A trampoline park has a trampoline that is 8 yards wide and 12 yards long. Approximate the distance (in
yards) between opposite corners of the trampoline to the nearest tenth.

Answer:

y=5x+6

Step-by-step explanation:

The equation of line passes through the point (2, 16) will be;

⇒ y = 5x + 6

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The point on the line are (2, 16).

And, The parallel line is,

⇒ y = 5x + 8

Now,

Since, The equation of line passes through the point (2, 16).

So, We need to find the slope of the line.

Since, The slope of the parallel line is same.

Hence, Slope of the line is,

y = 5x + 8

m = dy/dx = 5

m = 5

Thus, The equation of line with slope 5 is,

⇒ y - 16 = 5 (x - 2)

⇒ y - 16 = 5x - 10

⇒ y = 5x - 10 + 16

⇒ y = 5x + 6

Therefore, The equation of line passes through the point (2, 16) will be;

⇒ y = 5x + 6

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The speed that should be taken by Lionel to get to the destination will be 78 miles per hour.

From the information given, when Lionel drives from Barcelona to Madrid, 390 miles, it takes him about 6.5 hours.

The speed to make the trip in 5 hours will be:

Speed = Distance / Time

Speed = 390/5

Speed = 78 miles per hour.

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Answer:

To determine the speed, we can use the formula:

speed = distance / time

where distance is measured in feet and time is measured in minutes.

In this case, the distance is 264 feet and the time is 3 minutes. Plugging these values into the formula, we get:

speed = 264 feet / 3 minutes

simplifying, we get:

speed = 88 feet/minute

Therefore, the equipment is traveling at a speed of 88 feet per minute.

At first, let us find the measure of angle B

The sum of angles of a triangle is 180 degrees

Subtract 123 from both sides to fin m < B

Now, let us use the sin rule

Since b = 42, then

By using cross multiplication

Divide both sides by sin 57

Do the same to find c

By using cross multiplication

Divide both sides by sin 57

Answer:

the answer is x=4

Step-by-step explanation:

Distance can be defined as the amount of ground covered (traveled) by a physical object over a specific period of time and speed, regardless of its direction, starting point or ending point.

Mathematically, the distance (traveled) by a physical object can be calculated by using this formula:

Distance = speed × time

Making time the subject of formula, we have:

Time = distance/speed

Next, we would calculate the amount of time it will take for the two couriers to meet:

t = d/(Vm + Vn)

t = 8/(1 + 3)

t = 8/4

Time, t = 2 hours.

For the meeting time, we have:

Meeting time = 8:00 AM + 2 hours

Meeting time = 10:00 AM.

For the distance from M, we have:

Distance = 1 × 4

Distance = 4 km.

For the distance from N, we have:

Distance = 3 × 4

Distance = 12 km.

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Complete Question:

Two couriers leave two cities M and N(N is west of M) distant from each other 8kms and both go east. The one from M leaves at 6:00am and goes 1k/h and the one from N leaves at 8:00am and walks 3k/h. At what time did they meet and at what distance from M and N?

Answer:

a) P(t) = 5/6t + 20

b) 34.2 beetles

c) After 78 weeks.

Step-by-step explanation:

a) A general linear growth model can be expressed as P(t) = at + b, where P is the number of beetles in time t and t is the time in weeks.

It is known that:

P(0) = 20

P(6) = 25

These values can be substituted in the general equation to find a and b:

P(t) = at + b

P(0) = 20:

20 = a*0 + b

20 = 0 + b

20 = b

So,

P(t) = at + 20

Using P(6) = 25:

25 = a*6 + 20

25 - 20 = a*6

5 = a*6

5/6 = a

So, the linear growth model can the represented as:

P(t) = 5/6t + 20

b)

The number of beetles after 17 weeks is P(17):

P(17) = 5/6*17 + 20

P(17) = 14.1 + 20

P(17) = 34.2

34.2 beetles.

c)

P(t) = 85

85 = 5/6t + 20

85 - 20 = 5/6t

65 = 5/6t

t = 65*6/5

t = 78

After 78 weeks.

So, if the machine in 4.5.2 is traded in, approximately R615,060 extra needs to be paid.

To calculate the depreciated value of the machine after 6 years, we can use both simple interest and compound interest.

4.5.1 Depreciation at simple interest rate:
The formula for simple interest is:
Depreciated value = Initial value - (Initial value * depreciation rate * time)
In this case, the initial value is R900,000, the depreciation rate is 5% (or 0.05), and the time is 6 years. Plugging in these values into the formula, we get:
Depreciated value = R900,000 - (R900,000 * 0.05 * 6) = R900,000 - R270,000 = R630,000

So, the depreciated value of the machine after 6 years, with simple interest depreciation, is R630,000.

