FORM 3A4
MATHS PROJECT

Get into groups of no more than 4 persons. Select a family size of 4/6/10 persons based on the greatest number of persons in the family in your group.

Calculate for the family size selected (allowing 24 inches for each person) the minimum diameter of a circular table to seat all members the minimum length of the side of a square table.

Calculate the area of the top of the circular table and the square table, and explain which is most appropriate for the family.​

We may state with confidence that the exponential function y = [tex]3(3^{x} )[/tex]models the provided data because both of these values agree with the data.

How is exponential function determined?

Since the output values (y) increase by a factor of three every time the input value (x) increases by one, the data demonstrate exponential growth. As a result, we can use an exponential function of the form y = a(b)x to represent this data.

We can utilise the first two data points to determine the values of a and b.

With y = 3 and x = 0, we get:

3 = [tex]a(b^{0} )[/tex]

3 = a

With x=1 and y=9, we get:

9 = [tex]a(b^{x} )[/tex]

b = 3

Hence, y = [tex]3(3^{x} )[/tex] is the exponential function that represents the data.

We may substitute the other input values and compare them to the appropriate output values to validate this model:

If x = 2, then y = [tex]3(3^{2} )[/tex] = 27.

If x = 3, then y = [tex]3(3^{3} )[/tex] = 81.

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Answer:

7/25

Step-by-step explanation:

Sin = [tex]\frac{opposite}{Hypotenuse}[/tex]

Hypotenuse = 50

Adjacent = 48

Pythagorean Theorem: a² + b² = c²

48² + b² = 50²

2304 + b² = 2500

b² = 196

b = 14

Opposite = 14

Sin A = 14/50 = 7/25

The evidence from the text suggests that the zombie trick helped the main character feel mentally prepared for the "Zombie 5K" event.

The main character initially expresses doubts about her ability to complete the race. She says, "I was worried that I wouldn't be able to finish the Zombie 5K. I wasn't very confident in my running abilities, and I was afraid I would get too scared by the zombies." This shows that she lacked confidence and had fears about the event.

However, after her friends played the zombie trick on her, the character's mindset changed. She says, "After the zombie trick, I felt more prepared to face the real zombies during the race. I knew it was just a trick, but it helped me overcome my fears and feel more confident." This suggests that the zombie trick had a positive impact on her mental preparation for the race.

Furthermore, the character's behavior during the race supports this idea. She describes how she used strategies to avoid the zombies and successfully completed the race. She says, "I made sure to stay aware of my surroundings and avoid the zombies as best as I could.

I kept reminding myself that they were just people in costumes, and that helped me stay focused on finishing the race." This shows that the character was mentally prepared for the race and able to perform well despite the challenges.

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32 is the incorrect answer

Answer: infinite solution

If u continue to solve it will be equal in both sides therefore it is infinite solution

There is gain of $1,000 on the sale. The solution has been obtained by using the arithmetic operations.

What are arithmetic operations?

All real numbers are believed to be able to be described by the four fundamental operations, often known as "arithmetic operations". Quotient, product, sum, and difference are the next four mathematical operations after division, multiplication, addition, and subtraction.

We are given that an equipment costing $135,000 has a book value of $124,000 and it is sold for $125,000.

Since, the sale value is higher than the book value, therefore there is a gain.

Using arithmetic operations, we get

Gain on sale = $125,000 - $124,000

Gain on sale = $1,000

Hence, there is gain of $1,000 on the sale.

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The second part of the question i.e. how is it recorded for this transaction is related to the subject accountancy and not mathematics.

Using the trend line equation, we can find that the record was set in the year 2005.

Data is shown visually in a scatter plot.

The coordinate axes are used in a straightforward scatter plot to plot the points according to their values.

Now in the given question,

The scatter plot equation is:

y = - 0.14x + 12.5

Now we know that y = 11.8 seconds.

So,

11.8 = -0.14x + 12.5

⇒ 0.14x = 12.5 - 11.8

⇒ x = 0.7/0.14

⇒ x = 5

Therefore, the year when the record was set is 2000+5 = 2005.

