The lines below are perpendicular If the solid line has a slope of 2/3 what is the slope of the dashed line?

9514 1404 393

Answer:

  y = -3/5x +27/5

Step-by-step explanation:

Since we want a parallel line, we can use the same x- and y-coefficients to find the new constant in the given form:

  -3(4) -5(3) = -12 -15 = -27

In the given form, the equation of the desired line is ...

  -3x -5y = -27

Solving for y, we have ...

  -5y = 3x -27

  y = -3/5x +27/5

Answer:

y=-2/3x+9

Step-by-step explanation:

Hope this helps :-)

According to the trigonometric relations in a right triangle, we have:

Answer:

\(x = \sqrt 6\)

Step-by-step explanation:

Given

The attached triangle

Required

Find x

Considering angle 30 degrees,

\(Opposite = \sqrt{2\)

\(Adjacent = x\)

Using the tangent formula:

\(tan\ 30 = \frac{\sqrt 2}{x}\)

Make x the subject

\(x = \frac{\sqrt 2}{tan\ 30}\)

\(x = \frac{\sqrt 2}{1/\sqrt 3}\)

\(x = \sqrt 2 * \sqrt 3\)

\(x = \sqrt 6\)

Answer:

331.02

Step-by-step explanation:

Answer:

I believe that the answer is 22.

Step-by-step explanation:

The height would be 22, because the radius is 22, and 484/22 is 22, so I THINK this is the answer.

Given statement solution is :-

1) Gather your electricity bills from the period before the summer break.

2) Create a comprehensive list of all the electrical appliances used in your home.

Include major appliances like air conditioners, refrigerators, washing machines, and smaller devices like televisions, computers, and lights.

3) Research or locate the power consumption information for each appliance.

4) Identify areas where energy consumption can be reduced, such as:

Turning off lights when not in use.

Setting air conditioner temperatures at an optimal level.

Using energy-efficient appliances.

5) After the summer break, collect your electricity bill for the corresponding period.

6) Include details about your energy reduction plan, the changes implemented, and the resulting impact on energy consumption and cost.

Provide recommendations for further improvements or adjustments to achieve even greater sustainability.

To conduct a comparative study of consecutive electric bills and analyze the impact of a reduction plan, you can follow the steps below:

Examine your electricity bills of pre-summer break:

Gather your electricity bills from the period before the summer break.

Look for details such as total energy consumption (in kilowatt-hours or kWh), billing period, and the cost per unit of electricity.

List the various electrical appliances used in your home:

Create a comprehensive list of all the electrical appliances used in your home.

Include major appliances like air conditioners, refrigerators, washing machines, and smaller devices like televisions, computers, and lights.

Find out the power consumption and duration for each device in use:

Research or locate the power consumption information for each appliance.

This information is typically provided on the appliance itself or in the user manual.

Note down the power rating of each device in watts (W) or kilowatts (kW).

Estimate the average duration each device is used daily in hours (e.g., 2 hours for a television, 8 hours for a refrigerator).

Calculate the estimated electricity consumption and cost:

Multiply the power rating (in kW) of each device by its average daily usage (in hours) to find the daily energy consumption (in kWh).

Multiply the daily energy consumption by the number of days in the billing period to get the total energy consumption for that period.

Multiply the total energy consumption by the cost per unit of electricity to calculate the estimated cost for each appliance.

Sum up the estimated costs for all appliances to get the total estimated electricity bill.

Make an energy reduction plan and determine implementation:

Identify areas where energy consumption can be reduced, such as:

Turning off lights when not in use.

Setting air conditioner temperatures at an optimal level.

Using energy-efficient appliances.

Unplugging devices when not in use.

Determine the feasibility of implementing these energy reduction measures in your home.

Re-examine your electricity bill of post-summer break:

After the summer break, collect your electricity bill for the corresponding period.

Calculate the actual energy consumption and cost using the same method as in step 4.

Compare the actual post-summer break bill with the estimated pre-summer break bill.

Note any changes in energy consumption and cost, and analyze the effectiveness of your energy reduction plan.

Document your reduction plan and changes in the bill:

Write a report summarizing your findings and observations.

Include details about your energy reduction plan, the changes implemented, and the resulting impact on energy consumption and cost.

Provide recommendations for further improvements or adjustments to achieve even greater sustainability.

By following these steps, you can conduct a comparative study of consecutive electric bills, analyze the effectiveness of your energy reduction plan, and track changes in energy consumption and costs.

