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## There are 24 pictures on a roll of film. Adelle had 84 pictures from her trip home. She said that 12 other pictures were spoiled. How many rolls of film did Adelle use?

There are 24 pictures on a roll of film. Adelle had 84 pictures from her trip home. She said that 12 other pictures were spoiled. How many rolls of film did Adelle use?

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## On a vacation, DeVante and his family traveled 382 miles at 64 mph. How long did the trip take? (Round to the nearest hundredth)

On a vacation, DeVante and his family traveled 382 miles at 64 mph. How long did the trip take? (Round to the nearest hundredth)

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## Harley is on a trip with her dad. Her dad tells her that they've traveled 182.6 miles and they are 83% of the way to their destination. How many miles long is their trip?

Harley is on a trip with her dad. Her dad tells her that they’ve traveled 182.6 miles and they are 83% of the way to their destination. How many miles long is their trip?

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## The proper noun in the following sentence is not capitalized. Identify the proper noun. In order to go to the party, her cousin made the trip from boston. A. party B. cousin C. boston D. her

The proper noun in the following sentence is not capitalized. Identify the proper noun. In order to go to the party, her cousin made the trip from boston. A. party B. cousin C. boston D. her

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## Carlos and his family left for the amsuement park at 8:35 a.M. The trip took 1 hour and 55 minutes. What time did they arrive

Carlos and his family left for the amsuement park at 8:35 a.M. The trip took 1 hour and 55 minutes. What time did they arrive

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## For your fundraiser, you decide to hold a bake sale. In order to make bakery items, you had to purchase 12 pounds of sugar and 15 pounds of flour. Your total cost was \$9.30. On a second trip to the grocery store, you purchased 4 pounds of sugar and 10 pounds of flour for a total cost of \$4.60. Which of the following represent the system of equations for this problem.

C. Yes, because the population values appear to be normally distributed.

Step-by-step explanation:

Given is a graph which shows the distribution of values of a population

The graph has the following characteristics

i) Bell shaped

ii) symmerical about mid vertical line

iii) Unimodal with mode = median =mean

iv) As x deviates more from the mean probability is decreasing and also curve approaches asymptotically the x axis

Hence we find that the curve is a distribution of normal

Option C is right

C. Yes, because the population values appear to be normally distributed.

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Natural Forces Affecting the Driver:

1. While the car stops, the person continues moving the way that the car were moving and then hits the obstacle in the car or the person can be thrown out of the vehicle. If the person wears belt, he will stop moving with the vehicle and won’t hit the obstacle.

2. We count approximate kinetic energy using the formula K = v^2. So the vehicle which is moving at 30 mph will have four times less kinetic energy than vehicle which is moving at 60 mph. If they have the same road conditions, the breaking distance will be four times as great for the car moving twice as fast.

3. Kinetic energy depends on object’s mass and velocity and it has direct relationship with the stopping distance. The lesser mass of the vehicle = the lesser kinetic energy and lesser stopping distance. => If both vehicles have the same velocity, then small vehicle has lesser kinetic energy than large vehicle.

4. We know that kinetic energy has this relationship with velocity K = v^2. So the best way to prepare to enter sharp curves in the roadway is to lower the speed. The most appropriate speed is 20-30 mph, but it depends on road conditions and car’s breaks condition.

5. Car crashes can happen with everyone so the best way is to be prepared. First the driver should wear a seatbelt while he’s driving. He should check his tires and breaks condition regularly. And also it’s important to slow down the vehicle while entering sharp curves. Without following these rules, the driver can get catastrophic injuries in a car crash.

Signs, Signals, and Pavement Markings:

1. It doesn’t matter where you go. All you need is to learn highway code. It’s very different to know the meanings of every road sign. Also, it’s necessary to check your car’s conditions and you should take some spare parts for your car in case of accidents. So wherever you go, it’s important to be prepared.

2. You should stop before crossing and take few minutes to make sure there is no train approaching. If there is no train approaching, you can pass a railroad crossing. If you see approaching train, you should wait until it will pass a railroad crossing.

3. You should stop before the lights and wait to check the traffic movement and signs. Make sure that everything is safe and pass the intersection. Don’t move fast to avoid accidents.

4. Flashing yellow light means that it’s not necessary to stop but you should to pay attention on the traffic movement. So it would be better to yield before the lights and make sure if it’s safe to move. After that you can cross the intersection.