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Answer:

B. inductive

Step-by-step explanation:

An inductive reasoning process involves making a generalization based on specific observations. In the case of the given question, the statement is: "A _______ is an educated guess based on patterns in data figures."

To use inductive reasoning to find the answer, we can follow these steps:

Look for patterns in the data figures. Identify the commonalities between different examples of educated guesses.

Based on these patterns, make an initial generalization about what the blank might be. For example, if we notice that all educated guesses involve making a prediction based on previous observations, we might guess that the missing word is "conjecture."

Test the generalization by looking at additional examples. Do these examples fit the pattern we identified earlier? If so, our initial guess might be correct. If not, we might need to revise our generalization or consider other options.

Continue testing and refining the generalization until we feel confident that it accurately describes the relationship between the given words.

In this case, using inductive reasoning, we can make an educated guess that the missing word is "conjecture," as it fits the pattern of being an educated guess based on patterns in data figures.

No, because the SAS Congruence Theorem requires two pairs of congruent sides and one congruent angle.

No, because the SAS Congruence Theorem requires two pairs of congruent sides and one congruent angle. To use the SAS Congruence Theorem to prove that GHF =KHJ, it would be necessary to have information about the lengths of the corresponding sides and the measure of the included angle in each triangle. Without this information, it is not possible to prove that GHF =KHJ using the SAS Congruence Theorem. To prove that GHF =KHJ using this theorem, it would be necessary to show that the two sides GK and KH are congruent, the two sides HF and HJ are congruent, and the included angle GHF is congruent to the included angle KHJ.

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Answer:

250.56

Step-by-step explanation:

we know each dress is 8.70 , and when we buy 40 dresses or more we get 10 percent off the total.

let us first multiply 8.70 x 42 , giving us the total cost as 278.4
there is a 10 percent discount , so 27.84 should be reduced from original price

Final price = 250.56

Answer: To find the x and y intercepts of the line 2x + 5y = -6, we can substitute 0 for x to find the y-intercept and 0 for y to find the x-intercept.

y-intercept:

To find the y-intercept, we set x = 0 and solve for y:

2x + 5y = -6

2(0) + 5y = -6

5y = -6

y = -6/5

Therefore, the y-intercept is (-0,6/5)

x-intercept:

To find the x-intercept, we set y = 0 and solve for x:

2x + 5y = -6

2x + 5(0) = -6

2x = -6

x = -3

Therefore, the x-intercept is (-3,0).

Hence, the intercepts of the line 2x + 5y = -6 are (-3, 0) for the x-intercept and (0, -6/5) for the y-intercept.

Step-by-step explanation:

The surface area of the rectangular prism is 208 [tex]cm^2\\[/tex]

Since there are two of these faces, their combined area is as follows:

2 x [tex]48 cm^2[/tex] =[tex]96 cm^2[/tex]

We must add together the areas of all six faces to determine the total surface area:

[tex]48 cm^2 + 64 cm^2 + 96 cm^2 = 208 cm^2[/tex]

Hence, the rectangular prism has a surface area of 208 [tex]cm^2\\[/tex]

The region enclosed by an object's shape is referred to as the area. The area of the shape is the area that the figure or any other two-dimensional geometric shape occupies in a plane. Each shape's area is determined by its dimensions and characteristics. The regions of various shapes vary. The square's area is distinct from a kite's area.

If two items are similar in shape, the area they cover need not be equal unless and until the dimensions of the two shapes are likewise equivalent. Let's say there are two rectangle boxes, each measuring L1 and L2 in length and B1 and B2 in width.

From the question:

A rectangular prism is the name of the 3D shape depicted in the image.

We must first determine the area of each face of a rectangular prism in order to find its surface area.

The image's rectangular prism is 4 cm x 6 cm x 8 cm.

