Can somebody please tell me how do we solve this? Thank you.

The required vertices of hyperbola is given as (3, 5±√38).

Hyperbola is part of conic section, and its equation is given as,
[tex](x - h)^2/a^2 + (y - k)^2/b^2 = 1[/tex], where h,k is center and a and b are the lengths of the semi-major and the semi-minor axes.

Here,
Given equation of hyperbola,
36x²-y^²-216x+10y+261=0
Equation of hyperbola in vertex form is given as,
(x - 3)²/(19/18) - (y - 5)²/38 = 1

From above equation,
h = 3 k = 5 a = √38/6 and b = √38

Vertices of the  hyperbola is given as,
(h, k ± b) = (3, 5±√38)

Thus, the required vertices of hyperbola is given as (3, 5±√38).

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Answer:

the solution and explanation/work is in the images

Answer:

x+5 > 12

Step-by-step explanation:

A number plus 5 is greater than 12 represents x + 5 > 12.

The meaning of the y-intercept in this situation is ,

''For every additional mile the cab travels, the total fee increases by $12.00.''

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

From the table, we have the following parameters:

Points (x, y) = (2, 5) and (15.00, 19.50)

So, we would calculate the slope as follows:

Slope = (19.50 - 5)/(15.00 - 2)

Slope = 14.50/13

Slope = 1.11

Hence, We get;

Fixed fee = $15 - (1.12 x 2)

               = $15 - 2.24 ≈ $12.00

So, We get;

For every additional mile the cab travels, the total fee increases by $12.00.

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The numerator of the indicated expression is s+7.

The numbers 7, 14, 21, 28, 35, and 42 are the multiples of 7. 3 and 7 only share 21 as their smallest common number. 21 is the least common denominator as a result. The denominators can be multiplied by one another to find the common denominator for two or more fractions.

We were given the following rational expression:

where p is the numerator and q is the denominator, is the general representation of the rational expression.

So, the expression we provide is:

Assuming the LCM, the following expression can be rewritten as

Comparing (1) with the above-mentioned general rational expression

The numerator of the given expression is p=s+7.

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Using the formula a³ – b³ = (a – b)(a² + ab + b²), we have factor (8m – 1)(64m² + 8m + 1).

Factors are the positive integers that can divide a number evenly in mathematics. Say we want to create a product by multiplying two numbers. The factors of the product are the number that is multiplied. Each number has its own factor.

Examples of factors in real life include putting candies in a box, arranging numbers in a pattern, giving chocolates to kids, and many more.

Factors are the figures that can divide an amount precisely. As a result, there is no remainder after division. Factors are the sums of numbers that you multiply to produce another number. A factor is therefore the divisor of another number.

Using the formula

a³ – b³ = (a – b)(a² + ab + b²)

8m³ - 1³ = (8m – 1)(8m² + 8m + 1²)

8m³ - 1³ =  (8m – 1)(8m² + 8m + 1²)

8m³ - 1³ =  (8m – 1)((8m)² + 8m + 1²)

8m³ - 1³ =  (8m – 1)(64m² + 8m + 1)

8m³ - 1³ =  (8m – 1)(64m² + 8m + 1)

Thus, Using the formula a³ – b³ = (a – b)(a² + ab + b²), we have factor (8m – 1)(64m² + 8m + 1)

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Answer: ≈2.32

Step-by-step explanation: So, we can solve this in 2 ways:

1) 12.75 / 5.5 (easiest way)

= 2.3181818181818183

(Rounded to the nearest hundredth) ≈ 2.32

2) Set up a proportional relationship:

[tex]\frac{12.75}{5.5}[/tex] = [tex]\frac{?}{1}[/tex]

Now, divide 12.75 by 5.5, and get about 2.32

Now, let's check our answer:

2.32 x 5.5 = 12.76

So, he paid about 2.32 per pound.

I hope this helped!

Answer:

Step-by-step explanation:

3/5 because 10 is their GCF

Answer:

The answer is 3/5

Step-by-step explanation:

30/50 > 6/10 >3/5

Just divide 30/50 (both numbers by 5) and then divide 6/10 (both numbers by 2). Hope this helped :)

Answer:

Angle FSM = 92°  OPTION B

Step-by-step explanation:

[tex]5x+32=7x+8[/tex]

[tex]5x-7x=8-32[/tex]

[tex]-2x=-24[/tex]

[tex]x=\frac{-24}{-2} =12[/tex]

Angle FSM:

[tex]FSM=7x+28=7(12)+8=84+8=92[/tex]

Hope this helps

The estimated regression equation is :

          ŷ = 12.924 - 3.682[tex]x_{1}[/tex] + 45.216[tex]x_{2}[/tex]

S0, option(d) is the correct answer.

In statistics, an estimated regression equation is an equation constructed to model the relationship between dependent and independent variables.

The least squares method is the most widely used method for developing estimates of the model parameters.

For simple linear regression, the least squares estimates of the model parameters β0 and β1 are indicated [tex]b_{0}[/tex] & [tex]b_{1}[/tex]. Using these approximates, an estimated regression equation is constructed: ŷ = [tex]b_{0} + b_{1} x[/tex] . The graph of the estimated regression equation for simple linear regression is a straight-line approximation of the relationship between y and x.

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The set of ordered pairs that best represents the linear function f(x) = (1/2)x +2 is the third option.

