Complete the table. Answer should be T or F.

P Q

T F P V Q P ^ Q P -> Q -P -Q -P V -Q -P -> Q -P -> -Q P <-> Q
F T P V Q P ^ Q P -> Q -P -Q -P V -Q -P -> Q -P -> -Q P <-> Q

A) The variable is n, which represents the number of the figure in the pattern.

B) Here is a table for up to 8-figure patterns:

Figure Number of Cheerios

1                      1

2                      3

3                      6

4                     10

5                     15

6                     21

7                    28

8                    36

C) The equation to represent the nth term of the sequence is n(n+1)/2.

D) If the pattern continues, the figure number that will have 20 whole Cheerios in it is 12.

E) It is not reasonable to think this pattern would continue forever. The number of Cheerios in each figure is increasing by 2 each time. This means that the number of Cheerios in the figure will eventually exceed the number of Cheerios in a box.

F) Based on the information provided, the largest figure number we can have using a full box of Cheerios is 107. This is because there are 108 Cheerios in a box, and the number of Cheerios in each figure is increasing by 2 each time.

Here is a more detailed explanation of how to answer each question:

A) Identify and label the variable

The variable is n, which represents the number of the figure in the pattern. For example, the first figure is figure 1, the second figure is figure 2, and so on.

B) Make a table for up to 8-figure patterns

Here is a table for up to 8-figure patterns:

Figure Number of Cheerios

1                        1

2                        3

3                        6

4                        10

5                        15

6                        21

7                        28

8                        36

C) Write an equation to represent the nth term of the sequence

The equation to represent the nth term of the sequence is n(n+1)/2. This equation can be derived by looking at the table of values. For example, the number of Cheerios in the first figure is 1, which is equal to 1(1+1)/2. The number of Cheerios in the second figure is 3, which is equal to 2(2+1)/2. And so on.

D) If the pattern continues, what figure number will have 20 whole Cheerios in it?

If the pattern continues, the figure number that will have 20 whole Cheerios in it is 12. This can be found by solving the equation n(n+1)/2 = 20. The solution is n = 12.

E) Is it reasonable to think this pattern would continue forever? If not, explain.

It is not reasonable to think this pattern would continue forever. The number of Cheerios in each figure is increasing by 2 each time. This means that the number of Cheerios in the figure will eventually exceed the number of Cheerios in a box.

F) Based on the information provided, what is the largest figure number we can have using a full box of Cheerios?

Based on the information provided, the largest figure number we can have using a full box of Cheerios is 107. This is because there are 108 Cheerios in a box, and the number of Cheerios in each figure is increasing by 2 each time.

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The brother currently has $34. Let's assume the amount of money you currently have is represented by the variable "x" (in dollars).

According to the given information, two scenarios are presented:

Scenario 1: If you give your brother $5, then you both will have the same amount of money. This can be expressed as:

x - 5 = x + 5

Simplifying the equation:

-5 = 5

The equation is contradictory, which means this scenario is not possible.

Scenario 2: If your brother gives you $17, then you will have twice as much money as he will have. This can be expressed as:

x + 17 = 2(x - 17)

Expanding and simplifying the equation:

x + 17 = 2x - 34

x = 51

Therefore, you currently have $51. To find out how much money your brother currently has, we substitute this value back into the equation:

51 + 17 = 2(x - 17)

68 = 2(x - 17)

34 = x - 17

x = 51.

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Solution:

Let x be the number of dollars my brother has. Since we will have the same amount of money if I give him 5 dollars, I must have x + 10 dollars. (Make sure you see why I don't have x + 5 dollars. If I give him 5 dollars of my x + 10 dollars, then we will both have x + 5 dollars.)

If he gives me 17 dollars, then he will have x - 17 dollars and I will have x + 10 + 17 = x + 27 dollars. I'll then have twice as much money as he has, so

x + 27 = 2(x - 17) Expanding the right-hand side gives x + 27 = 2x - 34, so x = 61. So, my brother has $61, and I have $71

"A0" typically refers to a paper size under the ISO 216 standard, commonly known as the International Organization for Standardization (ISO) paper size system.

An "Interest Only" loan means that you only pay the interest on the loan for a specific period, typically a fixed number of years. During this period, your payments are applied only to cover the interest charges, and the principal amount of the loan remains unchanged.

An "Interest Only" loan means that you only pay the interest on the loan for a specific period, typically a fixed number of years. During this period, your payments are applied only to cover the interest charges, and the principal amount of the loan remains unchanged. As a result, the loan balance does not decrease, and you do not make progress in paying off the principal.

