Simplify (Write each expression without using the absolute value symbol)
|x+3| if x>5

Answer:

300 I think because when you repeat it 300 times it will give an exactly 7 300 times

Using congruent angles , we have been able to prove that the sum of the interior angles of ΔABC is 180°.

We are given that:

A, B, and C form a triangle.

The sum of the interior angles of ΔABC is 180°.

We want to find the complete the statements to prove that the sum of the interior angles of ΔABC is 180°

From the attached diagram, we have that:

A triangle ABC with angle 1, 2 and 3.

Line DE and AC are parallel and then BA is a traversal line.

Thus, the alternate interior angle is:

∠1 = ∠4

∠3 = ∠5

Therefore, the angle formed on line is:

∠4 + ∠2 + ∠5 = 180

∠1 + ∠2 + ∠3 = 180

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The answers are as:

a) The exponential distribution is a probability distribution

b) P(X = 10) =  0.006

c) P(X > 10) ≈ 0.16

d) P(X < 10) ≈ 0.015

What is probability?

Probability is the study of the chances of occurrence of a result, which are obtained by the ratio between favorable cases and possible cases.

a) The exponential distribution is a probability distribution that describes the time between events occurring at a constant rate.

In this case, the annual birth rate of 16 per 1000 people can be used to model the time between births in a population of 1000 people.

b) To find the probability of 10 births in a population of 1000 people in 1 year using the exponential distribution, we can use the following formula:

[tex]P(X = x) = \lambda\ ^{(-\lambda x)}[/tex]

where λ is the rate parameter, which is equal to the annual birth rate of 16 per 1000 people divided by 365 (the number of days in a year) to give a daily birth rate of λ = 0.044. x is the number of births we are interested in, which is 10.

Therefore, we have:

P(X = 10) = [tex]0.044e^{(-0.044*10)}[/tex]

≈ 0.006

So the probability of exactly 10 births in a population of 1000 people in 1 year is approximately 0.6%.

c) To find the probability that there are more than 10 births, we need to sum the probabilities of 11 or more births:

P(X > 10) = Σ P(X = x) for x > 10

[tex]= \Sigma 0.044e^{(-0.044x)}[/tex] for x > 10

[tex]= 1 - \Sigma 0.044e^{(-0.044x)}[/tex]for x ≤ 10

P(X > 10) ≈ 0.16

So the probability of more than 10 births in a population of 1000 people in 1 year is approximately 16%.

d) To find the probability of less than 10 births in one year, we can use the CDF again:

[tex]F(x) = 1 - e^{(-\lambda x)}[/tex]

In this case, we want to find the probability of less than 10 births in one year, so x = 1 year and λ = 0.016 births per person per year:

[tex]F(10) = 1 - e^{(-0.016)}[/tex]

P(10) ≈ 0.0158

So less than 10 births in one year are approximately 1.5%.

Hence, The answers are as:

a) The exponential distribution is a probability distribution

b) P(X = 10) =  0.006

c) P(X > 10) ≈ 0.16

d) P(X < 10) ≈ 0.015

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After answering the presented question, we can conclude that coordinates  Therefore, Khaled's house is located at approximately (-4.75, -1.5).

In mathematics, a coordinate is a number or combination of numbers that represents the location of a point or object in space. Coordinates are frequently used to define a point or object's position in a certain coordinate system, such as the Cartesian or polar coordinate systems. In the Cartesian coordinate system, a point is found by its distance from the origin along the x-axis and its distance from the origin along the y-axis. These distances are represented by two integers, the x-coordinate and the y-coordinate. The point's location in the plane is specified by the two coordinates.

