Mathematics: Write an equation from the given table that shows the relationship of y and x. Your answer should be in the form y = _ x-1012345 y1680-8-16-24-32

Write an equation from the given table that shows, №9557793, 05.04.2022 16:59

Mathematics

1.consider the average speed of a runner who jogs around a track four times. the distance (400m) remains constant for each lap. however, each lap is run 5 seconds slower than the first. the time for each lap increases. the average speed for each lap this is an example of a(n) relationship. a) increases, direct b) decreases, direct c) increases, inverse d) decreases, inverse larry and balky set up an experiment to analyze the motion of a marble as it rolled down an incline. they started the marble at the top of the ramp and set up photogates to

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1. D) decreases, inverse

The average speed for each lap is given by:

$v=\frac{S}{t}$

where S is the length of the lap (400 m) while t is the time taken to complete the lap. Since the time t increases at each lap, we see from the formula that v, the speed, decreases at each lap. This is an example of inverse relationship: when one of the two quantities increases (the time), the other one decreases (the speed).

2. A) Velocity on the y-axis, time on the x-axis

Acceleration is defined as the change in velocity divided by the time taken:

$a=\frac{\Delta v}{\Delta t}$

In a graph, the slope of a line is given by the increment in y divided by the increment in x:

$s=\frac{\Delta y}{\Delta x}$

Therefore, if we put velocity on the y-axis and time on the x-axis, we immediately see that the acceleration corresponds to the slope of the curve.

3. D)velocity

In fact, velocity consists of 1) speed and 2) direction. The speed can be calculated as:

$v=\frac{S}{t}$

where S is the distance covered and t the time taken. So, by knowing these two quantities, Tim can calculate the speed of the trip. Tim also knows the direction of motion, so he can determine the velocity of the trip.

4. B)equal, different

The difference between speed and velocity is simple: speed is a scalar, and it is just the magnitude of the velocity, so "how fast" is the object moving, while velocity takes also into account the direction of motion, so it is a vector.

Therefore: the two cars have same speed (25 m/s), but they have different velocities, since they are moving into different directions (car A is moving from NY to Miami, while car B is moving from NY to Chicago).

28. B) 11 m

The distance travelled by the bag in free fall is given by:

$S=\frac{1}{2}at^2$

where a=9.8 m/s^2 is the acceleration of gravity and t=1.5 s is the time. Replacing these numbers into the formula, we find

$S=\frac{1}{2}(9.8 m/s^2)(1.5 s)^2 =11 m$

29. B)10 m/s south

The boat is moving 20 m/s south, relative to the ground. The passenger is moving 10 m/s north, relative to the boat. Considering south as positive direction, the passenger's velocity relative to the ground is

v' = v_b + v_p = 20 m/s + (-10 m/s) = 10 m/s

and the positive sign means it is due south.

30. B)direction

In fact, velocity is a vector, so it consists of a magnitude (the speed) and a direction. The speed can be determined by the distance and the time, in fact speed is defined as

$v=\frac{d}{t}$

where d=distance and t=time; however, in order to determine velocity, we also need to know the direction of motion.

33. B)a velocity.

In fact, velocity is a vector, and it consists of a magnitude (the speed) and a direction. In this case, 10 m/s is the speed, while north is the direction.

34. C)Does the measurement include direction?

As stated in the previous question, a vector includes both magnitude and direction, while a scalar includes only a magnitude. Therefore, by asking if the measurement includes a direction, we are able to determine if the quantity is a vector or not.

Mathematics

1.consider the average speed of a runner who jogs around a track four times. the distance (400m) remains constant for each lap. however, each lap is run 5 seconds slower than the first. the time for each lap increases. the average speed for each lap this is an example of a(n) relationship. a) increases, direct b) decreases, direct c) increases, inverse d) decreases, inverse larry and balky set up an experiment to analyze the motion of a marble as it rolled down an incline. they started the marble at the top of the ramp and set up photogates to

Step-by-step answer

P Answered by PhD

3

1. D) decreases, inverse

The average speed for each lap is given by:

$v=\frac{S}{t}$

where S is the length of the lap (400 m) while t is the time taken to complete the lap. Since the time t increases at each lap, we see from the formula that v, the speed, decreases at each lap. This is an example of inverse relationship: when one of the two quantities increases (the time), the other one decreases (the speed).