5. The line change means that the lane changes and you can’t cross solid lines. Pay more attention on road marking because it shows how you should behave on the road or highway.

6. As you approach the next exit and  your passengers need to use the restroom and get some food, you should look for green signs which indicate food and rest stops. You should to slow down if you don’t want to skip the sign.

7. When you take the exit ramp off the expressway and merge onto the next road, you see yellow lines dividing the roadway which indicates that there is oncoming traffic and this is a two-way highway.

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## 1. 7.2 aliens =1 monster. 1 monster= 15.5 oranges. Using the conversion above, about how many oranges are equal to 1 alien? 2. In a scaled drawing, 1 millimeter represents 150 meters. How many square millimeters on the drawing represents 1 square meters? 3. While driving with his father, Amit holds his breath whenever they pass through a particular tunnel. Amit counts the number of seconds he holds his breath, from the beginning of the tunnel to the end of the tunnel, and finds that he holds his breath, on average for about 8 seconds. If his father drives the car at 60 mph through the tunnel, according to the average time, Amit holds his breath, about how long is the tunnel. 4. Lea’s car travels on average of 30 miles per gallon of gas. If she spent \$20.70 on gas for a 172.5 mile trip, what was the approximate cost of gas in dollars per gallon?

127=7 (mod n) means when 127 is divided by n, the division leaves a remainder of 7.

The statement is equivalent to
120=0 (mod n), meaning that n divides 120.

All divisors of 120 will satisfy the statement because 120 divided by a divisor (factor) will leave a remainder of 0.

Factors of 120 are:
n={1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120}, |n|=16.
You can count how many such values of n there are, and try to check that each one satisfies 127=7 mod n.

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## After a trip to Mars, the human heart would be much stronger than it was on Earth

First let us assign variables,

d = distance travelled

t = time it took

v = velocity of the commercial airline

In linear physics, the equation for velocity is given as:

v = d / t

Rewriting for d:

d = v t

We know that the distance to and from south America are equal
therefore:

d1 (going) = d2 (return)

Let us say that velocity of air is v3. Since going to South
America, the wind is against the direction of the plane and the return trip is
the opposite, therefore:

(v1 – v3) t1 = (v1 + v3) t2

(v1 – v3) 4 = (v1 + v3) 3.53

4 v1 – 4 v3 = 3.53 v1 + 3.53 v3

0.47 v1 = 7.53 v3

v1 = 16.02 v3

Since we also know that:

(v1 – v3) t1 = 784

(16.02 v3 – v3) * 4 = 784

60.085 v3 = 784

v3 = 13.05 mph

Therefore the speed of the plane in still air, v1 is:

v1 = 16.02 * 13.05

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## Against the wind a commercial airline in south america flew 784 miles in 4 hours. with a tailwind the return trip took 3.53 hours. what was the speed of the plane in still? air

a) The time the police officer required to reach the motorist was 15 s.

b) The speed of the officer at the moment she overtakes the motorist is 30 m/s

c) The total distance traveled by the officer was 225 m.

Explanation:

The equations for the position and velocity of an object moving in a straight line are as follows:

x = x0 + v0 · t + 1/2 · a · t²

v = v0 + a · t

Where:

x = position at time t

x0 = initial position

v0 = initial velocity

t = time

a = acceleration

v = velocity at time t

a)When the officer reaches the motorist, the position of the motorist is the same as the position of the officer:

x motorist = x officer

Using the equation for the position:

x motirist = x0 + v · t (since a = 0).

x officer = x0 + v0 · t + 1/2 · a · t²

Let´s place our frame of reference at the point where the officer starts following the motorist so that x0 = 0 for both:

x motorist = x officer

x0 + v · t = x0 + v0 · t + 1/2 · a · t²      (the officer starts form rest, then, v0 = 0)

v · t = 1/2 · a · t²

Solving for t:

2 v/a = t

t = 2 · 15.0 m/s/ 2.00 m/s² = 15 s

The time the police officer required to reach the motorist was 15 s.

b) Now, we can calculate the speed of the officer using the time calculated in a) and the  equation for velocity:

v = v0 + a · t

v = 0 m/s + 2.00 m/s² · 15 s

v = 30 m/s

The speed of the officer at the moment she overtakes the motorist is 30 m/s

c) Using the equation for the position, we can find the traveled distance in 15 s:

x = x0 + v0 · t + 1/2 · a · t²

x = 1/2 · 2.00 m/s² · (15s)² = 225 m

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## A company uses two vans to transport workers from a free parking lot to the workplace between 7:00 and 9:00 a.m. One van has 5 more seats than the other. The smaller van makes 2 trips every morning while tye larger one makes only one trip the 2 vans can only transport 71 people, maximum. let x be the seats in the small van and y the seats in the large van.how many seats does the larger on have?

