I assume the first equation is supposed to be
and not
As an augmented matrix, this system is given by
Multiply through row 3 by 1/2:
Add -1(row 2) to row 3:
Multiply through row 3 by 1/5:
Add -2(row 3) to row 1, and add 3(row 3) to row 2:
Add -3(row 2) to row 1:
Multiply through row 1 by -1:
Add -2(row 1) to row 2:
Multipy through row 2 by -1:
The solution to the system is then
Answer:
<h3>Q1</h3>
<u>Use slope formula</u>
- m = (y2 - y1)/(x2 - x1)
- m = (-2 - 6)/(3 - 7) = -8 / -4 = 2
- m = 2
<h3>Q2</h3>
Angles 2 and 6 are on the corresponding sides of the parallel lines, hence are corresponding angle
<u>Correct option is </u>
<h3>Q3</h3>
Congruent triangles have congruent corresponding parts
- ΔABC ≅ Δ GHI
- AB≅GH
- AB = GH = 13
<u>Correct choice is</u>
<h3>Q4</h3>
Option b is correct for any line and doesn't make the lines parallel. The rest of the options are correct for parallel lines.
<u>Correct option is the last one:</u>
The reason so many objects orbit the Sun in nearly the same plane (called the ecliptic) and in the same direction is that they all formed from this same disk.
While the planets were forming, there was not much peace in our solar system. Clumps of matter of all sizes often collided, and either stuck together or side-swiped each other, knocking off pieces and sending each other spinning. Sometimes the gravity of big objects would capture smaller ones in orbit. This could be one way the planets acquired their moons.
The correlation coefficient between two variables, r, is always going to be between -1 and 1.
- If the correlation coefficient is 0, means that there is no strong correlation relationship in one direction or the other direction.
- If the correlation coefficient is -1, means that these two variables move in opposite directions.
- If the correlation coefficient is 1, means that these two variables move in the same direction.