Triangle DEF has vertices at D(−3, 5), E(−10, 4), and F(−11, 8). Triangle D′E′F′ is the image of triangle DEF after a reflection. Determine the line of reflection if D′ is located at (3, 5).
y = 5
x = −3
y-axis
x-axis

The length of AB = CD and CD = AB based on the proof that :

Looking at the segments CD and AB, both segments are of equal length, hence they would be equal

Similarly , both segments are parallel and have the same end points. Hence, they are equal.

Therefore, AB = CD

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a)  the value of the tractor after two years is $10,400.

b)  the value of the tractor after six years is $5,200.

To find the value of the tractor after a certain number of years, we can substitute the value of t into the equation v = -1,300t + 13,000.

a) After two years:

Substituting t = 2 into the equation, we get:

v = -1,300(2) + 13,000

v = -2,600 + 13,000

v = 10,400

Therefore, the value of the tractor after two years is $10,400.

b) After six years:

Substituting t = 6 into the equation, we get:

v = -1,300(6) + 13,000

v = -7,800 + 13,000

v = 5,200

Therefore, the value of the tractor after six years is $5,200.

To find when the tractor will have no value, we need to find the value of t when v = 0. We can set the equation v = -1,300t + 13,000 equal to 0 and solve for t:

-1,300t + 13,000 = 0

-1,300t = -13,000

t = -13,000 / -1,300

t = 10

Therefore, the tractor will have no value after 10 years.

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Answer:

∠ ADE = 55° , ∠ ACE = 32.5° , ∠ BAD = 22.5°

Step-by-step explanation:

the measure of the inscribed angle ADE is half the measure of its intercepted arc AE , then

∠ ADE = [tex]\frac{1}{2}[/tex] × 110° = 55°

---------------------------------

the measure of the secant- secant angle ACE is half the difference of the measures of the intercepted arcs , that is

∠ ACE = [tex]\frac{1}{2}[/tex] (AE - BD) = [tex]\frac{1}{2}[/tex] (110 - 45)° = [tex]\frac{1}{2}[/tex] × 65° = 32.5°

-----------------------------------------

the measure of the inscribed angle BAD is half the measure of its intercepted arc BD , that is

∠ BAD = [tex]\frac{1}{2}[/tex] × 45° = 22.5°

The polynomial P(x) = x³ + 3x² - 8x + 140 divided by (x + 7), will give a quotient of x² - 3x + 2 and a remainder of 0 using the long division, we can write P(x) = (x + 7)(x² - 4x + 20) + 0

A polynomial is a mathematical expression which have a sum of powers in one or more variables with coefficients. The highest power of the variable in a polynomial is called its degree.

We shall divide the polynomial x³ + 3x² - 8x + 140 by x + 7 as follows;

x³ divided by x equals x²

x + 7 multiplied by x² equals x³ + 7x²

subtract x³ - x² from x³ + 3x² - 8x + 140 will result to -4x² - 8x + 140

-4x² divided by x equals -4x

x + 7 multiplied by -4x equals -4x² - 28x

subtract -4x² - 28x from -4x² - 8x + 140 will result to 20x + 140

20x divided by x equals 20

x + 7 multiplied by 20 equals 20x + 140

subtract 20x + 140 from 20x + 140 will result to a remainder 0

Therefore, the polynomial P(x) = x³ + 3x² - 8x + 140 divided by (x + 7), will give a quotient of x² - 3x + 2 and a remainder of 0 using the long division, we can write P(x) = (x + 7)(x² - 4x + 20) + 0

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The average rate of change over the interval from -3 to 1 is 2.000

To find the average rate of change over the interval from -3 to 1, we need to calculate the change in y divided by the change in x.

Δy = y₂ - y₁ = (-10) - (-18) = 8

Δx = x₂ - x₁ = 1 - (-3) = 4

Now, we can calculate the average rate of change using the formula:

Average Rate of Change = Δy / Δx

Average Rate of Change = 8 / 4 = 2

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Answer:

-1 - 6x = x - 15

Add 15 to both sides using the addition property of equality.

14 - 6x = x

14 = 7x

2 = x

D) -1 - 6x + 15 = x - 15 + 15

Answer and Step-by-step explanation:

Please refer to the photo for the solution!