The triangle ABC is similar to triangle LMP. The order here is very important. The letters correspond to one another
A corresponds to L (first letters of each sequence)
B corresponds to M (second letters of each sequence)
C corresponds to P (third letters of each sequence)

In a similar fashion, the segments also correspond to one another.
AB corresponds to LM (first two letters of each sequence)
AC corresponds to LP (first and last letters of each sequence)
BC corresponds to MP (last two letters of each sequence)

————————————

AB corresponds to LM. AB is 4 units long. LM is 2 units long. So AB is twice as long as LM. This ratio (of 2:1) will be applied to every paired corresponding value.

Also, the right angle is at angle M for triangle LMP. The right angle will be at angle B for triangle ABC (since B corresponds to M). The answer will have an x coordinate of 7. So the answer is either choice B or choice C.

If we move 4 units down from point B, we land on (7,-10). That isn’t listed as an answer choice. Let’s try moving 4 units up from point B. We land on (7,-2). This is an answer choice

So the final answer is choice C) (7,-2)

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## The graph indicates Linda’s walk. Which best describes the graph? Linda started out moving, and then stopped moving after 6 seconds. Linda started moving away from the start point, and then moved closer. Linda never moved the entire trip. Linda’s path results in a negative slope.

a) The time the police officer required to reach the motorist was 15 s.

b) The speed of the officer at the moment she overtakes the motorist is 30 m/s

c) The total distance traveled by the officer was 225 m.

Explanation:

The equations for the position and velocity of an object moving in a straight line are as follows:

x = x0 + v0 · t + 1/2 · a · t²

v = v0 + a · t

Where:

x = position at time t

x0 = initial position

v0 = initial velocity

t = time

a = acceleration

v = velocity at time t

a)When the officer reaches the motorist, the position of the motorist is the same as the position of the officer:

x motorist = x officer

Using the equation for the position:

x motirist = x0 + v · t (since a = 0).

x officer = x0 + v0 · t + 1/2 · a · t²

Let´s place our frame of reference at the point where the officer starts following the motorist so that x0 = 0 for both:

x motorist = x officer

x0 + v · t = x0 + v0 · t + 1/2 · a · t²      (the officer starts form rest, then, v0 = 0)

v · t = 1/2 · a · t²

Solving for t:

2 v/a = t

t = 2 · 15.0 m/s/ 2.00 m/s² = 15 s

The time the police officer required to reach the motorist was 15 s.

b) Now, we can calculate the speed of the officer using the time calculated in a) and the  equation for velocity:

v = v0 + a · t

v = 0 m/s + 2.00 m/s² · 15 s

v = 30 m/s

The speed of the officer at the moment she overtakes the motorist is 30 m/s

c) Using the equation for the position, we can find the traveled distance in 15 s:

x = x0 + v0 · t + 1/2 · a · t²

x = 1/2 · 2.00 m/s² · (15s)² = 225 m

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## The smith family bought a new tent for a camping trip with a base of 9 by 15 and a height of 7. What is the volume of their new tent?

So hmmm we’ll start off by using the decimal format for the percentage, thus 15% is just 15/100 or 0.15 and 7% is just 7/100 or 0.07 and so on

notice, the concentration of alcohol in the 15% is, well, 0.15 :), so for a quantity of whatever, it’d be 0.15whatever

anyway, for water… water has no alcohol whatsoever, so the concentration is 0%, or 0/100 which is 0.00 or a flat 0 we know that we’ll be adding “x” water with the 14mL to get “y”, thus 14+x = y

and the concentrated quantities will also add up to -> 14(0.15) = 2.1, thus
2.1 + 0x = 0.07y solve for “x”.

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## During a grade school field trip, ryan and his friends were running down a hill when he stepped on a snake. he was unharmed but shaken by the experience. when one of his friends mentioned the incident months later, ryan could not remember running down the hill that day. freud would say that this is an example of

The answer is C. In order to carefully control conditions and confirm or disconfirm a hypothesis about the causes of behavior, one must perform an experiment.

