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This construction is also known as the "perpendicular bisector" construction.

To construct a line through a given point that is perpendicular to a given line using a ruler and compass, you will need to follow these steps:

By following these steps, you have used the ruler and compass to construct a line through a given point that is perpendicular to a given line. This construction is also known as the "perpendicular bisector" construction.

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Step-by-step explanation:

a = 55° because angles on a straight line (around a single point on one side of the line) add up to 180°.

b = 75° because alternate angles (with parallel lines) are equal.

c = 50°, because alternate angles (with parallel lines) are equal.

d = 50°, because corresponding angles (with parallel lines) are equal.

The solution to the equation is x = 12.

The equation for "twice the difference of some number and 8 amounts to the quotient of 112 and 14" can be written as:

2(x - 8) = 112/14

Where x is the unknown number.

First, simplify the right side of the equation by dividing 112 by 14 to get:

2(x - 8) = 8

Next, distribute the 2 on the left side of the equation:

2x - 16 = 8

Finally, solve for x by isolating the variable on one side of the equation:

2x = 8 + 16

2x = 24

x = 24/2

x = 12

Therefore, the solution to the equation is x = 12.

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To find the new coordinates of the points after Louis multiplied each x-coordinate and y-coordinate of triangle ABC by -2, we can use the following formulas:

New x-coordinate = -2 * old x-coordinate

New y-coordinate = -2 * old y-coordinate

Let's apply these formulas to each point in triangle ABC:

Point A: (-3, 4)

New x-coordinate of A = -2 * (-3) = 6

New y-coordinate of A = -2 * 4 = -8

New coordinates of A: (6, -8)

Point B: (1, 1)

New x-coordinate of B = -2 * 1 = -2

New y-coordinate of B = -2 * 1 = -2

New coordinates of B: (-2, -2)

Point C: (5, -2)

New x-coordinate of C = -2 * 5 = -10

New y-coordinate of C = -2 * (-2) = 4

New coordinates of C: (-10, 4)

Therefore, the new coordinates of the points after Louis multiplied each x-coordinate and y-coordinate of triangle ABC by -2 are:

A: (6, -8)

B: (-2, -2)

C: (-10, 4)

According to the information we can infer that the statement that establishes a correct interpretation of the model is the model associates a score of 80 with 2 hours of studying.

To select the correct statement we must replace the value of (t) in the equation and check the relationship between the results of the students in the test and the hours spent studying.

According to the above, if we replace t by two we can infer that the result would be y = 80 as shown below:

So the correct answer would be statement C.

On the other hand, to identify the percentage to which the number of seventh grade students who have a laptop is equivalent, we must add the total number of students in this grade and then find the percentage with a rule of three:

So the correct answer would be 42% because this value is the closest and we could approximate it.

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Answer: d = [tex]\sqrt{109}[/tex]

Step-by-step explanation:

Use the distance formula. [tex]d=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y{1})^2[/tex]

[tex]d=\sqrt{(3-(-7))^2+(1-4)^2[/tex]

d = [tex]\sqrt{(10)^2+(-3)^2}[/tex]

d = [tex]\sqrt{100+9}[/tex]

d = [tex]\sqrt{109}[/tex]

Given- Two points as (-7,4) and (3,1)

To find- The exact distance between them

Explanation - we know the distance formula is

[tex]d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}[/tex]

here

[tex]x_1=-7, x_2=3\\y_1=4, y_2=1[/tex]

Substituting these values we get

[tex]d=\sqrt{(-7-3)^2+(1-4)^2} \\d=\sqrt{10^2+3^2} \\d=\sqrt{100+9} \\d=\sqrt{109} \\d=10.44[/tex]

Hence the distance between them is 10.44

Final answer- the distance between the points is 10.44

This expression will generate all angles coterminal with 240 degrees.

