<h3>Answer: Choice D</h3>
4x - 3y = 15
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Explanation:
The two points (-1,-1) and (2,3) are marked on the line
Let's find the slope of the line through those two points.
The slope is 4/3 meaning we go up 4 and to the right 3.
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Parallel lines have equal slopes, but different y intercepts. We'll need to see which of the four answer choices have a slope of 4/3.
Solve the equation in choice A for y. The goal is to get it into y = mx+b form so we can determine the slope m.
Equation A has a slope of -3/4 and not 4/3 like we want.
Therefore, this answer choice is crossed off the list.
Follow similar steps for choices B through D. I'll show the slopes of each so you can check your work.
- slope of equation B is 3/4
- slope of equation C is -4/3
- slope of equation D is 4/3
We have a match with equation D. Therefore, the equation 4x-3y = 15 is parallel to the given line shown in the graph.
You can use graphing tools like Desmos or GeoGebra to confirm the answer.
Answer:
1445.6 hours
Step-by-step explanation:
Distance between New York and San Francisco = 2902.8 miles (checked online)
Average speed of car = 2 mi/hr
Average speed of jet = 500 mi/hr
Time taken by Jet:
Time taken = Distance / speed
Time taken = 2902.8 / 500
Time taken = 5.8056 = 5.8 hours
Time taken by Car :
Time taken = Distance / speed
Time taken = 2902.8 / 2
Time taken = 5.8056 = 1451.4 hours
Time difference :
1451.4 - 5.8 = 1445.6 hours
None. ⅔ is greater than 1/6 but ⅔ equals 2 x (1/6).
Basically one half of ⅔ equals 1/6
Answer:
The two numbers following 1,-2,3,-4,5... are -6 and 7.
Step-by-step explanation:
index: 1 2 3 4 5 ....
value: 1 -2 3 -4 5
Let the index be n. Then the first term is a(1), the secon is a(2), and so on.
a(2) = 2*(-1)^(2-1) = 2*(-1) = -2 (correct)
a(3) = 3*(-1)^(3-1) = 3*(-1)^2 = 3 (correct)
a(4) = 4*(-1)^(4-1) = 4*(-1)^3 = -4 (correct)
So the general formula for a(n) is: a(n)=n(-1)^(n-1)
Thus,
a(5) = 5(-1)^4 = 5
a(6) = 6(-1)^5 = -6
a(7) = 7(-1)^6 = 7
The "next two numbers in the pattern" are -6 and 7. The first 7 numbers are
1,-2,3,-4,5, -6, 7
