Answer: (-3,5)
Step-by-Step Solution:
1. Set 1 equation equal to y
3y-2x=21
3y=2x+21
y=2/3x+7
2. Set the other equation equal to y
4y+5x=5
4y=-5x+5
y=-5/4x+5/4
3. Set the equations equal to each other, and solve for x
2/3x+7=-5/4x+5/4
2/3x+23/4=-5/4x
(Multiply by 12 on both sides to get rid of fractions)
8x+69=-15x
8x=-15x-69
23x=-69
x=-3
4. Solve for y
(Choose any of the equations)
y=2/3x+7
y=2/3(-3)+7
y=-2+7
y=5
ANSWER: (-3,5)
Answer:
20
Step-by-step explanation:
Use the distance equation to find the length of each side:
d = √((x₂ − x₁)² + (y₂ − y₁)²)
where (x₁, y₁) and (x₂, y₂) are the points (the order doesn't matter).
AB:
d = √((-2 − (-2))² + (-2 − 4)²)
d = 6
BC:
d = √((4 − (-2))² + (-2 − (-2))²)
d = 6
AC:
d = √((-2 − 4)² + (4 − (-2))²)
d = 6√2
So the perimeter is:
AB + BC + AC
6 + 6 + 6√2
≈ 20
4) You know slope-intercept form is y=mx+b. So using these two given points, you can find the slope!
(-8,5) (-3,10) [Use the y1-y2 over x1-x2 formula to solve for slope]
10 - 5 5
--------- = ----- = 1
-3-(-8) 5
Hurray! You got a slope of one. Now substitute this back into your original equation:
y=mx+b --> y=1x+b
Next, we find what our "b" is, or what our y-intercept is:
Using one of the previous points given, substitute them into the new equation:
[I used the point (-3, 10) ]
y=1x+b
10=1(-3)+b SUBSTITUTE
10=-3+b MULTIPLY
10=-3+b
+3 +3 ADD
----------
13=b SIMPLIFY
So, now we have our y-intercept. Use this and plug it into the equation:
y=1x+b --> y=1x+13
y=1x+13 is our final answer.
5) So for perpendicular lines, your slope will be the opposite reciprocal of the original slope. (Ex: Slope is 2, but perpendicular slope is -1/2)
We have the equation y= 3x-1, so find the reciprocal slope!
--> y=-1/3x-1
Good! Now we take our given point, (9, -4) and plug it into the new equation:
y=-1/3x-1
-4=-1/3(9)+b SUBSTITUTE and revert "-1" to "b", for we are trying to find the y- -4=-3+b intercept of our perpendicular equation.
+3 +3 ADD
--------
-1=b SIMPLIFY
So, our final answer is y=-1/3x+(-1)
6) I don't know, sorry! :(
Density = mass / volume
volume of 1 can = 12 * 40 = 480 cm^3
1.1 = mass / 480
mass = 528 grams Answer