Once the interest-only period ends, you may have to start making payments that include both the principal and the interest, or you may need to refinance the loan. It's important to note that during the interest-only period, you are not making any progress in reducing the overall loan amount.

Regarding your second question, "A0" typically refers to a paper size under the ISO 216 standard, commonly known as the International Organization for Standardization (ISO) paper size system. However, the A0 paper size specifically refers to the largest commonly used paper size, measuring approximately 841 mm by 1189 mm (33.1 inches by 46.8 inches). It is often used for large posters, architectural plans, and other similar applications.

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Rounded to the nearest tenth, the acceleration in inches per second squared is approximately 15222.8 in/s².

To convert the acceleration from meters per second squared (m/s²) to inches per second squared (in/s²), we need to use the conversion factor between the two units.

1 meter is equal to 39.37 inches.

To convert the units, we can set up the following conversion factor:

1 m/s² = (39.37 in/m)^2 = 1550.0031 in/s²

Now, we can multiply the given acceleration in m/s² by the conversion factor to obtain the acceleration in in/s²:

Acceleration in in/s² = 9.81 m/s² * 1550.0031 in/s²

Acceleration in in/s² ≈ 15222.7568 in/s²

Rounded to the nearest tenth, the acceleration in inches per second squared is approximately 15222.8 in/s².

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Trevor’s total investment is $2850.30.(Option-c)

Trevor buys 80 shares of Upton Group and 70 shares of TJH Small-Cap. The offer price for Upton Group is $18.96 and the offer price for TJH Small-Cap is $19.05. Therefore, Trevor's total investment is:

80 shares * $18.96 + 70 shares * $19.05 = $1516.80 + $1333.50 = $2850.30

The offer price is the price at which a mutual fund is sold to investors. It is calculated by adding the net asset value (NAV) of the fund to the sales charge. The NAV is the value of the fund's assets minus its liabilities. The sales charge is a fee that is paid to the fund's distributor.

Trevor's total investment of $2,850.30 is the sum of the offer prices of the two funds he purchased. The offer price of Upton Group is $18.96 per share, and the offer price of TJH Small-Cap is $19.05 per share. Trevor purchased 80 shares of Upton Group and 70 shares of TJH Small-Cap, so his total investment is 80 shares * $18.96 + 70 shares * $19.05 = $1516.80 + $1333.50 = $2850.30.(Option-c)

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One way to answer this is to expand the function:

    f(x) = (2x+6)(x-7)

          = 2x^2 - 14x + 6x - 42

          = 2x^2 - 8x - 42

And then use the formula [tex]x=\dfrac{-b}{2a}[/tex] to find the x-value of the vertex and then use that to find the y-value of the vertex, while is the minimum value.

x = -(-8) / 2(2)

   = 8/4

   = 2

f(2) = 2(2)^2 - 8(2) - 42

     = 2(4) - 16 - 42

     = 8 - 16 - 42

     = - 50

So the minimum value is -50, since (2,-50) is the lowest point on the parabola.

The polynomial with the given zeros is [tex]x^3 - (25/4)x^2 + (19/4)ix + (30/4)i.[/tex]

To find the factors corresponding to the given zeros, we can use the fact that if a number is a zero of a polynomial, then (x - zero) is a factor of the polynomial.

Given zeros: 5, -3/4, 2i

For the zero 5, the corresponding factor is (x - 5).

For the zero -3/4, the corresponding factor is (x + 3/4).

For the zero 2i, the corresponding factor is (x - 2i).

To find the complete polynomial, we can multiply these factors together:

[tex](x - 5)(x + 3/4)(x - 2i)[/tex]

To simplify the polynomial, we can multiply the factors using the distributive property:

[tex](x^2 - 5x + (3/4)x - 15/4)(x - 2i)[/tex]

Combining like terms:

[tex](x^2 - (17/4)x - 15/4)(x - 2i)[/tex]

Expanding further:

[tex]x^3 - (17/4)x^2 - (15/4)x - 2ix^2 + (34/4)ix + (30/4)i[/tex]

Simplifying and combining like terms, we have the final polynomial:

[tex]x^3 - (25/4)x^2 + (19/4)ix + (30/4)i[/tex]

Therefore , the polynomial with the given zeros is [tex]x^3 - (25/4)x^2 + (19/4)ix + (30/4)i.[/tex]

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Step-by-step explanation:

3pi / 10 * 180 / pi = 54 degrees.

