A(6,2), B(2,4) and C(8,-4) are three points in a plane. P is a point on the line BC and Q is a point in the plane such that PAQB is a rectangle. Find the:
(i) equations of the sides AP and BP,
(ii) coordinates of the point P,
(iii) area of the rectangle. ​

Answer:

Step-by-step explanation:

You want to know the values of x and y that make the angle measures consistent with the triangles being congruent in the given figure.

The side markings show congruent triangles with corresponding vertices (and angles) ...

  L (3x+24)° ⇔ P (8x -11)°

  M 84° ⇔ Q 84°

  N (2x +y)° ⇔ R (no marking)

Corresponding angles L and P have the same measure, so ...

  3x +24 = 8x -11

  35 = 5x . . . . . . . . add 11-3x

  7 = x . . . . . . . . . divide by 5

The measures of these angles are ...

  (3(7) +24)° = 45°

The sum of the angles in each triangle is 180°, so the measure of angle N is found to be ...

  L +M +N = 180°

  45° +84° +N = 180°

  N = 51°

This lets us find the value of y from ...

  (2x +y)° = 51°

  2(7) +y = 51

  y = 37 . . . . . . . . subtract 14

The value of x is 7. The value of y is 37.

Answer:

$10.5/hr

Step-by-step explanation:

210/20=10.5

Natalie can line up her textbooks in 24 different ways on her bookshelf.

Natalie has a Spanish book, a biology book,  physics book, and a health text book.

So, she has a total of 4 books in her book shelf.

So, the number of positions in which the books have to be put are four.

As we can see,

The books are only one in number each. So, the choices are not repeatable.

So,

In first position we have four choices, in third we will be left with three choices, in the seconds position we will have a total of two books as choice and in the last positive we have to put the book that is left.

So, the total different ways in which she can line up her books in the bookshelf are,

= 4×3×2×1

= 24

So, there are 24 different ways possible.

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If Yuvia also earns a base salary of $45 per day. The total amount she earned that day will be $245.

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

The usage of percentages is widespread and diverse. For instance, numerous data in the media, bank interest rates, retail discounts, and inflation rates are all reported as percentages. For comprehending the financial elements of daily life, percentages are crucial.

It is given that, Yuva works in a computer store, where she earns a commission of 8 percent of her sales. On Monday, her sales were $2,500.

Commission = 8 % of sales

Commission =($2,500)(0. 08)

Commission =$ 200

If yuvia also earns a base salary of $45 per day,

Total salary = base pay + commission].

Total salary =45 +200

Total salary =$245

f Yuvia also earns a base salary of $45 per day. The total amount she earned that day will be $245.

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From the graph provided, the coordinates of the two points are;

The distance between two points is;

Then, we substitute the values into the formula, we have;

The distance d, between the points is;

The equation of the line in point-slope form is; y=1.25 x+12.5 The slope of the line is 1.25.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let y is the total cost at the county fair and x is the number of tickets per ride

The variable in the linear equation;

y=mx+c

m=Cost per ticket ride

c= fair admission price

Given that;

y=$43.75

m=$1.25 per ticket ride

x=25 tickets

c=unknown

Now replacing;

43.75=(1.25×25)+c

c=43.75-31.25

c=12.5

The fair admission price will be; 12.5 dollar

The equation of the line in point-slope form is; y=1.25 x+12.5

The slope of the line is 1.25.

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Answer:

Equation of the line is 6x−y+8=0.

So I think Its A

Step-by-step explanation:

I rlly hope it helps u lol

we will use the next formula to find the rate of change of the given interval

in our case

a=-3

b=6

then we substitute the values in the formula

The average rate of change is 10/9=1.11

The correct answer is reflection. Option B.

Metamorphosis is a dramatic change in shape or appearance. Big events like getting a driver's license, going to college, or getting married can change your life. He has three basic fixed transformations of reflection rotation and translation. There is a fourth common transformation called expansion.

Simple Transformations is the SAP programming language for describing transformations between ABAP data and XML formats. ST is limited to ABAP data serialization and deserialization, the two most important modes of data integration. Transformation means change. A geometric transformation, therefore, means making some changes to a particular geometric shape. Transformation is a specific process by which exogenous genetic material is taken up and integrated directly into cells through the cell membrane.

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Answer:

24

Step-by-step explanation:

10 - 7(3 + 2) + 7²

10 - 7(5) + 49

10 - 35 + 49

10 - 35 = -25

-25 + 49 = 24

I hope this helps!

The function is given as,

The graph representing the above equation is green colour.

Given the system of equations. We have:

- For (5,0)

Substitute x = 5 and y = 0 in the equations:

Answer: No

- For (-7, -8)

x = -7 and y = -8

Answer: No

- For (3, -4)

This is satisfied for the first equation but not for the second. Therefore it is not a solution to the system.