Savings accounts and CDs are good options for people who want to save money without taking on a lot of risk.

If Anita and Miguel do not take any money from their accounts, Anita's account will grow faster than Miguel's.

This is because the interest rate for Anita's account is 6%, while Miguel's is 5%.

The interest rate is the percentage of the principal that a bank or other financial institution pays for the use of money.

It can be thought of as a fee charged for borrowing money.

The higher the interest rate, the more money a person can earn on their investment.

Anita and Miguel's accounts are probably savings accounts or CDs, which are low-risk investments that pay a fixed interest rate.

Savings accounts and CDs are good options for people who want to save money without taking on a lot of risk.

Anita and Miguel's accounts are probably savings accounts or CDs, which are low-risk investments that pay a fixed interest rate.

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According to the information we can infer that it will take approximately 31 years for the wolf population to reach 500.

The given function, w(x) = 14 * 1.08^x, models the number of wolves (w) in the years since 1995 (x).

To find the number of years it will take for the population to reach 500 wolves, we can set up the equation:

Dividing both sides by 14, we get:

Taking the logarithm (base 1.08) of both sides to solve for x:

Using a calculator, we find that x ≈ 31.

According to the above it will take approximately 31 years for the wolf population to reach 500 based on the given model.

Note: This question is incomplete. Here is the complete information:
Attached image

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Answer: 5/ 16

explanation: total= 4x4=16

red and yellow : (r,y) or (y,r)

n= 5

p= 5 1/1 16

p = 5 over 16

Answer:

P ≈ $12,654.89

Step-by-step explanation:

To calculate the amount of money that should be deposited today, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = the future value of the investment ($15,000 in this case)

P = the principal amount (the amount to be deposited today)

r = the annual interest rate (4.5% or 0.045 as a decimal)

n = the number of times the interest is compounded per year (monthly compounding, so n = 12)

t = the number of years (4 years in this case)

Substituting the given values into the formula, we have:

$15,000 = P(1 + 0.045/12)^(12*4)

Simplifying the equation:

$15,000 = P(1.00375)^(48)

To solve for P, we divide both sides of the equation by (1.00375)^(48):

P = $15,000 / (1.00375)^(48)

Using a calculator, we find:

P ≈ $12,654.89

Therefore, approximately $12,654.89 should be deposited today in order to accumulate to $15,000 in 4 years with a 4.5% annual interest rate compounded monthly.

As x tends to negative one from the left, the value of f(x) tends to positive infinity. As x → -1⁻, f(x) → ∞.

In Mathematics and Geometry, the vertical asymptote of a function simply refers to the value of x (x-value) which makes its denominator equal to zero (0).

By critically observing the graph of this rational function f(x) shown below, we can logically deduce that its vertical asymptote is at x = -1 and x = 2, and its horizontal asymptote is at y = 3.

In this context, we can logically deduce that the value of f(x) tends towards positive infinity, as x tends to negative one from the left;

As x → -1⁻, f(x) → ∞.

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25 quarter cups in 6 1/4 cups

answer: 61

The equation of the tangent line at the point (108, 6) on the curve y² = x²/(xy - 324) is: y = 6

The equation is given as:

y² = x²/(xy - 324) at (108, 6)

Differentiating implicitly with respect to x gives:

2y(dy/dx) = (2x(xy - 324) - x²(y - 324)(dy/dx)) / (xy - 324)²

Simplifying further using power rule and chain rule gives us:

[tex]\frac{dy}{dx} = \frac{x^{2}y - 648x }{2y(-324 + xy) +x^{3} }[/tex]

We can find the slope by plugging in x = 108 and y = 6 to get

[tex]\frac{dy}{dx} = \frac{(108^{2}*6) - 648(108) }{2(6)(-324 + (108*6)) + 108^{3} }[/tex]

dy/dx = 0

To find the equation of the tangent line, we use the point-slope form:

y - y₁ = m(x - x₁),

where:

(x₁, y₁) is the given point (108, 6) and m is the slope.

Substituting the values, we have:

y - 6 = 0(x - 108)

y = 6

This is the equation of the tangent line at the point (108, 6) on the curve y² = x²/(xy - 324).