To convert an angle from degrees to degrees, minutes, and seconds, we need to use the following formulas:
1 degree = 60 minutes
1 minute = 60 seconds

First, we need to convert the decimal part of the angle to minutes:
0.32 degrees * 60 minutes/degree = 19.2 minutes

Next, we need to convert the decimal part of the minutes to seconds:
0.2 minutes * 60 seconds/minute = 12 seconds

So, the angle 124.32 degrees is equal to 124 degrees, 19 minutes, and 12 seconds:
124.32 ∘ = 124 ∘ 19 ′ 12 ′′

To convert an angle from degrees, minutes, and seconds to decimal degrees, we need to use the following formulas:
1 degree = 60 minutes
1 minute = 60 seconds

First, we need to convert the minutes to degrees:
36 minutes / 60 minutes/degree = 0.6 degrees

Next, we need to convert the seconds to degrees:
36 seconds / 3600 seconds/degree = 0.01 degrees

So, the angle 48 degrees, 36 minutes, and 36 seconds is equal to 48.61 degrees:
48 ∘ 36 ′ 36 ′′ = 48.61 ∘

To find the angle of least positive measure that is coterminal with a given angle, we need to use the formula:
A = A + 360n

Where A is the given angle, and n is an integer. We need to find the smallest positive value of n that makes the expression equal to a positive angle less than 360 degrees.

For the given angle A = 725 degrees, we can use n = -2:
A = 725 + 360(-2) = 725 - 720 = 5 degrees

So, the angle of least positive measure that is coterminal with 725 degrees is 5 degrees.

To find an expression that generates all angles coterminal with a given angle, we can use the formula:
A = A + 360n

Where A is the given angle, and n is an integer. For the given angle A = 240 degrees, the expression is:
240 ∘ + 360n

This expression will generate all angles coterminal with 240 degrees.

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In order for the system of equations to be consistent, k must not be equal to 31.6087.

In order for the system of equations to be consistent, the determinant of the coefficient matrix must not be equal to zero. The coefficient matrix is:

| -3  4  7 |
| -11 24 k |
| 2  -5 -8 |

The determinant of this matrix is:

(-3)(24)(-8) + (4)(k)(2) + (7)(-11)(-5) - (7)(24)(2) - (4)(-11)(-8) - (-3)(k)(-5)

Simplifying this expression gives:

576 + 8k + 385 - 336 - 352 + 15k = 0

Solving for k gives:

23k = 727

k = 727/23

k ≈ 31.6087

Therefore, in order for the system of equations to be consistent, k must not be equal to 31.6087.

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Iliana needs to play for 16 hours to get a total of 200 XP.

What is  slope-intercept form ?

The slope-intercept form is a way to write the equation of a line in two variables, usually x and y. It is called "slope-intercept" form because it gives the slope of the line and the y-intercept of the line.

The slope-intercept form is given by:

y = mx + b

where m is the slope of the line and b is the y-intercept, which is the point where the line crosses the y-axis.

We can use the points on the graph to find the equation of the line that relates playing time (x) to total XP (y). To do this, we can use the slope-intercept form of a line:

y = mx + b

where m is the slope of the line and b is the y-intercept.

To find the slope, we can use any two points on the line. Let's use points A and B:

m = (y2 - y1) / (x2 - x1) = (50 - 25) / (4 - 2) = 25/2

Now we can write the equation of the line in slope-intercept form:

y = (25/2)x + b

To find the value of b, we can substitute one of the points on the line into the equation. Let's use point A:

25 = (25/2)(2) + b

b = 0

So the equation of the line is:

y = (25/2)x

Now we can use this equation to find how many hours Iliana needs to play to get 200 total XP. We can set y = 200 and solve for x:

200 = (25/2)x

x = (2/25) * 200

x = 16

Therefore, Iliana needs to play for 16 hours to get a total of 200 XP.

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Answer:

See below.

Step-by-step explanation:

We are asked to solve this expression.

We should first identify that (-5) will be a positive 5 due to 2 negatives cancelling each other out.

We should have;

[tex]-2 \frac{1}{3}+5[/tex]

To make adding a bit more simpler for this type of problem, we should turn both values into Improper Fractions.

Improper Fractions are 2 or more fractions that have a greater numerator than a denominator. You can see why they're called improper.

Good Examples:

[tex]\frac{4}{3} \ and \ \frac{3}{2} \\4 > 3\\ 3 > 2[/tex]

Bad Examples:

[tex]\frac{3}{4} \ and \ \frac{4}{4} \\3 < 4\\4 = 4[/tex]

Let's turn these values into Improper Fractions.