Distance from Khaled's house to the animal shelter:

[tex]d_1 = \sqrt((x - (-3))^2 + (y - (-5))^2) = \sqrt((x + 3)^2 + (y + 5)^2)[/tex]

Distance from Khaled's house to the grooming shop:

[tex]d_2 = \sqrt((x - 5)^2 + (y - (-1))^2) = \sqrt((x - 5)^2 + (y + 1)^2)\\d_1/d_2 = 1/3\\\sqrt((x + 3)^2 + (y + 5)^2) / \sqrt((x - 5)^2 + (y + 1)^2) = 1/3\\((x + 3)^2 + (y + 5)^2) / ((x - 5)^2 + (y + 1)^2) = 1/9\\8x + 38y + 4 = 0\\[/tex]

So the coordinates of Khaled's house are:

x = -4.75

y = -1.5

Therefore, Khaled's house is located at approximately (-4.75, -1.5).

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Answer:

Compounding goes from present value to future value.

4a² - 3b² + ab/(a- b)(a + b) is the solution of equation .

What does a math equation mean?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used.

                        For instance, the equation 3x + 5 = 14 contains two expressions, 3x + 5 and 14, which are separated by the 'equal' sign. When two expressions are joined by an equal sign, a mathematical statement is called an equation.

2ab/a² - b²  - b/a-b + 4

= 2ab/(a- b)(a + b) - b/(a - b) + 4

=    2ab/(a- b)(a + b) - b(a + b) +4(a- b)(a + b)/(a- b)(a + b)

= 2ab - ab - b² + 4a² - 4b²/(a- b)(a + b)

=  4a² - 3b² + ab/(a- b)(a + b)

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The area οf the actual bridge deck in square feet is 1,280 square feet.

Area refers tο the measurement οf the size οf a twο-dimensiοnal surface, usually measured in square units such as square inches, square feet, οr square meters. It represents the amοunt οf space that is inside the bοundary οf a flat οbject οr shape.

The scale οf the drawing is 40:1, which means that the dimensiοns οf the scaled bridge deck are 40 times smaller than the actual bridge deck. Tο find the area οf the actual bridge deck in square feet, we need tο cοnvert the dimensiοns οf the scaled bridge deck frοm inches tο feet and then multiply by the square οf the scale factοr (40² = 1600).

The dimensiοns οf the scaled bridge deck in feet are:

24 inches = 2 feet

4 and 4/5 inches = 0.4 feet

Sο, the area οf the scaled bridge deck in square feet is:

2 feet x 0.4 feet = 0.8 square feet

Tο find the area οf the actual bridge deck in square feet, we need tο multiply the area οf the scaled bridge deck by the square οf the scale factοr:

Area οf actual bridge deck = 0.8 square feet x (40²) = 1280 square feet

Therefοre, the area οf the actual bridge deck in square feet is 1,280 square feet.

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Answer:

Step-by-step explanation:

The scale factor indicates the actual bridge is 40 times larger than the drawing.

Increase the scale dimensions by the factor of 40.

24 times 40 = 960"

4.8 times 40 = 192" (I changed 4 4/5 to 4.8)

Area = length times width

960 times 192 = 184320 sq inches actual bridge deck in square inches

Divide 183320 by 144 (sq inches in a square foot) = 1280 sq feet

8.08 liters.

To find the volume of each water sample, we need to divide the total volume of water collected by the number of samples collected.

Volume of each water sample = Total volume of water collected / Number of samples collected

We are given that the total volume of water collected is 606 liters, and the number of samples collected is 75.

Volume of each water sample = 606 / 75

Volume of each water sample = 8.08 liters

Therefore, the volume of each water sample is 8.08 liters.

the measurements of the missing angles are-

c = 96°

a= 84°

b= 84°

e= 42°

d= 96°

f=96°

Both the largest and the tiniest walls of a skew are determined by an intersection of the lines that connect that make up its ends. A junction could possibly bring two routes together. Another result of two objects interacting is an angle. They most closely resemble dihedral shapes. Two line beams can be arranged in a variety of ways between their extremities to form a two-dimensional curve.

