College Algebua - „,1 Modellng with Quadratles Mahemet Koothall Thrun - Cine caact atswens, the and the fanctian ta ibcin your animen. - Show all necinary calnulations - Wrice par answis in ceptreste itriansich. reresest? 2. What a theytipenret' What dors it repericnt? Hha happris? ia at 10 irst be isurn wa fer be isle ta catis thin forchile College Algebra - 3.1 Modeling with QuadraticsMahomes Football Throw At a Kansas City Chiefs football practice, Patrick Mahomes is practicing his throws. He stands at one end of the football field and throws the ball. The ball's height, (in feet) as a function of horizontal distance,x(in feet), from Mahomes can be described by the following function:f(x)=−1201​(x−88)2+151058​- Give exact answers. Use only the function to obtain your answers. - Show all necessary calculations. - Write your answers in complete sentences. 1. What is the positivex-intercept? What does it represent? 2. What is they-intercept? What does it represent? 3. What is the maximum height that the foothall reaches?. What is the horizontal distance from Mahomes when this happens? 4. Travis Kelce is standing along the path of the football 160 feet from Patrick Mahomes. Travis can catch a ball that is at 10 feet or lower. Will he be able to catch this football? 5. What is the horizontal distance of the football from Patrick Mahomes when it first reaches a height of 40 feet?

1. domain: All real numbers. range: [2,4]

2. It is a function.

3. Not one to one function.

What is function?

A function is a relationship or expression involving one or more variables.  It has a set of input and outputs

1. domain of the given function would be, real numbers.

  range of the function is [2,4].

2. Yes. It is a function.

3. No it is not one to one function. It is many to one function?

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The total number of dimes in the container is 6 while the total number of quarters is 11.

To solve this problem, we will be using the simultaneous equation. The dimes and quarters will be assigned some figures:

First:

d + q = 17

10d + 25q = 335

This second equation is so because the value of the coins was converted to cents.

Where $1 = 100 cents

Next, we will resolve the figures to get the values for d and q as follows:

Multiply both sides of the first equation by -10

-10d - 10q = -170

Now, we shall minus the first equation from the second one to give:

15q = 165

q = 165/15

= 11

Substitute the value of q in the first equation:

d + 11 = 17

d = 17 - 11

d = 6

Substituting the values in the original equation will give the final sum of 335 for the coins.

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John must score 286 on his 8th game to achieve an average score of 215.

What is an Average?

Average, also known as the mean, is a mathematical concept that represents the central value of a set of numbers. It is found by dividing the sum of the numbers by the total count of the numbers.

To find out what John must score on his 8th game to achieve an average score of 215, we need to use the formula for calculating the average or mean:

Average = (Sum of Scores) / (Number of Scores)

We can use this formula to solve for the unknown score:

215 = (159 + 182 + 225 + 240 + 198 + 200 + 230 + x) / 8

Multiplying both sides by 8, we get:

1720 = 159 + 182 + 225 + 240 + 198 + 200 + 230 + x

Simplifying, we get:

1720 = 1434 + x

Subtracting 1434 from both sides, we get:

x = 286

Therefore, John must score 286 on his 8th game to achieve an average score of 215.

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Wyatt's mix will be more watery compared to Emma's mix.

What does it mean for a mixture to be "more watery"?

The percentage of water in a mix is an essential factor that determines its taste, texture, and consistency. A higher percentage of water in a lemonade mix will make it more watery and less concentrated. In contrast, a lower percentage of water will make the mix less watery and more concentrated. The right balance of water and lemon mix is crucial to make a perfect lemonade.

Calculation for percent of water in the lemon drink mix:

To find the percent of water in the lemonade mixes, we need to divide the amount of water by the total volume of the mix and then multiply by 100.

For Wyatt's mix:

Percent of water = (2 cups water / (2 cups water + 1 cup lemon mix)) x 100

Percent of water = 66.67%

For Emma's mix:

Percent of water = (12 cups water / (12 cups water + 7 cups lemon mix)) x 100

Percent of water = 63.16%

From the calculations, we can see that Wyatt's mix has a higher percentage of water than Emma's mix. Therefore, Emma's mix will be less watery compared to Wyatt's mix.

