The vertices of a triangle are A(2,5) B(1,2) and C(3,1). Find the coordinates of the image after a rotation 90° clockwise about the origin.

Let us discuss the 4 ways to find the slope:

1. The first case is where, you have two points (x1,y1)  and (x2,y2)

These points often may be intercepts of the x and/or y axes.

The equation of the slope is given by-

m= (y2−y1) / (x2−x1).

2. The second condition is where you are given the linear equation that is either in the form or can be manipulated into the form y=mx+b.

Here, the slope is m(the coefficient of x).

3. The third case is when you have a line that is a tangent to another function, you may have (or be able to determine) the slope of the tangent as the derivative of the function. Normally in such cases, the derivative is a function expressed in terms of x and all you need to do is substitute the value of x into this function for the required equation.

4. The fourth case is when you are given a graph as follows-

Here , the slope m = Δy/Δx

Also, note that tan θ = Δy/Δx

Hence, this tan θ is considered as the slope of the line.

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No , Dilation doesn't increase the measure of angles

Dilation is a transformation, which is used to resize the object. Dilation is used to make the objects larger or smaller.

This transformation produces an image that is the same as the original shape. But there is a difference in the size of the shape.

The new figure obtained after dilation is called the image and the original image is called the pre-image

We dilate any figure by scale factor.

Dilated figures will always be similar figures.

Similar figures have the same shape, angles with the same measures, and the lengths of corresponding sides have equal ratios. The ratio is the same as the scale factor of the dilation.

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Company B charges a $55 initial price plus an extra $0.90 for every mile traveled. For 70 miles, Company A will charge less than Company B.

The occurrence of an unfair and/or uneven distribution of opportunities and resources among the people that make up a society is referred to as inequality. To different individuals and in various settings, the word "inequality" may indicate different things.

$118 in change and unrestricted mileage

B affects the initial $550 and the cost per mile traveled.

Let m stand for the distance covered.

So inequality is

118 < 55 + 0.90 m

= 0.90 m > 118 - 55

= m > 63/0.90

= m > 70

So for 70 miles above company A changed less than company B.

Complete question:

Karen is going to rent a truck for one day. There are two companies she can choose from, and they have the following prices. Company A charges $118 and allows unlimited mileage. Company B has an initial fee of $55 and charges an additional $0.90 for every mile driven. For what mileages will Company A charge less than Company B? Use m for the number of miles driven, and solve your inequality for m.

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Answer:

It is not possible to determine whether the lines are parallel based on the information given. To determine whether two lines are parallel, we need to calculate the slope of each line and compare them. The slope is calculated as the change in the y-coordinate divided by the change in the x-coordinate, or (y2-y1)/(x2-x1). Since we only have the coordinates of the endpoints of the lines and not the equations of the lines, we cannot calculate the slope and therefore cannot determine whether the lines are parallel.

Answer: lines are parallel

Step-by-step explanation:

Lines are parallel if they have the same slope

                      [tex]\boxed {The\ slope\ m=\frac{y_2-y_1}{x_2-x_1} }[/tex]

1) (2,6)  (4,10)

x₁=2    x₂=4    y₁=6    y₂=10

Hence,

[tex]\displaystyle\\m=\frac{10-6}{4-2} \\\\m=\frac{4}{2}\\\\m=2[/tex]

2) (-2,3)  (3,13)

x₁=-2   x₂=3   y₁=3   y₂=13

Hence,

[tex]\displaystyle\\m_1=\frac{13-3}{3-(-2)} \\\\m_1=\frac{10}{3+2} \\\\m_1=\frac{10}{5}\\\\m_1=2[/tex]

m=m₁=2

Hence, lines are parallel

First, let's calculate the total number of marks for each group:

Then, we can calculate the mean mark for the whole group by adding up the total number of marks for each group and dividing by the total number of students:

(144 marks + 192 marks) / (8 students + 12 students) = 336 marks / 20 students = 16.8 marks/student

Therefore, the mean mark for the whole group is 16.8.

The mathematical mean is a measure of central tendency that is calculated by adding up all the values in a data set and dividing by the number of values in the set. It is also commonly known as the "average."

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Answer:

34.5

Step-by-step explanation:

The least common multiple(LCM) of 3, 8, and 12 is 24.

What is the least common multiple(LCM)?

The smallest positive integer that is divisible by both a and b is known as the least common multiple (lcm), lowest common multiple (lcm), or smallest common multiple of two numbers a and b in mathematics and number theory.

We have,

3, 8 and 12

and least common multiple of 3, 8, and 12?

LCM of 3, 8, and 12 is the smallest number among all common multiples of 3, 8, and 12.

The smallest number that can be divisible by 3, 8, and 12 exactly is the LCM.

Multiples of 3 = 3, 6, 9, 12, 15, 18, 21, 24, ….

