Consider the following equation:
(x + 1)²y" +5(x+1)y + 4y = 0. (a) Find all ordinary points and singular points of this equation. For singular points, are they regular or irregular? Explain your reason.
(b) Find the general solution of the equation.

If increasing the sides of a square field by five feet will increase the area by 245 ft², then the area of the original square is 484 ft².

To find the area of the original square, we can use the following formula:

Area of the original square = x²

where x is the original length of the square field.

Given that the increase in the length and width of the square field is 5 ft, the side length of the new square is (x + 5) ft. Therefore, the area of the new square is (x + 5)² ft².

Given that the area of the new square is 245 ft² more than the area of the smaller square, we can write:

(x + 5)² = 245 + x²

Expanding the left-hand side of the equation and simplifying, we get:

x² + 10x + 25 = 245 + x²

Solving for x, we get:

10x + 25 = 245

x = 22

Plugging x = 22 into the formula, we can find the area of the original square:

Area of the original square = x² = 22² = 484 ft²

Therefore, the area of the original square is 484 ft².

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The equation of the red graph is g(x) = x² + 3.

Option C.

The equation of the red graph can be determined by considering upscaling or transformation on the x - axis.

Since the equation focuses on the function g(x) and not on upscaling in the y-axis, any changes should not affect the x-axis. Therefore, we can eliminate (x - 3)² and (x + 3)² from the options given, since they involve modifying the x-axis.

In conclusion, as the transformation involves increasing the y-values along the y-axis, the correct choice is x² + 3 rather than x² - 3.

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Answer:

G

Step-by-step explanation:

The true comparison is 2/3 > 3/10.

Option (C) is correct.

What is a fraction?

A fraction is a mathematical representation of a part of a whole. It is written as two numbers separated by a slash (/) and represents the number of parts being considered out of the total number of parts in a whole. The number on the top is called the numerator and the number on the bottom is called the denominator.

To compare the amounts of water the scientist poured, we need to compare the fractions 2/3 and 3/10. To do this, we can convert both fractions to have a common denominator, which is the least common multiple of the denominators.

The least common multiple of 3 and 10 is 30. So, we can convert both 2/3 and 3/10 to 30 as the denominator:

2/3 = 20/30

3/10 = 9/30

Comparing the two fractions with a common denominator, we see that 20/30 is greater than 9/30. Therefore, the comparison that is true is:

C) 2/3 > 3/10

Hence, the true comparison is 2/3 > 3/10.

Option (C) is correct.

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Answer:

I can't see the fourth option, but the answer would be C.

Step-by-step explanation:

It's the only graph that fits the question.

The probability that the dart lands inside the triangle is \(\frac{1}{4}\).

we know that

Probability = \(\frac{Favourable outcomes}{total outcomes}\)

Probability = \(\frac{162}{648} = \frac{1}{4}\)

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Answer:

25%.

Step-by-step explanation:

The weight distribution of newborn African lions may not necessarily follow a normal distribution, and the actual percentages can vary based on the specific data available.

To determine the percentage of newborn African lions that weigh less than 3 pounds and the percentage that weigh more than 3.8 pounds, we would need statistical data on the weight distribution of newborn African lions. Since we don't have that information, we cannot provide the exact percentages.

However, if we assume that the weights of newborn African lions follow a normal distribution, we can use the properties of the standard normal distribution to make an estimation.

For the percentage of newborn African lions weighing less than 3 pounds:

We would need to know the mean and standard deviation of the weight distribution to calculate the Z-score for a weight of 3 pounds and then find the corresponding percentage using a standard normal distribution table. Without this information, we cannot provide an accurate estimation.

For the percentage of newborn African lions weighing more than 3.8 pounds:

Similarly, we would need the mean and standard deviation of the weight distribution to calculate the Z-score for a weight of 3.8 pounds and find the corresponding percentage using a standard normal distribution table. Without the required information, we cannot provide a specific estimation.

Please note that the weight distribution of newborn African lions may not necessarily follow a normal distribution, and the actual percentages can vary based on the specific data available.

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Answer:

80% or like 8 squares out of 10 oe=r 4 out of 5 ect

Step-by-step explanation:

Answer:

20 total friends

Step-by-step explanation: built different

Answer: Don't come at me if I'm wrong, but I believe it's 40 laps.