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Step-by-step explanation:

To find the value(s) for x such that f(x) = 23, we can set up the equation:

x^2 - 4x + 2 = 23

To solve this quadratic equation, we need to rearrange it into the standard quadratic form:

x^2 - 4x - 21 = 0

Now, we can solve this equation by factoring, completing the square, or using the quadratic formula. In this case, let's use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

For the equation x^2 - 4x - 21 = 0, the coefficients are: a = 1, b = -4, and c = -21.

Plugging these values into the quadratic formula, we get:

x = (-(-4) ± √((-4)^2 - 4(1)(-21))) / (2(1))

x = (4 ± √(16 + 84)) / 2

x = (4 ± √100) / 2

x = (4 ± 10) / 2

Now, we have two solutions:

x = (4 + 10) / 2 = 14 / 2 = 7

x = (4 - 10) / 2 = -6 / 2 = -3

Therefore, the values for x such that f(x) = 23 are x = 7 and x = -3.

The value of a and b in the given complex expression is  1/10 and -1/10 respectively.

This is a problem related to the complex numbers. The complex numbers has a general form of (a+bi) where 'i' is the imaginary number or √-1. The part without an 'i' is called Real Part and the part with an 'i' is called Imaginary Part.

(2i/2+i) - 3i/(3+i) = a + bi

{ 2i(3+i) - 3i(2+i) }/ (2 + i)(3 + i) = a+bi

6i + 2i² - 6i - 3i² / (2 + i)(3 + i) = a+bi

(-2 + 3) / (6 + 5i - 1) = s+bi

1 / (5 + 5i) = a+bi

Now we multiply top and bottom by 5 - 5i :

5 - 5i / (5 + 5i)(5 - 5i) = a+bi

5 - 5i / 25 -25i² = a+bi

5 - 5i / 50 = a+bi

1/10 - 1/10i = a+bi

On comparing the real and imaginary part on the both sides:

a= 1/10 , b= -1/10.

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Answer:

πr^2 h

π(11)^2 (15)

= 1815π or = 5701

Let's represent the number with the variable "x". According to the given property, we can write the following equation:

3(x + 4) < 7x

Now, let's solve this inequality to find the range of numbers that satisfy the property.

3x + 12 < 7x

Subtract 3x from both sides:

12 < 4x

Divide both sides by 4 (since the coefficient of x is 4):

3 < x

So, the range of numbers that satisfy the given property is x > 3.

Therefore, any number greater than 3 will satisfy the condition. For example, 4, 5, 6, 7, 8, etc.Step-by-step explanation:

An output value for (fog)(x) is 55/(x² + 2x).

Domain = (-∞, 1) U (-2, 0) U (0, ∞) or {x|x ≠ 0, -2}.

In this exercise, we would determine the corresponding composite function of f(x) and g(x) under the given mathematical operations in simplified form as follows;

(fog)(x) = 5/(x + 2) × 11/x

(fog)(x) = 55/x(x + 2)

(fog)(x) = 55/(x² + 2x)

For the restrictions on the domain, we would have to equate the denominator of the rational function to zero and then evaluate as follows;

x² + 2x ≠ 0

x² ≠ -2x

x ≠ -2

Domain = (-∞, 1) U (-2, 0) U (0, ∞) or {x|x ≠ 0, -2}.

In conclusion, we can reasonably infer and logically deduce that x must not be equal to 0 and -2.

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The equations of the other line are:

BC: y = 2x

AD: y = 2x + 2

CD = -¹/₂x + 5.5

The formula for the equation of a line between two coordinates is expressed as:

(y - y₁)/(x - x₁) = (y₂ - y₁)/(x₂ - x₁)

Thus, for the lines we have:

BC has B(-2, 4) and C(-1, 6)

Thus:

BC: (y - 4)/(x - 2) = (6 - 4)/(-1 + 2)

BC: (y - 4)/(x - 2) =2

BC: y - 4 = 2x - 4

BC: y = 2x

AD has  A(2,2) and D(3, 4)

Thus:

AD: (y - 2)/(x - 2) = (4 - 2)/(3 - 2)

AD: y - 2 = 2x - 4

AD: y = 2x + 2

CD has C(-1, 6) and D(3, 4)

CD: (y - 6)/(x + 1) = (4 - 6)/4

CD: y - 6 = -¹/₂(x + 1)

CD = -¹/₂x + 5.5

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Answer:

False

Step-by-step explanation:

When calculating volume, units of measurement are cubed. When calculating surface area, units of measurement are squared.

