Answer:
5 units
Step-by-step explanation:
3x + 4y = 8
4y = -3x+8
y = -3/4+2
The shortest distance between a point and a line is the perpendicular line.
Slope of the perpendicular line: 4/3 and point (-3,-2)
b = -2-(4/3)(-3) = 2
Equation of the perpendicular line: y=4/3x+2
y is equal y
4/3x+2= -3/4x+2
4/3x +3/4x = 2-2
x = 0
Plug x=0 into one of the equations to find y
y = 4/3(0) + 2
y = 2
(0,2) and (-3,-2)
Distance = sqrt [(-3-0)^2 + (-2-2)^2]
Sqrt (-3)^2+ (-4)^2
Sqrt 25 = 5
Answer:
0.3
Step-by-step explanation:
The margin of error is calculated as ...
(standard deviation)/√(sample size) × (z*-score)
where the z*-score is chosen based on the desired confidence level.
Here, you have ...
- standard deviation = 2.7
- √(sample size) = √225 = 15
- z*-score for 90% confidence level = 1.645
Putting these values in the above expression for margin of error gives ...
2.7/15·1.645 = 0.2961 ≈ 0.3
Setup 2 problems
2x - 7 < 15 and 2x - 7 > -15
2x < 22 2x > -8
x < 11 x > -4
Or you can write it -4 < x < 11
<h3><u>The first number, x, is equal to 7.</u></h3><h3><u>The second number, y, is equal to 2.</u></h3>
x + 2y = 11
2x + y = 16
We can subtract 2y from both sides of the first equation to get a value for x.
x = 11 - 2y
Because we have a value for x, we can plug it into the second equation.
2(11 - 2y) + y = 16
Distributive property.
22 - 4y + y = 16
Combine like terms.
22 - 3y = 16
Subtract 22 from both sides.
-3y = -6
Divide both sides by -3.
y = 2
Now that we have a value for y, we can plug it into either equation to solve for x.
x + 2(2) = 11
x + 4 = 11
Subtract 4 from both sides.
x = 7