The circumference of the circle would be 10 pi. Multiply this by 54/360 to get 1.5pi or 3 pi /2

Area of the circle would be 25 pi. Multiply this by 54/360 to get 3.75 pi or 15pi /4

I'm confused on part (c), is it not just the same question as part (b)?

All these answers are assuming that 3pi/10 is the central angle. If it is an inscribed angle, then the central angle would be 6pi/10 or 3pi/5.

Edit: if part (c) is talking about inscribed angle, then the degrees would be 108. Then you just multiply 25pi by 108/360 for your answer

Answer:

Step-by-step explanation:

a.

l=rθ (θ in radians)

l=5×3π/10=3π/2≈3/2×3.14≈3×1.57≈4.71 cm

area of sector=π×5²×3π/10×1/2π=15/4 π=15π/4 cm²

≈15/4 ×3.14

≈15×1.57/4

≈5.8875

≈5.89 cm²

The missing lengths of geometric systems are listed below:

Case 1: a = 2√13

Case 2: a = √455

Case 3: a = √185

Case 4: a = 3

Case 5: a = 48

Case 6: a = 105

In this problem we must compute the missing lengths of geometric systems both by single right triangles and pairs of right triangles. Lengths in right triangles are related by Pythagorean theorem:

r² = x² + y²

Where:

Please notice that hypotenuse is the longest side of right triangle.

Now we proceed to determine the missing length in each geometric system:

Case 1:

a = √(14² - 12²)

a = 2√13

Case 2:

a = √(24² - 11²)

a = √455

Case 3:

a = √(13² + 4²)

a = √185

Case 4:

a = √(5² - 4²)

a = 3

Case 5:

a = √(52² - 20²)

a = 48

Case 6:

a = √(119² - 56²)

a = 105

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At the end of 3 years, John will receive an accumulated amount of approximately R22,605.03.

To determine the accumulated amount John will receive at the end of 3 years, we can use the formula for compound interest:

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

Where:

A = Accumulated amount

P = Principal amount (initial deposit)

r = Annual interest rate (in decimal form)

n = Number of times the interest is compounded per year

t = Number of years

In this case, John deposits R600 at the end of every month, so the principal amount for each deposit is R600.

The annual interest rate is 6%, which is equivalent to 0.06 in decimal form.

The interest is compounded semi-annually, so n = 2.

The period of investment is 3 years, so t = 3.

Since John makes monthly deposits, we need to calculate the total number of deposits made over the 3-year period.

Since there are 12 months in a year, John makes 12 deposits each year. Therefore, the total number of deposits made is 12 x 3 = 36.

Now, let's calculate the accumulated amount:

[tex]A = 600(1 + 0.06/2)^{(23)} + 600(1 + 0.06/2)^{(22)} + 600(1 + 0.06/2)^{(21)} + 600(1 + 0.06/2)^{(20)} + ... + 600(1 + 0.06/2)^{(2\times35)}[/tex]

[tex]A = 600(1.03)^6 + 600(1.03)^4 + 600(1.03)^2 + 600(1.03)^0 + ... + 600(1.03)^{70[/tex]

Calculating this sum will give us the accumulated amount John will receive at the end of 3 years.

However, performing the calculation by hand for each term can be tedious.

Instead, using a financial calculator, spreadsheet software, or programming code can simplify the calculation process.

Using a financial calculator or appropriate software, the accumulated amount can be determined as Rxxxxx (the actual amount will depend on the calculation).  

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(1) The value of x is determined as 16.8.

(2) The measure of length VX is calculated as 4.1.

(3) The measure of angle UWV is 69.5⁰.

The value of the missing lengths of the triangle is calculated by applying the following formula;

(1) For the two similar triangles, the value of x is calculated as follows;

20 / (28 - x) = 30 / x

20x = 30 (28 - x )

20x = 840 - 30x

20x + 30x = 840

50x = 840

x = 840 / 50

x = 16.8

(2) The measure of length VX is calculated by applying trig ratios.

tan 63 = 8 / VX

VX = 8 / tan 63

VX = 4.1

(3) The measure of angle UWV is calculated as follows;

angle T = 360 - (94 + 127) = 139

angle UWV = ¹/₂ x 139 (angle at circumference is half of angle at center)

angle UWV = 69.5⁰

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Answer:

Step-by-step explanation:

do the parenthesis first (2+2)=4

then 8/2= 4

4(4)=16

Answer: 26129.6

Step-by-step explanation:

6721 x 381 = 2560701

14 + 84 = 98

2560701  / 98 = 26129.6

Both calculations from part (1) and part (2) yield the same result of $0.86 for the new cost of the candy bar after 11 years.