Answer: No

- For (-2, -2)

Answer: No

The more appropriate domain for Han is values between 0 and 4, while the minimum surface area is 20.

Given that,

Han discovers an equation for S(r) that, in terms of the radius r in inches, yields the surface area in square inches of any cylindrical container with a particular fixed volume. If Han lets r to take on any value between -1 and 5, he will obtain the graph shown above.

The more appropriate domain to use

The function's finishing graph is added as an attachment.

We can make the following observations based on the graph.

Minimum x value = 0

Maximum x value = 4

The following is a representation of the domain of the function's graph:

Minimum x value  <=  x <= Maximum x value

Substitute the known values in the above equation

So, we have

0 <= x <= 4

0 and 4 are represents a more appropriate domain.

The minimum surface area

The graph that completes the function is added as an attachment

From the graph, we have the following observation

Minimum y value = 20

20 is the minimum surface area of the cylindrical can.

Therefore, The more appropriate domain for Han is values between 0 and 4, while the minimum surface area is 20.

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The expression which is equivalent to fog(x), is

fog(x) = 3x² + 5

Given, the functions f(x) and g(x), as follows

f(x) = 3x + 2 and g(x) = x² + 1

Now, we have to find the fog(x),

fog(x) = 3( x² + 1 ) + 2

fog(x) = 3x² + 3 + 2

fog(x) = 3x² + 5

So, the value of fog(x) = 3x² + 5

Hence, the expression which is equivalent to fog(x), is

fog(x) = 3x² + 5

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All the pairs of ratios that form a proportion are;

B. 7/9, 28/36

C. 14/18, 21/27

What is Proportional?

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

Given that;

All the ratio are,

A. 1/6,4/20

B.7/9 ,28/36

C. 14/18 ,21/27

D. 30/80 , 6/18

Now,

Solve the ratio in simplest form as;

A. 1/6, 4/20

1/6 = 1 / 6

And, 4 / 20 = 1 / 5

Thus, It is not form a proportion.

B. 7/9, 28/36

7 / 9 = 7 / 9

And, 28 / 36 = 7 / 9

Thus, It is form a proportion.

C. 14/18 ,21/27

14 / 18 = 7 / 9

And, 21 / 27 = 7 / 9

Thus, It is form a proportion.

D. 30/80 , 6/18

30 / 80 = 3 / 8

And, 6 / 18 = 1 / 3

Thus,  It is not form a proportion.

Therefore, All the pairs of ratios that form a proportion are;

B. 7/9, 28/36

C. 14/18, 21/27

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The standard form of the equation of the line

The equation of the line can be expressed in several forms. One of them is the standard form:

Ax + By = C

Where A, B, and C are constants, and x and y are the variables.

We have the equation:

Multiplying by 3:

Subtracting 4x:

Is the required standard form of the line

The slopes of the rays of the absolute value function, y = -3·|x + 2| + 8 are 3 and -3

In an absolute value function, an algebraic expression is contained within an absolute value symbol.

The given absolute value function is; y = -3·|x + 2| + 8

The slope of the rays are found as follows;

The general form of the absolute value function is; f(x) = a·|x - h| + k

The vertex of the function is the point (h, k)

The slope of the function is a

Comparing the specified function, y = -3·|x + 2| + 8, to the general function, we get;

The vertex of the function is (h, k) = (-2, 8)

The slope of the rays of the function are; a = 3

Slope of the ray 1 = (8 - (-19))/(-2 - (-11)) = 3

Slope of ray 1 is therefore; 3

Slope of ray 2 = (8 - (-19))/(-2 - 7) = -3

The slope of the ray 2 is therefore; -3

The slope of the rays are; 3 and -3

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The equation of the line that passes through the point (5,3) and has a slope of 3/5 is  y = 3 / 5x .

The equation of a line in slope intercept form can be represented as follows:

y = mx + b

where

The equation of the line passes through the point (5,3) and has a slope of 3/5. Therefore, let's find the y-intercept of the line using (5, 3)

y = 3 / 5 x + b

3 = 3 / 5 (5) + b

3 = 3 + b

b = 3 - 3

b = 0

Therefore, the equation of the lines is y = 3 / 5x

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The perimeter measures around 36 metre.

The perimeter refers to the area surrounding an object. For instance, your house has a fenced-in yard. The perimeter is the length of the fence. If the yard is 50 feet by 50 feet, your fence is 200 feet long.

While 12.74 rounds up to 13, 5.45 rounds down to 5. Recatangle created a total of four sides, two of which are identical in length to the other two (which is a poor way to explain it). There are two sides that are 13 inches long and two sides that are 5 inches long, which is the solution to this question. When added together, the perimeter would be 13+13+5+5.

