Which do you think would have a higher value if c and d are positive decimal numbers:

4c + 2d or 6c + 3d? How can you be sure?

The coordinates for the image after the translation of EFG would be E'(-2, 3), F'(-4, 0), and G'(-1, -2).

To translate a point, you simply add or subtract the specified units from its x and y coordinates. In this case, you are asked to translate the points 3 units left and 1 unit down.

To translate 3 units left, subtract 3 from the x-coordinate, and to translate 1 unit down, subtract 1 from the y-coordinate.

For point E (1, 4):

E' = (1 - 3, 4 - 1) = (-2, 3)

For point F (-1, 1):

F' = (-1 - 3, 1 - 1) = (-4, 0)

For point G (2, -1):

G' = (2 - 3, -1 - 1) = (-1, -2)

The translated points are E'(-2, 3), F'(-4, 0), and G'(-1, -2).

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If john has a new house. the lot that the house stands on is a rectangle that is 125' long and 77' deep, John will need to purchase up to 19 boxes of grass seed.

First, we need to calculate the total area of the lot. The area of a rectangle is given by its length multiplied by its width, so:

Area of lot = 125 ft * 77 ft = 9625 square feet

Next, we need to determine the area of the portion of the lot that is not covered by the house. Since the house is located near the center of the lot, we can find the area of the rectangle that represents the space around the house and subtract it from the total area of the lot:

Area around house = (125 ft - 40 ft - 40 ft)/2 * (77 ft - 36 ft - 36 ft)/2 = 22.5 ft * 16.5 ft = 371.25 square feet

Area to be planted = 9625 square feet - 371.25 square feet = 9253.75 square feet

Now we can calculate the number of boxes of grass seed needed by dividing the area to be planted by the coverage of each box:

Number of boxes = 9253.75 square feet / 500 square feet per box = 18.51 boxes

Since you can't purchase a fraction of a box, John will need to round up to 19 boxes of grass seed.

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Answer: the height of the hockey puck is approximately 0.835 inches.

Step-by-step explanation: The formula for determining the volume of a cylinder is as follows:

The formula for the volume (V) of a cylinder can be expressed mathematically as V = πr2h, where r represents the radius of the cylinder's base and h represents the height of the cylinder. This formula is derived from the concept that the volume of a cylinder can be calculated by multiplying the area of its base (which is represented by the term πr2) by its height (h).

The present study utilizes the conventional nomenclature in which V denotes the volume, r represents the radius, and h stands for the height.

As the diameter of the hockey puck is measured to be 3 inches, it follows that the radius is equivalently calculated as 1.5 inches, or precisely half of the diameter.

It is established that the hockey puck has a volume of 7.1 cubic inches; accordingly, by substituting these known values into the relevant formula and performing the appropriate calculations, the measurement of h may be ascertained.

The expression 7.1 = π(1.5)^2h can be reformulated in a more academic manner. It can be said that the equation represents the mathematical relationship between the volume of a cylinder and its dimensions, wherein the value of 7.1 denotes the volume of the cylinder, whereas π, 1.5, and h refer to the mathematical constants of pi, radius, and height, respectively. Thus, the formula can be expressed as V = πr^2h, where V represents the volume of the cylinder, r denotes the radius, and h denotes the height.

The process of reducing something to its simplest form. Rewritten: The act of simplification involves distilling a concept or idea to its most basic, essential components. This process aims to facilitate a clear and concise understanding of the subject matter, allowing for greater comprehension and ease of communication.

The numerical expression 7.1 = 2.25πh can be written in a more formal and academic manner. Specifically, the equation can be rephrased as an algebraic relationship between the variables involved. More concisely, the equation describes the result of a multiplication between the constant factor 2.25π and the variable h, which according to the equation equals 7.1. As such, it can be represented by the following expression: 2.25πh = 7.1

Dividing each side by 2.25π is a logical mathematical operation utilized to simplify an equation or expression.

The aforementioned equation may be expressed in an academic tone as follows: The value of h is equivalent to the quotient obtained from dividing 7.1 by 2.25 times the mathematical constant π.