2. A) Velocity on the y-axis, time on the x-axis

Acceleration is defined as the change in velocity divided by the time taken:

$a=\frac{\Delta v}{\Delta t}$

In a graph, the slope of a line is given by the increment in y divided by the increment in x:

$s=\frac{\Delta y}{\Delta x}$

Therefore, if we put velocity on the y-axis and time on the x-axis, we immediately see that the acceleration corresponds to the slope of the curve.

3. D)velocity

In fact, velocity consists of 1) speed and 2) direction. The speed can be calculated as:

$v=\frac{S}{t}$

where S is the distance covered and t the time taken. So, by knowing these two quantities, Tim can calculate the speed of the trip. Tim also knows the direction of motion, so he can determine the velocity of the trip.

4. B)equal, different

The difference between speed and velocity is simple: speed is a scalar, and it is just the magnitude of the velocity, so "how fast" is the object moving, while velocity takes also into account the direction of motion, so it is a vector.

Therefore: the two cars have same speed (25 m/s), but they have different velocities, since they are moving into different directions (car A is moving from NY to Miami, while car B is moving from NY to Chicago).

28. B) 11 m

The distance travelled by the bag in free fall is given by:

$S=\frac{1}{2}at^2$

where a=9.8 m/s^2 is the acceleration of gravity and t=1.5 s is the time. Replacing these numbers into the formula, we find

$S=\frac{1}{2}(9.8 m/s^2)(1.5 s)^2 =11 m$

29. B)10 m/s south

The boat is moving 20 m/s south, relative to the ground. The passenger is moving 10 m/s north, relative to the boat. Considering south as positive direction, the passenger's velocity relative to the ground is

v' = v_b + v_p = 20 m/s + (-10 m/s) = 10 m/s

and the positive sign means it is due south.

30. B)direction

In fact, velocity is a vector, so it consists of a magnitude (the speed) and a direction. The speed can be determined by the distance and the time, in fact speed is defined as

$v=\frac{d}{t}$

where d=distance and t=time; however, in order to determine velocity, we also need to know the direction of motion.

33. B)a velocity.

In fact, velocity is a vector, and it consists of a magnitude (the speed) and a direction. In this case, 10 m/s is the speed, while north is the direction.

34. C)Does the measurement include direction?

As stated in the previous question, a vector includes both magnitude and direction, while a scalar includes only a magnitude. Therefore, by asking if the measurement includes a direction, we are able to determine if the quantity is a vector or not.

Mathematics

2. geoff planted dahlias in his garden. dahlias have bulbs that divide and reproduce underground. in the first year, geoff’s garden produced 6 bulbs. in the second year, it produced 12 bulbs, and in the third year, it produced 24 bulbs. if this pattern continues, how many bulbs should geoff expect in the eighth year? (1 point) 48 bulbs 384 bulbs 768 bulbs 1,536 bulbs 3. what are the first four terms of the sequence represented by the expression n(n – 1) – 5? (1 point) –7, –5, –3, 1 –5, –10, –15, –20 0, 2, 6, 12 –5, –3, 1, 7 6. given the function

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2. In the first year, Geoff’s garden produced 6 bulbs. In the second year, it produced 12=6·2 bulbs, and in the third year, it produced 24=12·2 bulbs. If this pattern continues, then he can expect 24·2=48 bulbs in the fourth year, 48·2=96 bulbs in the fifth year, 96·2=192 bulbs in the 6th year, 192·2=384 bulbs in the 7th year and 384·2=768 bulbs in the 8th year.

