parallel.

2.

2 lines are parallel only if their slopes are equal.

3.

if the equation of a line l is given in the form y=mx+t, then m, the coefficient of x, is the slope of that line.

4.

so given lines a, b, c with equations:

$a: y=m_1x+t\\\\b: y=m_2x+u\\\\c: y=m_3x+v$

if $m_1 \neq m_2 \neq m_3$ , then the lines intersect, forming thus a triangle.

5.

let the 3 lines be:

$a: y=2x+5\\\\b: y=-4x+13\\\\c: y=x+7$

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How do you write this in standard form? (6-7i)/(1-2i)

xenn [34]

$\frac { \left( 6-7i \right) }{ \left( 1-2i \right) } \cdot 1\\ \\ =\frac { \left( 6-7i \right) }{ \left( 1-2i \right) } \cdot \frac { \left( 1+2i \right) }{ \left( 1+2i \right) } \\ \\ =\frac { 6+12i-7i-14{ i }^{ 2 } }{ 1+2i-2i-4{ i }^{ 2 } }$

$\\ \\ =\frac { 6+5i-14\left( -1 \right) }{ 1-4\left( -1 \right) } \\ \\ =\frac { 6+5i+14 }{ 1+4 } \\ \\ =\frac { 20+5i }{ 5 } \\ \\ =\frac { 20 }{ 5 } +\frac { 5i }{ 5 } \\ \\ =4+i$

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3 years ago

What happens to the particles in iodine when you increase

Tju [1.3M]

Answer:

When you have iodine gas at 200 degrees, the temperature and thus pressure as so high, that when cooling down you enter the liquid phase. And when some of this gas then condenses, the pressure drops. So the remaining part of the gas can sublime.

Step-by-step explanation:

5 0

3 years ago

2. What is the slope passing through the points (2, -1) and (-4, 11)

algol [13]

Answer:

I believe it is y equals 3 minus 2x.

4 0

3 years ago

(X to the fourth power) squared equals

Viktor [21]

Answer:

$(x^4)^2=x^8$

Step-by-step explanation:

Because of the power of a power property, which states that $(x^n)^m=x^{n\times{m}}$ , where m and n are real numbers, the expression you mentioned can be simplified by applying this property like this: $(x^4)^2=x^{4\times2}=x^8$

4 0

3 years ago

Can someone please help!!!

RideAnS [48]

Answers:

System 1: x = 3 and y = -5
System 2: x = 1 and y = 2

==========================================================

Explanation:

For now, let's focus on system 1.

We have identical copies of "2y" in each equation, which means that if we were to subtract the equations straight down, then the y terms cancel out. That allows us to solve for x.

The x terms subtract to 7x-x = 6x
The y terms subtract to 0 and go away
The right hand sides subtract to 11 minus (-7) = 11-(-7) = 11+7 = 18

After doing those subtractions, we have the new equation 6x = 18 which solves to x = 3. Divide both sides by 6 to isolate x.

Once we know x, we can find out y.

7x+2y = 11

7(3)+2y = 11

21+2y = 11

2y = 11-21

2y = -10

y = -10/2

y = -5

or we can say

x+2y = -7

3+2y = -7

2y = -7-3

2y = -10

y = -10/2

y = -5

We should lead to the same y value either way. This helps confirm we have the correct x value.

Overall, the solution to system 1 is (x,y) = (3, -5)

----------------------------

Now onto system 2.

Unfortunately, we don't have identical y terms this time. But what we can do is double everything in the second equation to go from -x+y = 1 to -2x+2y = 2.

The new equivalent system is

$\begin{cases}7x+2y = 11\\-2x+2y = 2\end{cases}$

Now we have the same situation as before: Subtract straight down, solve for x.

The x terms subtract to 7x-(-2x) = 7x+2x = 9x
The y terms go away when subtracting
The right hand sides subtract to 11-2 = 9

So we have 9x = 9 and that solves to x = 1.

We'll use this x to find the y value.

7x+2y = 11

7(1)+2y = 11

7+2y = 11

2y = 11-7

2y = 4

y = 4/2

y = 2

Or you could pick on the second equation

-x+y = 1

-1+y = 1

y = 1+1

y = 2

6 0

2 years ago