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Answer:

a) 100π

Step-by-step explanation:

A = πr²

A = (10²)π

A = 100π

Answer: 25

Step-by-step explanation:

10           6

/       =      /

x             15

Just cross multiply, so do 10*15 = 6*x

10*15 = 6*x

150 = 6*x

Divide by 6 on both sides to isolate x.

25 = x

Answer:

x = 25

Step-by-step explanation:

first simplify the 6/15 by dividing 6 and 15 both with 3
10/x = 2/5
then multiply with 5x on both sides to get rid of the fraction:
5x * (10/x) = 5x * (2/5)
then shorten and solve:
5 * 10 = x * 2
50 = x * 2
25 = x

Answer:

x² + y² = 74

Step-by-step explanation:

given

(x - y) = 8 ( square both sides )

(x - y)² = 8² ← expand left side using FOIL

x² - 2xy + y² = 64 ← substitute xy = 5

x² - 2(5) + y² = 64

x² - 10 + y² = 64 ( add 10 to both sides )

x² + y² = 74

It should be noted that to prove that G is connected, we can use proof by contradiction. Suppose that G is not connected, which means that there exist two vertices u and v that are not connected by any path in G. Since every vertex in G has degree at least 1, both u and v must have at least one neighbor each.

Let w be a neighbor of u, and x be a neighbor of v. Since u and v are not connected, there is no edge between w and x. But then, the vertices u, w, x, and v form a cycle of length 4, which contradicts the fact that G has minimum degree 1.

Therefore, G must be connected. To show that every pair of vertices is of distance at most 2, let u and v be any two vertices in G. If u and v are adjacent, then they are clearly at distance 1 from each other. Otherwise, let w be a neighbor of u. Since G is connected, there exists a path from w to v, and so the vertices u, w, and v form a path of length 2 from u to v.

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Answer:

64

Step-by-step explanation:

\(\sqrt[3]{512} = 8\\8x8 = 64\)

You need to add 3 5/9 to make 8. If you want to know what 4 4/9 goes to, to make 8, do the opposite which is subtracting. 8 turn to 7 9/9 and then subtract 4 4/9 and then you get the answer aka 3 5/9.

the vertex of the parabola is the point in which the parabola stops decreasing and starts increasing.

Vertex: (-2,2)

the axis of simitry is the vertical line between the parabola that acts as a mirror and divides the parabola exactly on two

Axis ox simetry: x = -2

the minimum or maximum values is as the name says the maximum or minimum values that a function can take place, in quadratic functions the maximum or minimum value that the function can take place will be the vertex and it will depend on the form of the parabola

minimum value: y = 2

lastly, the range of the parabola is all the values that the function can have, in this case from the minimum value to the maximum value, however since there is no maximum value it would be to infinite

range: [2,∞)

The area of carpet required to be bought for the living room is 127.75 square feet.

Thus the area of carpet required is 127.75 square feet.

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The disadvantages of the mode are: For many sets of data there is no mode.

The mode is a measure of central tendency that represents the most frequently occurring value in a dataset.

However, one of the disadvantages of the mode is that for many sets of data, there may not be a distinct mode. In such cases, the data may have a uniform distribution where all values occur with equal frequency, or it may have multiple modes with similar frequencies.

The mode is not affected by extremely large or small values. It only considers the frequency of values and not their magnitude. Therefore, extreme values do not influence the mode.

The statement that the mode can only be computed for interval-level data or higher is incorrect. The mode can be computed for any type of data, including nominal, ordinal, interval, and ratio data. It is applicable to categorical as well as numerical data.

The main disadvantage of the mode is that for many datasets, there may not be a distinct mode.

The correct option is: For many sets of data there is no mode.

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Answer:

the value of a - b is 4.

Step-by-step explanation:

We have been given the following two equations:

a + b = 10 ------------(1)

a² - b² = 40 -------(2)

We can factor the left-hand side of equation (2) using the difference of squares identity:

(a + b)(a - b) = 40

Substituting equation (1) into this equation, we get:

10(a - b) = 40

Dividing both sides by 10, we get:

a - b = 4

Therefore, the value of a - b is 4.

Step-by-step explanation:

if I understand this correctly :

a + b = 10

a² - b² = 40

(a² - b²) = (a + b)(a - b) = 40

10(a - b) = 40

(a - b) = 4

Answer:

180 fb*lb

45 ft*lb

Step-by-step explanation:

We have that the work is equal to:

W = F * d

but when the force is constant and in this case, it is changing.

 therefore it would be:

\(W = \int\limits^b_ a {F(x)} \, dx\)

Where a = 0 and b = 30.