Step-by-step explanation:

First, you need to figure out how many laps James runs in 1 minute and you can do this by dividing the number of laps and minutes (8 laps/14 minutes). This should give you 4/7 laps/minute.

Next, you figure out how many minutes 1 hour and 10 minutes is (just to make things easier) 1 hour and 10 minutes = 70 minutes

Then, you multiple 4/7 and 70 and you get 40 laps.

Answer:

40 laps

Step-by-step explanation:

I just put this into a proportion

so basically i just did 8/14 = ?/70

Then i just worked it like any other problem

8 x 70 then divide 14 and i got 40.

so James ran 40 laps in one hour and tens minutes

NOTE that i turned one hour and ten minutes into minutes

pls mark brainleist

Not all rational numbers a and b satisfy the equation |a+b|=|a|+|b|.

As a result, |a+b|=|a|+|b|.

If |a+b|=|a|+|b| for all rational numbers a and b, we must verify this.

P/Q is the format for rational numbers, where p and q are open-ended integers and q 0. Thus, natural numbers, whole numbers, integers, fractions of integers, and decimals are all examples of rational numbers (terminating decimals and recurring decimals).

Now,

a=-3 and b=5

|-3+5|=|-3|+|5|

⇒2≠8

A = 2 and B = 4

|2+4|=|2|+|4|

⇒6=6

As a result, we realized from the examples above that |a+b|=|a|+|b| isn't always true.

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Answer:

99

Step-by-step explanation:

(√3−(−2√3))^2+(−√2−5√2)^2

Subtracting a negative is like adding

(√3+(2√3))^2+(−√2−5√2)^2

Taking the first term

(√3+(2√3))(√3+(2√3))

sqrt(3)^2 +2 sqrt(3) * sqrt(3) +2 sqrt(3) * sqrt(3)  + (2 sqrt(3))^2

3 + 2 *3 + 2*3 + 4*3

3 +6+6+12

27

Second term

(−√2−5√2)(−√2−5√2)

-sqrt(2)*-sqrt(2) -sqrt(2)*-5sqrt(2) -sqrt(2)*-5sqrt(2) -5sqrt(2)*(-5sqrt(2))

2 +5*2 +5(2) +25(2)

2+10+10+50

72

Add the two terms together

27+72

99

Answer:

d = 6(√3 - 2√2)

Step-by-step explanation:

d = (√3 - (-2 √3) * 2 + (-√2 - 5√2) * 2

d = (√3 + 2√3)   * 2 + (-√2 - 5√2) * 2

d = 3√3              * 2 + (-6√2)         * 2

d = 6√3                   + (-12√2)

d = 6√3 - 12√2

d = 6(√3 - 2√2)

Answer:

\((x+1)^{2} -5\)

Step-by-step explanation:

\(-2x=x^{2} -6 \\x^{2} +2x-6\\(\frac{b}{2}) ^{2} =(\frac{2}{2}) ^{2} =1^{2} =1\\so, (x^{2} +2x+1)-6+1\\ x^{2} +2x+1=(x+1)^{2} \\-6+1=5\\(x+1)^{2} -5\)

Sorry it took so long

Answer:

-13° Fahrenheit

Step-by-step explanation:

-10 - 3 is the same as 10 + 3 and then adding a negative sign, so 10 + 3 = 13 = -13

The function S to represent the sequence of transformations applied to the point (x, y) is  (-y, -x - 6)

Transformation is a technique used to change the position of an object on an xy-plane.

Given the coordinate (x, y)

Rotation of the coordinate by 180° clockwise about the origin will given;

(x, y) - > (-x, -y)

If the result is translated 6 units to the left, then;

(-x, -y) -> (-x-6, -y)

If it is then reflected across the line y = x, we will switch the coordinates to have:

(-x-6, -y) -> (-y, -x - 6)

The function S to represent the sequence of transformations applied to the point (x, y) is  (-y, -x - 6)

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Answer: 1 tablespoon

Step-by-step explanation:

Answer:

The rate charged by first mechanic per hour= x =$85

The rat charged by second mechanic per hour =y = $70

Step-by-step explanation:

Two mechanics worked on a car. The first mechanic worked for 10 hours, and the second mechanic worked for 15 hours. Together they charged a total of $1900. What was the rate charged per hour by each mechanic if the sum of the two rates was $155 per hour?