Answer 2: correct choice is C.

3. Given n(n – 1) – 5 you can find:

for n=1, 1·(1-1)-5=-5;for n=2, 2·(2-1)-5=-3;for n=3, 3·(3-1)-5=1;for n=4, 4·(4-1)-5=7.

Answer 3: correct choice is D.

6. Given the function rule f(x) = x² – 5x + 1,

f(-3)=(-3)²-5·(-3)+1=9+15+1=25.

Answer 6: correct choice is C.

7. Suppose you earn $10 each hour you babysit and your total earnings E depending on the number of hours h you babysit is

E(h)=10·h.

Answer 7: correct choice is A.

8. If Melanie charges $4.50 per hour, then she she charges $4.50·x for x hours. Plus $5.00 for supplies, then the function rule is

y=4.50x+5.00.

Answer 8: correct choice is B.

14. The sale price of apples at a local grocery store is $1.35 for the first pound and $1.10 for each additional pound. If x is the number of sold pounds then 1 was sold for $1.35 and rest x-1 were sold for $1.10. This means that

y=1.10(x-1)+1.35

Answer 14: correct choice is A.

Mathematics

2. geoff planted dahlias in his garden. dahlias have bulbs that divide and reproduce underground. in the first year, geoff’s garden produced 6 bulbs. in the second year, it produced 12 bulbs, and in the third year, it produced 24 bulbs. if this pattern continues, how many bulbs should geoff expect in the eighth year? (1 point) 48 bulbs 384 bulbs 768 bulbs 1,536 bulbs 3. what are the first four terms of the sequence represented by the expression n(n – 1) – 5? (1 point) –7, –5, –3, 1 –5, –10, –15, –20 0, 2, 6, 12 –5, –3, 1, 7 6. given the function

Step-by-step answer

P Answered by PhD

1

2. In the first year, Geoff’s garden produced 6 bulbs. In the second year, it produced 12=6·2 bulbs, and in the third year, it produced 24=12·2 bulbs. If this pattern continues, then he can expect 24·2=48 bulbs in the fourth year, 48·2=96 bulbs in the fifth year, 96·2=192 bulbs in the 6th year, 192·2=384 bulbs in the 7th year and 384·2=768 bulbs in the 8th year.

Answer 2: correct choice is C.

3. Given n(n – 1) – 5 you can find:

for n=1, 1·(1-1)-5=-5;for n=2, 2·(2-1)-5=-3;for n=3, 3·(3-1)-5=1;for n=4, 4·(4-1)-5=7.

Answer 3: correct choice is D.

6. Given the function rule f(x) = x² – 5x + 1,

f(-3)=(-3)²-5·(-3)+1=9+15+1=25.

Answer 6: correct choice is C.

7. Suppose you earn $10 each hour you babysit and your total earnings E depending on the number of hours h you babysit is

E(h)=10·h.

Answer 7: correct choice is A.

8. If Melanie charges $4.50 per hour, then she she charges $4.50·x for x hours. Plus $5.00 for supplies, then the function rule is

y=4.50x+5.00.

Answer 8: correct choice is B.

14. The sale price of apples at a local grocery store is $1.35 for the first pound and $1.10 for each additional pound. If x is the number of sold pounds then 1 was sold for $1.35 and rest x-1 were sold for $1.10. This means that

y=1.10(x-1)+1.35

Answer 14: correct choice is A.

Mathematics

A new school randomly assigns a six-character student code to every prospective student. The school uses the characters 1, 2, 3, 4, 5, X, Y, and Z. If none of the student codes contain a repeated character, what is the total number of codes that can be randomly assigned?

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The total nom of code that can be used is equal to 5+3 = 8

Mathematics

A 4300-N force from a car s engines produces an acceleration of 3.3 m/s2. What is the mass of the car? A. 4300 kg B. 1300 kg C. 14,000 kg D. 390 kg

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F=ma