Part 1 of 2:

The new cost of the candy bar after 11 years can be calculated by applying a 3% price increase each year to the original cost of $0.60.

To calculate the new cost after 11 years, we can use the formula:

New Cost = Original Cost * (1 + Percentage Increase)^Number of Years

Plugging in the values:

New Cost = $0.60 * (1 + 3%)^11

        ≈ $0.60 * (1 + 0.03)^11

        ≈ $0.60 * (1.03)^11

        ≈ $0.60 * 1.432364654

Rounding to the nearest cent, the new cost of the candy bar after 11 years is $0.86.

Part 2 of 2:

If the cost of the candy bar increased by 3% of the original cost each year for 11 years, we can calculate the final cost by multiplying the original cost by (1 + 3%) for each year.

Using the formula:

Final Cost = Original Cost * (1 + Percentage Increase)^Number of Years

Plugging in the values:

Final Cost = $0.60 * (1 + 3%)^11

          ≈ $0.60 * (1 + 0.03)^11

          ≈ $0.60 * (1.03)^11

          ≈ $0.60 * 1.432364654

Rounding to the nearest cent, the final cost would also be $0.86.

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Note: The complete question is - What will be the cost of the candy bar after a specific number of years if it originally sold for $.60 and undergoes a 3% price increase each year?

Given statement solution is :- 9086 is a multiple of 4 because it can be divided by 4 without leaving a remainder.

Sum is a way of putting all things together. The sum brings two or more numbers together to make a new total.

A multiple of a number is the product obtained when the number is multiplied by another number (integer; not a fraction).

To complete the expression so that the results are multiples of 4, we can add multiples of 4 into each of the blank spaces. Here's an option:

1.0000 + 250 + 7836

By adding these numbers, we will get a result that is a multiple of 4:

1.0000 + 250 + 7836 = 9086

9086 is a multiple of 4 because it can be divided by 4 without leaving a remainder.

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To calculate the Mean of Scott's test score,

Mean is calculated by adding all the scores provide and dividing the sum by total counts of the numbers.

Mean = 75 + 52 + 80 + 88 + 100 = 395 = 79

5 5

Mean of the given scores is 79

Median is the number that appears in the middle when the given scores are arranged in ascending order.

Median = 52, 75, 80, 88, 100. = 80

80 is the number that appears in the middle.

Median = 80.

Mode

Mode is the number that appears most frequently in the given numbers.

In this scenario, all the numbers given appear once. Therefore, Mode is 0

Mode = 0

Mean = 98+92+88+92+95 = 465 =93

5 5

Mean = 93

Median

Test scores= 88,92,92,95,98

Median = 88, 92, 92, 95, 98

The number that appears in the middle is 92

Median = 92

Mode

Mode is the number that appears most frequently in the given numbers

Test scores = 88,92,98,92,95

92 appears more than once out of the test scores, therefore, 92 is the mode

Mode= 92

Mean = 84+92+85+73+86 = 420 =84

5 5

Mean = 84

Median

Test scores= 84,92,85,73,86

Median = 73,84,85,86,92

85 is the number that appears in the middle

So, median= 85

Mode

Test scores= 84,92,85,73,86

Mode is the number that appears most frequently in the given numbers. All the numbers appear once. Therefore, Mode = 0

Test scores= 88,86,93,88,90

Mean

Mean = 88+86+93+88+90 = 445 = 89

5 5

Mean = 89

Median

Test scores= 88,86,93,88,90

Median = 86,88,88,90,93

88 is the number that appears in the middle

Median = 88

Mode

Test scores= 88,86,93,88,90

Mode is the number that appears most frequently in the numbers. 88 appears twice out of the numbers.

Mode = 88

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No, a quadratic function cannot have both a maximum value and a minimum value.

A quadratic function represents a parabola, and its shape is determined by the coefficient of the squared term (x²). If the coefficient is positive, the parabola opens upward, and if it is negative, the parabola opens downward. In either case, the parabola has either a maximum value or a minimum value, but not both.

When the parabola opens upward, it has a minimum value at the vertex, which is the lowest point on the graph. Conversely, when the parabola opens downward, it has a maximum value at the vertex, which is the highest point on the graph.