Solution

Let

x= hourly rate of the first mechanic

y= hourly rate of the second mechanic

Derive two equations to solve for the two unknowns

10x + 15y = 1900 (1)

x + y = 155 (2)

From (2)

x + y = 155

x=155-y

Substitute x=155-y into (1)

10x + 15y = 1900

10(155-y) + 15y =1900

1550 -10y + 15y =1900

5y =1900-1550

5y=350

Divide both sides by 5

y= 70

Substitute y=70 into (2)

x + y = 155

x + (70) =155

x=155 - 70

= 85

x= 85

The rate charged by first mechanic per hour= x =$85

The rat charged by second mechanic per hour =y = $70

Answer: Exact Form:

x= −35/12

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Answer:

-32

Step-by-step explanation:

-32/4=-8

-8+5=-3

A scatter plot in Excel is the type of chart that can plot a point at its Cartesian coordinates using an x-coordinate and a y-coordinate.

The type of chart in Excel that plots a point at its Cartesian coordinates using an x-coordinate and a y-coordinate is a Scatter Plot. A scatter plot is a type of graph in which individual data points are represented by dots on a graph. Each data point has two coordinates: the x-coordinate and the y-coordinate, which are used to plot the point on the graph.

In Excel, to create a scatter plot, you need to first select your data, then go to the Insert tab and click on the Scatter chart button. You can then choose the type of scatter plot you want to create. Once the chart is created, you can add data labels to show the x-coordinate and y-coordinate of each data point.

In summary, a scatter plot in Excel is the type of chart that can plot a point at its Cartesian coordinates using an x-coordinate and a y-coordinate.

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2x=3

x=3/2 =1.5

The solution to the system of equations is x = 5 and y = -1.

Simultaneous equations, a system of equations Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution.

There are four methods for solving systems of equations: graphing, substitution, elimination, and matrices.

Given a system of equation 2x - 6y = 16 and x + y = 4

Let's start with the second equation:

x + y = 4

We can solve for one of the variables, say y, by subtracting x from both sides:

y = 4 - x

Now we can substitute this expression for y into the first equation:

2x - 6y = 16

2x - 6(4 - x) = 16

Expanding and simplifying, we get:

2x - 24 + 6x = 16

Combining like terms, we get:

8x - 24 = 16

Adding 24 to both sides, we get:

8x = 40

Dividing both sides by 8, we get:

x = 5

Now we can substitute this value of x into either of the original equations to find y. Let's use the second equation:

x + y = 4

5 + y = 4

Subtracting 5 from both sides, we get:

y = -1

Therefore, The solution to the system of equations is x = 5 and y = -1.

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Answer:

the answer is c 95

Step-by-step explanation:

180-41-44=95

a  triangle has 180 degrees

Answer: I think A. 75

Step-by-step explanation: why not pick A……

Hope this helps^^

=================================================

Explanation:

Adding an even number to an odd number always results in an odd number

even + odd = odd

odd + even = odd

So if 'a' is odd, adding 2 onto it (even number), leads to an odd result of a+2.

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

Extra Information (optional section)

If you are curious why the two equations shown above are true, then here's a proof.

Let 'a' be an odd number. This means a = 2k+1 for some integer k. We add 1 to any multiple of 2 and it goes from even (2k) to odd (2k+1).

If we made b an even number, then b = 2m for some integer m.

Adding 'a' and b gives us...

c = a + b

c = ( a ) + ( b )

c = ( 2k+1 ) + ( 2m )

c = (2k+2m) + 1

c = 2(k+m) + 1

c = 2n + 1 .... where n = k+m

The result a+b is an odd number since it is in the form 2*(integer)+1

It verifies the claim that odd+even = odd.

So this shows that a+2 is also odd, since we let b = 2.

through my working i got to 41² is the hypotenuse.