The employment of a calculator to compute the aforementioned expression:

The observed value of h is approximately equal to 0.835 inches.

Answer: 18 square feet im pretty sure

Step-by-step explanation:

Answer:  B)  216

Step-by-step explanation:

The requried, there are 8998912 possible license plates that can be generated using this format.

There are 8 digits that can be used for each of the three digits on the license plate, with two digits (4 and 5) that cannot be used. Therefore, there are 8 choices for each of the three digits, giving us 8 x 8 x 8 = 512 possible combinations for the digits.

Similarly, there are 26 letters that can be used for each of the three letters on the license plate. Therefore, there are 26 choices for each of the three letters, giving us 26 x 26 x 26 = 17576 possible combinations for the letters.

Total number of license plates = number of choices for the digits x number of choices for the letters

= 512 x 17576

= 8998912

Therefore, there are 8998912 possible license plates that can be generated using this format.

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Buying bulk topsoil is less expensive than buying bags of topsoil in this case.

Volume is a measure of the amount of space occupied by a three-dimensional object. It is typically measured in cubic units, such as cubic meters (m³), cubic centimeters (cm³), or cubic feet (ft³).

To find the volume of a simple object such as a cube, rectangular prism, or cylinder, you can use a formula that involves multiplying the length, width, and height of the object. For example, the formula for the volume of a rectangular prism is V = lwh, where V is the volume, l is the length, w is the width, and h is the height.

For more complex objects, such as irregular shapes or those with curved surfaces, you can use techniques such as integration or approximation to find the volume.

First, we need to determine how many cubic feet of topsoil Austin needs to cover his backyard with a 4 inch layer. We can start by calculating the volume of his backyard in cubic feet:

Volume = length x width x depth

Volume = 70 ft x 60 ft x (4 in / 12) ft

Volume = 1400 ft³

So Austin needs 1400 cubic feet of topsoil to cover his backyard with a 4 inch layer.

Option 1: Bags of Topsoil

Each bag of topsoil covers 3 cubic feet, so Austin needs 1400 / 3 = 466.67 bags of topsoil. Since he can only buy whole bags, he will need to buy 467 bags. Each bag costs $2.50, so the total cost of the topsoil would be:

Total cost = number of bags x cost per bag

Total cost = 467 x $2.50

Total cost = $1167.50

Since delivery is free, the total cost of the topsoil is $1167.50.

Option 2: Bulk Topsoil

Bulk topsoil costs $22.00 per cubic yard, and Austin needs 1400 / 27 = 51.85 cubic yards. Since he can only buy whole yards, he will need to buy 52 yards. The cost of the topsoil itself would be:

Cost of topsoil = volume of topsoil x cost per cubic yard

Cost of topsoil = 52 yd³ x $22.00/yd³

Cost of topsoil = $1144.00

There is also a $20 delivery fee, so the total cost of the topsoil would be:

Total cost = cost of topsoil + delivery fee

Total cost = $1144.00 + $20.00

Total cost = $1164.00

Therefore, buying bulk topsoil is less expensive than buying bags of topsoil in this case.

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Answer:

15%

Step-by-step explanation:

0.15 x 100 = 15%

The mean and standard deviation of a sampling distribution of sample means with sample size 249 are 71 and approximately 1.267 respectively when the population has a mean of 71 and standard deviation of 20.

We know that, if the population has mean [tex]=\mu[/tex] and standard deviation [tex]=\sigma[/tex] and if the sampling distribution has sample size of n then

mean of the sampling distribution will be [tex](\mu_{\bar{x}})=\mu[/tex]

and the standard deviation of sampling distribution will be [tex](\sigma_{\bar{x}})=\frac{\sigma}{\sqrt{n}}[/tex]

Here in this problem,

Mean of the population [tex](\mu)[/tex] = 71

Standard Deviation of the population [tex](\sigma)[/tex] = 20

And the sample size of the sampling distribution (n) = 249

So, the mean of sampling distribution [tex](\mu_{\bar{x}})=\mu[/tex] = 71

Standard Deviation of sampling distribution [tex](\sigma_{\bar{x}})=\frac{\sigma}{\sqrt{n}}=\frac{20}{\sqrt{249}} \approx 1.267[/tex] (Correct up to three decimal places)

Hence, the mean and standard deviation of the sampling distribution of sample means with sample size 249 are 71 and 1.267 (approximately) respectively.