[tex]\frac{1}{3} - \frac{3}{3} - \frac{3}{3} = -\frac{7}{3}[/tex]

[tex]5=\frac{5}{1}[/tex]

Make the Denominators Equal:

[tex]\frac{5}{1} \times \frac{3}{3} = \frac{15}{3} \ (5)[/tex]

Now, we can simply add.

[tex]-\frac{7}{3} + \frac{15}{3} = \frac{8}{3}[/tex]

Reverse, turn [tex]\frac{8}{3}[/tex] into a mixed fraction.

[tex]\frac{8}{3} - \frac{3}{3} \ (1) - \frac{3}{3} \ (2) = 2\frac{2}{3}[/tex]

Our final answer is [tex]2\frac{2}{3} .[/tex]

Answer:

9/7 is smallerrrr

The equation x^(4)+6x^(3)-3x^(2)-24x-4=0 has possible rational roots ± 1, 2, 4, ± 1/2, 1/4.

Given the equation: $x^4+6x^3-3x^2-24x-4=0$

To identify possible rational roots we use Rational Root Theorem which states that:

If a polynomial function with integer coefficients has any rational roots then the numerator must divide the constant term and the denominator must divide the leading coefficient. Let's identify possible rational roots. The constant term is -4 and the leading coefficient is 1. Therefore, the possible rational roots are as follows:± 1, 2, 4± 1/2, 1/4

We use synthetic division to test several possible rational roots in order to identify the roots of the equation.

x−40−3−2−4−4−4−4−2+2-2+2-2+2+2-1+1-1+1-1+1+1+4-2+4-2+4-2+4+0-4+0-4+0-4±1 is the root of the equation since the remainder is zero. Therefore, divide the polynomial by x − 1.x^4+6x^3-3x^2-24x-4 = (x-1)(x^3+7x^2+4x+4x+4) = (x-1)(x^3+7x^2+8x+4)

The roots of the equation are x = 1, -2 ± i, where i = √(-1).

Hence, we have completed the following:

Possible rational roots: ± 1, 2, 4, ± 1/2, 1/4

Synthetic division to test possible rational roots: x−40−3−2−4−4−4−4−2+2-2+2-2+2+2-1+1-1+1-1+1+1+4-2+4-2+4-2+4+0-4+0-4+0-4

Possible rational root: ±1

Divide polynomial by (x-1): x^4+6x^3-3x^2-24x-4 = (x-1)(x^3+7x^2+4x+4x+4) = (x-1)(x^3+7x^2+8x+4)

Roots of the equation: x = 1, -2 ± i, where i = √(-1).

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Answer:

$2.50

Step-by-step explanation:

Answer:

See explanation

Step-by-step explanation:

50 is 5*10, so multiply 3 by 5 also to get 5 and 15/50. First answer is 15

5 and 15/50 is also equal to 4 and 65/50. second answer is 65

carry the numerator on the second line to get 30 for the third answer.

finally, subtract 3 from 4 to get 1, and subtract 30 from 65 to get 35/50.

last two answers are 1, and 35.

The length of the top of the workbench is 13m and the width is 7m.

To find the length and the width, we can use the formula for the area of a rectangle, which is A = L x W, where A is the area, L is the length, and W is the width. We can plug in the given values and solve for the unknowns.

Let's start by assigning variables to the length and the width. Let's call the width x and the length x + 6 (since the length is 6m greater than the width).

Now we can plug these values into the formula:

A = L x W

91 = (x + 6) x x

91 = x2 + 6x

Now we can rearrange the equation to solve for x:

x2 + 6x - 91 = 0

We can use the quadratic formula to solve for x:

x = (-6 ± √(62 - 4(1)(-91))) / (2(1))

x = (-6 ± √(36 + 364)) / 2

x = (-6 ± √400) / 2

x = (-6 ± 20) / 2

The two possible solutions are:

x = (-6 + 20) / 2 = 7

x = (-6 - 20) / 2 = -13

Since the width cannot be negative, the only valid solution is x = 7. This means that the width is 7m and the length is x + 6 = 7 + 6 = 13m.

So the length of the top of the workbench is 13m and the width is 7m.