Explanation:

Experimental research allows the researcher to control all the variables in order to create the conditions that can confirm or disconfirm a hypothesis. This method aimes to establish a relation of causality between two variables, which means that one variable is generated and determined by the other; this is posible because all of the other variables that can influence it have been controlled.

When a researcher conducts a survey or engages in naturalistic observation, he can’t control the variables, therefore, he can only establish a correlation between two variables, but not of causality.

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## Randy made a business trip of 204 miles. he averaged 52 mph for the first part of the trip and 50 mph for the second part. if the trip took 4 hours, how long did he travel at each rate?

Option C – BD=76 cm

Step-by-step explanation:

Given : You are designing a diamond-shaped kite. you know that AD = 44.8 cm, DC = 72 cm, and AC = 84.8 cm.

To find : How long BD should it be?

Solution :

First we draw a rough diagram.

The given sides were AD = 44.8 cm, DC = 72 cm and AC = 84.8 cm.

According to properties of kite

Two disjoint pairs of consecutive sides are congruent.

DC=BC=72 cm

The diagonals are perpendicular.

So, AC ⊥ BD

Let O be the point where diagonal intersect let let the partition be x and y.

AC= AO+OC

AC= …….

Perpendicular bisect the diagonal BD into equal parts let it be z.

BD=BO+OD

BD=z+z

Applying Pythagorean theorem in ΔAOD

where H=AD=44.8 ,P= AO=x , B=OD=z  ………

Applying Pythagorean theorem in ΔCOD

where H=DC=72 ,P= OC=y , B=OD=z  …………

Subtract  and    ……….

Add equation  and , to get values of x and y   Substitute x in   Substitute value of x in equation , to get z     We know, BD=z+z

BD= 38.06+38.06

BD= 76.12

Nearest to whole number BD=76 cm

Therefore, Option c – BD=76 cm is correct.

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## Which detail from “The Monkey’s Paw” is an example of conflict? A. When all of Mr. White’s wishes are gone, he is worse off than before. B. Mr. White comments that he would enjoy making a trip to India. C. The night the story begins, the weather outside is cold and wet. D. Mr. White feels uncomfortable when his son Herbert outsmarts him.

Since a tiny tender child of four,
There’s nothing that I dreamt of more,
Than to jump aboard a great big ship,
A telescope, a map, a sword, by my hip,
To feel the sea breeze in my hair,
To stroke my parrot on the wood chair,
To be bold and brave and happy as can be,
To trek and travel and sail the seven seas.

8 lines. Rhyme scheme aabbccdd. If I managed to write that in about 4 minutes, you could write something much better and longer in like 30 minutes. You can use my rubbish poem as inspiration lol. Good luck X

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## A trip to the ocean can be a relaxing escape from the everyday pressures of life. A sailboat glistening on the horizon provides a mental escape to faraway places. The rhythm of the ocean beating against the sand is sedating music to a troubled mind. A slow, gentle breeze can relax your tensions. You should always be careful to avoid overexposure to the sun at the beach. 1.a.Write the sentence that is the topic sentence of the paragraph. b.Write the sentence that is unrelated to the topic and can be eliminated. 2.List four things to look for when you’re proofreading. 3.Complete the following two steps: a. Define the term cliché. b. Use a cliché in a sentence that you create. 4.Name and explain two types of prewriting.

Hey there!

Correct answer is D. Comma or Period Inside Rule

A. Question mark or exclamation point inside: those are not really necessary.

B. Colon or semicolon: not, a semicolon would divide the whole sentence and it would be shorten; a colon would work but after requested, when there is already a comma.

C. Question mark or Exclamation Point Outside Rule: would not work, becase it is an very polite and affirmative sentence.

D: A comma or period inside rule: actually, just a comma would work. Please, Cooper’s dad requested, go… Cooper’s dad requested must be in between commas as it is a vocative.

Hope this helps

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## You are going shopping and you plan to buy 3 new pairs of pants, 2 new shirts, and a pair of boots. The total cost of this shopping trip can be represented by the expression 3p + 2s + b where p stands for the cost of each pair of pants, s stands for the cost of each shirt, and b stands for the cost of the boots. If each pair of pants cost \$39.99, each shirt costs \$17.89, and the boots cost \$49, what is the total cost of the shopping trip? Show Work Here: Final answer here:

Employee                                 Mary      Zoe         Greg         Ann           Tom

Cumulative Pay                       \$6,800   \$10,500  \$8,400    \$66,000   \$4,700

