Newton's Second Law states acceleration equals force
divided by mass, a = F/M. This graph shows f(x) = 5/x , an
acceleration based on a constant force of 5 Newtons
applied to different objects. How is f(x) transformed to
get g(x) and what is the new equation?

Answer:

(x - 2)(x + 4)

Step-by-step explanation:

What are the factors of: f(x) = \(x ^2 + 2x - 8\)

\(x ^2 + 2x - 8\)

a = 1

b =  2

c = -8

Find two numbers that add to 2 and multiply to -8:

-2 + 4 = 2

-2(4) = -8

factors are:

(x - 2)(x + 4)

Answer:

Let's Convert yards into inches

Base = 40 yards = 1440 inches

Height = 25 yards = 900 inches

Base (Map)/Base (Actual)

40/1440 = 1 : 36

Height (Map)/Height (Actual)

25/900 = 1 : 36

I hope it helps you!

Step-by-step explanation:

Let's expand our knowledge even more by explaining.

The scale of the height and the width is 1 inch equals 1 yard.

the scale of the area would be 1 square inch equals 1 square yard.

for example:

the area of a triangle is equal to 1/2 * base * height.

the base on the map is 40 inches and the height on the map is 25 inches.

the area on the map is therefore 1/2 * 40 * 25 = 500 square inches.

the base in the real world is 40 yards and the height in the real world is 25 yards.

the area in the real world is therefore equal to 1/2 * 40 * 25 = 500 square yards.

the ratio of the area on the map to the area in the real world is 500 square inches / 500 square yards equals 1 square inch / 1 square yard.

that's 1 square inch to 1 square yard.

in general, if the scale in the linear measurements were a/b, then the scale in area would be (a/b)^2.

since your scale in linear measurements is 1/1, then the scale in area would be (1/1)^2 which is equal to 1/1.

assuming the scale in linear measurements were 1/2, then the scale in area would be (1/2)^2 = 1^2/2^2 = 1/4.

Answer:

Below

Step-by-step explanation:

Find unit rate (since it starts at 0,0)

at 45 seconds  it is 900 bottles

             900 bottles / 45 seconds = 20 bottle / sec

20 bottles / sec * 80 sec = 1600 bottles

Answer:

the correct answer is A. 25 sandwiches.

Step-by-step explanation:

Assuming you have plenty of bread and jelly, you can make 25 sandwiches from the jar of peanut butter.

Each sandwich typically requires 2 tablespoons of peanut butter, one slice of bread with peanut butter and one slice of bread with jelly.

So, if you have 50 tablespoons of peanut butter, you can make 25 sandwiches with it, because 50 / 2 = 25.

Therefore, the correct answer is A. 25 sandwiches.

Answer: 25

Step-by-step explanation:

We have 50 tablespoons of peanut butter and we know that it requires 2 tablespoons to make a single sandwich. In order to find how many sandwiches we can make with our 50 tablespoons, we would have to do 50 divided by 2.

2+2...=50

Answer:

6 is in ten place and its place value is 60, 3 is in ones place and its place value is 3.

The given values into the equation AE = 2a + 10. Therefore, The value of AE is 3 - x.

To find the value of AE, we can substitute the given values into the equation AE = 2a + 10.

Given:

AB = 10

AE = 2a + 10

ED = x + 3

CD = 4

Since AB is a segment on the line, it can be divided into AE and ED. Therefore, AB = AE + ED.

We know that AB = 10 and CD = 4. So, if we subtract CD from AB, we get AE + ED = 10 - 4.

AE + ED = 6.

Now, we can substitute the value of ED, which is x + 3, into the equation: AE + x + 3 = 6.

To find the value of AE, we need to isolate it on one side of the equation. Let's subtract x and 3 from both sides:

AE = 6 - x - 3.

Simplifying further, we get;

AE = 3 - x.

Therefore, the value of AE is 3 - x.

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Answer:

1863/275=6.7745recurring

Step-by-step explanation:

Dont u have a calculator

Answer:

(4,-6)

x=4, y=-6

It wants me to type it longer help I just know the answer

Answer: Sam was 2.5 Km far from his house

Step-by-step explanation:

Sam's parents gave him a map to reach his house.

As per Map Sam was =1.5cm from his home.

To find actual distance from house

If we consider actual distance  of sam house =X

We have,

If each 3 cm on scale drawing equals 5 km

We know on map 3cm  = 5Km

If 1.5 cm = X Km

We need to cross multiple

 3X =1.5 × 5

 3X = 7.5

X= 7.5÷3

X= 2.5 Km

Sam was 2.5 Km far from his house.

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Answer: y = 9x - 3

That's y=mx + b, the usual slope intercept form of a line with slope m and y intercept b.

