Answer:
Have them solve mathematical problems and those with the top two scores can go
Step-by-step explanation:
Fair game
x-intercept = 4, y-intercept = - 3
to find the intercepts, that is where the graph crosses the axes
let x = 0, in the equation for y- intercept
let y = 0, in the equation for x- intercept
x = 0 : - 4y = 12 ⇒ y = - 3 ⇒ (0, - 3) ← y - intercept
y = 0 : 3x = 12 ⇒ x = 4 ⇒ (4, 0 ) ← x- intercept
<h3>
Answer: SSS Postulate</h3>
The tickmarks tell us which pairs of sides are the same length.
- AB = BC due to the single tickmarks
- AD = CD due to the double tickmarks
So far we have two pairs of congruent sides.
The third pair of congruent sides are the overlapping or shared sides BD = BD which is true by the reflexive property (anything is congruent to itself).
Overall we have three pairs of congruent sides allowing us to use SSS. Each "S" stands for "Side".
Step One
Add the first and third
-2x + 2y + 3z = 0
<u>2x + 3y + 3z = 5</u>
5y + 6z = 5
Step Two
Add the second and third together.
- 2x - y + z = -3
<u>2x + 3y + 3z = 5</u>
2y + 4z = 2 Divide this result by 2
y + 2z = 1 multiply this result by 5
5y + 10z = 5
Step three
Subtract the result of step 2 from the result of step one
5y + 10z = 5
<u>5y + 6z = 5 </u> Subtract
4z = 0
z = 0
Step Four
Solve for y
5y + 6z = 5 But z = 0
5y = 5
y = 1
Step Four
Solve for x . Use equation 3 in the givens.
2x + 3y + 3z = 5
2x + 3*1) + 3*0 = 5
2x = 5 - 3
2x = 2
x = 1
Answer
x = 1
y = 1
z =0 This has been checked and found to be correct.
Problem 2
Substitution is not the best way to do this. Divide the last equation by 2 and add it to the first one.
Step One
divide equation 3 by 2.
x + z = 2
Step Two
Add step one to equation 1
-x - y - z = - 8
<u>x + z = 2</u>
- y = - 6
y = 6
Step Three
Put this result into equation 1.
-x - 6 - z = - 8
-x - z = - 2
x + z = 2 Multiply this equation by 4
4x + 4z = 8
Step four
Put y = 7 into the second equation.
-4x + 4y + 5z = 7
-4x + 4*6 + 5z = 7
-4x + 24 + 5z = 7
-4x +5z = -17
Step 5
Add the results from Step 3 and Step 4 together.
-4x + 5z = - 17
4x + 4z = 8
9z = - 9
z = - 1
Step 6
Find x
-x - y - z = - 8
-x -6 + 1 =- 8
-x - 5 = - 8
-x = - 3
x = 3
Answers
x = 3
y = 6
z = -1 verified to be correct.