Pay subject to FICA S.S.         \$421.60  \$651.00  \$520.80 \$4092.00 \$291.40
6.2%, (First \$118,000)

Pay subject to FICA Medicare \$98.60 \$152.25    \$121.80    \$957.00    \$68.15
1.45% of gross

Pay subject to FUTA Taxes      \$40.80  \$63.00     \$50.40    \$396.00  \$28.20
0.6%

Pay subject to SUTA Taxes   \$367.20  \$567.00  \$453.60  \$3564.00 \$253.80
5.4% (First \$7000)

Totals                                     \$928.20 \$1,433.25 \$1,146.60 \$9,009.00 \$641.55

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## A motorist travels for 3.0 h at 80 km/h and 2.0 h at 100 km/h. What is her average speed for the trip?

a) The time the police officer required to reach the motorist was 15 s.

b) The speed of the officer at the moment she overtakes the motorist is 30 m/s

c) The total distance traveled by the officer was 225 m.

Explanation:

The equations for the position and velocity of an object moving in a straight line are as follows:

x = x0 + v0 · t + 1/2 · a · t²

v = v0 + a · t

Where:

x = position at time t

x0 = initial position

v0 = initial velocity

t = time

a = acceleration

v = velocity at time t

a)When the officer reaches the motorist, the position of the motorist is the same as the position of the officer:

x motorist = x officer

Using the equation for the position:

x motirist = x0 + v · t (since a = 0).

x officer = x0 + v0 · t + 1/2 · a · t²

Let´s place our frame of reference at the point where the officer starts following the motorist so that x0 = 0 for both:

x motorist = x officer

x0 + v · t = x0 + v0 · t + 1/2 · a · t²      (the officer starts form rest, then, v0 = 0)

v · t = 1/2 · a · t²

Solving for t:

2 v/a = t

t = 2 · 15.0 m/s/ 2.00 m/s² = 15 s

The time the police officer required to reach the motorist was 15 s.

b) Now, we can calculate the speed of the officer using the time calculated in a) and the  equation for velocity:

v = v0 + a · t

v = 0 m/s + 2.00 m/s² · 15 s

v = 30 m/s

The speed of the officer at the moment she overtakes the motorist is 30 m/s

c) Using the equation for the position, we can find the traveled distance in 15 s:

x = x0 + v0 · t + 1/2 · a · t²

x = 1/2 · 2.00 m/s² · (15s)² = 225 m

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## Situation i andrew loves to go camping and hiking in the fall. about two weeks after his last camping trip, he noticed an expanding red rash on his arm. andrew is most likely suffering from

The answers to the given blanks above are NORMS, and CONFORMITY PRESSURES CHANGE ATTITUDES, respectively.
This research is actually based from Jean Watson (1950), an American nurse theorist who is known for her theory of Human Caring. According to her, when the given standards in an environment are changed, this also affects how a person deals with the people around his or her environment. Given above that there is lesser prejudice, this also changed their attitude by being less prejudiced.

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## Cory predicts it will take him 64 minutes to travel to Baltimore from Washington D.C. If the trip actually took 74 minutes, what was Cory’s percent error? Round your answer to the nearest tenth of a percent.

The basis to respond this question are:

1) Perpedicular lines form a 90° angle between them.

2) The product of the slopes of two any perpendicular lines is – 1.

So, from that basic knowledge you can analyze each option:

a.Lines s and t have slopes that are opposite reciprocals.

TRUE. Tha comes the number 2 basic condition for the perpendicular lines.

slope_1 * slope_2 = – 1 => slope_1 = – 1 / slope_2, which is what opposite reciprocals means.

b.Lines s and t have the same slope.

FALSE. We have already stated the the slopes are opposite reciprocals.

c.The product of the slopes of s and t is equal to -1

TRUE: that is one of the basic statements that you need to know and handle.

d.The lines have the same steepness.

FALSE: the slope is a measure of steepness, so they have different steepness.

e.The lines have different y intercepts.

FALSE: the y intercepts may be equal or different. For example y = x + 2 and y = -x + 2 are perpendicular and both have the same y intercept, 2.

f.The lines never intersect.

FALSE: perpendicular lines always intersept (in a 90° angle).

g.The intersection of s and t forms right angle.

TRUE: right angle = 90°.

h.If the slope of s is 6, the slope of t is -6

FALSE. – 6 is not the opposite reciprocal of 6. The opposite reciprocal of 6 is – 1/6.

So, the right choices are a, c and g.