Here,

c = 96 °(A pair of vertically opposite angles are always equal to each other)

a + c = 180°(a vertical angle and its adjacent angle are supplementary angles, i.e., they add up to 180 degrees)

so, a= 180°-96°

a= 84°

therefore, b = 84°(A pair of vertically opposite angles are always equal to each other)

as shown in figure, 2e = 84°

that is, e = 84°/2

e = 42°

2e+f = 180°(a vertical angle and its adjacent angle are supplementary angles, i.e., they add up to 180 degrees)

f=180°-2e (placing the value of e)

f = 180° -84°

so, f=96°

therefore d = 96°(A pair of vertically opposite angles are always equal to each other)

therefore, the measurements of the missing angles are-

c = 96°

a= 84°

b= 84°

e= 42°

d= 96°

f=96°

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The product between functions f(x) and g(x) gives:

(f·g)(x) = x⁵ - 2x³ + 2x² - 8x + 4

Here we have the functions:

f(x) = x³ - 4x + 2

g(x) = x² + 2

The product:

(f·g)(x) is just the product between the two functions, this gives:

f(x)·g(x)

Replacing these functions we will get.

(x³ - 4x + 2)*( x² + 2)

Expanding that product, we will get:

x³*x² + 2x³ - 4x*x² - 8x + 2x² + 4

x⁵ - 2x³ + 2x² - 8x + 4

That is the product.

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he asked me what my name was into direct speech

Answer:The correct dot plot is:

Step-by-step explanation:

LV

1

2

1

2

1

1

2

5 2 3

2

2

3

1

1

2 2

1

3 2

3

1

2

1

2 2

3₁

3

In this dot plot, each dot represents one household, and its position on the vertical axis corresponds to the number of televisions in that household. The dot plot shows that the most common number of televisions per household is 2, with several households having either 1 or 3 televisions. There are also a few households with 5 televisions.

The equation for the hanger is 2x + 2x + 2 = 11 and x = 9/4

Algebraic expressions are defined as mathematical expressions that are composed of variables, constants, factors, coefficient and terms.

They are also made up of arithmetic operations, such as;

From the diagram shown, we have that;

2x, 2x + 2 = 11

x + 2 + x + 2 + x as the remaining expression for the hanger

Then, this can be represented as;

2x + 2x + 2= 11

collect the like terms and add the terms

4x =11 - 2

4x = 9

Make 'x' the subject

x = 9/4

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Answer:

[tex] \sf \: 13.36\%[/tex]

Step-by-step explanation:

The coefficient of variation (CV) is a measure of relative variability, which expresses the standard deviation as a percentage of the mean. It can be calculated as follows:

[tex] \sf \: CV = \frac{standard \: deviation}{mean} \times 100%[/tex]

In this case, the mean number of citations is 23.2, and the standard deviation is 3.1. Thus, the coefficient of variation is:

[tex] \sf \: CV = \frac{3.1}{23.2} \times 100% [/tex]

[tex] \sf = 13.36\%[/tex]

Therefore, the coefficient of variation for the number of citations is approximately 13.36%.

A. The equatiοn that relates these variables is: d = s × t.

B. The biker wοuld travel 10 miles in 20 minutes.

C. The biker wοuld bike fοr 96 minutes tο travel 48 miles.

A. To find the values Let's define the variables:

t = time in minutes

d = distance traveled by the biker in miles

s = speed οf the biker in miles per minute

The equatiοn that relates these variables is:

d = s * t

b. If the biker travels fοr 20 minutes, we can use the equatiοn abοve tο find the distance traveled:

d = s * t

d = s * 20 (since t = 20 minutes)

We need tο knοw the speed οf the biker tο calculate the distance traveled. Let's assume that the biker's speed is 0.5 miles per minute (which is equivalent tο 30 miles per hοur):

d = 0.5 * 20

d = 10

Therefοre, the biker wοuld travel 10 miles in 20 minutes.

c. If the biker traveled 48 miles, we can rearrange the equatiοn abοve tο find the time:

d = s * t

t = d / s

We need tο knοw the speed οf the biker tο calculate the time. Let's assume that the biker's speed is still 0.5 miles per minute:

t = 48 / 0.5

t = 96

Therefοre, the biker wοuld bike fοr 96 minutes tο travel 48 miles. Rοunded tο the nearest tenth, this is 96.0 minutes.

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a.) So the monthly payment is $550.27. b.) the total amount paid over the term of the loan is $99,048.60. c.)  Approximately 50.43% of the total amount paid goes towards principal, and 49.57% goes towards interest.

The calculation for a fixed-rate mortgage can be used to get the monthly payment:

Monthly Payment is equal to P * r * [(1 + r)n - 1] / [(1 + r)n]

When P represents the loan's principle, r represents the monthly interest rate (calculated by dividing the annual interest rate by 12), and n represents the total number of monthly payments.

When we enter the values, we obtain:

Monthly Payment is equal to 50,000 * (0.11/12) * (1 + 0.11/12) * [((1 + 0.11/12))*180 - 1)]

= $550.27 (rounded to the nearest cent) (rounded to the nearest cent)

the amount due each month is $550.27.

We can multiply the monthly payment by the number of payments to get the total amount paid over the course of the loan. There will be 180 payments total in this instance (15 years times 12 months per year).

Monthly Payment * Number of Payments = $550.27 * 180 to get the total amount paid.

= $99,048.60 (rounded to the nearest cent) (rounded to the nearest cent)

Hence, the total amount paid during the loan's period is $99,048.60.

An amortization schedule can be used to calculate the portion of the total payment that goes to principle and interest. According to this arrangement, the principal and interest portions of each monthly payment are separated.

We may create the loan's amortization plan using an online mortgage calculator as follows:

Month      Payment      Principal      Interest      Balance

1                $550.27      $265.85      $284.42     $49,734.15

2               $550.27      $265.85      $284.42     $49,734.15

...                    ...                ...                   ...                    ...

179             $550.27      $529.26     $21.02        $840.96

180             $550.27      $532.69     $17.58        $0.00

This table shows that the total amount paid in interest is $49,048.60, whereas the total amount paid in principal during the course of the loan is $50,000 (the original loan amount).

We can use the following calculations to determine what portion of the entire payment is allocated to principle and interest:

Principal Paid / Total Paid * 100% = $50,000 / $99,048.60 * 100% is the percentage of principal.

= 50.43%

Interest Paid / Total Paid * 100% = $49,048.60 / $99,048.60 * 100% = 49.57% is the percentage of interest.

Hence, around 49.57% of the total payment is spent on interest, and 50.43% is spent on principal.

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Complete question is: Consider a home mortgage of ​$5000 at a fixed APR of 7​% for 12years.

a. Calculate the monthly payment.

b. Determine the total amount paid over the term of the loan.

c. Of the total amount​ paid, what percentage is paid toward the principal and what percentage is paid for interest.

Answer:

  0.2

Step-by-step explanation:

You want to know the value of 0.199...repeating 9s.

Let the value be represented by x:

  x = 0.1999...

Then 10x is ...

  10x = 1.9999...

The difference is ...

  10x -x = 1.9999... -0.1999... = 1.8

  9x = 1.8 . . . . . simplify

  x = 1.8/9 = 0.2

The value of the repeating decimal is 0.2.

__

Additional comment

The repeating decimal 0.99... is equivalent to 9/9 = 1. The repeating portion of 0.1999... has the value 0.1, Added to the first non-repeating digit, the sum is ...

  [tex]0.1\overline{9}=0.1+0.0\overline{9}=0.1+0.1=0.2[/tex]

A graph of the coordinates of the vertices of the image after a dilation by the given scale factor and center of dilation is shown in the image below.

In Geometry, dilation simply refers to a type of transformation which typically changes the size of a geometric object, but not its shape.

Next, we would apply a dilation to the coordinates of the pre-image by using a scale factor of 0.5 centered at the origin as follows:

Ordered pair J (-8, 0) → J' (-8 × 0.5, 0 × 0.5) = J' (-4, 0).

Ordered pair K (-4, 4) → K' (-4 × 0.5, 4 × 0.5) = K' (-2, 2).

Ordered pair L (-2, 0) → L' (-2 × 0.5, 0 × 0.5) = L' (-1, 0).

Next, we would have to dilate the coordinates of the preimage by using a scale factor of 1/3 centered at the point B (3, 3) by using this mathematical expression:

(x, y)  →  (k(x - a) + a, k(y - b) + b)

For coordinate A, B, and C, we have;

Coordinate A = (9, 9)  →  (1/3(9 - 3) + 3, 1/3(9 - 3) + 3) = (5, 5).

Coordinate B = (3, 3)  →  (1/3(3 - 3) + 3, 1/3(3 - 3) + 3) = (3, 3).

Coordinate C = (6, 0)  →  (1/3(6 - 3) + 3, 1/3(0 - 3) + 3) = (4, 2).

For coordinate D, E, and F, we have;

Coordinate D = (2, -2)  →  (1.5(2 - 4) + 3, 1.5(-2 + 2) + 3) = (0, 3).

Coordinate E = (4, -2)  →  (1.5(4 - 4) + 3, 1.5(-2 + 2) + 3) = (3, 3).

Coordinate F = (1, -4)  →  (1.5(1 - 4) + 3, 1.5(-4 + 2) + 3) = (-1.5, 0).

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Answer:

Yes, these two triangles are similar. Triangle similarity can be proved by the measurement of the angles. Angle A= Angle J. Angle B= Angle K and Angle C= Angle L. Triangle ABC ≈(similar to) Triangle JKL.

Explanation:

Triangle JKL is dilated with a scale factor of 2. (all side lengths were doubled; multiplied by 2) which is an enlargement any scale factor greater then 1 is an enlargement which means the triangle size is being increased. Any scale factor less than one is a shrinkage. The 2 triangles have the same angle but not the same side lengths.

What is a dilation:

A dilation is a geometric transformation that changes the size of a shape. The only thing the changes in a dilation is the size. It can either get bigger or smaller (angle measurements DO NOT change)

Conclusion:

triangle similarity can be proved by AA similarity postulate.

i hope this helps :)

happy geometry studying!!

Answer:

To find the monthly lease payment, we need to use the formula:

Monthly lease payment = (Net capitalized cost - Residual value) / Lease term in months

where:

Net capitalized cost = negotiated price - down payment

Residual value = percentage of MSRP x MSRP

Lease term in months = 36

First, we need to calculate the net capitalized cost:

Net capitalized cost = $49,000 - $4,000 = $45,000

Next, we need to calculate the residual value:

Residual value = 49% x $51,500 = $25,235

Now we can plug in the values and solve for the monthly lease payment:

Monthly lease payment = ($45,000 - $25,235) / 36 = $548.76

Therefore, the monthly lease payment is approximately $548.76.

From the time you are 21 until the time you turn 51, if you put $500 away quarterly in an account that produces 12% compound interest, you will have around $1,299,994.09 in it by the end of the 30 years.

Four quarters, numbered Q1, Q2, Q3, & Q4, make up an entire year. There are 3 months in each quarter. About 91 days make up each quarter. Quarterly is defined as once every quarter, or around every 91 days.

The calculation for future value of the an annuity can be used to resolve this issue:

FV = PMT x ((1 + r/n)nt - 1) / (r/n), where FV is just the future value of a annuity, PMT is indeed the payment amount (in this case, $500), r is indeed the interest rate (the value of which in this case is 12% or 0.12), n refers to the number of occasions a year the interest is greatly exacerbated (which in this case is four for quarterly cumulative), and t is the duration of the annuity .

When we enter the data, we get the following result: FV = 500 x (1.03120 - 1) / 0.03 = $1,299,994.09

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Answer:

➠ 11.7 + 19.1

➠ 30.8

Answer: 30.8

1. Add 11 and 19

2. Add .7 and .1

3. Put the results together

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x^2 - 12x + 11 = (x-11)(x-1)

Step-by-step explanation:

To find the missing term in the equation x^2 + __x + 11 = (x-11)(x-1), we can expand the right side to get:

x^2 - 12x + 11

Comparing this to the left side, we see that the missing term is -12x. Therefore, the complete equation is:

x^2 - 12x + 11 = (x-11)(x-1)

Answer:

+ 7

Step-by-step explanation:

Answer: A. To find the equation that models this relation, we can plot the data and look for a trend.

From the graph, we can see that the data follows an exponential growth pattern. The equation for exponential growth is:

y = ab^x

where y is the final population, a is the initial population, b is the growth rate, and x is the time in hours.

Using the data from the table, we can find the value of b:

b = y/x

where y is the population after x hours.

For example, after 2 hours, the population is 5000:

b = 5000/2 = 2500

We can repeat this process for each time period and find the average value of b:

b = (2500 + 3125 + 3906.25 + 4882.81 + 6103.51 + 7629.38) / 6 = 4275.5

Now that we have the value of b, we can find the equation that models the relation:

y = 2000(4275.5)^x

Rounding to one decimal place:

y = 2000(4.3)^x

B. Using the equation, we can find the population after 12 and 24 hours:

y = 2000(4.3)^12 ≈ 8,898,335.7

y = 2000(4.3)^24 ≈ 7.42 x 10^13

Step-by-step explanation:

The student used 6 toonies (worth $12) and 8 $10 bills (worth $80) to pay for the bike.

what is distribution?

Distribution can refer to various things depending on the context, but in general, it means the act of dividing or sharing something among a group of people or things.

In mathematics and statistics, distribution refers to the pattern or spread of values of a variable in a population or a sample. It describes how the values of a variable are distributed or arranged, and can be represented by a probability distribution or a frequency distribution.

In business and economics, distribution refers to the process of getting products or services from the manufacturer or producer to the consumer or end user. It involves various activities such as transportation, warehousing, and retailing, and is an important part of the supply chain management.

In politics and social sciences, distribution can refer to the allocation of resources or benefits among individuals or groups in a society. It can involve issues such as income distribution, wealth distribution, and resource allocation, and is a key concern in social justice and welfare policies.

In general, distribution is a fundamental concept that involves the division or sharing of something, and can be applied in various fields and contexts.

Let's start by using algebra to solve the problem. Let x be the number of toonies and x + 2 be the number of $10 bills.

The total cost of the bike is $92, which is equivalent to 9200 cents. The number of toonies is x, which is worth 200 cents each, so the total value of the toonies is 200x cents. The number of $10 bills is x + 2, which is worth 1000 cents each, so the total value of the $10 bills is 1000(x + 2) cents. Therefore, we can write the equation:

200x + 1000(x + 2) = 9200

Simplifying and solving for x:

1200x + 2000 = 9200

1200x = 7200

x = 6

Therefore, the student used 6 toonies (worth $12) and 8 $10 bills (worth $80) to pay for the bike.

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Answer: y = (1/12)x^2 - 2

Step-by-step explanation:

The equation of a parabola in vertex form is given by:

y = a(x-h)^2 + k

where (h,k) is the vertex of the parabola and "a" is a coefficient that determines the shape of the parabola.

In this case, the vertex is given as (0, -2), so h = 0 and k = -2. Also, the parabola passes through the point (6, 1), which means that when x = 6, y = 1. We can use this information to solve for "a".

Substituting the values of h, k, x, and y in the equation, we get:

1 = a(6-0)^2 - 2

Simplifying this equation, we get:

1 + 2 = 36a

3 = 36a

a = 3/36

a = 1/12

Now that we know the value of "a", we can substitute it in the vertex form equation to get the final equation of the parabola:

y = (1/12)(x-0)^2 - 2

Simplifying this equation, we get:

y = (1/12)x^2 - 2

Therefore, the equation of the parabola in vertex form is y = (1/12)x^2 - 2.

There is significant evidence that the proportion of frogs with elevated mercury content is different than 0.5, The p-value is approximately 0.038.

What is significant evidence?

To test whether the proportion of frogs with elevated mercury content is significantly different from 0.5, we can use a one-sample proportion test. The null hypothesis is that the true proportion is 0.5, and the alternative hypothesis is that it is different from 0.5.

Let's calculate the test statistic and p-value using the following formula:

z = (p - P0) / √(P0*(1-P0)/n)

where p is the sample proportion (17/50 = 0.34), P0 is the null hypothesis value (0.5), and n is the sample size (50).

z = (0.34 - 0.5) / √(0.5*0.5/50) = -2.07

The calculated z-value is -2.07. We can find the p-value by looking up the area to the left of -2.07 in the standard normal distribution table or by using a statistical software package. The p-value is approximately 0.038.

Since the p-value (0.038) is less than the alpha level of 0.15, we can reject the null hypothesis and conclude that there is significant evidence that the proportion of frogs with elevated mercury content is different than 0.5.

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The third side of the right angled triangle is 45.

What is right angled triangle?

A right angled triangle, also known as a right triangle, is a type of triangle that has one angle that measures exactly 90 degrees, called the right angle. This angle is formed where the two shorter sides of the triangle meet.

To solve this problem, we can use the concept of special right triangles, specifically the 3-4-5 right triangle. In a 3-4-5 right triangle, the sides are in the ratio of 3:4:5.

Let's label the length of the triangle as [tex]$L$[/tex], the height as [tex]$H$[/tex], and the hypotenuse as [tex]X[/tex].

The Pythagorean theorem states that in a right triangle, the sum of the squares of the legs is equal to the square of the hypotenuse. Therefore, we can set up the following equation:

[tex]$$ L^2 + H^2 = X^2 $$[/tex]

Substitute the given values.

We are given that [tex]$L = 27$[/tex] and [tex]$H = 36$[/tex], so we can substitute these values into the equation:

[tex]$$ 27^2 + 36^2 = X^2 $$[/tex]

Simplify the equation.

Evaluating the squares on the left side, we get:

[tex]$$ 729 + 1296 = X^2 $$[/tex]

Simplifying the right side, we get:

[tex]$$ 2025 = X^2 $$[/tex]

Solve for X.

Taking the square root of both sides, we get:

[tex]$$ X = \sqrt{2025} $$[/tex]

[tex]$$ X = 45 $$[/tex]

Therefore, the third side of the triangle is 45.

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The system of equation the 4x−6y = −24 and 2x−3y = −6 have no solution.

In mathematics, a system οf equatiοns, alsο knοwn as a set οf simultaneοus equatiοns οr an equatiοn system, is a finite set οf equatiοns fοr which we sοught cοmmοn sοlutiοns. In systems οf equatiοns, variables are related in a specific way in each equatiοn. i.e., the equatiοns can be sοlved simultaneοusly tο find a set οf values οf variables that satisfies each equatiοn.

Multiplying the second equation by 2, we get:

4x - 6y = -24

4x - 6y = -12

Lets graph these equations in a coordinate plane and see.

As we can see that the graph line do not intersect and is parallel to each other we can conclude that,

The system of equation the 4x−6y = −24 and 2x−3y = −6 have no solution.

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In the exponential decay, A) r = -0.0839 , B) r = -8.39% , C) Value=$11,800.

What is exponential decay?

The term "exponential decay" in mathematics refers to the process of a constant percentage rate reduction in an amount over time. It can be written as y=a(1-b)x, where x is the amount of time that has passed, an is the initial amount, b is the decay factor, and y is the final amount.

To find the annual rate of change between 1992 and 2006, we can use the formula:

r = [tex](V_2/V_1)^{1/n}-1[/tex]

where V1 is the initial value, V2 is the final value, and n is the number of years between the two values.

=>r = -0.0839

Therefore, the rate of change between 1992 and 2006 is -0.0839.

To express the rate of change in percentage form, we can multiply the result from part A by 100:

=>r = -0.0839 x 100

=> r = -8.39%

Therefore, the rate of change between 1992 and 2006 is a decrease of 8.39%.

To find the value of the car in the year 2009, we can assume that the value continues to drop at the same percentage rate as calculated in part A.

From 2006 to 2009, there are 3 years. So, using the formula for exponential decay, we have:

where V0 is the value in 2006, r is the rate of decrease, and n is the number of years between 2006 and 2009.

=>V = 11792.51

Therefore, the value of the car in the year 2009 would be approximately $11,800 (rounded to the nearest $50).

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