Multiples of 8 = 8, 16, 24, 32, 40, 48, 56, …..

Multiples of 12 = 12, 24, 36, 48, 60, 72, 84, …..

Hence, the least common multiple(LCM) of 3, 8, and 12 is 24.

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The given ray is a bisector of a given angle.

So, the option (b) is the correct answer.

What is bisector?

Bisection in geometry is the division of an object into two equal or congruent parts, typically by a line, which is then referred to as a bisector. The segment bisector and the angle bisector are the two types of bisectors that are most frequently used.

An angle is divided into two equal parts by a ray known as an angle bisector or angle bisector. For instance, if ray AX divides a 60 degree angle into two equal parts, each measurement will be 30 degrees.

Consider, the given angle.

The given angle is bisects by a ray equally.

Hence, the given ray is a bisector of a given angle.

So, the option (b) is the correct answer.

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The equation of the line passing through the point (-6, -3) and perpendicular to JK with J(-2, -7) and K(6, 5) is y =  -2 / 3x - 7, so option B is correct.

An object having an endless length and no width, depth, or curvature is called a line. Since lines can exist in two, three, or higher-dimensional environments, they are one-dimensional things.

Given:

A line passing through the point (-6, -3) and perpendicular to JK with J(-2, -7) and K(6, 5)

Calculate the slope of the line,

m = 5 - (-7) / 6 - (-)

m = 12 / 8

m = 3 / 2

The slope of a line perpendicular to JK, M = - 1 / 3 / 2 = -2 / 3

Calculate the equation of the line as shown below,

y - (-3) = -2 / 3[x - (-6)]

y + 3 = -2 / 3x - 4

y =  -2 / 3x - 7

Therefore, the equation of the line passing through the point (-6, -3) and perpendicular to JK with J(-2, -7) and K(6, 5) is y =  -2 / 3x - 7.

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An example of discrete data is the number of pencils in a pencil case. Option D

Discrete data can be defined as a numerical type of data including concrete or whole numbers with fixed and specific data values determined by counting.

Some features of discrete data are;

Examples of discrete data are;

Hence, the correct option is the number of pencils in a pencil case.

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The first rider the displacement is, 17 km.

And the 2nd river the displacement is 20.22 km.

What is right triangle?

A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or formerly rectangled triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and other angles of the right triangle.

It is asked in this problem is who's displacement is greater (not distance) it means that the shortest distance of starting and ending point with direction from start and end.

Here we have two triangle with two arm know for both.

So we have to find the 3rd arm for both triangle.

Now we have for a right triangle

a^2 + b^2 = c^2

For other triangle we know the cosine law of triangle is,

a^2 + b^2 - 2ab cosθ = c^2

θ is the opposite angle of c

For the first rider the displacement is,

c = [tex]c = \sqrt{a^2 + b^2} = \sqrt{8^2 + 15^2} = 17 km\\[/tex]

For the 2nd river the displacement is

[tex]c = \sqrt{a^2-b^2 -2abcosheta}[/tex],  θ = 120°

[tex]c = \sqrt{8^2 + 15^2 - 2ab cos(120)} \\c = \sqrt{289 - 240cos(120)} \\c = \sqrt{289 - (-120)} \\c = \sqrt{289 + 120}\\ c = \sqrt{409} \\c = 20.22km[/tex]

Hence, the first rider the displacement is, 17 km.

And  the 2nd river the displacement is 20.22 km.

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The value of x is 3√2/2.

A triangle with one angle being a right angle is called a right-angled triangle.

Given a right-angled triangle, with both acute angles equal to 45°

Since, acute angles = 45°

Therefore, both the legs of the triangle are equal.

Applying Pythagoras theorem,

x²+x² = 3²

2x² = 9

x² = 9/2

x = 3/√2

Rationalizing the denominator,

x = 3√2/√2x√2

x = 3√2/2

Hence, The value of x is 3√2/2.

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The maximum number of friends that he can invite without going over his limit is 9.

A difference between two values indicates whether one is smaller, larger, or basically not similar to the other.

In essence, a comparison of any two values reveals whether one is less than, larger than, or equal to the value on the opposite side of the equation.

As per the given,

Fixed fee = $50

Suppose the number of people is x.

Total fee = 50 + 5.50x

Total fee ≤ budget

50 + 5.50x ≤ 100

5.50x ≤ 50

x ≤ 9.09 thus, x = 9

Hence "The maximum number of friends that he can invite without going over his limit is 9".

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In 42 6/7 minutes the pool will get filed when all 3 pumps work together.