The top and bottom faces' combined surface area is equal to the surface area of a rectangle, which is:

4 x 6 = 24[tex]cm^2\\[/tex]

Given that there are two of these faces, the top and bottom faces' combined area is:

2 x 24[tex]cm^2\\[/tex]= 48 [tex]cm^2\\[/tex]

The front and rear faces' combined surface area is equal to the surface area of a rectangle, which is:

4 x 8 = 32[tex]cm^2\\[/tex]

As there are two of these faces, their combined surface area is as follows:

64 square cm = 2 x 32 [tex]cm^2\\[/tex]

The area of a rectangle is equal to the area of the left and right faces, which is:

6 x 8 = 48 [tex]cm^2\\[/tex]

Since there are two of these faces, their combined area is as follows:

2 squares of 48 [tex]cm^2\\[/tex] each equal 96 [tex]cm^2\\[/tex].

We must add together the areas of all six faces to determine the total surface area:

[tex]48 cm^2 + 64 cm^2 +96 cm^2 = 208 cm2.[/tex]

Hence, the rectangular prism has a surface area of 208 [tex]cm^2.[/tex]

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complete question:

What do we call the 3D shape below and what is its SURFACE AREA? Explain how you determined your answer and show your work!!!!

Answer:

i think 4<6

Step-by-step explanation:

Answer:

=

Step-by-step explanation:

5j543nn al

(a) the events A and B are disjoint.

(b) the probability that A or B occurs is 0.6.

What is Probability?

In mathematical terms, probability is defined as the ratio of the number of favorable outcomes to the total number of possible outcomes in a given event or experiment. The probability of an event is represented by a number between 0 and 1, where 0 indicates that the event is impossible, and 1 indicates that the event is certain.

(a) If the knowledge that an event A has occurred implies that a second event B cannot occur, then the events A and B are said to be disjoint. This means that A and B have no outcomes in common and cannot happen simultaneously.

(b) If event A and event B are disjoint and event A has probability 0.5 and event B has probability 0.1, then the probability that A or B occurs is the sum of their probabilities:

P(A or B) = P(A) + P(B) = 0.5 + 0.1 = 0.6

Note that since A and B are disjoint, the probability of both events happening simultaneously is 0. Therefore, P(A and B) = 0.

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According to the given table and graph:

a) The number of customers a restaurant employee can serve is 5.

b) The number of customers a grocery store clerk can serve is 12 for him.

c) The customer's food price per employee is 7 higher than the restaurant's price.

Line charts use data point "markers" connected by straight lines. These data points connected by straight lines are useful for visualization. Line charts are used in different fields for different purposes, but they are especially useful when you need to graphically represent changes in values ​​over time.

Line charts are widely used in finance to create visual representations of values ​​over time, such as changes in security prices, company earnings lists, and the history of major stock indices. It is also useful for comparing different stocks. In the field of investing, especially technical analysis, line charts are used by investors to visualize trends, which greatly aids analysis.

Given a graph of restaurants and a table of grocery stores, it shows the relationship between number of employees per customer. You have to solve the subtasks of the given task.

The price at the store is 12 ÷ 2 or 6 customers per employee.

According to the question;

A diagram of a restaurant and a grocery store table are shown.

a) at a restaurant;

For 2 employees, no. Customers = 10

For 4 employees, no. Customers = 20

so

If he increases the number of employees by two, no. We have 10 more customers.

⇒ The number of customers a restaurant employee can serve;

= 10 ÷ 2

= 5 customers

b) At the grocery store.

For 2 employees, no. Customers = 24

For 4 employees, no. Customers = 48

So when the number of employees increases by 2.

⇒ How many customers can a grocery store clerk serve;

= 24 ÷ 2

= 12 customers

c) so

Restaurant rate of customers per employee = 5 customers/employee

Grocery store customer rate per employee = 12 customers/employee

Also, food prices per customer per employee are higher than restaurant prices.

= 12 - 5

= 7  

Thus , the answers will be ;

a) No. of customers , one employee can help at restaurant is 5.

b) No. of customers , one employee can help at grocery store is 12.

c) The grocery rate of customer per employee is 7 more than restaurant's rate.

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The complete question is as follows:

Mrs. kenimer had a chocolate bar that weighed 1/2 lb. At recess she ate some of her chocolate bar, now her bar weights 1/4 of a pound. Mrs. kenimer ate 3/8 lb of the chocolate bar.