Further explanation:

Let's say you are finding the area of a rectangle. The length is 5in and the width is 7 in.

since you know l*w is area, you need to multiply 5in and 7in. 5*7=35 and then the two units of measurement, in*in=in^2 so 5in*7in=35in^2. the unit is squared not cubed.

The units of measurement for surface area are always SQUARED. Hence the correct answer is FALSE.

In 2-D, the total space covered by any two-dimensional figure is called Area while if we talk about 3-D, the total area of all the outer surfaces when added, sums up to form the Surface Area. Hence, the surface area is the multiplication of any two of the physical quantities.

For example,

Area of a square=(side x side)

                           =(metre x metre) or (cm x cm) [in terms of units]

                           = [tex]metre^{2}[/tex] or [tex]cm^{2}[/tex]

Similarly,

Surface Area of cube=6x(side x side)  [summation of the area of 6 faces of cube]

                                   =(metre x metre) or (cm x cm) [in terms of units]

                                    = [tex]metre^{2}[/tex] or [tex]cm^{2}[/tex]  (again)

Therefore, The units of measurement for the surface area are always SQUARED. Hence the correct answer is FALSE.

When talking of volume, since volume is the amount of space taken by any object or any 3-Dimensional body, the units of measurement of Volume are always cubed. For example, [tex]metre^{3}[/tex] or [tex]cm^{3}[/tex].

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Answer:

In summary, the faster cyclist cycles at a speed of 18 mi/h since they travel 36 of the 54 miles in 2 hours while cycling twice as fast as the slower cyclist.

Explanationn:

The two cyclists are 54 miles apart and heading toward each other.

One cyclist cycles 2 times as fast as the other. We will call the faster cyclist A and the slower cyclist B.

They meet 2 hours after starting. This means they travel a total distance of 54 miles in 2 hours.

Since cyclist, A cycles 2 times as fast as cyclist B, cyclist A travels 2/3 of the total distance, and cyclist B travels 1/3 of the total distance.

In two hours, cyclist A travels (2/3) * 54 miles = 36 miles.

We need to find the speed of cyclist A in miles per hour.

Speed = Distance / Time

So the speed of cyclist A is:

36 miles / 2 hours = 18 miles per hour

Therefore, the speed of the faster cyclist is 18 mi/h.

Answer: 2×2×5×7 or, in exponent form, [tex]2^2[/tex]×[tex]5^1[/tex]×[tex]7^1[/tex]

Step-by-step explanation:

We can use a factor tree to determine the prime factorization of 140. You may notice that there are several factors to choose from that will give us 140, but you can choose any because in the end it will give you the same answer!

                                                         140

                                                     14   ×  10

                                                   2×7      2×5

That is all, because the final numbers listed are prime and we cannot perform any further actions.

Hope this helps!

The correct range for the piecewise graph is [-4, 2].

We need to find the minimum and maximum values of the y-coordinates.

The first segment goes from (-3, 2) to (0, 1), so the range for this segment is from 1 to 2.

The second segment goes from (0, 1) to (5, -4), so the range for this segment is from -4 to 1.

We must take into account the minimum and maximum values from each segments in order to determine the overall range. The minimum and highest values are -4 and 2, respectively.

Therefore, the correct range for the piecewise graph is [-4, 2].

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If sinθ = 5/13 and θ is in Quadrant II, then sin (θ/2) will be equal to  [tex]\frac{5}{\sqrt{26}}[/tex]

To find sin(θ/2), we can use the half-angle identity for sine, which states that:

sin(θ/2) = ±[tex]\sqrt{\frac{(1 - cos\theta)}{2}}[/tex]

Given that sinθ = 5/13 and θ is in Quadrant II, we can determine the value of cosθ using the Pythagorean identity

sin²θ + cos²θ = 1

sinθ = 5/13

sin²θ = (5/13)² = 25/169

cos²θ = 1 - sin²θ = 1 - 25/169 = 144/169

cosθ = ±√(144/169) = ±12/13

Since θ is in Quadrant II, the cosine is negative. Therefore, cosθ = -12/13.

