Explain why when you reflect a point across the line y=x, the x−coordinate and the y−coordinate change places, and when you reflect a point across the line y = −x, the x−coordinate and the y−coordinate change places and their signs are changed.

A triangle's internal angles add up to a total of 180°. This indicates that a triangle's complete turn from one angle to another is equivalent to 180 degrees. Regardless of the triangle's size or shape, there is a link between the measurements of its internal angles.

The sum of the two angles' measurements would also equal 180° if we think of a straight line as a degenerate triangle with two of its angles each measuring 180°. So, the equation for the connection between two angles' measurements is:

Mangle1 + Mangle2 = 180°

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The probability of flipping at least two heads in a row when a fair coin is flipped three times can be calculated by determining the favorable outcomes and dividing it by the total number of possible outcomes. The probability is 1/8 or 0.125.

To calculate the probability, we need to determine the favorable outcomes and the total number of possible outcomes.

In this case, the favorable outcomes are when we have at least two consecutive heads. There are three possible scenarios: (1) HHH, (2) THH, and (3) HHT.

The total number of possible outcomes when flipping a fair coin three times is 2^3 = 8, since each flip has two possible outcomes (head or tail), and we multiply them together for three flips.

Therefore, the probability of flipping at least two heads in a row is 3 favorable outcomes out of 8 total possible outcomes. This can be expressed as 3/8 or 0.125.

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Answer:

360ft^2

Step-by-step explanation:

We know that the height is always 8 ft. So lets find the area of two of the 4 walls.

We multiply by 2 because there are two of the same wall.

2(8ft x 10ft) = 160ft^2

Now lets find the area of the other wall.

2(8ft x 15ft) = 240ft^2

Now we add it up

160 + 240 = 400

400ft^2

But wait! We aren't done yet! We still have to subtract out the door and window which is 60ft^2.

400 - 60 = 360

360ft^2

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Answer:

Infinite number of solutions.

Step-by-step explanation:

Are the equations written correctly?  They are identical.  Since they overlap, every point is a solution for as long as the lines reach.  Since no one is stopping them, the answers are infinite.

Answer:

you are correct

Step-by-step explanation:

since this was a random sampling, there can be no source of bias.

Answer:

-200 isn't higher than 450 but 450 is:

450 is 250 higher than -200

Step-by-step explanation:

Answer:

The missing value of the inverse function is 20

Answer:

No Solution or 0

Step-by-step explanation:

Combine like terms: constant numbers

Isolate x

Plug back into equation but the answers x=0 and x greater than or equal to 3/29 overlap so no solution.

Answer:

x = 5, -5, 3, -3

Step-by-step explanation:

First, substitute u = x^2 into the equation, and we have

u^2 - 34u + 225 = 0

u = x^2

Factor u^2 −34u +225 using the AC method, and we get

( u - 25) ( u - 9) = 0

We know If any individual factor on the left side of the equation is equal to

0, the entire expression will be equal to 0, so

u - 25 = 0

u - 9 = 0

Next, we set u - 25 equal to 0  and solve for u, and we get

u = 25

Then set u - 9 equal to 0 and solve for u, and we get

u = 9

The final solution is all the values that make (u−25)(u−9) = 0  true.

u =25,9

Substitute the real value of u=x^2 back into the solved equation.

x^2 = 25

(x^2)^1 = 9

x^2 = 25

x = 5, -5

Now we solve the second equation

(x^2)^1 = 9

x = 3, -3

So, the answers are: 5, -5, 3, -3

D = M/12 + N/4 represents the relationship between Elena's distance in miles, D, and her biking speed.

Speed = distance/ time

Here, we are given that Elena bikes 20 minutes each day for exercise. She bikes at a constant speed of M miles per hour for the first 5 minutes, then at N miles per hour for the last 15 minutes.

Therefore, distance covered by her in the first 5 minutes = speed x time

time = 5 minutes = 5/60 hours

= 1/12 hours

Thus, distance = M(1/12)

= M/12

Now, similarly, distance covered by her in the last 15 minutes = N(15/60)

=N/4

Thus, the total distance in miles, D, covered by her in the last 15 minutes = N(15/60)

= N/4

Thus, the total distance in miles, D, covered by her is D = M/12 + N/4

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Answer:

QUESTION 1

The given system of equation,

We simplify to get.

The correct answer is option A.

1.

A.) (4, −2)

2.

x = -7

y = 2

3.

x = 5

y = 14

QUESTION 2

The given system of equations is

and

We make y the subject in equation (2) to get,

We put equation (3) into equation (1) to obtain,

We group like terms to get,

This implies that,

we divide through by  to get,

Hence the x-coordinate is  

QUESTION 3

The given system is

and

We make  the subject in equation (2)

We put equation (3) into equation (1) to obtain,

We expand the bracket to get,

Group like terms to get,

We simplify to get;

This implies that,

Therefore the y-coordinate is 14.

