For line l to intersect line m at point (2, 1/2), line m must have the point (2,1/2) on its graph. It is implied that line l already has the point (2, 1/2). If line m does not have it, then there will be no intersection at that specific point.
Try checking every choice to see if it has point (2,1/2) on the graph.
Note that (x,y) = (2,1/2); check by using x=2 and y=1/2.
For A,
2x = y/2
2(2) = (1/2) / 2
4 <span>≠ 1/4
</span>
Cannot be choice A as it results in a false equation; this choice will not go through (2,1/2)
For B:
2y = 3 - x
2(1/2) = 3 - 2
1 = 1
This is a true equation so the point (2,1/2) is on the graph of 2y=3-x. This means that if this is the equation for line m, then line m will have a point at (2,1/2) and therefore intersect with line l. Therefore, B is the answer.
The rest of the choices are false as shown:
For C:
2x + 4y = 8
2(2) + 4(1/2) = 8
4 + 2 = 8
6 ≠ 8
Cannot be choice C as it results in a false equation; this choice will not go through (2,1/2)
For D:
y = 4 - (5/4)x
1/2 = 4 - (5/4)(2)
1/2 = 4 - 5/2
1/2 = 8/2 - 5/2
1/2≠ 3/2
Cannot be choice D as it results in a false equation; this choice will not go through (2,1/2)
2P + 2 + 3P + 6 > 2
5P + 8 > 2
Subtract 8 from both sides.
5P > -6
Divide each side by 5.
P > -6/5
Answer:
-23.99048X + 310.7619
Step-by-step explanation:
Given the following :
Time(weeks) - - - mass(grams)
0 - - - - - - - - - - - - - 400
3 - - - - - - - - - - - - - 201
6 - - - - - - - - - - - - - 98
9 - - - - - - - - - - - - - 50
12 - - - - - - - - - - - - 24
15 - - - - - - - - - - - - 12
Using the regression calculator, the model for Mass(time), which best fits the data is represented by the equation:
ŷ = -23.99048X + 310.7619
Where, - 23.99044 is the slope or gradient
X is the time(t)
y is the Mass
310.7619 is the intercept. Point where the graph crosses the y-axis.
You would need two bottles, because 4 ounces is the same as 24 teaspoons, so if you buy two bottles for 30 teaspoons you will have 18 teaspoons left (3 ounces) I hope this helps!
If you mean just to simplify it, it's done like this: use the fact that tan is the same as sin/cos, and cot is the same as cos/sin. So when you make these substitutions, you have 2 * (sin/cos)*(cos/sin). The two sets of parenthesis cancel each other out (they equal 1), so the answer, or simplification, of that is 2.