21²+20²=c²

factor out the square

(21+20)²=c²

41²=c²

and 41² is 1681

Answer:

29 units

Step-by-step explanation:

i just took the quiz

Answer:

(0,-9)

Step-by-step explanation:

To find the y-intercept, substitute x=0

y=(0)^2+4(0)-9

=-9

Here's a tip to help you find the y-intercept faster, it is usually the constant of the graph equation

Answer:

see explanation

Step-by-step explanation:

Given a parabola in standard form

y = ax² + bx + c ( a ≠ 0 )

The equation of the axis of symmetry which is also the x- coordinate of the vertex is

x = - \(\frac{b}{2a}\)

y = x² + 4x - 9 ← is in standard form

with a = 1, b = 4 , then

x = - \(\frac{4}{2}\) = - 2

x = - 2 is the equation of the axis of symmetry

Substitute x = - 2 into the equation for corresponding y- coordinate of vertex

y = (- 2)² + 4(- 2) - 9 = 4 - 8 - 9 = - 13

vertex = (- 2, - 13 )

To find the y- intercept let x = 0 and solve for y

y = 0² + 4(0) - 9 = 0 + 0 - 9 = - 9

y- intercept = (0, - 9)

From the standard form of the parabola

• If a > 0 then vertex is a minimum

• If a < 0 then vertex is a maximum

Here a = 1 , that is > 0

vertex (- 2, - 13 ) is a minimum

Answer:

8

Explanation:

First, we need to find the mean, so the sum of all values divided by the number of values is equal to:

Then, we need to find the population standard deviation, so we need to find the square of the difference between each value and the mean:

(87 - 64.44)² = 508.75

(63 - 64.44)² = 2.08

(39 - 64.44)² = 647.41

(67 - 64.44)² = 6.53

(66 - 64.44)² = 2.41

(63 - 64.44)² = 2.08

(62 - 64.44)² = 5.97

(67 - 64.44)² = 6.53

(66 - 64.44)² =2.41

Now, the standard deviation will be the square root of the sum of these values divided by the number of values, so:

Therefore, the data that is within 2 population standard deviations to the mean is the data that is located within the following limits:

mean + 2s = 64.44 + 2(11.47) = 87.38

mean - 2s = 64.44 - 2(11.47) = 41.5

So, from the 9 values, 8 are within 2 population standard deviations of the mean.

Therefore, the answer is 8.

Answer:

I'd say the answer is A or B

Step-by-step explanation:

Since the colonists overtime had so many laws passed over that were cruel and unfair they went against the British with acts like the Tea Act which were preformed to turn against the British. (sorry if im wrong ^-^)

If the expression \(r(x) = 3x - 1\) and the expression \(s(x) = 2x + 1\) , then the expression equivalent to \(\frac{r}{s} (6)\) is (a) \(\frac{3(6)-1}{2(6) +1}\) .

What are Algebraic Expression ?

The algebraic Expression are defined as the expressions that are written with the combination of variables and constants joined by mathematical operators , For Example : \(3x+7\) .

Here the two expressions are given as \(r(x) = 3x - 1\) and \(s(x) = 2x + 1\) ;

we have to find equivalent expression for \(\frac{r}{s} (6)\) ;

By the Division Property of Algebraic Expression ;

it can be written as : \(\frac{r(6)}{s(6)}\) ;

So , Substituting \(x=6\) , in r(x) ,

we get ; \(r(6) = 3(6) - 1\) , ......equation(1)

On Substituting \(x=6\) , in s(x) ,

we get ; \(s(6) = 2(6)+1\) ,  ....equation(2) ;

Substituting the values of r(6) and s(6) from equation(1) and equation(2) in \(\frac{r(6)}{s(6)}\) ;

we get ;

⇒ \(\frac{r(6)}{s(6)} = \frac{3(6)-1}{2(6) +1}\) ;

Therefore , the expression equivalent to \(\frac{r}{s} (6)\) is \(\frac{3(6)-1}{2(6) +1}\) .

The given question is incomplete , the complete question is

If r(x) = 3x - 1 and s(x) = 2x + 1, which expression is equivalent to r/s(6) ?

(a) \(\frac{3(6)-1}{2(6) +1}\)

(b) \(\frac{(6)}{2(6)+1}\)

(c) \(\frac{36-1}{26+1}\)

(d) \(\frac{(6)-1}{(6)+1}\)

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Each twelve-inch square tile weighs approximately 27 ounces.

To calculate the weight of each tile in ounces, we need to convert the weight of the box from pounds to ounces and divide it by the number of tiles in the box. Since there are 16 ounces in a pound, the weight of each box is 36 pounds * 16 ounces/pound = 576 ounces.

If there are 20 tiles in each box, we divide the weight of the box (576 ounces) by the number of tiles (20) to get the weight of each tile: 576 ounces / 20 tiles = 28.8 ounces. Rounding to the nearest ounce, each twelve-inch square tile weighs approximately 27 ounces.


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