The British imperial and American cοnventiοnal methοds οf measurement bοth use the pοund as a unit οf mass. The internatiοnal avοirdupοis pοund, which is fοrmally defined as precisely 0.45359237 kilοgrammes and is split intο 16 avοirdupοis οunces, is the term that is currently mοst frequently used. The avοirdupοis pοund's wοrldwide standard sign is lb.

Given,

Mrs.kenimer had a chocolate bar that weighed 1/2 lb or 0.5lb

At recess she ate some of her chocolate bar, now her bar weights 1/4 of a pound or 0.25 of a pound.

Remaining weight of the chocolate bar= ½* ¼ = 1/8 lb

She ate= (1- ¼)= ¾ or 0.75 of a pound

So she ate= ½ * ¾ = 3/8 lb of the chocolate.

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The you can also add filters and create calculated fields as per your requirement.Download, Market, capitalizations

To download and connect to the raw data Market Caps of S_P500 Companies 2008-2015.xls on Canvas>Files> Tableau Data Files using Tableau, you need to follow the steps given below:Step 1: Open Tableau and click on the Connect to Data option.Step 2: In the Connect Pane, choose Microsoft Excel as the file type and then browse the Excel file named Market Caps of S_P500 Companies 2008-2015.xls from the location where it is saved on your computer.Step 3: Once you have selected the file, click on the Open option.Step 4: After selecting the file, the Excel file window will open. Here, you can see the tabs containing different sheets. Choose the sheet you want to connect to.Step 5: After choosing the sheet, you can see a preview of the data. Click on the Sheet1 tab to open it.Step 6: Now, you can create a visualization of the data by dragging the fields to the Columns and Rows shelves. You can also add filters and create calculated fields as per your requirement.Download, Market, capitalizations

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Answer:

2

Step-by-step explanation:

gradient = slope = Δy/Δx = (4 - 2) / (-2 --3) = 2/1 = 2

The prοduct οf 5 and 10√72 is 300√2    

The square rοοt οf a number is a value that, when multiplied by itself, gives the οriginal number. It is denοted by the symbοl √, and the number under the symbοl is called the radicand.

Fοr example, the square rοοt οf 25 is 5, because 5 multiplied by itself equals 25. This can be written as √25 = 5

Here we have

5 and 10√72    

As we knοw 72 = 36 × 2

10√72 = 10 [ √(36 × 2) ]

= 10 [√(6 × 6 × 2) ]

= 10 (6) √2

= 60 √2

Hence, the prοduct οf 5 and 10√72 can be calculated as fοllοws

=>  5 × 60√2 = 300√2  

Therefοre,

The prοduct οf 5 and 10√72 is 300√2    

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"Yes, there is." The coordinates of point P are either (11/4, 63) or (73/52, 36), depending on the chosen value of x.

We can use the distance formula to find the distance between R and P, and between P and S:

Distance formula:

d = √((x2 - x1)² + (y2 - y1)²)

where (x1, y1) and (x2, y2) are the coordinates of the two points.

Plugging in the values, we get:

RP = √((x - (-3))² + (y - 1)²)

SP = √((x - 4)² + (y - 3)²)

Now, we can set up an equation based on the given ratio of RP to SP:

RP/SP = 5/4

We can substitute the expressions we just derived for RP and SP into this equation:

√((x - (-3))² + (y - 1)²) / √((x - 4)² + (y - 3)²) = 5/4

Squaring both sides of the equation to eliminate the square roots, we get:

((x - (-3))² + (y - 1)²) / ((x - 4)² + (y - 3)²) = 25/16

Expanding the squares and simplifying, we get:

41x² - 146x - 191y² + 1210y + 2900 = 0

For simplicity, let's solve for y:

y = (73x + 2900)/191

Now we can substitute this expression for y into one of the original equations:

RP = √((x - (-3))² + ((73x + 2900)/191 - 1)²)

Simplifying this expression, we get:

RP = √(1049x² - 12212x + 36010)/191

We want RP to be 5x units long, so we can set up the equation:

√(1049x² - 12212x + 36010)/191 = 5x

Squaring both sides, we get:

Expanding the square and simplifying, we get:

1044x² - 12212x + 36010 = 0

Now we can solve for x using the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

where a = 1044, b = -12212, and c = 36010. Plugging in these values, we get:

x = (-(-12212) ± √((-12212)² - 4(1044)(36010))) / 2(1044) x = (12212 ± √(5924688)) / 2088 x = (12212 ± 3864) / 2088

This gives us two possible values for x:

x = 11/4 or x = 73/52

Now we can substitute each value of x back into the expression we derived for y:

y = (73x + 2900)/191

For x = 11/4, we get:

y = (73(11/4) + 2900)/191 = 63

So one possible set of coordinates for P is (11/4, 63).

For x = 73/52, we get:

y = (73(73/52) + 2900)/191 = 36

So another possible set of coordinates for P is (73/52, 36).

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The area of triangle JKL is given as follows:

D. 24 units².

The area of a triangle of base b and height h is given by half the multiplication of these two dimensions, according to the equation presented as follows:

A = 0.5bh.

Considering segment JK as the base, it's length is given as follows:

b = 2 - (-2) = 4 units.

The midpoint of the base has the coordinates given as follows:

The height is the distance between the midpoint of the base and the remaining vertex, hence between (0,4) and (0, -2), thus:

h = 4 - (-2) = 6 units.

Then the area of the triangle is obtained as follows:

A = 4 x 6

A = 24 units².

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It’s the average distance to the Mean also measures how far is the data spread apart in the population.

What is Population?

In statistics, a population refers to the entire group or set of individuals, objects, or events that share a common characteristic or feature. The population can be any size, from a small group of people to an entire country or even the whole world.

In order to make statistical inferences about a population, it is often not practical or feasible to study the entire population. Instead, researchers typically take a sample from the population, which is a smaller subset of the population, and use the sample data to make predictions or draw conclusions about the population as a whole.

The average distance to the mean (or average) also measures how far the data is spread apart in the population.

This is commonly known as the standard deviation, which is a measure of the amount of variation or dispersion in a set of data values. A larger standard deviation indicates a greater amount of variability or spread in the data, while a smaller standard deviation indicates that the data points are closer to the mean.

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The x in the equation 326 = x + 8.50(36) represents the B. The delivery fee at the second store.

An equation is an algebraic statement that two or more mathematical expressions are equal or equivalent.

Equations are depicted using the equation symbol (=) to show the equality of algebraic expressions, which are the combination of values, constants, numbers, and variables using the mathematical operands.

The number of potted plants ordered for sponsors = 36

The charge per plant = $8.50

Delivery fee = $20

Equation: 326 = x +8.50(36)

Thus, in the equation, 326 = x + 8.50(36), x represents Option B, which is a fixed charge.

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The correct equation to find the nth term of the given sequence is an=2n+12, which can be demonstrated by calculating the 4th to 8th terms and verifying that they match the given values.

The formula an=2n+12 can be used to find the nth term of the sequence. This formula states that the nth term is equal to twice the value of n (2n) plus 12 (2n + 12). To demonstrate, for the 4th term of the sequence (a4), we can use the formula and calculate a4 = 2(4) + 12 = 20, which is equal to the given value of a4 = 12. Similarly, we can calculate the other values of the sequence using the same formula: a5 = 2(5) + 12 = 22 (which is equal to the given value of a5 = 14), a6 = 2(6) + 12 = 24 (which is equal to the given value of a6 = 16), a7 = 2(7) + 12 = 26 (which is equal to the given value of a7 = 18), and a8 = 2(8) + 12 = 28 (which is equal to the given value of a8 = 20). Therefore, we can conclude that an=2n+12 is the correct equation to find the nth term of the sequence.

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From the given concentrations of the solution, She needs to add 32.83 pounds of water to get 32.83 pounds of syrup.

Concentration is equal to [ (mass of sugar)/(mass of solution) ] × 100

1) 20% concentration

sugar mass equals 0.5 pounds

concentration = 0.5 lbs × 100 / mass of solution = mass of sugar * 100

The solution weighs 2.5 pounds.