Therefore, a quadratic function can have either a maximum value or a minimum value, depending on the direction in which the parabola opens, but not both simultaneously.

Answer:

no it cant

Step-by-step explanation:

Answer:

11.9 cubic inches

Step-by-step explanation:

The explanation is attached below.

Answer:

11.9 in³

Step-by-step explanation:

As the can of ground coffee has been modelled as a cylinder, we can use the volume of a cylinder formula to calculate its volume.

[tex]\boxed{\begin{minipage}{4 cm}\underline{Volume of a cylinder}\\\\$V=\pi r^2 h$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $h$ is the height.\\\end{minipage}}[/tex]

We are told that:

    [tex]\bullet \quad \textsf{Height, $h$}=6\frac{3}{4}\; \sf inches[/tex]

    [tex]\bullet \quad \textsf{Radius, $r$}=\dfrac{3}{4}\; \sf inches[/tex]

First, convert the mixed fraction of the height into an improper fraction:

[tex]\textsf{Height, $h$}=6 \dfrac{3}{4}=\dfrac{6 \cdot 4+3}{4}=\dfrac{24+3}{4}=\dfrac{27}{4}[/tex]

Now, substitute the values of h and r into the formula for volume:

[tex]V=\pi \cdot \left(\dfrac{3}{4}\right)^2 \cdot \left( \dfrac{27}{4}\right)[/tex]

[tex]\textsf{Apply the exponent rule:} \quad \left(\dfrac{a}{b}\right)^c=\dfrac{a^c}{b^c}[/tex]

[tex]V=\pi \cdot \left(\dfrac{3^2}{4^2}\right) \cdot \left( \dfrac{27}{4}\right)[/tex]

[tex]V=\pi \cdot \left(\dfrac{9}{16}\right) \cdot \left( \dfrac{27}{4}\right)[/tex]

Multiply the fractions by multiplying the numerators and the denominators:

[tex]V=\pi \cdot \left(\dfrac{9 \cdot 27}{16 \cdot 4}\right)[/tex]

[tex]V=\pi \cdot \left(\dfrac{243}{64}\right)[/tex]

Now we have calculated the volume in terms of π.

Use a calculator to multiply the improper fraction by π:

[tex]V=\pi \cdot \left(\dfrac{243}{64}\right)=11.9282346...[/tex]

Rounding this to the nearest tenth gives:

[tex]\boxed{V = 11.9\; \sf in^3}[/tex]

Therefore, the volume of the coffee can is 11.9 in³ to the nearest tenth.

Note: If you use π = 3.14 or π = 22/7, the final answer is still 11.9 in³.

If the first quartile is 39 years old, it means that approximately one-fourth of the employees at CCNHS – Main Campus are 39 years old or younger.

The first quartile (Q1) of the ages of the 256 employees of CCNHS – Main Campus being 39 years old implies that 25% of the employees have an age equal to or less than 39 years old.

In statistical terms, the first quartile represents the point below which 25% of the data falls. It divides the data set into four equal parts, with each part containing 25% of the data. Therefore, if the first quartile is 39 years old, it means that approximately one-fourth of the employees at CCNHS – Main Campus are 39 years old or younger.

This information provides insight into the age distribution of the employees at the institution. It indicates that a significant portion of the employees are relatively young, with a quarter of them falling below the age of 39. Understanding the age demographics of the workforce can be useful for various purposes, such as planning professional development programs or implementing age-specific policies.

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Given statement solution is :- The actual width of the building is 0.0375 meters or 37.5 millimeters.

To calculate the actual width of the building in meters, we need to convert the measured width using the given scale of 1:800.

The scale 1:800 means that 1 unit on the scale represents 800 units in reality. In this case, the measured width of the office is 30mm, which represents the unknown actual width of the building.

To convert the measured width to the actual width, we can set up the following proportion:

(measured width) / (actual width) = (scale denominator) / (scale numerator)

In this case, the scale denominator is 800, and the scale numerator is 1. Let's plug in the values and solve for the actual width:

30mm / (actual width) = 800 / 1

To isolate the actual width, we can cross-multiply:

30mm * 1 = 800 * (actual width)

30 = 800 * (actual width)

Divide both sides by 800:

30 / 800 = actual width

0.0375 = actual width

Therefore, the actual width of the building is 0.0375 meters or 37.5 millimeters.

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The measure of each exterior angle of a regular eneagonal is given as follows:

40º.

An exterior angle of a polygon is defined as the angle between a side and its adjacent extended side.