Step-by-step explanation:

The equation of a line is y = mx + b, where m is the slope and b is the y-intercept. We know that m = 9 and b = -3, and when we plug those in, we get y = 9x - 3. Hope this helps!

a.

$70,440 is the loan on 12 months by Credit union

$88,050 is the loan on 24 months, the loan on 12 months to compare is $44,025

B.the loan by Credit union will cost less but it must be paid in less time

C.we do the subtraction of each total loan

the first method would cost $17,610 less

The perimeter is given by:

Since the length of a rectangle is 5 meters less than 3 times the width:

Answer:

c. The period is 2π

Step-by-step explanation:

The period of a function is the smallest value of $p$ for which\( f(x+p) = f(x)\) for all x.

For the function f(x) = 2cos(x^2), we can see that f(x+2π) = f(x) for all x.

This is because the cosine function has a period of 2π. Therefore, the period of f(x) = 2cos(x^2) is \(\boxed{2\pi}\)

Answer:

11 pieces

Step-by-step explanation:

19 1/4 ÷ 1 3/4

19 x 4 = 76 + 1 = 77

1 x 4 = 4 + 3 = 7

77/4 ÷ 7/4

77/4 ÷ 7/4 = 11/1

11 pieces

(Just copy my work above for Part B)

Answer:

0.666

Step-by-step explanation:

I don't know. i just used a calculator

Answer:

38 = 1 x 38 or 2 x 19. Factors of 38: 1, 2, 19, 38. Prime factorization: 38 = 2 x 19

Answer:

I believe answer is 0.041

Answer:

Step-by-step explanation:

Answer:

This cinder block has gravitational potential energy.

This cinder block has 15 484 joules of potential energy

Step-by-step explanation:

PE = mass*gravity*height and g= 9.8 m/s^2

PE = 79 * 9.8 * 20

PE = 15 484

a) Approximately 77.94% of possums have heads less than 95.4 mm.

b) Approximately 96.93% of possums have heads more than 85.8 mm.

c) Approximately 74.93% of possums have heads between 85.8 and 95.4 mm.

d) The maximum head length of the shortest 10% of possum heads is approximately 87.68 mm.

a) We can use the normal distribution to answer this question. Let X be the head length of a brushtail possum. Then X has a normal distribution with mean μ = 92.6 mm and standard deviation σ = 3.6 mm. We want to find P(X < 95.4 mm).

Using the standard normal distribution table or a calculator, we can find the z-score corresponding to a head length of 95.4 mm:

\(z = \frac{(95.4 - 92.6)}{3.6} = 0.78\)

Then, using the standard normal distribution table, we can find the probability that a standard normal variable is less than 0.78:

P(Z < 0.78) = 0.7794

Therefore, approximately 77.94% of possums have heads less than 95.4 mm.

b) Again, using the normal distribution with mean μ = 92.6 mm and standard deviation σ = 3.6 mm, we want to find P(X > 85.8 mm).

Finding the corresponding z-score:

\(z = \frac{(85.8 - 92.6)}{3.6} = -1.89\)

Using the standard normal distribution table, we find:

P(Z > -1.89) = P(Z < 1.89) = 0.9693

Therefore, approximately 96.93% of possums have heads more than 85.8 mm.

c) To find the percentage of possums with heads between 85.8 and 95.4 mm, we can subtract the probability of heads less than 85.8 mm from the probability of heads less than 95.4 mm:

P(85.8 < X < 95.4) = P(X < 95.4) - P(X < 85.8)

Using the same calculations as in parts (a) and (b), we get:

P(85.8 < X < 95.4) = 0.7794 - 0.0301 = 0.7493

Therefore, approximately 74.93% of possums have heads between 85.8 and 95.4 mm.

d) We want to find the maximum head length of the shortest 10% of possum heads. This is equivalent to finding the 10th percentile of the distribution. Using the normal distribution with mean μ = 92.6 mm and standard deviation σ = 3.6 mm, we want to find the head length x such that P(X < x) = 0.1.

Using the standard normal distribution table or a calculator, we can find the z-score corresponding to the 10th percentile:

P(Z < z) = 0.1

z = -1.28

Then, we can find the corresponding head length x:

x = μ + zσ = 92.6 + (-1.28)(3.6) = 87.68

Therefore, the maximum head length of the shortest 10% of possum heads is approximately 87.68 mm.

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Answer:

54 cm

Step-by-step explanation:

Because the perimeter of the square is 81 cm, each of its sides will be 81 ÷ 4 = 20.25 cm.

When we divide the square into rectangles, two sides remain the same lengths, and two others are \(\frac{1}3\) their original lengths.