F (x) = 0.4 * x

Therefore, we replace and we would be left with:

\(W = \int\limits^b_a {0.4*x} \, dx\)

We integrate and we have:

W = 0.4 / 2 * x ^ 2

W = 0.2 * (x ^ 2) from 0 to 30, we replace:

W = 0.2 * (30 ^ 2) - 0.2 * (0 ^ 2)

W = 180 ft * lb

Now in the second part it is the same, but the integral would be from 0 to 15.

we replace:

W = 0.2 * (15 ^ 2) - 0.2 * (0 ^ 2)

W = 45 ft * lb

Following are the calculation to the given value:

Given:

\(length= 30 \ ft\\\\mass= 0.4 \ \frac{lb}{ft}\\\\edge= 80 \ ft \\\\\)

To find:

work=?

Solution:

Using formula:

\(\to W=fd\)

\(\to W=\int^{30}_{0} 0.4 \ x\ dx\\\\\)

\(= [0.4 \ \frac{x^2}{2}]^{30}_{0} \\\\= [\frac{4}{10} \times \frac{x^2}{2}]^{30}_{0} \\\\= [\frac{2}{10} \times x^2]^{30}_{0} \\\\= [\frac{1}{5} \times x^2]^{30}_{0} \\\\= [\frac{x^2}{5}]^{30}_{0} \\\\= [\frac{30^2}{5}- 0] \\\\= [\frac{900}{5}] \\\\=180\)

Therefore, the final answer is "\(180\ \frac{ lb}{ft}\)".

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Answer:

69.53 or 70(depending on rounding)

Step-by-step explanation:

The squares area is (9*2)^2 which is 324.

The circles area is 9^2 pi or 254.47 approx.

Subtract and you get 69.53 or 70

Answer:

To find the average speed of the truck, we can divide the total distance travelled by the total time taken.

Average speed = Total distance / Total time

In this case, the truck travelled 261 miles in 4 hours.

Average speed = 261 miles / 4 hours

Average speed = 65.25 mph (rounded to two decimal places)

Therefore, the truck was averaging approximately 65 mph on this trip.

The correct option is (a) 65 mph.

Answer:

i hope it helps mapriend

Answer:

7 < x < 9

Step-by-step explanation:

x^2 – 16x + 63 < 0

this is a parabola that opens up.

The parabola will be < 0 for values between the roots.

to picture this see the graph below.

Factor

(x - 7)(x - 9) < 0

Roots

x = {7, 9}

solution

7 < x < 9

First, recall the definition of the remaining trigonometric functions in terms of sin(x) and cos(x):

On te other hand, recall the Pythagorean Identity:

We can obtain an expression for cos(x) in terms of sin(x) using the Pythagorean Identity as follows:

Find cos(B) using the expression for cosine in terms of sine. Then, use the values of cos(B) andsin(B) to find the values of tan(B), sec(B), csc(B) and cot(B):

Then:

Therefore, the answers are:

Using linear function you would need to cross the bridge 30 times for the costs of the two toll options to be the same.

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Answer:

\( c(1+2+4+5) =1\)

\( c =\frac{1}{12}\)

Now we can find the expected value with this formula:

\( E(Y) =\sum_{i=1}^n Y_i P(Y_i) =\sum_{i=1}^n cy_i *y_i = cy^2_i\)

And replacing we got:

\( E(Y) = \frac{1}{12} (1^2 + 2^2 + 4^2 +5^2) = \frac{46}{12}= \frac{23}{6}\)

Step-by-step explanation:

For this case we know the following probability mass function given:

\( P(y) = cy , y= 1,2,4,5\)

For this case we need to satisfy the following condition in order to have a probability distribution function:

\(\sum_{i=1}^n P(y_i) =1\)

And we have this:

\( c(1+2+4+5) =1\)

\( c =\frac{1}{12}\)

Now we can find the expected value with this formula:

\( E(Y) =\sum_{i=1}^n Y_i P(Y_i) =\sum_{i=1}^n cy_i *y_i = cy^2_i\)

And replacing we got:

\( E(Y) = \frac{1}{12} (1^2 + 2^2 + 4^2 +5^2) = \frac{46}{12}= \frac{23}{6}\)

Answer:

$2100

Step-by-step explanation:

p x r x t

15000 x 0.07 x 2

Answer:7

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

Since v=7, put 7 where the v is. 7+9=16.

(hope this helps :P)

Answer:

16

Step-by-step explanation:

1. substitute 7+9=?

2. add 7+9=16

3. find answer 16