9514 1404 393
Answer:
(a) 4/3
(b) y -3 = 4/3(x -1)
(c) y -3 = -3/4(x -1)
(d) r = 5
Step-by-step explanation:
a) The slope is given by the slope formula:
m = (y2 -y1)/(x2 -x1)
m = (7 -3)/(4 -1) = 4/3
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b) The radius is normal to the circle. The point-slope form of the equation for a line can be useful here:
y -k = m(x -h) . . . . . line with slope m through point (h, k)
For slope 4/3, the line through point (1, 3) will have the equation ...
y -3 = 4/3(x -1) . . . . point-slope equation of the normal
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c) The tangent is perpendicular to the radius. It will have a slope that is the opposite reciprocal of the slope of the radius: -1/(4/3) = -3/4.
y -3 = -3/4(x -1) . . . . point-slope equation of the tangent
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d) The radius can be found from the distance formula.
d = √((x2 -x1)² +(y2 -y1)²)
d = √((4 -1)² +(7 -3)²) = √(3² +4²) = √25 = 5
The radius of the circle is 5.
The boxes can weight at most 5 grams less than the desired amount, so they can't be lighter than
grams
Similary, they can't weight more than 5 grams more than the desired amount, so they can't be heavier than
grams
So, the acceptable range is between 208 and 218.
1. 300 T-shirt in 10 Minutes, thus: 300/10=30 T-shirts per minute.
3. 2 Liters in 10 seconds, thus: 2/10 = 0.2 Liters or 2 deciliters each second
4. Bill is paid $200 for 5 days, thus, $200/5 = $40 per day.
Answer:
um 2x=45 because it is alternate interior
Step-by-step explanation:
2x=45
divide both by 2
x=22.5
Answer: x = 6
<u>Step-by-step explanation:</u>
<em>multiplied by common denominator</em>
18 + 2x = 5x
<u> -2x</u> <u>-2x</u>
18 = 3x
<u>÷3 </u> <u>÷3 </u>
6 = x
Since "x" is in the denominator, the restriction is that x ≠ 0. If the solution was x = 0, then the solution would not be valid and would be eliminated as an answer.
Remember that "x" is just an unknown value. It is possible to add two fractions together and have their sum be a fraction.
For example: 
could be written as 
. When we solve it, we will get x = 5.
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Answer: Edward
<u>Step-by-step explanation:</u>
The denominator cannot equal zero, so:
- x + 1 ≠ 0 → x ≠ -1
- x - 2 ≠ 0 → x ≠ 2
- x - 4 ≠ 0 → x ≠ 4
Those x-values are the asymptotes, which is where the function is undefined.