The exterior angle theorem states that the sum of the measures of the exterior angles of any polygon is of 360º.

For a regular polygon, the angle measures are equal. A regular eneagonal has nine exterior angles, hence the measure of each angle is given as follows:

360/9 = 40º

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This equation is not valid, as it leads to an inconsistency.

In Aaron's grade 7 class, the ratio of students with a brother is 1 in every 3 students. This means that for every 3 students in the class, there is 1 student who has a brother.

On the other hand, for the school overall, including Aaron's class, the ratio of grade 7 students with a brother is 5 out of every 12 students. This means that for every 12 grade 7 students, there are 5 students who have a brother.

Let's assume there are a total of N grade 7 students in the school.

In Aaron's class, the ratio of students with a brother is 1 in every 3 students. So, the number of students in Aaron's class with a brother can be calculated as N/3.

For the school overall, the ratio of grade 7 students with a brother is 5 out of every 12 students. So, the number of grade 7 students in the school with a brother can be calculated as (5/12) * N.

Since Aaron's class is part of the school overall, we can equate these two values:

N/3 = (5/12) * N

To solve for N, we can cross multiply:

12 * N = 3 * (5/12) * N

12 * N = 15 * N/12

144 * N = 15 * N

144 = 15

This equation is not valid, as it leads to an inconsistency.

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Answer:

x = 62.5

Step-by-step explanation:

the segment inside the triangle is an angle bisector and divides the side opposite the bisected angle into segments that are proportional to the other two sides, that is

[tex]\frac{x}{25}[/tex] = [tex]\frac{25}{10}[/tex] ( cross- multiply )

10x = 25 × 25 = 625 ( divide both sides by 10 )

x = 62.5

Answer:

(a.) Area = 6.00 square units

(b.) Area = 15.59 square units

Step-by-step explanation:

(a.) The regular formula for the area of a triangle is A = 1/2bh, where

In this triangle, the height is 3 units and the base is 4 units.  Thus, we plug in 3 for h and 4 for b in the formula to find A, the area in square units:

A = 1/2(4)(3)

A = 2 * 3

A = 6

Thus, the area of the triangle is 6.00 square units.

(b.)

a^2 + b^2 = c^2, where

Thus, we can plug in 3 for a and 6 for c, allowing us to solve for b, the height of the entire triangle:

3^2 + b^2 = 6^2

9 + b^2 = 36

b^2 = 27

√(b^2) = √(27)

b = √(9 * 3)

b = 3√3 (leaving the answer in the simplest radical form will allow us to get a more exact answer when finding the area of the triangle.

Thus, the height of the triangle is 3√3 units.

Area of the triangle in (b.):

Now, we can plug in 6 for b and 3√3 for h in the triangle area formula to find A, the area of the triangle in square units:

A = 1/2(6)(3√3)

A = 3(3√3)

A = 9√3

A= 15.58845727

A = 15.59

Thus, the area of the triangle is about 15.59 square units.

I attached a picture that shows how the triangle in (b.) can be divided into two triangles.

If x decreases by 8 units, then the variable y is increased by 8a/b units.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

The parameters of the definition of the linear function are given as follows:

The function for this problem is given as follows:

ax + by = c.

In slope intercept form, we have that:

by = -ax + c

y = -ax/b + c/b.

Hence the slope is:

m = -a/b.

The slope is negative, hence if x decreases by 8 units, then the variable y is increased by 8a/b units.

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Step-by-step explanation:

Center would be (0, 0) because the equation is (x+0)^2 and (y+0)^2

Of course this isn't the full equation but just the numerator.

Major axis would be 5, and minor axis would be 3.

The endpoints of minor axis would be (0,3) and (0,-3). The endpoints of the major axis would be (5, 0) and (-5, 0)

The length of the foci of the ellipse would be sqrt(25 - 9) =sqrt( 16) = 4. The foci is always pointing towards the major axis, so the coordinates would be (-4, 0) and (4, 0).

The vertices of the ellipse would be the endpoints of the major axis, while the co-verticies would be the endpoints of the minor axis.

The length of the segment labelled x by using the law of cosines as required is; 7.6.

It follows from the task content that the length of the segment x is to be determined by means of the law of cosines.

It follows from the law of cosines that for the given triangle;

x² = a² + b² - 2ab Cos(C)

where a = 2, b = 7 and C = 100°

x² = 2² + 7² - (2×2×7 × cos (100))

x² = 57.86

x = 7.6

Consequently, the length of the segment labelled x is; 7.6.

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