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## Using a map for trip planning can make driving _____________. A. less stressful B. more stressful C. fuel efficient D. slower

1. I am definitely sure that correct option is: a. It will continue to move to the right, its speed increasing with time. If the object is experiencing a net force to the right, it always accelerates to the right => the velocity is increasing, because the greater the force, the larger the acceleration.

2. In my opinion the answer should be

b. The table top will break and the object will fall to the floor. We should count the normal force of the object. According to the conditions, we can use N=mg; N=165*9,8 = 1617 N. 1617 > 1600. That’s why I’ve picked this option.

3. It’s tricky question, because the weight of the rock depends only on the force of gravity. Speed doesn’t affect the weight of the object. So it doesn’t matter what the acceleration is, its force will be 138 N. So the answer is D.

4. The friction doesn’t matter. We should use Newton’s laws to define

the normal force that the floor exerts on the chair.
So the solution is: ; where  ;
so the most approximate answer is B. 340 N.

5. I am pretty sure that correct answer is: b. extremely small values, such as the distances between particles in an atomic nucleus. According to its definition, strong interaction is a mechanism that is responsible responsible for the acts between subatomic particles of matter.

6. As far as I remember the correct option is: a. The action force and the reaction force act on different objects. Action and reaction forces are very important forces of a single interaction and they are not exist without each other. They’re both equal in strength but opposite in direction.

7. I am not completely sure, but I think that the answer should be 48 N. We have normal force which is equal to the box’s weight, so n = 320 N. Then we can count force of friction using the formula f = n*μ where μ = 0.15.  8. –

9. We have and . And this is all we need to find the real force that pulls the wagon forward.
The formula is: ; ;

So the most approximate answer is C. 245 N.

10. According to the free-body diagram given above, the answer should be d. a woman jumping off the floor. Because in this option the object is experiencing a vertical acceleration, and this means that the normal force acting on the object will not be equal to the weight of the object.

11. According to the Newton’s second law of motion  So the answer is  A. 8 m/s^2

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## Jody drives 120 miles south from Kingston, NY to Princeton, NJ. If she drives 60 mph, how long will it take her to make the trip?

1. To understand this, consider first that the 60 feet of fencing goes all the way around a rectangle and is the perimeter. So, if one side is x, so is the opposite side; and if another side is (30-x), so is its opposite side, so the total perimeter, 60 = 2x + 2(30-x). So, they’ve arranged it so that sides x and (30-x) always provide the 60 foot perimeter, even though you can change x.
Secondly, to maximize the area, A, consider that A = x (30-x), or -x^2 +30x, a quadratic equation, a parabolic curve facing down (the x^2 term is negative, so it faces down), and has a maximum, which will be where the derivative is zero. So, take the derivative: -2x + 30, set it to zero and solve and you find: x = 15. Plunk the 15 back into the original equation for area A, -x^2 + 30x, and you find it’s -15*15 + 30*15 = 15(30-15) = 15*15 = 225 square feet. (I hope… feel free to check!) But it’s x they wanter, which will be the 15 feet.
2. 3x^2=15x-2 They ask for the discriminant: that’s the part of the Quadratic Equation under the square root sign, isn’t it? so first put this into standard form and it should become obvious, just read it from the equation: 3x^2 – 15x + 2 = 0, the discriminant (call it N) is b^2 -4ac if my memory’s working, a = 3, b = -15, c = 2, so N = 225 – 4*3*2 = 225 – 24 = 201 (do please check, I’m hurring ’cause I have to put supper on soon!). Since that’s positive, there should be two solutions. Use sthe Quadratic Formula: [ -b ± √(D) ] / 2a. should be the 2 solutions, [15 ± √(201)] / 6, take it from there.
3. Those four choices should make it obvious to you, as they’re all in slope-intercept form, all have slope 100. Trick is to substitute x = 2,000 for that point, and find out what y would be, the 100*x would be 200,000, and you’re subtracting something from a choice, to get 3,000 for that point, so the something had better be 197,000 … 🙂 Or you could say they’re giving you y = 100x – S (S for “something” to tell which answer to choose), and it has got to work for x = 2,000 and y = 3,000, so solve it for S, that is
S = 100x – y, then put in your point (2,000, 3,000) and you’ll have S = 100*(2,000) – (3,000) and from that you’d find your answer.
But you’re right: aim to understand how they work, then the method’s easy to remember, and easy to use in a zillion similar questions. The methods do make sense, and work quite well;)

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