Step-by-step explanation:

Answer:

Rhombuses

Step-by-step explanation:

It has four vertical lines, then draw a Venn Diagram, opposite to opposite.

Order from Venn Diagrams:

Quadrilaterals

Rectangles

Squares

Rhombuses.

The metric unit that would be best to measure the capacity of a cereal bowl is milliliters (ml).

Capacity is a measure of the amount of fluid that a container can hold. Cereal bowls are typically used to hold liquids such as milk or yogurt along with cereal. Milliliters are a commonly used metric unit of volume that would be appropriate for measuring the capacity of a cereal bowl. Other metric units of volume such as liters or cubic centimeters could also be used, but milliliters would provide a more precise measurement for a smaller container such as a cereal bowl. To measure the capacity of a cereal bowl in milliliters, one would simply pour a known amount of water into the bowl and measure the volume of the water using a measuring cup or a graduated cylinder.

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Answer:i have same question

Step-by-step explanation:

Answer:

3/4 or 0.75 vertical change per unit of horizontal change

Step-by-step explanation:

Its basically asking what the slope is without stating it directly, to find slope use the equation y2-y1/x2-x1, which coordinate pair you make 1 or 2 doesn't matter as long as it is consistent, this ends up being (0-(-3)) / (0-(-4)) to get 3/4 or 0.75 vertical change per unit

There will be 660 digits which are used to print page numbers of a 256- page book.

To find out the total number of digits. First split the pages into three parts:

(1 - 9), (10 - 99), (100 - 256)

First is (1 - 9) pages

There are 9 pages from 1 to 9 and it will require 9 digits to print the page numbers.

Second is (10 - 99) pages

There are 90 pages from 10 to 99 and it will require 90 multiply by 2 that is 180 digits

Third is (100 - 256) pages

There are 256 - (90+9) = 157 pages and it will require 157 multiply by 3 that is 471 digits.

The total number of digits required is 9 + 180 + 471 = 660.

Therefore, the total number of digits required is 660.

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Answer:

45 gallons

Step-by-step explanation:

60/4=15 so each quarter is 15 gallons. He already has 15 gallons so he needs 45 more.

Answer:

45 gallons

Step-by-step explanation:

60*1/4=15

15*3= 45

Answer:

x=4

Step-by-step explanation:

-x=1-5 (subtract 5 from both sides to isolate the x variable)

-x= -4 (1-5= -4)

x=4  (divide both sides by -1 so the x will not be a negative.)

Therefore, your answer will be x=4. Hope this helps! :)

Answer:

4

Step-by-step explanation:

First, let's move "+5" on the other side. We should change "+" on "-":

-x=1-5

1-5=-4:

-x=-4 |• (-1)

x=4

Answer: look at the attachment I wrote it out

Step-by-step

Answer: A. A relation that is a function.

Step-by-step explanation:

A relation is said to be a function if each input value is associated with one unique output value.

Here, Number of miles run by car is directly proportional to the quantity of gasoline.

Independent variable - quantity of gasoline.

Dependent variable - Number of miles

On assuming the condition of car as good, the number of miles a car can run highly depends on the gallons of gasoline in the tank .

As quantity of gasoline increases number of miles driven would also increases.

i.e. Number of miles driven is a function with respect to quantity of gasoline.

Hence, the given line best describe as : A relation that is afunction.

An convenient to make measurements in centimeters and grams  summary the conversions to 5t units are (a) 0.78 cm ≈ 0.078 5t units,(b) 126.2 s ≈ 126.2 5t units,(c) 42.4 cm³≈ 0.0424 t³,(d) 75.7 g/cm³≈ 75.7 t²

To convert the given measurements to 5t units,  to establish the conversion factors between centimeters/grams and 5t units.

1 t = 10 cm (since 1 meter = 100 cm and 1 meter = 10 t)

1 t = 1 kg (since 1 kg = 1000 g and 1 kg = 1 t)

Now, let's convert each measurement to 5t units:

(a) 0.78 cm:

To convert from centimeters to 5t units, we divide by 10 since 1 t = 10 cm.

0.78 cm / 10 = 0.078 t

Therefore, 0.78 cm is approximately 0.078 5t units.

(b) 126.2 s:

Since no conversion factor is given, we assume that 1 second remains the same in both systems. Thus, 126.2 s remains the same in 5t units.

Therefore, 126.2 s is approximately 126.2 5t units.

(c) 42.4 cm^3:

To convert from cm³to 5t units, we need to consider the conversion for volume, which is (1 t)³ = 1 t³= 1000 cm³

42.4 cm³ / 1000 = 0.0424 t³

Therefore, 42.4 cm³is approximately 0.0424 t³ in 5t units.