4.5.2 Depreciation at compound interest rate:
The formula for compound interest is:
Depreciated value = Initial value * (1 - depreciation rate)^time
Again, the initial value is R900,000, the depreciation rate is 5% (or 0.05), and the time is 6 years. Plugging in these values into the formula, we get:
Depreciated value = R900,000 * (1 - 0.05)^6 = R900,000 * 0.95^6 ≈ R900,000 * 0.7351 ≈ R661,590

So, the depreciated value of the machine after 6 years, with compound interest depreciation, is approximately R661,590.

4.6 To determine the price of the new machine in 4.5 after 6 years, we need to take into account the rate of inflation, which is 6% compounded annually. This means that the price of the new machine will increase by 6% each year.

To calculate the price of the new machine, we can use the formula for compound interest:
New price = Initial price * (1 + inflation rate)^time
In this case, the initial price is R900,000, the inflation rate is 6% (or 0.06), and the time is 6 years. Plugging in these values into the formula, we get:
New price = R900,000 * (1 + 0.06)^6 ≈ R900,000 * 1.4185 ≈ R1,276,650

So, the price of the new machine after 6 years, with the 6% inflation rate, is approximately R1,276,650.

To calculate how much extra needs to be paid if the machine in 4.5.2 is traded in, we need to subtract the depreciated value of the machine in 4.5.2 from the price of the new machine.
Extra payment = Price of new machine - Depreciated value of machine in 4.5.2
Plugging in the values, we get:
Extra payment = R1,276,650 - R661,590 ≈ R615,060

So, if the machine in 4.5.2 is traded in, approximately R615,060 extra needs to be paid.

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Answer:

44/3

Step-by-step explanation:

Reduce 22/2 to 11, 3/9 to 1/3:

11(1/3)(4)

Working from left to right:

11(4)

------ = 44/3

  3

Answer:

Step-by-step explanation:

simplify 22/2 then multiply it by 3/9

then multiply that answer by 4 and your total will be 14.6

Answer:

an enlargement or a reduction of the figure

a slide of the figure

a turning of the figure about some fixed point

a mirror image of the figure

The best description of a dilation of a figure is a slide of the figure.

What is dilation?

A dilation is a transformation that changes the size of a figure. It can become larger or smaller but the shape of the figure does not change.

Now,

The best description of a dilation of a figure is a slide of the figure.

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Answer:

community property addition

Answer:

Kenny found 80% of the eggs.

Step-by-step explanation:

(4 ÷ 5) × 100 = x

0.8 × 100 = x

80% = x

Kenny found 80% of the eggs.

Answer:

well if you have 10 and you subtract 2 you get 8 it really simple  

Step-by-step explanation:

Answer:

6*n < - (39 + 3/4)

Step-by-step explanation:

Let's do it in steps:

"Six times a number" can be written as:

6*n

Where n is the "number"

"... is less than negative thirty-nine and three-quarters "

then we have:

6*n < - (39 + 3/4)

This is the inequality we wanted, now we can also solve this for n as:

n < -(39 + 3/4)/6

Answer:

Find out for yourself.

Step-by-step explanation:

4th is 16

6th is 36

Based on the numbers that are the 6th and the 4th square numbers, the difference between those numbers is 20.

The 6th square number is:

= 6 x 6

= 36

The 4th square number is:

= 4 x 4

= 16

The difference is:

= 36 - 16

= 20

In conclusion, the difference is 20.

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Answer: Alex 28

Frank 22

Step-by-step explanation: Age difference is 6. Addition is 50

Answer:

%10

Step-by-step explanation:

If the gold steadily increased $400 over a four-month period, we need to figure out how much the gold increased each month.

400 ÷ 4 = 100

Now that we figured out that the gold steadily increased $100 every month, we now need to figure out what percent it grew.

1000 ÷ 100 = 10

The price grew %10 every month.

Answer:

They have large leaves with holes in them that the Toucan can use to reach the fruit inside. The Toucan's beak is also used to break open hard-shelled fruits, such as coconuts. The Toucan's beak is also used for defence against predators, as it can be used to peck and jab at them. The adaptations of the rainforest plants are examples of convergent evolution. Both the Toucan and Monstera Plants have adapted to their environment in order to survive. The Toucan has a large beak that helps it to reach fruit in the canopy, while the Monstera Plant has long, grooved leaves with drip tips that allow water to run off and prevent mould. Both adaptations are beneficial for the survival of the species in the rainforest.