So the perimeter of each rectangle is

\(2*20.25+2*(20.25 \div 3)\\=40.5+13.5\\=54 (cm)\)

Answer:

I love math

Step-by-step explanation:

The formula for simple interest is:

I = P * r * t

where:

I = interest earned

P = principal amount

r = interest rate (as a decimal)

t = time (in years)

In this case, we know that:

P = $1,264

r = 2.75% = 0.0275 (as a decimal)

t = 2.5 years

So, we can plug in these values and solve for I:

I = 1,264 * 0.0275 * 2.5 = $87.55

Therefore, the interest earned over 2.5 years is $87.55. To find the ending balance, we need to add the interest earned to the principal:

Ending balance = $1,264 + $87.55 = $1,351.55

So, Quentin's account balance will be $1,351.55 at the end of 2.5 years.

Answer:

Let's calculate the "cups of sugar per dozen cookies" ratio:

2 cups

---------- = 0.8  (Rina)        

  2.5                                  

2.25 cups

------------- = 0.75 (Jonah)

     3

Rina uses more sugar for a dozen cookies.

The situation Veronica receives $21 for babysitting, and then spends the same amount, $21, on a new shirt quantities combine to make 0.The correct answer is option C.

When we add +21 (the money she receives) and subtract -21 (the money she spends), the result is 0. This means that the net change in Veronica's money is zero, indicating that the quantities combine to make 0.

In situations A, B, and D, the quantities do not combine to make 0. In situation A, the player earns 4 points for getting an answer right and then earns an additional 4 points for making it around the board.

The total points earned in this situation would be 8, which is not equal to 0.

In situation B, the car is initially filled with 10 gallons of gas, but then half of that, which is 5 gallons, is used on a day's drive. The remaining fuel in the car would be 5 gallons, which is also not equal to 0.

In situation D, the bird flies 25 feet up in the air and then 25 feet across to its nest. The total distance traveled by the bird would be 50 feet, which is not equal to 0.

Therefore, only in situation C, where Veronica receives and spends the same amount of money, do the quantities combine to make 0.

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The probable question may be:

In which of these situations do the quantities combine to make 0?

A. A player a game earns 4 points for getting an answer right. She then earns 4 points for making it around the board.

B. A car is filled with 10 gallons of gas. Half of the 10 gallons are then used on a day's drive.

C. Veronica receives $21 for babysitting. She then spends $21 on a new shirt.

D. A bird flies 25 feet up in the air. It then flies 25 feet across to its nest.

The Operating income is $172,500.

To calculate the margin of safety, contribution margin ratio, and operating income, we need to use the given information.

a. Margin of Safety:

Margin of Safety = Actual Sales - Break-even Sales

Given that the break-even point is at $750,000 in sales revenue and actual sales are $1,100,000, we can calculate the margin of safety:

Margin of Safety = $1,100,000 - $750,000 = $350,000

Therefore, the margin of safety is $350,000.

b. Margin of Safety as a Percentage of Sales:

Margin of Safety Percentage = (Margin of Safety / Actual Sales) * 100

Using the values from the previous calculations:

Margin of Safety Percentage = ($350,000 / $1,100,000) * 100 = 31.82%

Therefore, the margin of safety expressed as a percentage of sales is approximately 31.82%.

c. Contribution Margin Ratio:

Contribution Margin Ratio = (Contribution Margin / Sales) * 100

To calculate the contribution margin, we need to subtract variable costs from sales:

Contribution Margin = Sales - Variable Costs = $1,100,000 - $645,000 = $455,000

Using the values, we can calculate the contribution margin ratio:

Contribution Margin Ratio = ($455,000 / $1,100,000) * 100 = 41.36%

Therefore, the contribution margin ratio is approximately 41.36%.

d. Operating Income:

Operating Income = Sales - Variable Costs - Fixed Costs

Using the values provided:

Operating Income = $1,100,000 - $645,000 - $282,500 = $172,500

Therefore, the operating income is $172,500.

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The statement about geometric figures

that is true is B. On a coordinate plane, parallel lines have the same slope.

Geometric shapes can be created by combining points, lines, and planes. Angles are created between lines, segments, or rays in virtually every geometric figure that we'll study.

That would appear like this in the coordinate plane: These two lines' slopes are both when we look at them more closely.

Any pair of parallel lines can be used as a generalization of this. Parallel lines always have different intercepts and the same slope. In coordinate geometry, the slopes of two parallel lines are identical and are always equal.

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Answer:

9 oz I think not entirely sure

\(\dfrac{x+4}{3} =7\)

Multiply both sides by 3:

\((\dfrac{x+4}{3} )\times3=(7)\times3\)

\(x+4=21\)

Subtract 4 from both sides:

\(x+4-4=21-4\)

\(\boxed{x=17}\)