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Cash received for interest during  2014 was $3,500 .The following equation can be used to determine the amount of money received as interest in 2014:

Amount received as interest equals Interest Income for 2014 plus the decline in Interest Receivable

The difference between the balance of interest receivable at December 31, 2013, and at December 31, 2014, can be used to calculate the decline in interest receivable:

Reduced interest due = Interest due at December 31, 2013, minus Interest due at December 31, 2014, which equals $1,100 minus $1,400, or -$300.

The fact that the balance of interest receivable increased from 2013 to 2014 indicates that the company produced more interest money during the year than it received. In light of this, the money earned on interest in 2014 is:

Interest income from 2014 plus a decrease in interest receivable equals $3,200 minus (-$300) to $3,500 in interest payments received.

Hence, $3,500 is the correct response (C).

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Answer: 50

Step-by-step explanation
One method to estimate the number of fish in the pond is to use the mark-and-recapture method. This method assumes that the proportion of marked fish in the second sample is the same as the proportion of marked fish in the entire population. Using this assumption, we can estimate the total number of fish in the pond as follows:

Let N be the total number of fish in the pond.

Let M be the number of fish caught in the first sample (50 fish).

Let R be the number of marked fish caught in the second sample (8 fish).

Let r be the unknown total number of marked fish in the pond.

According to the mark-and-recapture method, we have the following proportion:

M/N = R/r

We can rearrange this equation to solve for N:

N = M * r / R

Substituting the values given in the problem, we have:

N = 50 * r / 8

Simplifying, we get:

N = 6.25 * r

This means that the estimated total number of fish in the pond is 6.25 times the number of marked fish in the second sample. Since we know that 8 fish were marked in the second sample, the estimate for the total number of fish in the pond is:

N = 6.25 * 8 = 50

Therefore, the estimated number of fish in the pond is 50

The measure of the angle MSP, m∠MSP, obtained using the relationship between linear pair angles is 80°

Linear pair angles are angles that have a sum of 180°. Linear pair angles come together to form a straight line.

The specified measure of the angle NSM is m∠NSM = 100°

The angles ∠NSM and ∠MSP are linear pair angles therefore;

m∠NSM + m∠MSP = 180°

Plugging in the known value of the angle NSM, we get;

100° + m∠MSP = 180°

Therefore; m∠MSP = 180° - 100° = 80°

The measure of the angle MSP, m∠MSP is 80°

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Answer:

-18.67.

Step-by-step explanation:

If you think math is boring, think again. Here is a fun way to learn how to find the rational number that we need to divide -15/56 by to get -5/7. It's like a puzzle, but with fractions!

First, we need to make -15/56 look nicer. How do we do that? By dividing both the top and the bottom by -1. That's like flipping the sign. So we get 15/56. Much better!

Next, we need to find a mystery number that makes -5/7 and 15/56 equal when we multiply them. That's like finding a missing piece of a jigsaw puzzle. How do we do that? By cross-multiplying! That's when we multiply the top of one fraction by the bottom of the other and set them equal. So we get:

-5 times 56 equals 15 times mystery number

Now we just need to solve for the mystery number. How do we do that? By dividing both sides by 15. That's like cutting a cake into equal slices. So we get:

Mystery number equals (-5 times 56) divided by 15

Now we just need to simplify. How do we do that? By using a calculator or our brains. Either way, we get:

Mystery number equals -18.67

And that's it! We found the rational number that we need to divide -15/56 by to get -5/7. It's -18.67. Isn't math fun?

The evaluated probability for chances of  randomly selecting an employee who will  have a starting salary of at least $31,000 is 11.51%. Here, we have to depend on the principles of standard normal distribution to find the percentage of probability,


Let us take  z-score for a starting salary of $31,000 as

z = (31000 - 25000) / 5000
= 1.2

Now after using a standard normal distribution table , the probability of a z-score of 1.2 or greater is approximately 0.1151
Converting it into percentage
0.1151 x 100
= 11.51%
The evaluated probability for chances of  randomly selecting an employee who will  have a starting salary of at least $31,000 is 11.51%.