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By answering the above question, we may state that As a result, y = function 3(x2)2+6 is identical to the function y = 3x212x+18.

Mathematicians research numbers, their variants, equations, forms, and related structures, as well as possible locations for these things. The relationship between a group of inputs, each of which has a corresponding output, is referred to as a function. Every input contributes to a single, distinct output in a connection between inputs and outputs known as a function. A domain, codomain, or scope is assigned to each function. Often, functions are denoted with the letter f. (x). The key is an x. There are four main categories of accessible functions: on functions, one-to-one capabilities, so many capabilities, in capabilities, and on functions.

The vertex of the function y = 3(x2)2+6 lies at (2, 6), and the coefficient 3 denotes that the parabola widens upwards.

This function needs to be expanded and simplified in order to be written in standard form:

y = 3(x−2)2+6 y = 3(x−2)(x−2)

6 y equals 3 (x24x+4) + 6 y equals 3 (x212x+18)

As a result, y = 3(x2)2+6 is identical to the function y = 3x212x+18.

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(2,1) is a solution to the system of equations 8x+7y=11 and x+y=3.

Two or more expressions with an Equal sign is called as Equation.

To check if (2,1) is a solution to the system of equations:

8x + 7y = 11

x + y = 3

We substitute x = 2 and y = 1 into both equations:

For the first equation: 8(2) + 7(1) = 16 + 7 = 23

For the second equation: 2 + 1 = 3

Hence, we can see that both equations are true when x = 2 and y = 1.

Therefore, (2,1) is a solution to the system of equations.

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By those 2 ways of solution, a total of 3,105 packs of juice drinks were distributed to different schools.

To find out how many packs of juice drinks were distributed to different schools, we need to add the number of packs given to each school.

950 (La Paz Elementary School) + 785 (Igdarapdap Elementary School) + 1,370 (Cabalaynan Elementary School) = 3,105 packs of juice drinks

So, a total of 3,105 packs of juice drinks were distributed to different schools.

To find out how many packs of juice drinks were not given, we need to subtract the number of packs distributed to different schools from the total number of packs available.

5,000 (total number of packs) - 3,105 (number of packs distributed to different schools) = 1,895 packs of juice drinks

So, a total of 1,895 packs of juice drinks were not given.

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The LCM of the polynomials x² + 8x + 16 and x² + 11 x + 28 is (x + 4)(x + 4)(x + 7).

To determine the LCM of the given polynomials, we need to find the smallest polynomial that is a multiple of both  x² + 8x + 16 and x² + 11 x + 28.

First, let's factor the given polynomials:
x² + 8x + 16 = (x + 4)(x + 4)

x² + 11 x + 28 = (x + 4)(x + 7)

Now, we can see that the LCM of these two polynomials is the product of the highest power of each factor:

LCM = (x + 4)(x + 4)(x + 7)

So, the LCM of the given polynomials in factored form is (x + 4)(x + 4)(x + 7).

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Answer:

Unfortunately, the sale price of the sweater and the original price are not given in the problem, so we cannot calculate the exact change that Rachel will receive. We need more information to solve the problem.

Answer:

864.3

Step-by-step explanation:

Since the substance is increasing continuously at a relative rate of 7% per day, we can use the continuous exponential growth formula:

P(t) = P(0) * e^(rt)

where:

P(t) is the mass of the substance after "t" days

P(0) is the initial mass of the substance (552 grams in this case)

e is the mathematical constant e (approximately equal to 2.71828)

r is the relative growth rate (0.07 per day in this case)

Substituting the given values, we get:

P(t) = 552 * e^(0.07t)

To find the mass after 6 days, we can substitute t = 6:

P(6) = 552 * e^(0.07*6)

Using a calculator, we get:

P(6) ≈ 864.3 grams

Therefore, the mass of the substance after 6 days is approximately 864.3 grams rounded to the nearest tenth.

The expression x -2 y-4 3 sqrt 64xy³ can be written in the form axby as follows:

ax -2by-4c 3 sqrt 64xy³

Coefficient in mathematics is a numerical value that is used to represent the magnitude of a given quantity in an equation. It is normally the numerical factor associated with the variables in an equation that represent a certain amount of change in the equation. For example, the coefficient of x in the equation y = 5x + 7 is 5, which indicates that x is multiplied by 5 in the equation.

In this expression, a, b, and c refer to the coefficients of the x, y, and the cube of y respectively. Thus, a is equal to 1, b is equal to -2, and c is equal to -4. Therefore, the product of a, b and c is equal to 8.

To break down the expression further, the coefficient of x is a, which is equal to 1. The coefficient of y is -2b, which is equal to -2. The coefficient of the cube of y is -4c, which is equal to -4. Finally, the coefficient of the square root of 64xy³ is 3, which is equal to 3.

Thus, when written in the form axby, the expression x -2 y-4 3 sqrt 64xy³ is equal to 1 -2 -4 3 sqrt 64xy³. The product of a, b, and c in this expression is equal to 8.

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The value of angle A and C is 68° respectively

The sum of angle In a triangle is 180°. This means that A+B+C = 180°.

An isosceles triangle is a triangle that has two sides of equal length. Sometimes it is specified as having exactly two sides of equal length, and sometimes as havingat least two sides of equal length.

Since AB = BC, then the triangle is an isosceles triangle.

The sum of angle in a triangle is 180. This means that A+B+C = 180

Since AB = BC , then angle A = angle C

therefore , substitute C for A

C +B + C = 180

2C + 44 = 180

2C = 180-44

2C = 136

divide both sides by 2

C = 136/2

C = 68°

then A= C = 68°

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The best estimate of the volume of the stack once it has been bumped/shifted is 4πt³ cubic centimeters.

A cylinder is a three-dimensional geometric shape that consists of two parallel circular bases connected by a curved surface. The volume of a cylinder is the amount of space occupied by the shape and is given by the formula:

Volume = πr²h

where π (pi) is a mathematical constant approximately equal to 3.14, r is the radius of the circular base, and h is the height of the cylinder.

Assuming that the coins have the same dimensions and are perfectly circular, the original stack of 15 coins formed a cylinder with a height of 15 times the thickness of a single coin, and a radius equal to the radius of a single coin.

The volume of this cylinder can be calculated using the formula V = πr²h, where r is the radius and h is the height.

Since the volume of the original stack is 8 cubic centimeters, we can set up the equation:

8 = πr²(15t)

where t is the thickness of a single coin.

Solving for r, we get:

r = √(8/15πt)

When the stack is bumped and shifts to a leaning position, the new shape will still be a cylinder, but the height will be shorter than before. Let's say that the new height is h2. We can calculate the new volume using the same formula:

V2 = πr²h2

To estimate the new height, we can use the fact that the coins are now leaning against each other, so the new height will be less than 15t. Let's say that the new height is approximately 12t.

Substituting in the values, we get:

V2 = π(√(8/15πt))²(12t)

Simplifying, we get:

V2 = 4πt³

Therefore, the best estimate of the volume of the stack once it has been bumped/shifted is 4π³ cubic centimeters.

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$600

B. $600 per week

For Activity 2, the Normal Cost is $1,000 and the Crash Cost is $4,600, so the Crash cost per week is $60.

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As a result, the circle's precise size is (529/4)π³  square centimetres.

A circle is a closed, two-dimensional shape where every point in the surface is equally spaced from a central point. The line of mirror symmetry is formed by all lines that traverse the circle. Additionally, every point has circular symmetry around the centre.

The circumference of a circle is given by the formula:

C = 2πr

where r is the radius of the circle. We can rearrange this formula to solve for the radius:

r = C / 2π

When we substitute the circumference's specified number, we obtain:

r = (23r) / (2π)

Simplifying:

r = (23/2)π

Now that we know the radius, we can use the formula for the area of a circle:

A = πr²

Substituting the value we found for the radius, we get:

A = π[(23/2)π]²

Simplifying:

A = π(529/4)π²

A = (529/4)π³

Therefore, the exact area of the circle is (529/4)π³ square cm.

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The probability of a randomly selected tester from this group having a score between 1497 and 1819 is approximately 0.68.

Probability is the measure of how likely a certain event is to occur. It is a mathematical concept that is used to quantify the likelihood of a certain outcome from a given set of circumstances. Probability is expressed as a number between 0 and 1, where 0 indicates that the event is impossible, and 1 indicates that the event is certain. Probability is used in many fields, including mathematics, finance, and decision making.

This is because approximately 68% of the data is within one standard deviation of the mean, and the data is normally distributed. The area between the mean and the upper limit of 1819 is 0.68, which means that the graph probability of a randomly selected tester from this group having a score between 1497 and 1819 is 0.68.

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The better buy is given by the following brand:

Brand A.

The better buy is obtained applying the proportions in the context of the problem.

A proportion is applied as the cost per ounce is given dividing the total cost by the number of ounces.

Then the better buy is given by the option with the lowest cost per ounce.

The cost per ounce for each brand is given as follows:

$8 per ounce is a lesser cost than $9.3 per ounce, hence the better buy is given by Brand A.

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The complete factorization of the expression 144p² - 9q² is (12p + 3q)(12p − 3q). The correct answer is B.

To factor 144p² - 9q², we can use the difference of squares formula, which states that:

a² - b² = (a + b)(a - b)

We can see that 144p² is a perfect square, as it is the square of 12p. Similarly, 9q² is a perfect square, as it is the square of 3q. So we can write:

144p² - 9q² = (12p)² - (3q)²

Now we can use the difference of squares formula to factor:

(12p)² - (3q)² = (12p + 3q)(12p - 3q)

Simplifying, we can also write this as:

144p² - 9q² = 3²(16p² - q²)

So, the factored form of 144p² - 9q² is:

144p² - 9q² = 3²(16p² - q²) = (12p + 3q)(12p - 3q)

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Answer:

scalene triangle

Step-by-step explanation:

in a scalene triangle, all the sides are not equal

IH is not equal to HJ and also is not equal to JI

The scale factor is 11.

Scale factor is a numerical value used to proportionally enlarge or reduce a size of an object or image. It is also used to compare two similar shapes or objects. When the scale factor is greater than 1, it indicates an increase in size and when the scale factor is less than 1, it indicates a decrease in size. Scale factors are usually expressed as a ratio, such as 1:2, which means that the object has been doubled in size.

To calculate it, divide the first number by the second number and multiply by the third number: (35/42) x 11 = 10.714. Therefore, the scale factor is 11.

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The ratios of online sales to shop sales of A jewelery shop which sold 240 necklaces in a month is equals to the 3:1.

We have a jewelery shop and they sold there necklaces to the different shops.

Total number of sold necklaces in a month = 240

Number of online sold necklaces in a month = 180

Total online sales of jewelery shop = 180

and rest of necklaces were sold in a high street shop. So, the number of sold necklaces in high street shop during a month = total number of sold necklaces - online sold necklaces

= 240 - 180 = 60

Total shop sales jewelery shop = 60 necklaces

Ratio is used to determine the relationship between two or more things ( like size, quantity, etc.). It is represented by a/b or a : b ( read as a ratio b). Here, we have to calculate the ratios of online sales to shop sales. So, the ratio of online sales to shop sales = 180 : 60 or 180/60

Simplify the expression,

=> 180/60 = 3

Hence, required ratio is 3: 1.

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Answer:

the answer is 8

Step-by-step explanation:

subtract 11
67 - 11 = 56

Divide 7 to find the answer

56/7 = 8

If you could provide me more details, including the dimensions of the two triangle ' angles and sides, I might be able to evaluate whether or not they are comparable.

A triangle is a polygon because it includes four or so additional parts. It features a simple rectangular shape. A rectangle having edges A, B, and C is referred to as a triangle. When the sides are actually not collinear, Euclidean geometry yields a single plane and cube. If a triangle contains three parts and three angles, it is a polygon. The intersections of a triangle's three sides are referred to as its corners. The sum of a triangle's sides is 180 degrees.

Two polygons must have congruent corresponding angles and proportionate corresponding sides in order to be considered comparable.

If you could provide me more details, including the dimensions of the two polygons' angles and sides, I might be able to evaluate whether or not they are comparable.

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The difference between their sound levels is 9.9W/m².

The preceding number, which is always put before a number, is referred to as the predecessor. A number's successor is the one that is written just after it. Take the list of natural numbers 1, 2, 3, 4, and 5, for instance. 1 is the precursor of 2, and 2 is the successor of 1. Consecutive numbers are those that come after one another in ascending sequence, from smallest to largest. The typical difference between every two numbers is 1.

Here, we have

Given: It is known that the sound levels of two consecutive thunderstorms in the storm are 0.1W/m² and 10W/m² respectively.

We have to find the difference between their sound levels.​

S₁ = 0.1W/m²

S₂ = 10W/m²

Difference = S₂ - S₁

Difference = 10W/m² - 0.1W/m²

Difference  = 9.9W/m²

Hence, the difference between their sound levels is 9.9W/m².

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variables y = 1.5, x = 5, hence, the value of y is 9 when x is 30

Two variables, such as x and y, are proportional to one another and their ratio is constant when they vary directly. In other words, if y and x vary directly, their relationship can be written as y = kx, where k is the proportionality constant. With the knowledge that y = 1.5 when x = 5 as provided, we can utilise this information to find the value of y when x equals 30:

1.5 = k(5) \sk = 1.5/5 \sk = 0.3

We can use the equation y = kx to get the value of y for x = 30 now that we know the value of k:

y = 0.3(30) \sy = 9

Hence, the value of y is 9 when x is 30.

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Part A) Estimated Populations of Cities A and B are given.

Part B)  City A's estimated population is increasing at a faster rate than City B's estimated population for each decade.

Part C) the estimated population of City A first exceeds the estimated population of City B at the start of the 4th decade (t = 3)

Part D) The models may not realistically predict population growth over very long time scales, as they do not take into account other factors  

Part A:

Estimated Populations of Cities A and B

Decades Since 1980  City A (in thousands)          City B (in thousands)

0                                       15                                           16

1                                  19.5                                   16.4

2                                  25.2                                   17.8

3                                  32.7                                   19.2

4                                  42.4                                    20.6

Part B:

Population Increases from the previous Decade for Cities A and B

Decades Since 1980 City A (in hundreds)           City B (in hundreds)

0                                         -                                                   -

1                                       450                                              40

2                                       570                                               140

3                                       750                                               140

4                                       970                                               140

Interpretation:

From the table, we can see that City A's estimated population is increasing at a faster rate than City B's estimated population for each decade. This indicates that City A is growing more rapidly than City B, and may continue to do so in the future.

Part C:

To find the start of the decade when the estimated population of City A first exceeds the estimated population of City B, we need to solve the equation:

15[tex](1.03)^t[/tex] > 0.4t + 16

where t is the number of decades since 1980.

One way to solve this is to use a graphing calculator to graph both functions and find their intersection point. Alternatively, we can use trial and error to test different values of t until we find the smallest one that satisfies the inequality.

Using a graphing calculator, we find that the estimated population of City A first exceeds the estimated population of City B at the start of the 4th decade (t = 3), when the estimated population of City A is approximately 32.7 thousand people, and the estimated population of City B is approximately 19.2 thousand people.

Part D:

The models may not realistically predict population growth over very long time scales, as they do not take into account factors such as changes in birth and death rates, migration patterns, and economic or environmental changes that may affect population growth. Additionally, the models assume that population growth will continue to follow a linear or exponential pattern, which may not be accurate in the long term. Therefore, while the models can provide useful estimates for short- to medium-term population trends, they should be used with caution when making long-term projections.

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The correct question should be:

The estimated population, in thousands of people, of city A can be modeled by the function SO) = 15(1.03), where is the number of decades (10-year period) since 1980 The estimated population, in thousands of people, of the city can be modeled by the function (1)-0.41 +16, where is the number of decades since 1980

Part A)     Complete this table, showing both estimated population values, rounded to the nearest tenth for each city based on the number of decades since 1980 Estimated Populations of Cities A and B City Decades Since 1980 City B (thousands of people) (thousands of people) 0 . 2 3 4

Part B)      Using the table in Part A, complete this table showing population increases, in hundreds of people, cach decade Population Increases from previous Decade for Cities A and B Decades Since 1980, Increase of City A Increase of City B (hundreds of people), (hundreds of people), fin)-(-1) g) -R-1) 2 3 4 Interpret the differences in the increases of the estimated populations of the two cities based on the functions that model cach city's population. Provide evidence to support your answer

Part C)    At the start of which decade will the estimated population of city A first exceed the estimated population of city B? What will be the estimated populations of each city at the start of that decade? Provide evidence to support your answers.