Step-by-step explanation:

Answer:

Step-by-step explanation:       Step 1

1 of 2

step 1.2659 ;[26 Discovery Group

October 20

Last

Trade Time

Chg

Open

52-week High

52-week Low

Sales in 100s

High

Low

​

$38.50

4:00 P.M. ET

$1.56

$37.22

$76.19

$22.78

19,700

$40.10

$36.77

​

\begin{matrix} \text{Discovery Group} & \text{}\\ \text{October 20} & \text{}\\ \text{Last} & \text{\$42.00}\\ \text{Trade Time} & \text{4:00 P.M. ET}\\ \text{Chg} & \text{\$1.50}\\ \text{Open} & \text{\$42.50}\\ \text{52-week High} & \text{\$76.19}\\ \text{52-week Low} & \text{\$22.78}\\ \text{Sales in 100s} & \text{23,600}\\ \text{High} & \text{\$42.50}\\ \text{Low} & \text{\$42.00}\\ \end{matrix}

Discovery Group

October 20

Last

Trade Time

Chg

Open

52-week High

52-week Low

Sales in 100s

High

Low

​

$42.00

4:00 P.M. ET

$1.50

$42.50

$76.19

$22.78

23,600

$42.50

$42.00

​

Answer:

-1.2 Hope this helps!

Step-by-step explanation:

Answer:

\(\frac{3^{10} }{3^{2} }\) , \((3*3)^{4}\), \((3^{4})^{2}\)  

Step-by-step explanation:

The expressions 3¹⁰/3², (3⁴)², and (3·3)⁴ are equivalent to the given expression. which is the correct answer would be options (B), (D), and (E).

Exponential expressions, as the name indicates, involve exponents. We already know that the exponent of a number (base) specifies how many times the number (base) has been multiplied. To answer the exponential expressions, we may need to apply the relationship between exponents and logarithms.

As per option (B), we have

3¹⁰/3²

3¹⁰⁻²

Apply the subtraction operation in the exponent

3⁸

As per option (D), we have

(3⁴)²

3⁴ˣ²

Apply the multiplication operation in the exponent

3⁸

As per option (E), we have

(3·3)⁴

(3²)⁴

3⁴ˣ²

3⁸

Thus, the expressions 3¹⁰/3², (3⁴)², and (3·3)⁴ are equivalent to the given expression.

Hence, the correct answer would be options (B), (D), and (E).

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We have to solve the following inequality:

Answer:

It is also called Archimedes constant which was named after the Greek mathematician, Archimedes, who created an algorithm to approximate the pi value. The value of pi is irrational, which means that the count of digits after the decimal point is infinite.

I hope this helped (;

Answer:

of a Circle. The circumference divided by the diameter of a circle is always π, no matter how large or small the circle is! To help you remember what π is ... just draw this diagram.

...

Step-by-step explanation:

A demand curve is a graph that shows the relationship between the price of a product or service and the quantity of that product or service that consumers are willing to buy at that price.

A graph is a visual representation of data that is used to show the relationship between two or more variables. Graphs are used in many fields, such as mathematics, science, economics, and social sciences, to display and analyze data in a way that is easy to interpret.

There are several types of graphs, each with its own unique features and uses. Some common types of graphs include:

Line graphs: A line graph is used to display data that changes over time. The data points are connected by lines to show the trend of the data.

Bar graphs: A bar graph is used to compare data across different categories. The height or length of the bars represents the quantity or value of the data.

Pie charts: A pie chart is used to display the proportion of data in different categories. The size of each slice of the pie represents the percentage of the total data.

Scatter plots: A scatter plot is used to display the relationship between two variables. Each data point is represented by a dot on the graph, and the position of the dot represents the value of the two variables.

A demand curve is a graph that shows the relationship between the price of a product or service and the quantity of that product or service that consumers are willing to buy at that price. The demand curve is downward sloping, meaning that as the price of the product or service increases, the quantity demanded decreases, and as the price decreases, the quantity demanded increases.

TRIBE is an acronym that stands for the five factors that can affect the demand for a product or service. These factors are:

An increase in demand, represented by the curve D1, could be caused by a shift in one or more of these factors. For example, if a new study finds that consuming the product has health benefits, the taste and preferences of consumers may shift, leading to an increase in demand for the product.

A decrease in demand, represented by the curve D2, could also be caused by a shift in one or more of these factors. For example, if the price of a related good or service decreases, consumers may switch to that alternative, leading to a decrease in demand for the original product.

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The quantity of more flour that she needs to add would be = 3/4

A fraction is defined as the representation of the part of a whole data in a form of numerator and denominator.

The quantity of flour Ryan needs for baking = 3¼

The quantity of flour she has already added = 2½

The remaining amount that she needs to add;

= 3¼-2½

= 3/4

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Answer: its (4f 5) ^3

Step-by-step explanation:

Answer:

The approximate distance between points D and E is 8.25

Step-by-step explanation:

The figure is as follows :

To find - What is the approximate distance between points D and E ?

Solution -

By Pythagoras Theorem, we get

(DE)² = (FE)² + (DF)²

        = (8)² + (2)²

        = 64 + 4

        = 68

⇒(DE)² = 68

⇒DE = √68

⇒DE = 8.246

∴ we get

The approximate distance between points D and E is 8.25