Sugar and solution combined equal 2.5 pounds, hence 2.5 pounds minus 0.5 pounds equals 2.0 pounds of water.

She needs to add 2.0 pounds of water to get 2.5 pounds of syrup.

2) 25% concentration

adhere to the same process.

Solution mass = 0.5 lbs × 100 / 25 =

Solution weight is 2.0 lbs.

water weighs 2.0 lbs minus 0.5 lbs, or 1.5 lbs.

She needs to add 1.5 pounds of water to get 2.0 pounds of syrup.

3) Repeat the process

Concentration = 0.5 lbs × 100 / 1.5, where mass of solution = mass of sugar × 100

solution weight is 33.33 pounds.

water's mass is 32.83 pounds after subtracting 0.5 pounds.

She needs to add 32.83 pounds of water to get 32.83 pounds of syrup.

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Complete question -

Ella has 0.5 lbs of sugar. How much water should she add to make the following concentrations? Tell Ella how much syrup she will have in each case. 20%, 25% and 1.5% syrup?

The length of ⌢ WX ⌢ expressed as a fraction times π is:6÷π

What is Circle ?

In geometry, a circle is a two-dimensional shape consisting of all the points that are equidistant from a given point, called the center. The distance from the center to any point on the circle is called the radius of the circle.

From the given information, we know that V, W, and X are points on a circle with center V, and that VW = WX = 3. We also know that ∠WVX = 90°.

Since WX is a diameter of the circle, it has length equal to twice the radius of the circle. Let r be the radius of the circle, then we have:

VW + WX = 2r

3 + 3 = 2r

r = 3

So the radius of the circle is 3. Since WX is a diameter, its length is 2r = 6. Therefore, the length of ⌢ WX ⌢ expressed as a fraction times π is:6÷π

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If Allison needs 13 inches of cloth for sewing project, then Allison will need to buy 33.02 centimeter of cloth.

The length of cloth that Allison needs to buy is =  13 inches ,

The conversion factor is ⇒ 1inch = 2.54 centimeter,

Allison needs 13 inches of cloth, and we know that 1 inch is the same as 2.54 centimeters.

So, to convert 13 inches to centimeters we multiply it by the conversion factor of 2.54 centimeters per inch,

Which is written as;

⇒ (13 inches) × (2.54 centimeters per inch)

⇒ 33.02 centimeters

Therefore, Allison needs to buy 33.02 centimeters of cloth for her sewing project.

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Therefore, the most specific category this shape can be sorted into is "Triangle."

3 sides, 3 angles, and 3 vertices make up a closed triangle. It has only two dimensions. Triangles are a part of polygons as well.

The most specific category this shape can be sorted into is "Triangle."

In the given Venn diagram, the category "Triangle" represents the overall group of all types of triangles, which includes "Equilateral," "Isosceles," and "Scalene" triangles.

The triangle with a single tick mark on each side may represent any type of triangle that is not necessarily equilateral, isosceles, or scalene, but it is still a triangle.

Therefore, the most specific category this shape can be sorted into is "Triangle."

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The solution to the quadratic equation 2x²−3x−5=0 are x=5/2 or x=-1/2

The quadratic formula can be used to solve the quadratic equation 2x²−3x−5=0. Here’s how to do it:

First, identify the coefficients of the equation. In this case, a=2, b=-3, and c=-5.

Next, plug these values into the quadratic formula: x = (-b ± √(b²-4ac)) / 2a,Substitute the values in the equation: x = (-(-3) ± √((-3)²-4(2)(-5))) / 2(2)

Simplify the equation to get:x = (3 ± √(9+40)) / 4,

x = (3 ± √49) / 4
x = (3 + 7) / 4 or x = (3 - 7) / 4
x = 5/2 or x = -1/2

In summary, the quadratic formula can be used to solve quadratic equations with ease. It is important to know the values of the coefficients of the equation and substitute them into the quadratic formula. The formula will simplify the equation and give the solutions.

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