Triangle XYZ is drawn with vertices X(−2, 4), Y(−9, 3), Z(−10, 7). Determine the line of reflection that produces Z′(10, 7).

y-axis
x-axis
y = 3
x = −4

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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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

Answer:

9/7 is smallerrrr

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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The solutions are x ≈ -2.744 and x ≈ -17.106.

To solve this equation, we need to get rid of the fractions by multiplying each term by the least common multiple (LCM) of the denominators. The LCM of x+6 and 5x+30 is (x+6)(5x+30).

Multiplying each term by the LCM gives us:
(5)(x+6)(5x+30)/(x+6) = (7)(x+6)(5x+30)/(5x+30) - 2(x+6)(5x+30)

Simplifying the fractions and distributing the terms gives us:
5(5x+30) = 7(x+6) - 2(x+6)(5x+30)

Expanding and simplifying the terms gives us:
25x + 150 = 7x + 42 - 10x^2 - 180x - 360

Combining like terms and rearranging gives us:
10x^2 + 198x + 468 = 0

Using the quadratic formula, we can find the values of x:
x = (-198 ± √(198^2 - 4(10)(468)))/(2(10))

Simplifying gives us:
x = (-198 ± √(39204 - 18720))/(20)

x = (-198 ± √20484)/(20)

x = (-198 ± 143.126)/(20)

The two solutions for x are:
x = (-198 + 143.126)/(20) ≈ -2.744
x = (-198 - 143.126)/(20) ≈ -17.106

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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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Answer:

hope this helps.

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.

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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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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The linear functions of the scenario are y = 12x and y = 24/2x

From the question, we have the following parameters that can be used in our computation:

(1, 12) and (2,24)

From the question, we understand that the function is a linear function

A linear function is represented as

y = mx + c

Using the above as a guide, we have the following equations

m + c = 12

2m + c = 24

Subtract the equations

m = 12

Substitute 12 for m in m + c = 12

12 + c = 12

Evaluate

c =0

So, the equation is y = 12x

An equivalent equation is y = 24x/2

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Answer:

0.00265251989

Hope this helped.

Answer:

,15

Step-by-step explanation:

ez

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

To find out how many points Ava had at the end of round one, we need to work backwards from the end of the game using probability. Here are the steps to do so:

Step 1: At the end of the game, Ava had 50 points. This was after she lost 2/7 of her total points in the fifth round. Let's call the number of points she had before the fifth round X. So:

50 = X - (2/7)X

Step 2: Solve for X by combining like terms:

50 = (5/7)X

Step 3: Multiply both sides of the equation by 7/5 to isolate X:

X = 70

Step 4: Now we know that Ava had 70 points before the fifth round. This was after she increased her total points by 75% in the fourth round. Let's call the number of points she had before the fourth round Y using probability. So:

70 = Y + (75/100)Y

Step 5: Solve for Y by combining like terms:

70 = (175/100)Y

Step 6: Multiply both sides of the equation by 100/175 to isolate Y:

Y = 40

Step 7: Now we know that Ava had 40 points before the fourth round. This was after she decreased her point total by 3/5 in the third round. Let's call the number of points she had before the third round Z. So:

40 = Z - (3/5)Z

Step 8: Solve for Z by combining like terms:

40 = (2/5)Z

Step 9: Multiply both sides of the equation by 5/2 to isolate Z:

Z = 100

Step 10: Now we know that Ava had 100 points before the third round. This was after she increased her point total by 25% in the second round. Let's call the number of points she had before the second round A using probability. So:

100 = A + (25/100)A

Step 11: Solve for A by combining like terms:

100 = (125/100)A

Step 12: Multiply both sides of the equation by 100/125 to isolate A:

A = 80

Step 13: Now we know that Ava had 80 points before the second round, which means she had 80 points at the end of the first round.

Therefore, the answer is 80 points using probability.

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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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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]

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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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)

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 correct statement regarding the monthly payments is given as follows:

D. Yes, because $320 is greater than the amount of interest he is

charged per year.

The monthly payment formula is defined by the equation as follows:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

In which the parameters are listed as follows:

The parameter values for this problem are given as follows:

P = 2700, r = 0.12, n = 12.

Hence:

r/12 = 0.12/12 = 0.01.

Hence the monthly payment is calculated as follows:

A = 2700 x 0.01 x (1.01)^12/(1.01^12 - 1)

A = $240.

The interest is less than $320, hence he will manage to pay off the loan.

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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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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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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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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]

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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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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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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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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Answer:

$2.50

Step-by-step explanation: