You are fencing in a rectangular area of a garden you have only 150 feet of fence do you want the length of the garden to be at least 40 feet you want the width of the garden to be at least 5 feet what is a graph showing the possible dimensions your garden could have? What vegetables will you use? What will they represent? How many inequalities do you need to write?

Answer:

x = 20

Step-by-step explanation:

using the cosine ratio in the right triangle and the exact value

cos45° = [tex]\frac{\sqrt{2} }{2}[/tex] , then

cos45° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{10\sqrt{2} }{x}[/tex] = [tex]\frac{\sqrt{2} }{2}[/tex] ( cross- multiply )

x × [tex]\sqrt{2}[/tex] = 20[tex]\sqrt{2}[/tex] ( divide both sides by [tex]\sqrt{2}[/tex] )

x = 20

The equation of the line is 3y-5x=3 and the graph is attached.

Geometrically speaking, a line is a one-dimensional figure because it has length but no width. A group of points can be extended endlessly in opposing directions to form a line. Two points in a two-dimensional plane determine it. There are, however, additional ways to formulate the equation of a line in a two-dimensional coordinate system. The three most popular methods are the point-slope form, slope-intercept form, and general or standard form of the equation of a line. As its name suggests, the point-slope form combines a line point and a straight-line slope. The equations of infinite lines with a particular slope can be expressed, however when we specify that the line passes through a particular point, we get a singularity.

the equation of a line is

y-y'=m(x-x')

[tex]y+4=\frac{5}{3}(x+3)\\\\3y+12=5x+15\\3y-5x=3[/tex]

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The population will exceed 2627 after approximately 6.08 units of time.

A lοgarithm is a mathematical functiοn that tells us what expοnent is needed tο prοduce a given number, when that number is expressed as a pοwer οf a fixed base. In οther wοrds, lοgarithms tell us hοw many times we need tο multiply the base by itself tο get the desired number.

To solve for t when the population exceeds 2627, we can set the equation equal to 2627 and solve for t:

p(t) = 1000[tex]e^{(0.21t)}[/tex] = 2627

Dividing both sides by 1000, we get:

[tex]e^{(0.21t)}[/tex] = 2.627

Taking the natural logarithm of both sides, we get:

0.21t = ln(2.627)

Solving for t, we get: t = ln(2.627)/0.21 ≈ 6.08

Therefore, the population will exceed 2627 after approximately 6.08 units of time.

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Answer:

Step-by-step explanation:

For the 90°/right angle part, we can subtract 35° from 90° to get the degree of that area.

90° - 35° = 55°

We can check off the "55°" box

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

Now, for the other half of the straight angle including the right angle, we can subtract 90° from 180°.

Getting 90°

We can check off the "90°" box

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

To find the degree of the "(7x + 5°)" -- assuming that that angle is vertical to the "other" -- we can make an equation of

⇒ 7x + 5° = 90° + 55°

Solve:

Add together 90 and 55 which is 145°

New equation:

7x + 5° = 145°

Subtract 5° from both sides, getting the equation

7x = 140°

Isolate x by dividing both sides by 7

x = 20°

Substitute what we have for x into the equation "7x + 5°"

7(20°) + 5

= 145°

We can check off the "145°" box

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

All the boxes checked off:

Hopefully this helps! -- mark me brainliest if you want ofc

Step-by-step explanation:

a) Since the temperature of the oven is decreasing by a percentage of its current temperature each minute, the function that best represents this situation is an exponential function.

b) Let T be the temperature of the oven in degrees Fahrenheit at time x minutes after it was turned off. The initial temperature of the oven was 450° F, and the temperature decreases by 10% each minute. This can be expressed as:

T = 450(0.9)^x

Therefore, the function that models the situation is:

f(x) = 450(0.9)^x

where f(x) is the temperature of the oven in degrees Fahrenheit x minutes after it was turned off.

To win the game, your team needs to score more than   [tex]35[/tex] points, which means: 3f + 7t > 35 three possible game-winning combinations are:

[tex]t = 5, f = 11: 3(11) + 7(5) = 63[/tex]

[tex]t = 6, f = 8: 3(8) + 7(6) = 62[/tex]

[tex]t = 7, f = 5: 3(5) + 7(7) = 56[/tex]

Each of these combinations would result in your team scoring more than 35 points and winning the game.

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=).

For example, the argument [tex]"2x + 3 = 9"[/tex]  asserts that the phrase [tex]"2x + 3"[/tex]  equals the number "9." The purpose of equation solving is to determine the value or values of the variable(s) that allows the equation to be true.

Equations can be simple or complicated, regular or nonlinear, and include one or more elements. The variable x is raised to the second power in the equation. [tex]"x2 + 2x - 3 = 0."[/tex]    Lines are utilised in many different areas of mathematics, such as  algebra, calculus, and geometry.

Let's let f be the number of field goals scored by your team and t be the number of touchdowns scored by your team.

a) To win the game, your team needs to score more than 35 points, which means:

3f + 7t > 35

We can simplify this inequality by dividing both sides by 1:

3f + 7t/1 > 35/1

3f + 7t > 35

b) Now, we need to find possible values for f and t that make this inequality true. Since we are looking for positive integer values for f and t, we can start by testing different values for t and solving for f:

If t = 5, then 3f + 7(5) > 35, so 3f > 0 and f > 0. Possible solutions are f = 1, f = 2, f = 3, and so on.

If t = 6, then 3f + 7(6) > 35, so 3f > 7 and f > 2. Possible solutions are f = 3, f = 4, f = 5, and so on.

If t = 7, then 3f + 7(7) > 35, so 3f > 14 and f > 4. Possible solutions are f = 5, f = 6, f = 7, and so on.

c) So, three possible game-winning combinations are:

[tex]t = 5, f = 11: 3(11) + 7(5) = 63[/tex]

[tex]t = 6, f = 8: 3(8) + 7(6) = 62[/tex]

[tex]t = 7, f = 5: 3(5) + 7(7) = 56[/tex]

Each of these combinations would result in your team scoring more than 35 points and winning the game.

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Answer:

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

Supplementary angles add up to 180°:

Substitute and solve for x:

Find the measure of ∠B:

Answer:

Step-by-step explanation:

To express the difference in mean weights as a multiple of the MAD for both dog breeds, we can use the formula:

(difference in means) / (mean absolute deviation)

Let's plug in the values given in the problem:

(difference in means) = 13 - 11.5 = 1.5

(mean absolute deviation) = 2 + 1.8 / 2 = 1.9 (taking the average of the two MADs)

Now we can calculate:

(difference in means) / (mean absolute deviation) = 1.5 / 1.9 ≈ 0.7895

Therefore, the difference in mean weights between the two breeds is approximately 0.7895 times the average MAD for both breeds.

If the equation is changed from y = x^2 to y = (1/4)x^2, the parabola will become wider.

Answer:

It will take Jaime 36 days to run 96 miles.

Step-by-step explanation:

The formula for rate is:

[tex]\boxed{\sf Rate=\dfrac{Distance}{Time}}[/tex]

Therefore, Jaime's run rate is:

[tex]\implies \sf Rate=\dfrac{8\;miles}{3\;days}=\dfrac{8}{3} \;miles\;per\;day[/tex]

Rearrange the rate formula to isolate time:

[tex]\implies \sf Time=\dfrac{Distance}{Rate}[/tex]

To find how long it will take for Jaime to run 96 miles, substitute the distance and rate into the formula and solve for time:

[tex]\implies \sf Time=\dfrac{96\;miles}{\frac{8 \;miles}{3\;days}}[/tex]

[tex]\implies \sf Time=96\;miles \times \dfrac{3\;days}{8\;miles}[/tex]

[tex]\implies \sf Time= \dfrac{288}{8}\;days[/tex]

[tex]\implies \sf Time= 36\;days[/tex]

Therefore, it will take Jaime 36 days to run 96 miles.

Answer: 363+368=731

Step-by-step explanation:

The required perimeter of the given triangle is 23 units respectively.

Triangles are closed, two-dimensional shapes with three sides, three angles, and three vertices.

A triangle is part of a polygon. A triangle is a polygonal form with three sides.

These points meet at the vertex, which forms an internal angle at the junction of two triangle sides.

Every triangle has three sides, three vertices, and three internal angles.

So, to get the perimeter of the triangle, count the unit as follows:

7 units + 7 units + 9 units

To find the triangle, we need to add the length of the 3 sides as follows:

7 + 7 + 9 = 23 units

Therefore, the required perimeter of the given triangle is 23 units respectively.

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 the income tax payable on a salary of Birr 5200 is Birr 320.

In Ethiopia, income tax is calculated based on a progressive tax system where the tax rate increases as the taxable income increases. The formula for calculating income tax on monthly salary is as follows:

Taxable income = Gross monthly salary - Deductions

Tax payable = Tax rate * (Taxable income - Tax threshold) - Allowances

Where:

1. Gross monthly salary: Total salary before any deductions.

2. Deductions: Includes mandatory deductions such as employee social security contributions, pension contributions, and other authorized deductions.

3. Taxable income: Gross monthly salary minus deductions.

4. Tax rate: The percentage of tax applicable to the taxable income based on the tax bracket.

5. Tax threshold: The minimum amount of taxable income before tax is applicable.

6. Allowances: Includes authorized tax deductions such as dependant's allowance and other authorized allowances.

To calculate the income tax on a salary of Birr 5200, we need to determine the taxable income first. Let's assume that the gross monthly salary is Birr 5200, and there are no deductions.

Taxable income = Birr 5200 - 0 = Birr 5200

Next, we need to determine the tax rate applicable to this taxable income based on the tax bracket. For the taxable income range of Birr 5251 to 7800, the tax rate is 10%. Therefore, the tax rate applicable to Birr 5200 is 10%.

Tax rate = 10%

Now, we need to determine the tax threshold and the allowances applicable to this taxable income. Let's assume that the tax threshold is Birr 2000, and there are no allowances.

Tax threshold = Birr 2000

Allowances = 0

Using the formula mentioned earlier, we can calculate the income tax payable as follows:

Tax payable = 10% * (Birr 5200 - Birr 2000) - 0

Tax payable = Birr 320

Therefore, the income tax payable on a salary of Birr 5200 is Birr 320.

To derive the formula to calculate income tax on Birr x, we can use the same formula mentioned earlier. We can express the formula in terms of x as follows:

Taxable income = x - Deductions

Tax payable = Tax rate * (Taxable income - Tax threshold) - Allowances

Where:

1. x: Gross monthly salary.

2. Deductions: Includes mandatory deductions such as employee social security contributions, pension contributions, and other authorized deductions.

3. Taxable income: Gross monthly salary minus deductions.

4. Tax rate: The percentage of tax applicable to the taxable income based on the tax bracket.

5. Tax threshold: The minimum amount of taxable income before tax is applicable.

6. Allowances: Includes authorized tax deductions such as dependant's allowance and other authorized allowances.

We can use this formula to calculate the income tax payable on any salary falling within the Birr 5251 to 7800 taxable income range.

In conclusion, income tax in Ethiopia is calculated based on a progressive tax system, where the tax rate increases as the taxable income increases. To calculate income tax on a salary of Birr 5200, we need to determine the taxable income, tax rate, tax threshold, and allowances applicable to that salary. We can use the same formula to calculate income tax on any salary within the Birr 5251 to 7800 taxable income range.

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Rounding to the same number of significant digits as the measurement with the least number of significant digits (which is "350 ppm"), the expected CO₂ level by the end of 2030 would be 430 ppm.

Significant digits, also known as significant figures or sig figs, are the digits in a number that are considered to be accurate or meaningful. They represent the precision or reliability of a measurement or calculation.

In a number, all digits except for leading zeros are considered to be significant. For example, in the number 0.00456, there are three significant digits (4, 5, and 6), while the zeros before the 4 are not significant.

The rules for determining the number of significant digits in a number are:

All non-zero digits are significant.

Zeros between non-zero digits are significant.

Leading zeros are not significant.

To find the expected CO₂ level in the atmosphere by the end of 2030, we need to calculate the total increase in CO₂ levels from 2012 to 2030 and then add it to the 2012 CO₂ level of 396 ppm.

To calculate the total increase in CO₂ levels, we can use the following formula:

Total increase in CO₂ levels = rate of increase × time

where the rate of increase is 2.10 ppm per year and the time is the number of years from 2012 to 2030, which is 18 years.

Total increase in CO₂ levels = 2.10 ppm/year × 18 years = 37.8 ppm

Therefore, the expected CO₂ level in the atmosphere by the end of 2030 would be:

Expected CO₂ level = 2012 CO₂ level + total increase in CO₂ levels

Expected CO₂ level = 396 ppm + 37.8 ppm

Expected CO₂ level = 433.8 ppm

Rounding to the same number of significant digits as the measurement with the least number of significant digits (which is "350 ppm"), the expected CO₂ level by the end of 2030 would be 430 ppm.

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2 1/6 years in months is 26/1 as a fraction.

Answer:26 months or 26/1 months

Answer:

I think its 75 degrees and brainliest would be greatly appreciated

Answer:

The file is attached below.

I disagree with Meghan.

Step-by-step explanation:

Hello!

The line plot is attached below.

I disagree with Meghan as the least amount of time someone recited the alphabet is 4 seconds and the greatest is 7.5 seconds.

The difference between these two numbers would be 3.5 seconds, which is not the same as 4 seconds.

The function f(x) = 2x³-3x² - 12x + 1 does not have any local maximum or minimum values over the interval [2, 3].

To find the local maximum and minimum of a function over a given interval, we need to find the critical points of the function within that interval and then apply the second derivative test to classify those critical points as local maximum or minimum.

To find the critical points, we first take the derivative of the given function:

f'(x) = 6x² - 6x - 12 = 6(x² - x - 2)

x = -1 or x = 2

Both of these critical points fall outside the given interval [2, 3]. Therefore, there are no critical points of the function within the interval [2, 3], and so there are no local maximum or minimum values of the function over this interval.

In other words, the function f(x) = 2x³-3x² - 12x + 1 does not have any local maximum or minimum values over the interval [2, 3].

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Answer:

Step-by-step explanation:

a) The steering committee of 5 can be chosen from 15 members in 15 nCr 5 ways. Once the committee is chosen, the chair can be selected in 5 ways and the secretary can be selected in 4 ways (since the chair cannot also be the secretary). Therefore, the total number of different sets of committees (including officer selection) is:

15 nCr 5 * 5 * 4 = 3,003,600

b) Each of the 6 raffle prizes can be awarded to any of the 100 people, so there are 100 choices for the first prize, 99 choices for the second prize, and so on, down to 95 choices for the sixth prize. However, since the three $25 prizes are equivalent, we need to divide by 3! to account for the ways in which the $25 prizes can be arranged. Therefore, the total number of different raffle ticket winner selections is:

(100 * 99 * 98 * 97 * 96 * 95) / (3!) = 903,450,240,000

c) Since repeats are allowed and the code cannot begin with 0, there are 9 choices for the first digit and 10 choices for each of the remaining digits. Therefore, the total number of six-digit PIN codes that can be made is:

9 * 10^5 = 9,000,000

Answer:

Step-by-step explanation:

To find:-

Answer:-

We are here given that the right angle is made up of two angles viz 8z° and (3z+2)° .

As we know that the measure of a right angle is 90° , so the sum of the two angles would also be 90° . Hence here ,

→ 8z + 3z + 2 = 90

→ 11z + 2 = 90

→ 11z = 90-2

→ 11z = 88

→ z = 88/11

→ z = 8

Hence the value of z is 8 .

The function is decreasing for x < -6, or over the interval (–∞, –6).

What is a graph?

In computer science and mathematics, a graph is a collection of vertices (also known as nodes or points) connected by edges (also known as links or lines). Graphs are often used to represent relationships between objects or to model complex systems.

The derivative of the function y = |x + 6| is equal to -1 for x < -6 and 1 for x > -6. At x = -6, the derivative is undefined, but the function is not decreasing there, so we don't need to consider that point.

Thus, the function is decreasing for x < -6, or over the interval (–∞, –6). Therefore, the answer is A. (–∞, –6).

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The limit of the determinant as [tex]t[/tex] approaches 0 is [tex]-\infty[/tex].

To evaluate this limit, we can use the fact that the determinant is a linear function of each row, and that the limit of a sum is the sum of the limits. Therefore, we can compute the limit of each row separately.

Starting with the first row, we have:

[tex]\lim_{t\to 0} \int_0^t \frac{u}{\sinh(u)} du

= \lim_{t\to 0} \frac{\int_0^t \frac{u}{\sinh(u)} du}{t} \cdot t

= \lim_{t\to 0} \frac{\frac{t}{\sinh(t)} - 1}{t} \cdot t

= \lim_{t\to 0} \frac{1-\sinh(t)}{t\sinh(t)} = 1[/tex]

[tex]\lim_{t\to 0} \cos(t)

= 1[/tex]

[tex]\lim_{t\to 0} \sum_{n=1}^{\infty} \frac{1}{n+t+i}

= \sum_{n=1}^{\infty} \lim_{t\to 0} \frac{1}{n+t+i}

= \sum_{n=1}^{\infty} \frac{1}{n+i}

= \psi(i+1) \approx 0.643 + 0.41i[/tex]

where [tex]\psi(z)[/tex] is the digamma function.

Therefore, the limit of the first row is [tex]1 \cdot 1 \cdot \psi(i+1) = \psi(i+1)[/tex].

Moving on to the second row, we have:

[tex]\lim_{t\to 0} \frac{d}{dt} \left(e^t \ln \left(\frac{1}{t}\right) \right)

= \lim_{t\to 0} \frac{e^t}{t} - \lim_{t\to 0} \frac{e^t}{t^2}

= 1 - \infty = -\infty[/tex]

[tex]\lim_{t\to 0} \binom{5}{2} t^2

= 0[/tex]

[tex]\lim_{t\to 0} \prod_{n=1}^4 \left(\sqrt{1+nt} - 1\right)

= \prod_{n=1}^4 \lim_{t\to 0} \left(\sqrt{1+nt} - 1\right)

= \prod_{n=1}^4 \sqrt{1+n} - 1

= 4\sqrt{2} - 5[/tex]

Therefore, the limit of the second row is [tex]-\infty \cdot 0 \cdot (4\sqrt{2} - 5) = 0[/tex].

Finally, for the third row, we have:

[tex]\lim_{t\to 0} i\binom{5}{3} t^3 \sin(2t) = 0[/tex]

[tex]\lim_{t\to 0} \sum_{n=1}^{5} n^2 e^{int}

= \sum_{n=1}^{5} n^2 \lim_{t\to 0} e^{int}

= \sum_{n=1}^{5} n^2

= 55[/tex]

[tex]\lim_{t\to 0} \binom{8}{2} t^2 + i\binom{5}{2} t^3 \cos(3t) = 28[/tex]

Therefore, the limit of the third row is [tex]0 \cdot 55 \cdot 28 = 0[/tex].

Putting everything together, we get:

[tex]\lim_{t\to 0} \det\left(\begin{bmatrix} \displaystyle \int_0^t \frac{u}{\sinh(u)} du & \cos(t) & \displaystyle \sum_{n=1}^{\infty} \frac{1}{n+t+i} \\ \displaystyle \frac{d}{dt} \left(e^t \ln \left(\frac{1}{t}\right) \right)

& \binom{5}{2} t^2 & \displaystyle \prod_{n=1}^4 \left(\sqrt{1+nt} - 1\right) \\ i\binom{5}{3} t^3 \sin(2t) & \displaystyle \sum_{n=1}^{5} n^2 e^{int} & \binom{8}{2} t^2 + i\binom{5}{2} t^3 \cos(3t) \end{bmatrix}\right) = \det\left(\begin{bmatrix} \psi(i+1) & 1 & 0 \\ -\infty & 0 & 4\sqrt{2}-5 \\ 0 & 55 & 28 \end{bmatrix}\right) = -\infty[/tex]

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Answer:

4/64

Step-by-step explanation:

The spinner is independent (the total won't be effected)

we know there is 2 whites with 8 coloured option.

we want the probability of getting two whites.

2/8 x 2/8 = 4/64

there is 3 ways to work out probability, fraction, decimal and percentage (i'd personally say fraction is the most easiest)

Answer: Let's call the scale factor between the two containers "k". Then, we know that the ratio of their surface areas is equal to the square of the scale factor:

(surface area of B) / (surface area of A) = k^2

We also know that the ratio of their volumes is equal to the cube of the scale factor:

(volume of B) / (volume of A) = k^3

We can rearrange the first equation to solve for k:

k^2 = (surface area of B) / (surface area of A) = 10478 mm^2 / 1550 mm^2 = 6.75

Taking the square root of both sides, we get:

k = sqrt(6.75) = 2.6 (rounded to one decimal place)

Now we can use the second equation to find the volume of container A:

(volume of B) - (volume of A) = 62160 mm^3

(k^3)(volume of A) - (volume of A) = 62160 mm^3

Simplifying and solving for the volume of A, we get:

volume of A = 62160 mm^3 / (k^3 - 1) = 62160 mm^3 / (2.6^3 - 1) ≈ 4477 mm^3

Therefore, the volume of container A is approximately 4477 mm^3.

Step-by-step explanation:

As 80 percentage of 25 classmates is equal to 20. Krysti should have ordered 20 small t-shirts for her 25 classmates

Error is when a mistake is made while solving a mathematical problem.

Krysti's error in finding the number of small t-shirts is that she forgot to multiply the percentage by the total number of classmates.

If Krysti wanted to find the number of small t-shirts she should have ordered, she should have multiplied

80% * 25.

=0.8 * 25

= 20.

To explain it in another way, Krysti could have also 100/25 and then 80 divided by the answer that is 4. This would also give the same result of 20.

Krysti's error was that she did not correctly use percentages to find the number of small t-shirts she should have ordered.

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Answer:

a = 8

Step-by-step explanation:

4 x 2 = 8

8 x 2 = 16

Helping in the name of Jesus.

The best height he can jump is 2.5 meters. The solution has been obtained by using the arithmetic operations.

What are arithmetic operations?

It is believed that the four fundamental operations, often known as "arithmetic operations," adequately explain all real numbers. Division, multiplication, addition, and subtraction are the mathematical operations that come before quotient, product, sum, and difference.

We are given that Ivan Ukhov  jumps 2.4 metres which is 4% lower than the best height he can jump.

Let the best height be 'x'.

So, from the above information, we get

⇒ x - 0.04x = 2.4

⇒ 0.96x = 2.4                     (Using subtraction)

⇒ x = 2.5                             (Using division)  

Hence, the best height he can jump is 2.5 meters.

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To translate a shape, all of its vertices must be moved in the same direction and by the same amount. The responses to the five sections of the question are as follows:

Coordinates are used to identify the position of an object on a two-dimensional grid or in three-dimensional space. They are usually written as pairs of numbers, separated by a comma.

1. We must deduct 2 from all of the y-coordinates of the vertices of the parallelogram ABCD in order to translate it two units down. Let's assume that the vertices' initial coordinates are A(a,b), B(c,d), C(e,f), and D. (g,h). The vertices will then have the new coordinates A'(a,b-2), B'(c,d-2), C'(e,f-2), and D' (g,h-2). To obtain the translated parallelogram, plot these new vertex points.

2. To move the rhombus EFGH 2 units to the left and 4 units down, we must deduct 2 from all of its vertices' x-coordinates and 4 from all of its y-coordinates. Let's assume that the vertices' initial coordinates are E(a,b), F(c,d), G(e,f), and H. (g,h). The vertices will then have the new coordinates E'(a-2,b-4), F'(c-2,d-4), G'(e-2,f-4), and H' (g-2,h-4). To obtain the translated rhombus, plot these additional vertices.

3. If we want to translate a square with coordinates L(-5,5), M(-5,5), N(5,5), and O(5,5) 3 units to the right and 2 units up, we must add 3 to all of its x-coordinates and subtract 2 from all of its y-coordinates. The vertices' new coordinates are L'(-2,-7), M'(-2,3), N'(8,3), and O' (8,-7). To obtain the translated square, plot these new vertex points.

4. The new coordinates of triangle XYZ after translating 4 units down will be X' (2,-3), Y' (4,1) and Z' (5,-2). This is happening because when a triangle is translated 4 units down, the y-coordinate of each vertex is decreased by 4 units, while the x-coordinate remains the same.

5. I (4,-2) P (-4,-2) G (5,2) Q (6,-4) R (-2,2)

S (6,4) J (1,-1) U (-5,0) H (3,-1) K (-6,-5)

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The initial investment was approximately $2,603.88, which is option (b).

Probability is a measure of the likelihood of an event occurring.

We can use the formula for compound interest:

A = [tex]P(1+r/n)^{nt}[/tex]

where A is the final amount, P is the principal (initial investment), r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the time period in years.

In this case, we know that the final amount A is $3,820, the annual interest rate r is 5.5% (or 0.055 as a decimal), the interest is compounded 6 times a year (n = 6), and the time period is 7 years.

So we can rearrange the formula to solve for P:

P = A/[tex]P(1+r/n)^{nt}[/tex]

Plugging in the values, we get:

P = 3820 / [tex](1+0.055/6)^{6*7}[/tex]

P ≈ $2,603.88

Therefore, the initial investment was approximately $2,603.88, which is option (b).

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