As an expression,

2(13)+2(5)

=26+10

=36.

The perimeter is approximately 36 meters.

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Answer:

[tex] - 120[/tex]

that would be your answer thank you very much

Equation of line having passing points (-6,0) and (0,-24) is 4x + y + 24 = 0

What do you mean by equation of line?

The general equation for every straight line is y = mx + c, where m is the gradient (or degree of steepness) of the line and c is the y-intercept (the point in which the line crosses the y-axis).

The variables x and y are related to coordinates on the line in the linear equation y = mx + c.

The formula y = mx + c yields a result for y when we enter a value for x.

As y depends on the value of x, it follows that x is an independent variable and y is a dependent variable.

Two passing points of line are (-6,0) and (0,-24)

Equation of line having two passing points as (a,b) and (c,d) is

[tex](y-b) = \frac{d-b}{c-a} (x-a)[/tex]

So, here equation of line become ,

[tex](y - 0) = \frac{-24-0}{0+6}(x+6)[/tex]

⇒ [tex]y = \frac{-24}{6}(x+6)[/tex]

⇒ y = -4(x+6)

⇒ y = -4x - 24

⇒ 4x + y + 24 =0

Hence, equation of line having passing points (-6,0) and (0,-24) is 4x + y + 24 = 0

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3589.9 m is the height at which air pressure equals 65% of the air pressure at the surface of the Earth

Given: the function P(h) =P₀ e^(-0.00012h)

When air pressure equals 65% of the air pressure at the surface of the Earth. That means P = 0.65P₀

Substitute P = 0.65P₀ into the function:

P(h) = P₀ e^(-0.00012h)

0.65P₀  = P₀ e^(-0.00012h)

Dividing both sides by P₀ gives:

0.65  = e^(-0.00012h)

Take ln of both sides (ln is the inverse of e):

ln 0.65 = -0.00012h

h = ln 0.65/ (-0.00012)

h = 3589.9 m

Therefore, the height at which air pressure equal 65% of the air pressure at the surface of the Earth is 3589.9 m. Option D is the answer

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Solution

we need to convert the following expression:

four less than half a number n

Then the best answer is:

Solution

If a single die is rolled twice, we would have

Answer:

========================

Let the central angle be α.

Note: You could get it more easily if considered 360° = 2π in your calculations.

Answer:

[tex]\dfrac{78}{5} \pi = 15.6 \pi[/tex]

Step-by-step explanation:

Given values:

As the arc length is given in terms of pi, use the formulas where the angle is measured in radians.

[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Arc length}\\\\Arc length $=r \theta$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $\theta$ is the angle measured in radians.\\\end{minipage}}[/tex]

Substitute the given values into the arc length formula to calculate the central angle (in radians):

[tex]\implies 6\pi=5.2\; \theta[/tex]

[tex]\implies \theta=\dfrac{6\pi}{5.2}[/tex]

[tex]\implies \theta=\dfrac{15}{13}\pi[/tex]

[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Area of a sector of a circle}\\\\Area of a sector = $\dfrac12 r^2 \theta$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $\theta$ is the angle measured in radians.\\\end{minipage}}[/tex]

Substitute the radius and the found angle into the formula and solve for area:

[tex]\begin{aligned}\implies \textsf{Area of the sector}&=\dfrac{1}{2}(5.2)^2 \left(\dfrac{15}{13}\pi\right)\\\\&=\dfrac{1}{2}(27.04) \left(\dfrac{15}{13}\pi\right)\\\\&=(13.52) \left(\dfrac{15}{13}\pi\right)\\\\&=\dfrac{78}{5}\pi \\\\&=15.6 \pi\end{aligned}[/tex]

The given expression is represented in scientific notation as (1.77 × 10⁶).

What do we mean by scientific notation?

So, the given expression in scientific notation:

Therefore, the given expression is represented in scientific notation as (1.77 × 10⁶).

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Correct question?

2.2⋅10^6 −4.3⋅10^5 scientific notation

Answer:

D

Step-by-step explanation:

Two of the same X's

The distance each player ran for warm up laps is 875 cm and the distance each player ran for the store is 1.47 meters.

According to the question,

We have the following information:

Adrianna’s football team ran some warm up laps with a total distance of 6125 centimeters. There are 7 players on her football team.

The distance to the store = 10.31 meters

Now, we can find the distance ran by each player by dividing the total distance by number of players.

Distance for warm up laps = 6125/7

Distance ran by each player = 875 cm

Distance for the store = 10.31/7

Distance for the store = 1.47 m

Hence, the distance each player ran for warm up laps is 875 cm and the distance each player ran for the store is 1.47 meters.

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The rate of cahne of rate with respect to bags is.

Therfore, the rate is 30.

Since, the slope of the graph is positive. The variation is direct.