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1. 1-cos²x / sinx = sin²x / sinx = sinx
2. Cos X – Cos x = 0
3. (sin^2 + tan^2 u + cos^2 u) / (sec u) = (1 + tan^2 u) / (sec u) = sec^2 u / sec u = sec u
4. (sec^2 x – tan^2 c) / (cos^2 x + sin^2 x) = (1/cos^2 x - sin^2 x / cos^2 x) / 1 = (1 - sin^2 x) / cos^2 x = cos^2 x / cos^2 x = 1
5. (sec^2 + csc^2 x) - (tan^2 x + cot^2 x) = (1/cos^2 x + 1/sin^2 x) - (sin^2 x / cos^2 x + cos^2 x / sin^2 x) = (sin^4 x + cos^4 x) / (sin^2 x cos^2 x) = 1 / (sin x cos x)
6. tan x cot x = (sin x / cos x) * (cos x / sin x) = 1
7. cot u sin u = (cos u / sin u) * sin u = cos u
8. sec (-x) cos (-x) = (1 / cos (-x)) * cos (-x) = 1
9. cot (-θ) tan (-θ) = (cos (-θ) / sin (-θ)) * (sin (-θ) / cos (-θ)) = 1
10. sec^2 (-x) – tan^2 (-x) = (1/cos^2 (-x)) - (sin^2 (-x) / cos^2 (-x)) = (1 - sin^2 (-x)) / cos^2 (-x) = cos^2 (-x) / cos^2 (-x) = 1
11. sec u sin u = (1 / cos u) * sin u = sin u / cos u = tan u

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The answers are given in the solution below.

A circle is a round-shaped figure that has no corners or edges. In geometry, a circle can be defined as a closed, two-dimensional curved shape.

Given that, are circles, we need to find the value of x in each of them,

Using the property of circle,

1) ∠ TSU = 1/2(arc LV + arc TU)

98° = 1/2(70° + 25x+1)

196 = 71+25x

25x = 125

x = 5

2) ∠ BAC = 1/2(arc DR + arc CB)

10x-5 = 1/2(4x+18 + 132)

20x-10 = 4x+18+132

16x = 160

x = 10

3) arc FR = 360° - 245°

arc FR = 115°

∠ FSR = 1/2(245-115)

8x+1 = 65

8x = 64

x = 8

4) ∠ EDF = 1/2(arc CF - arc DF)

5x+1 = 1/2(13x+19-4x-5)

5x+1 = 1/2(9x+14)

10x+2 = 9x+14

x = 12

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Answer:

hope this helps.

Step-by-step explanation:

In the triangle ABC, the value of AC is obtained as 5 units.

What are triangles?

Triangles are a particular sort of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here. An example of a 3-sided polygon is a triangle. The total of a triangle's three angles equals 180 degrees. One plane completely encloses the triangle.

A triangle ABC is given.

The measure of AB is given as 10 units.

The measure of KB is given as 2 units.

The measure of KM is given as 1 unit.

According to the indirect measurement -

AB / AC = KB / KM

Substitute the values in the equation -

10 / AC = 2 / 1

2 AC = 10

AC = 5  

Therefore, the value of AC is obtained as 5 units.

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Answer:

0.00265251989

Hope this helped.

The possible arrangement is 3960.

Permutation is a mathematical calculation of the number of ways a particular set can be arranged, where the order of the arrangement matters.

Given that, Bart wants to plant 8 trees in a row along his fence.

Possible arrangement of 4 birches = 5 x 4 x 3 x 2 x 1 = 120

If 3 birches are next to each other, therefore, 6 possible arrangement are possible = A₄⁴ x A₅² = 480

Similarly,

If 2 birches are next to each other, therefore, 6 possible arrangement are possible = A₄⁴ x A₅² = 480

If 4 birches are not next to each other, therefore, possible arrangement are possible = A₄⁴ x A₅⁴ = 2880

Therefore, total arrangements = 120+480+480+2880 = 3960

Hence, the possible arrangement is 3960.

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If both a and b are positive numbers and (b)/(a) is greater than 1, then a-b will be negative.

This is because when (b)/(a) is greater than 1, it means that b is greater than a. So when you subtract a from b, you will get a negative number.

For example, let's say a = 2 and b = 5.

(b)/(a) = (5)/(2) = 2.5, which is greater than 1.

So when we subtract a from b, we get:

b - a = 5 - 2 = 3, which is a positive number.

But when we subtract b from a, we get:

a - b = 2 - 5 = -3, which is a negative number.