Given,

Time taken by the pump 1 to fill a pool = 50 minutes

Time taken by pump 2 to fill the same pool = 60 minutes

The time taken by pump 3 to drain the pool = 75 minutes

When all the 3 pumps work together, we have to find the time taken to fill the pool;

Here,

In every minute,

Pump 1 fills 1/50 of pool

Pump 2 fills 1/60 of pool

Pump 3 drains 1/75 of pool

That is,

1/50 + 1/60 - 1/75 = 6/300 + 5/300 - 4/300 = 11 - 4 / 300 = 7/300

The time taken = 300/7 minutes = 42 6/7 minutes

Therefore,

When the 3 pumps work together, it will take 42 6/7 minutes to fill the pool.

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The degree measure of the exterior angle triangle is ∠D = 137°.

Having three vertices and three angles that add up to 180 degrees, a triangle is a three-sided polygon.

given this, the angles D, E, and F in the triangle DEF are (4x + 15), (5x + 32), and 70 respectively.

The sum of the angles of a triangle is now 180°.

Therefore, we may write:  m ∠D m∠ E m ∠F = 180

When all the numbers are substituted, we obtain the following results: (9x + 117 = 180) 9x

= 180 -117 (4x + 15) + (5x + 32) + 70

⇒ 9x = 63

⇒ x = 7

As a result, we obtain m∠ D = (4x + 15)°,

m∠ D = (4 x 7 + 15)°,

m ∠D = (28 + 15)°, and m∠ D = (43)°.

Furthermore, m∠ E = (5x + 32)°

m ∠E = (5 x 7 + 32)°

m ∠E = (35 + 32)°

m ∠E = 67°

Since, The measure of the exterior angle to ∠D = m ∠E + m ∠F

= 67° + 70

= 137°

Thus, The measure of the exterior angle  ∠D will be 137°.

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Therefore ,  95% confidence interval for the difference in mean mcls levels is 95% C.I = {4.0978 , 3.1423}.

In frequentist statistics, a confidence interval is a range of estimates for an unobserved parameter. The most frequent confidence level is 95%, while other levels, such 90% or 99%, are occasionally used for computing confidence intervals.

Here,

Given:

c= 1.95 M.E = 0.5 ,n=?,C.V=1.96

Using formula,

=> M.E = C.V + [tex]\frac{c}{\sqrt{n} }[/tex]

=> 0.5 = 1.96 + 1.95/[tex]\sqrt{n}[/tex]

=> 0.5 = 3.822/[tex]\sqrt{n}[/tex]  

=> [tex]\sqrt{n}[/tex]  = 3.822/0.5

=> [tex]\sqrt{n}[/tex]  = 7.644

=> n =58.43

=> n ≈ 58

So, n = 64 , [tex]x^{'}[/tex]=3.62,α=1.95

=> u = [tex]x^{'}[/tex] ± C.V * α/[tex]\sqrt{n}[/tex]

=> u = 3.62 ±  1.96 * 1.95/√64

=>  u = 3.62 ± 0.47775

=>  u = 3.62+ 0.47775 = 4.0978

 or u=3.62-0.47775 = 3.1423

95% C.I = {4.0978 , 3.1423}

Therefore ,  95% confidence interval for the difference in mean mcls levels is 95% C.I = {4.0978 , 3.1423}.

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Theory is the correct answer, theory  represents the lowest degree of certainty.

What is certainty?
The epistemic attribute of beliefs that one cannot rationally reject is certainty, often known as epistemic certainty or objective certainty. Epistemic certainty is commonly defined as a belief being certain if and only if the person holding it could not be wrong in holding it. Other popular definitions of certainty refer to the beliefs' incontrovertibility or describe certainty as a characteristic of those beliefs with the strongest foundation. Although certainty and knowledge are closely related, modern philosophers frequently treat knowledge as having less conditions than certainty.

The rest of the options given in the questions which are conclusion, fact, hypothesis are evidence based and they provides comparatively higher degree of certainty than theory.

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Point E's coordinates are (-7, -1).

The formulas for our new x and y are provided to us. We must first establish our points 1 and 2 before applying this formula. Due to the fact that the issue was sole with the point E that divides the line segment "from J to K,"

the following formula: point 1 = point J = (x1, y1)

Points 2 and K are equal (x2, y2)

The partition segments JE and EK take up a certain amount of the original segment, as indicated by the variables m and n. Given that the ratio is 1:1, then

JE = m = 1

EK = n = 4

Consequently, using the above formulas to calculate for x and y:

x = [1 / (1 + 4)] (25 – (-15)) + (-15) (-15)

x = -7

y = [1 / (1 + 4)] (15 – (-5)) + (-5) (-5)

y = -1

Consequently, point E's coordinates are (-7, -1)

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The two points, along with the [x] - intercept are joined are joined.

        [tex]y =log_{e} x[/tex]

We have the following function -

y = log (1/8)x

We can write -

y = log (1/8)x

y = log(x/8)

y = log(x) - log(8)

Refer to the graph attached. The two points, along with the [x] - intercept are joined.

Therefore, the two points, along with the [x] - intercept are joined are joined.