Part D)   Based on the behavior of the functions, do the models realistically predict population growth over very long time scales? Provide evidence to support your answer.

The sample size needed to detect µ1 - µ2 = 1 with power at least 80% is approximately 323.

The power of a test is the probability of correctly rejecting the null hypothesis when the alternative hypothesis is true. In this case, we wish to find the power of the z-test to detect a difference of δ1 - δ2 = 0.1 when the sample size is 100 and the significance level is 0.05.

a) First, we need to find the critical value for the z-test at a significance level of 0.05. This can be found using a z-table or a calculator. The critical value is 1.645.

Next, we need to find the standardized difference between the two means, which is (δ1 - δ2)/√(2δ^2/n) = (0.1)/√(2(1)^2/100) = 0.1/√(0.02) = 0.7071.

Finally, we can find the power of the test by subtracting the standardized difference from the critical value and finding the corresponding probability from a z-table or calculator. The power is 1 - P(Z < 1.645 - 0.7071) = 1 - P(Z < 0.9379) = 1 - 0.8264 = 0.1736.

Therefore, the power of the z-test to detect a difference of δ1 - δ2 = 0.1 with a sample size of 100 and a significance level of 0.05 is 0.1736.

b) To find the sample size needed to detect µ1 - µ2 = 1 with power at least 80%, we can use the formula for power:

Power = 1 - P(Z < (critical value - standardized difference))

We can rearrange this formula to solve for the sample size:

Standardized difference = (critical value - Z value corresponding to power)/√(2δ^2/n)

n = (2δ^2(critical value - Z value corresponding to power)^2)/(standardized difference)^2

Plugging in the values for critical value (1.645), Z value corresponding to power (0.8416), and standardized difference (1), we get:

n = (2(1)^2(1.645 - 0.8416)^2)/(1)^2 = 322.69

Therefore, the sample size needed to detect µ1 - µ2 = 1 with power at least 80% is approximately 323.

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The given quadratic equation does not have a real solution.

Quadratic equations are polynomial equations of second degree.

The general form of a quadratic equation is ax² + b x + c = 0.

The given quadratic equation is,

4a² + 6 = 0

We have to find the solution of the quadratic equation.

Subtracting both sides by 6,

4a² + 6 - 6 = 0 - 6

4a² = -6

a² = -6/4

a² = -3/2

Taking square root on both sides,

a = √(-3/2), which implies that the given quadratic equation does not have a real solution.

Hence there are no real solution for the given equation.

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The value of y that satisfies the equation is y = -11.

An equation is a mathematical statement that expresses the equality of two expressions. It typically consists of two sides, separated by an equals sign (=), with each side containing one or more terms that may include variables, constants, and mathematical operators.

We can start by setting up the equation:

(y+1)/(y-5) + 10/(y+5) = (y+1)/(y-5) × 10/(y+5)

To solve for y, we need to simplify and manipulate the equation:

Multiply both sides by (y-5) × (y+5) to eliminate the denominators:

(y+1)(y+5) + 10(y-5) = 10 × (y+1)

Expand and simplify:

y² + 6y - 15 + 10y - 50 = 10y + 10

Combine like terms:

y² + 16y - 55 = 0

Factor the quadratic:

(y + 11)(y - 5) = 0

Solve for y:

y = -11 or y = 5

However, we need to check if either solution makes the denominators of the original equation equal to zero, since division by zero is undefined:

For y = -11, the denominators are -16 and -6, respectively, which are both nonzero. Therefore, y = -11 is a valid solution.

For y = 5, the denominator of the first fraction is 0, which is not allowed. Therefore, y = 5 is an extraneous solution and should be discarded.

Therefore, the value of y that satisfies the equation is y = -11.

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