(d) 75.7 g/cm³:

To convert from g/cm³ to 5t units, we need to consider both the conversion for mass and volume. We have 1 g = 1/1000 kg = 1/1000 t and 1 cm^3 = 1/1000 t³

75.7 g/cm³ × (1/1000 t / 1/1000 t³) = 75.7 t / t³ = 75.7 t²

Therefore, 75.7 g/cm³ is approximately 75.7 t² in 5t units.

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Answer:

181/65

Step-by-step explanation:

If cos theta is 5/13 then sin theta is equal to 12/13. This is because 5 squared (25) + 12 squared (144) = thirteen squared (169). Tan is sin/cos or opposite/adjacent, so it is equal to 12/5. To add 12/5 and 5/13 you need a common denominator, 65 in this case. 12 times 13 = 156 and 5 times 5 = 25. 156 + 25 = 181. Final answer is 181/65.

While in the blueprint, each square is 1/4...in real life, it's 4 feet per square.

Meaning, the area of each square is (4 x 4) 16 square feet.

Since there are 8 squares/tiles in the bathroom...

...multiply 8 x 16 = 128 square feet in real life.

Multiply that with the cost, and since it costs $5 per square feet:

Do it in similar steps.

Living room: 4 x 7 = 28 tiles

Bedroom: 4 x 5 = 20 tiles

20 + 28 = 48 tiles (in blueprint)

...multiply 48 x 16 = 768 feet square (in real life)

[Convert feet into yards...3 feet equals 1 yard]

a square yard would be 3 feet x 3 feet = 9 feet...

...divide 768 by 9

768 ÷ 9 = 85.33 square yards (rounded up)

Multiply that with the cost, and since it costs $18 per square feet:

Answer:

point form:(2,-2),(-3,13)

Step-by-step explanation:

You solve for the first variable in one of the equations, then substitute the result into the other equation.

Answer:

The x-intercepts of the function are \(x = 3\) and \(x = -5\).

Step-by-step explanation:

We are given the function \(\displaystyle f(x) = x^2 + 2x - 15\).

In order to find the x-intercepts of the equation, we need to solve this quadratic. We can use factoring methods to solve it.

The parent function for a quadratic is \(f(x) = ax^2 + bx + c = 0\).

We can use this information to determine what factoring technique we want to use.

There are several different methods, including using the quadratic formula, but because this is easily factorable, we can avoid using it.

We see that our a is equal to 1 (there is no coefficient in front of x²), so we can use the easier of the techniques:

Therefore, let's determine what our c is: 15.

Now, let's label the factors for 15.

Therefore, our two factors are 3 and 5 since they cannot be broken down any further (they are prime numbers - we just performed prime factorization).

Now, we need to pay attention to the sign for c. It's negative, so one of our factors needs to be negative. Therefore, we can test this out:

Now, we check for which one matches the sign for b. This is positive 2, so our two factors are 5 and -3.

Finally, to factor, we add or subtract the factors from x depending on the sign. If the factor is positive, we add it. If the factor is negative, we subtract it. Therefore, we can set up our equations.

\(x + 5 = 0\\\\x = -5\)

\(x - 3 = 0\\\\x = 3\)

Therefore, for when x = 3 or x = -5, the line crosses the x-axis. These are the x-intercepts of the function.

Our answers are x = -5 and x = 3.

we have the ratio

447 to 166.

so

447:166

Simplify

Its a irreducible fraction

so

answer is

To perform a "pooled variance t-test" in Excel, you should use the "t-Test: Two-Sample Assuming Equal Variances" data analysis tool.

Step-by-step explanation on how to use this tool:

1. Open Excel and ensure that the "Data Analysis ToolPak" add-in is installed. If it's not, go to File > Options > Add-Ins, select "Excel Add-ins" from the drop-down menu, click "Go", and then check the box for "Analysis ToolPak" and click "OK".

2. Organize your data into two columns, one for each sample group. Make sure there are no gaps or missing data points.

3. Click the "Data" tab at the top of the Excel window.

4. In the "Analysis" group, click "Data Analysis".

5. In the "Data Analysis" dialog box, scroll down and select "t-Test: Two-Sample Assuming Equal Variances" and click "OK".

6. In the "t-Test: Two-Sample Assuming Equal Variances" dialog box, enter the cell range for the first sample in the "Variable 1 Range" field and the cell range for the second sample in the "Variable 2 Range" field.

7. Choose the desired level of significance (commonly 0.05) in the "Alpha" field.

8. Select an output range or choose "New Worksheet Ply" to display the results.

9. Click "OK" to perform the pooled variance t-test.

The results will show the t-statistic, degrees of freedom, and p-value, which you can use to determine if there is a significant difference between the two sample groups.

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The graph is in the image uploaded.

Given equation:

y = 3x-7

compare this with standard equation y =mx+b

so slope m = 3

y-intercept b = -7

so the point is (0,-7)

Table:

x        y

1        -4

0       -7

we can plot the graph with two points.

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