Therefore, if both a and b are positive numbers and (b)/(a) is greater than 1, then a-b will be negative.

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The location of B' after the rotation on the coordinate plane of 90 degrees clockwise about the origin is

90 degree clockwise rotation refers to the rotation of a figure on a coordinate plane about a fixed point in the clockwise direction. Every point (x, y) will rotate to in order to rotate the figure 90 degrees clockwise around a point (y, -x).

This then means that the B will go from B ( 7, 3 ) to B' ( 3, - 7 ) after a clockwise rotation about the origin.

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Answer:

,15

Step-by-step explanation:

ez

The standard form to this equation is x=2/3.

This equation is in the form of a linear equation in one variable, where the variable is x.

The equation is written as x=2/3, meaning that the value of x is equal to 2/3.

The equation can be interpreted as the ratio of two numbers, 2 and 3. The numerator, 2, represents the number of parts, and the denominator, 3, represents the total number of parts.

This equation can be used to solve for the fraction of the total number of parts represented by the numerator. In this case, the fraction is 2/3, or 2 parts out of a total of 3 parts.

The equation can also be interpreted as a proportion. If we make the numerator the unknown value, x, then the equation becomes x/3 = 2/3. This equation can be solved using the cross-multiplication method.

By multiplying the denominators together and setting them equal to each other, then solving for x, we get x = 2/3. This equation shows that the value of x is equal to 2/3 of the total number of parts.

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The average rate of change of g(x) over the interval [2, 5] is -2.1.

The formula to calculate the slope of a line passing through two points (x₁, y₁) and (x₂, y₂) is:

slope = (y₂ - y₁) / (x₂ - x₁)

Using this formula, we can calculate the slopes of the two secant lines for f(x) and g(x) over the interval [2, 5]. Let's start with f(x):

slope_f = (f(5) - f(2)) / (5 - 2)

= (-0.1(5)² - (-0.1(2)²)) / (5 - 2)

= (-0.1(25) + 0.1(4)) / 3

= (-2.5 + 0.4) / 3

= -2.1 / 3

= -0.7

Therefore, the average rate of change of f(x) over the interval [2, 5] is -0.7.

Now, let's calculate the average rate of change of g(x):

slope_g = (g(5) - g(2)) / (5 - 2)

= (-0.3(5)² - (-0.3(2)²)) / (5 - 2)

= (-0.3(25) + 0.3(4)) / 3

= (-7.5 + 1.2) / 3

= -6.3 / 3

= -2.1

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Complete Question:

how do the average rates of change for the pair of functions compare over the given interval

f(x)= -0.1x²

g(x)= -0.3x²

2≤x≤5

The final velocity of the jet flying in the north direction after accelerating for 15s is 473 m/s.

When observed from a specific point of view and as measured by a specific unit of time, velocity is the direction at which an item is moving and serves as a measure of the pace at which its position is changing. How quickly or slowly an object is travelling can be determined by its velocity and speed. Being a vector quantity, we need to define velocity in terms of both magnitude (speed) and direction. A body is considered to be accelerating if the magnitude or direction of its velocity changes.

Given,

The initial velocity u = 200 m/s

Acceleration of jet a = 18.2 m/s²

Time taken t = 15s

We are asked to find the final velocity v of the jet.

W can use the following formula to find the final velocity.

v = u+ at

  = 200 + (18.2) × 15

 = 473 m/s (north)

Therefore the final velocity of the jet flying in the north direction after accelerating for 15s is 473 m/s.

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Answer: the last option

Step-by-step explanation:

Standard derivation reflects the degree if dispersion  of a data set

so the answer is 1,1,1,1,2,2,2,2

Answer:

12/18, 2/3, and 18/27.

Step-by-step explanation:

In order to find ratios that are equivalent to a certain fraction they must have common divisibles.

In this case...
[tex]\frac{6}{9}[/tex]
If the common divisible is two....
[tex]6\times2=12[/tex]
[tex]9\times2=18[/tex]
[tex]=\frac{12}{18}[/tex]

You could also simplify the ratio:
[tex]\frac{6}{9} \div3=\frac{2}{3}[/tex]
[tex]=\frac{2}{3}[/tex]

If the common divisible is three:
[tex]6\times3=18[/tex]
[tex]9\times3=27[/tex]
[tex]=\frac{18}{27}[/tex]