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Answer:

6+d-1

Step-by-step explanation:

Answer:

2d+4

Step-by-step explanation:

2(3+d-1)

2(3)+2(d)+2(-1)

6+2d-2

2d+4

hopes this helps

The slopes of the secant lines do not appear to be approaching a limit.

For each value of x, calculate y and then use the slope formula to find the slope of P Q for the given limit.

x = 2 → y = 0 : Q(2, 0) ⇒ m =0 − 0 / 2 − 1 = 0

x = 1.5 → y ≈ 0.866 : Q(1.5, 0.866) ⇒ m = 0.866 − 0/ 1.5 − 1 ≈ 1.73

x = 1.4 → y ≈ −0.434 : Q(1.4, −0.434) ⇒ m =−0.434 − 0 / 1.4 − 1 = −1.08

x = 1.3 → y ≈ −0.823 : Q(1.3, −0.823) ⇒ m = −0.823 − 0/1.3 − 1 = −2.74

x = 1.2 → y ≈ 0.866 : Q(1.2, 0.866) ⇒ m = 0.866 − 0 / 1.2 − 1 = 4.33

x = 1.1 → y ≈ −0.282 : Q(1.1, −0.282) ⇒ m = −0.282 − 0/1.1 − 1 = −2.82

x = 0.9 → y ≈ −0.342 : Q(0.9, −0.342) ⇒ m = −0.342 − 0/0.9 − 1 = 3.42

x = 0.8 → y = 1 : Q(0.8, 1) ⇒ m = 1 − 0/ 0.8 − 1 = −5

x = 0.7 → y ≈ 0.782 : Q(0.7, 0.782) ⇒ m = 0.782 − 0/0.7 − 1 = −2.61

x = 0.6 → y ≈ 0.866 : Q(0.6, 0.866) ⇒ m = 0.866 − 0 / 0.6 − 1 = −2.17

x = 0.5 → y = 0 : Q(0.5, 0) ⇒ m = 0 − 0 / 0.5 − 1 = 0

Hence, The slopes of the secant lines do not appear to be approaching a limit.

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Answer:

it’s no solution

Step-by-step explanation:

Answer:

The answer is none its that easy i dont need to explain it

Step-by-step explanation:

your words.

Answer: 2x+3=15 and 81/x-3=6

Step-by-step explanation:

[tex]\displaystyle\\Answer:\ r=\sqrt{\frac{a}{nh} }[/tex]

Step-by-step explanation:

a=nr^2h

Divide both parts of the equation by nh:

[tex]\displaystyle\\\frac{a}{nh} =r^2\\[/tex]

Extract the square root of both parts of the equation:

[tex]\displaystyle\\\sqrt{\frac{a}{nh} } =\sqrt{r^2} \\\\\sqrt{\frac{a}{nh} } =r\\\\Thus,\ r=\sqrt{\frac{a}{nh} }[/tex]

Answer:

200

hope you like it

By using the fact that the sum of the internal angles must be equal to 360°, we will see that x = 18

Suppose we have a figure of N sides, the sum of the internal angles of that figure will be equal to:

S = (N - 2)*180°

In this case, we have 4 sides, then:

S = (4 - 2)*180° = 360°

Also notice that the figure is symmetrical around the two vertical vertices, then the angle at the left side (the only one that we don't know) also measures 101°, like the one in the right side.

Then we can write the linear equation:

100° + 101° + 101° + (4 + 3x)° = 360°

Now we can try to solve this for x.

(100° + 101° + 101°) + (4 + 3x)° = 360°

302° + (4 + 3x)° = 360°

(4 + 3x)° = 360° - 302°

4 + 3x = 58

3x = 58 - 4 = 54

x = 54/3

x = 18

That is the value of x in the kite.

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The options that are done by translational research or science are given as follows:

c. Take laboratory findings for development for use with patients at the bedside

d. Use clinical research findings to ask new questions for research in the laboratory

e. Discover practical applications for scientific theories and laws.

Translational research is a field of science that studies strategies to convert research results or data into strategies that actually benefit humans.

Hence statements c, d and e are correct, as they all involve strategies that benefit humans.

Statements a and b are incorrect, as:

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The y-intercept of the line on the graph is -60.

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

y = mx + b

where

Therefore, the y-intercept is the point where the graph intersects the y-axis.  The y-intercept is the value of y when x = 0.

Therefore, on the graph the value of y when x is equals to zero is -60.

Hence,

y-intercept = -60

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Answer:

5.25c + 116 = 719.75

Step-by-step explanation:

Let c = cost of labor per hour

He worked for 5.25 hours, so the part of the cost due to the hourly rate is

5.25c

You must the add the cost of the parts.

5.25c + 116

Now you set the total cost expression equal to the actual total cost.

5.25c + 116 = 719.75