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Answer: in2

Step-by-step explanation:

answerd

The volume of the rectangular prism for the given dimensions length , width , and the height is equal to 168 cubic inches.

Dimensions of the rectangular prism is equal to,

length of the rectangular prism = 12 inches

width of the rectangular prism = 8 inches

height of the rectangular prism = 1.75 inches

The formula for the volume of a rectangular prism is equal to,

Volume of the rectangular prism = length x width x height

Plugging in the given values of the dimensions , we have,

⇒ Volume of the rectangular prism  = 12 inches x 8 inches x 1.75 inches

Simplifying this expression to get the volume of rectangular prism, we get,

⇒ Volume of the rectangular prism = 168 cubic inches

Therefore, the volume of the rectangular prism is 168 cubic inches.

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Answer:

Let's denote:

M: the set of students who like maths

S: the set of students who like science

n(M): the number of students who like maths

n(S): the number of students who like science

n(M ∩ S): the number of students who like both maths and science

n(M ∪ S): the number of students who like maths or science (or both)

We can use the principle of inclusion-exclusion to find n(M ∪ S):

n(M ∪ S) = n(M) + n(S) - n(M ∩ S)

From the problem statement, we know:

n(M) = 10

n(S) = 15

n(M ∩ S) = ? (unknown)

We also know that 10 students like neither maths nor science, which means that:

n(M ∪ S)' = 10

where (M ∪ S)' denotes the complement of M ∪ S, i.e., the set of students who do not like maths or science.

We can use the formula:

n(A') = N - n(A)

where N is the total number of students (N = 50).

n(M ∪ S)' = n((M ∪ S))' = N - n(M ∪ S) = N - (n(M) + n(S) - n(M ∩ S))

Substituting the known values:

n((M ∪ S))' = 50 - (10 + 15 - n(M ∩ S)) = 25 + n(M ∩ S)

Simplifying:

n(M ∩ S) = n((M ∪ S))' - 25 = 10

Therefore, we have:

n(M ∪ S) = n(M) + n(S) - n(M ∩ S) = 10 + 15 - 10 = 15

The ratio of the students who like maths or science is:

n(M ∪ S) / N = 15 / 50 = 3/10

So the required ratio is 3:10.

Step-by-step explanation:

The equation that represents your balance after x years is: [tex]250 * (1.0725)^x[/tex]

what is interest ?

To calculate simple interest, multiply the principal by the rate of interest rates, the duration, and several other variables. The marketing formula is simple returns = capital + interests + hours.

Initial Value (a): $250

Rate (r): 7.25% per year (or 0.0725 as a decimal)

Time (x): x years

The formula for calculating the balance after x years is:

[tex]Balance = a * (1 + r)^x[/tex]

Plugging in the values, we get:

[tex]Balance = 250 * (1 + 0.0725)^x[/tex]

So the equation that represents your balance after x years is:

[tex]Balance = 250 * (1.0725)^x[/tex]

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Answer:

Step-by-step explanation:

The problem shows a 90° angle split by a ray, we know that both angles are equal to 90° because the whole is equal to the sum of its parts therefore adding 6b+7 and 7b-8 gives us 90° which is simplified as

13b°-1°= 90°

add 1  to both sides

13b°-1° + 1° = 90° +1°

13b° = 91°

divide by 13

13b°/13 = 91°/13

b= 7°

The equation with the fewest symbols is 30x - 18, which represents the simplified form of the given expression.

An equation is a mathematical statement that shows the equality between two expressions. The given expression is not an equation since there is no equality sign present. However, we can simplify the expression to get an equivalent equation with the fewest symbols.