Now, we can calculate sin(θ/2):

sin(θ/2) = ±√((1 - cosθ) / 2) = ±√((1 - (-12/13)) / 2) = ±√((1 + 12/13) / 2) = ±√(25/26) = ±5/√26

Since θ is in Quadrant II, sin(θ/2) will be positive.

Therefore, sin(θ/2) = 5/√26.

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The solution to the piecewise-defined function is shown in the attached graph.

The function g(x) is defined as follows:

g(x) = -4     if x ≠ 0

g(x) = 5       if x = 0

On the graph, when x is any value other than 0, the function takes the value of -4. This means that there will be a horizontal line at y = -4 for all x ≠ 0. The point (0, 5) will be represented by a solid dot since it's the only point where g(x) equals 5.

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The square root of the expression -36 is DNE

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

[tex](-36)^\frac 12[/tex]

By definition, the square root of negative numbers are complex numbers

using the above as a guide, we have the following:

[tex](-36)^\frac 12[/tex] is not a real number

Hence, the solution is DNE

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A line segment is a fundamental concept in geometry, representing a portion of a line that has a definite beginning and end. It consists of an infinite number of points situated between two endpoints.

The endpoints themselves are distinct points on a line, and they are included as part of the line segment. Unlike a line, which extends indefinitely in both directions, a line segment is confined to a specific length.

This length is often referred to as the 'measure' of the line segment. Additionally, line segments serve as building blocks for various geometrical shapes and figures by connecting multiple points in space.

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The Question in English

What is the definition of a line segment?

The area of the parallelogram ABCD is (a) 13 square units.

Area of a parallelogram = Length × Width

Length = distance AB

Where

A = (3, 6) and B = (6, 5)

So, we have

[tex]Length = \sqrt{ {(3 - 6)}^{2} + (6 - 5) ^{2} }[/tex]

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

[tex] = \sqrt{ 9 + 1 }[/tex]

[tex]= \sqrt{10}[/tex]

Next, we have

Width = distance AD

Where

A = (3, 6) and D = (2, 2)

So, we have

[tex]width = \sqrt{ {(3 - 2)}^{2} + (6 - 2) ^{2} }[/tex]

[tex] = \sqrt{ {( 1)}^{2} + (4) ^{2} }[/tex]

[tex]= \sqrt{ 1 + 16 }[/tex]

[tex]= \sqrt{17}[/tex]

Recall that

Area of a parallelogram = Length × Width

So, we have

= √10 × √17

Evaluate the products

√170

Take the square rppt

= 13.03840481040529

Approximately, 13 square units

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Complete question:

What is the area of parallelogram ABCD?

O 13 square units

O 14 square units

O 15 square units

O 16 square units

See attachment

Rounding to the nearest whole number, the membership of the Network Club in 2020 will be approximately 5,564.

Therefore, the correct answer is: E. 5,564.

To calculate the membership of the Network Club in 2020, we can use the continuous growth formula:

[tex]A = P \times e^{(rt)[/tex]

Where:

A is the final amount or membership in 2020,

P is the initial amount or membership in 2010,

e is the mathematical constant approximately equal to 2.71828,

r is the annual growth rate as a decimal,

t is the number of years.

Given:

P = 2,500 (membership in 2010),

r = 8% = 0.08 (annual growth rate),

t = 2020 - 2010 = 10 years (number of years).

Plugging in the values into the formula, we have:

[tex]A = 2,500 \times e^{(0.08 \times 10)}[/tex]

Calculating the exponent:

[tex]A = 2,500 \times e^{(0.8)[/tex]

Using a calculator, we find that[tex]e^{(0.8)[/tex]  is approximately 2.22554.

Now, we can calculate the final amount A:

A ≈ 2,500 [tex]\times[/tex] 2.22554 ≈ 5,563.85  

Therefore, the correct answer is: E. 5,564.

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Answer: The answer is 5564

Step-by-step explanation: P=I[tex]e^rt[/tex]=2500e^(0.08)(10)=5563.85

The calculated period of the function is 12

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

The graph

By definition, the period of the function is calculated as

Period = Difference between cycles or the length of one complete cycle

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

Period = 13 - 1

Evaluate

Period = 12

Hence, the period of the function is 12

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