To simplify the expression, we use the distributive property of multiplication over addition/subtraction. We multiply 6 with each term inside the parentheses, i.e., 5x and -3. This gives us:

6(5x - 3) = 6(5x) - 6(3) = 30x - 18

This simplified expression is an equation that shows the equality between the left-hand side (LHS) and the right-hand side (RHS). The LHS is 30x - 18, and the RHS is also 30x - 18, which means that they are equal.

Therefore, the equation with the fewest symbols is 30x - 18, which represents the simplified form of the given expression.

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The length of the side w is 55mm. Option C

Note that the different trigonometric identities are;

From the triangle shown, we have;

x = 45mm

z = 80mm

We also have tangent where the star is located is 1

Then,

tan θ = 1

find the tangent inverse of the values

θ = 45 degrees

As given in the diagram, the diagrams are similar

So both angles are 45 degrees

However, we can deduce that since the angles are equal, then, the sides are equal

x = w = 55mm

w = 55mmm

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3⁴ is 3 times larger than 3³, 5³ is 5 times larger than 5², 7¹⁰ is 49 times larger than 7⁸ and 17⁶ is 289 times larger than 17⁴.

3⁴ / 3³ = (3 × 3 × 3 × 3) / (3 × 3 × 3) = 3

This means that 3⁴ is 3 times larger than 3³.

5³ is 5 times larger than 5².

5³ / 5² = (5 × 5 × 5) / (5× 5) = 5

7¹⁰ is 49 times larger than 7⁸.

7¹⁰/ 7⁸ = 7² =49

17⁶ is 289 times larger than 17⁴.

17⁶ /17⁴ = 289

Hence, 3⁴ is 3 times larger than 3³, 5³ is 5 times larger than 5², 7¹⁰ is 49 times larger than 7⁸ and 17⁶ is 289 times larger than 17⁴.

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The area of the polygon containing the given triangle and rectangle is 45 square units.

What exactly is a rectangle?

A rectangle is a quadrilateral having four straight sides, four right angles, and parallel and equal-length opposing sides. A rectangle's opposing sides are also congruent, which implies they have the same length.

The formula A = lw gives the area of a rectangle, where A is the area, l is the length, and w is the width. A rectangle's perimeter is determined by the formula P = 2l + 2w, where P is the perimeter.

Now,

To find the area of the polygon containing the triangle and rectangle, we need to find the individual areas of the triangle and rectangle, and then add them together.

The area of a triangle

A = (1/2)bh

where b= base and h = height. Substituting the given values, we get:

A_triangle = (1/2)(9)(6) = 27 square units

The area of a rectangle is

A = lw

where l = length and w = width. Substituting the given values, we get:

A_rectangle = (9)(2) = 18 square units

Therefore, the total area of the polygon is:

A_polygon = A_triangle + A_rectangle

A_polygon = 27 + 18

A_polygon = 45 square units

Therefore, the area of the polygon containing the given triangle and rectangle is 45 square units.

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The evaluated solution for the  given  question comprises of sample point of a that are  {HHT, HTH, THH, HHHT, HHTH, HTHH, THHH} , the event probability is 0.875 and the probability of implementing a, b is 3/4  below under the condition of a fair coin is tossed three times, and the events a and b are defined.

a)  Points sample  for event a: {HHT, HTH, THH, HHHT, HHTH, HTHH, THHH}
Points  sample  for event b: {HTT, THT, TTH, HHH}
Points  sample  for event a b: {HTT, THT, TTH, HHH, HHT, HTH, THH}
  Points  sample for event ac: {TTT}
  Points  sample for event a c: {TTT, HHHH}

b)  Event a probability= 7/8 = 0.875
  Event b probability= 1/2 = 0.5
  Event ab probability = 3/8 = 0.375
  Event ac probability   = 1/8 = 0.125
  Event a c probability  = 1/16 + 1/8 = 0.1875

c) Probability of a b implementing additive rule
    P(a b) = P(a) + P(b) - P(a ∩ b)
     P(a ∩ b) = P(a) + P(b) - P(a b)
     P(a ∩ b) = (7/8) + (1/2) - (3/8)
     P(a ∩ b) = 9/8 - 3/8
     P(a ∩ b) = 6/8
     P(a ∩ b) = 3/4

d)  Hence, events a and b are not mutually exclusive due to the lack of chances of having common sample points {HHH}.


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Answer:

2((6(14) + 6(5) + 14(5)) = 2(84 + 30 + 70) =

2(184) = 368 square centimeters

Juliana and Brody hiked a total distance of 6 1/2 miles, which is the sum of the distances of the two trails they hiked 3 2/3 miles and 2 5/6 miles.

To find the total distance hiked by Juliana and Brody, we need to add the distances of the two trails they hiked.

3 2/3 + 2 5/6 can be written as a common fraction by finding the least common multiple (LCM) of the denominators, which is 6.

3 2/3 can be written as 11/3, and 2 5/6 can be written as 17/6.

So, 3 2/3 + 2 5/6 = 11/3 + 17/6

We need to find a common denominator, which is 6

11/3 + 17/6 = 22/6 + 17/6

Adding the two fractions, we get

22/6 + 17/6 = 39/6

Simplifying the fraction, we get

39/6 = 6 3/6

Therefore, Juliana and Brody hiked a total distance of 6 3/6 or 6 1/2 miles.

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The given linear equation in slope intercept form is y = -1/4(x) - 2/7.

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;

y = mx + c

Where:

By making "y" the subject of formula, we have the following:

1/4x + y = -2/7

y = -1/4(x) - 2/7

By comparison, we have the following:

Slope, m = -1/4.

y-intercept, c = -2/7.

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Understanding the meaning of addition and subtraction will allows us to make predictions about how changing the value of a variable will affect the value of an expression.

In mathematics, integers are a set of whole numbers that include both positive and negative numbers, as well as zero. The set of integers is denoted by the symbol Z, and it includes all the natural numbers (1, 2, 3,...), their negatives (-1, -2, -3,...), and zero (0). Integers are used in a variety of mathematical contexts, including algebra, number theory, and geometry. Integers can be used to represent many real-world situations, such as temperatures above or below zero, changes in altitude, gains or losses in money, and more. They are also used extensively in computer programming and other fields that rely heavily on mathematics.

Knowing what addition and subtraction mean allows you to understand how changing the value of a variable can affect the value of an expression.

For example, consider the expression x + 2. If x has a value of 3, then the value of the expression is 5. However, if x increases to 4, then the value of the expression increases to 6. This is because we are adding 2 to the value of x.

On the other hand, if we have the expression x - 2 and x has a value of 3, then the value of the expression is 1. If x increases to 4, then the value of the expression decreases to 2. This is because we are subtracting 2 from the value of x, so as x increases, the value of the expression decreases.

Understanding the meaning of addition and subtraction is essential to be able to manipulate expressions and variables, and it allows us to make predictions about how changing the value of a variable will affect the value of an expression.

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Rewriting 11,000,000 as a power of 10 using scientific notation is: 1.1 * 10⁷

A number is written in scientific notation whenever a number between 1 and 10 is multiplied by a power of 10. For example, 650,000,000 can be written in scientific notation as 6.5 * 10^8.

Now, we want to write the number 11000000 as a power of 10. Using the concept of scientific notation, we have:

11000000 = 1.1 * 10⁷

That is the final expression of the given number as a power of 10

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1. 7 x^2 - 9 y^2 = 343 is a hyperbola

2. x^2 + y^2 - 4 x + 6 y - 5 = 1 is a circle

3. 4 x^2 + 9 y^2 = 1 is a ellipse

4. x^2 - 6 y = 0 is a parabola

A conic section conic or a quadratic curve is described as  a curve obtained from a cone's surface intersecting a plane.

The three types of conic section are :

All conics are  written in terms of the following equation:

Ax2 + Bxy + Cy2 + Dx + Ey + F = 0.

In conclusion, a conic is the intersection of a plane and a right circular cone.

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#Complete question:

Match the following equations with the conic sections formed by them. 1. x 2 + y 2 - 4x + 6y - 5 = 0 hyperbola 2. x 2 - 6y = 0 circle 3. 4x 2 + 9y 2 = 1 ellipse 4. 7x 2 - 9y 2 = 343 parabola