H { (-4, 0), (-1, 1.5), (2, 3), (4, 4)}

We want to see which one of the given sets best represents the linear function:

f(x) = (1/2)x +2

To identify the correct option, we need to see which set of ordered pairs only includes points that are on the linear equation.

For example, the first set starts with the point (-4, -7.5)

Replacing these values in our function we will get:

-7.5 = (1/2)*-4 + 2

-7.5 = -2 + 2

-7.5 = 0

This is false, so we can discard the first equation.

(We also can see that f(-4) = 0, so we can also discard the second option).

Now let's look at the third option, the second point is (-1, 1.5)

f(-1) = 1.5 = (1/2)*-1 + 2

        1.5 = -0.5 + 2

         1.5 = 1.5

This point belongs to the functions graph.

(and on the other set we have the point (-1, 3), that point clearly does not belong to the graph, so we can also discard this option).

Finally, the only remaining option is the third one, H.

{ (-4, 0), (-1, 1.5), (2, 3), (4, 4)}

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For estimation, she have to make calculation as 320x50/

Using one significant figure as an example 3692 should be converted to one square foot (s.f.). The number 3 is the first significant digit because it is the first non-zero digit.6 exceeds 5 in number.We round up because 6 is greater than 5 One plus three equals four, and 3692 is four thousand square feet.

each number to the nearest significant figure.Use the 'approximately equal to' symbol to build the new estimated calculation.Consider units when calculating and use the rounded numbers to provide an approximation.

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The value for the proportional constant, for given data, is 5/6.

A linear function is a function that, when plotted, creates a straight line. Typically, it is a polynomial function with a maximum degree of 1 or 0. Nevertheless, calculus and linear algebra are also used to represent linear functions.

Given that b  varies directly as m

so b ∝ m

it says b is directly proportional to m,

removing the proportional sign apply a constant k,

b = km

where k is the proportional constant,

and m = 6 and b = 5

5 = 6k

k = 5/6

Hence the value of the constant is 5/6.

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Answer:

follow me if this helped you

Step-by-step explanation:

Area of inscribed square.

A circle is inscribed into a square, find the area of the circle if one side of the square is 15 m

The diameter of the inscribed circle is equal to the length of the square's diagonal, which is equal to the length of one side of the square multiplied by the square root of 2 (since the diagonal of a square is equal to the square root of 2 times the length of one side). Therefore, the diameter of the inscribed circle is 15m * sqrt(2) = 15m * 1.41421356237 = 21.213203435596424m

The area of a circle is given by the formula A = π * r^2, where r is the radius of the circle. Since the diameter of the circle is 21.213203435596424m, the radius is half of that, which is 10.60660171779821m.

So the area of the circle is A = π * r^2 = π * 10.60660171779821^2 = 353.09

Given the number lines (attached) the correct one is Option B) because it represents the right placement of values.

A number line is a depiction of a graded straight line that serves as a visual representation of real numbers in primary mathematics. Every point on a number line is presumed to be a real number, and every real number is assumed to be a point.

We can tell that option B is correct because:

Thus, option B is correct in the given number line.

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Inferential statistics is a branch or method of statistics that makes the use of various analytical tools to draw or conclude inferences about the population data from sample data. Apart from inferential statistics, another part is descriptive statistics forms another branch of statistics.

Inferential statistics help to make conclusions about the population while descriptive statistics summarizes the features of the data set.

Inferential statistics helps to develop a good grasp of the population data by analyzing the samples obtained from it.

It helps in making concept about the population by using different analytical tests and tools.

Inferential statistics can be classified into two types of hypothesis testing and regression analysis. Hypothesis testing also includes the use of belief intervals to test the parameters of a population.

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[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

[tex]\qquad \sf  \dashrightarrow \: f(x) = 2 {x}^{2} - 2x - 4[/tex]

[tex]\qquad \sf  \dashrightarrow \: f(3) = 2(3) {}^{2} - 2(3) - 4[/tex]

[tex]\qquad \sf  \dashrightarrow \: f(3) = 2(9) {} - 6- 4[/tex]

[tex]\qquad \sf  \dashrightarrow \: f(3) = 18{} - 10[/tex]

[tex]\qquad \sf  \dashrightarrow \: f(3) = 8[/tex]

Classifying  the scenarios as an observational study, an experiment, or a sample survey.

Scenario A: Counties in eastern Iowa that received either an above typical or below typical rainfall in a given year are compared in terms of corn production - observational study.

Scenario B: Eight students were chosen at random from the cafeteria and asked if their favorite sport was soccer- a sample survey

Scenario C: To determine which drug is most effective in treating the common cold, drug A or drug B, cold patients were randomly given one of the two drugs and the results were compared-  a sample survey.

Scenario D: To determine which hair growth treatment was most effective in regrowing hair, GrowHair or ReGain, participants were assigned a treatment to determine which showed the most new hair growth- experiment.

Scenario E: Students who were taught reading by two different methods are compared in terms of their reading standardized test scores  observational study.

Scenario F: Ten employees are randomly selected and asked whether they would be in favor of a new management position in their department- a sample survey.

Sample Survey can be defined as the way in which people are randomly choose or pick from a large population so as to draw or reach a conclusion.

Observational study is a type of research method in which  people are be observed before conclusion are drawn.

Experiment study is research method in which something is been  tested before conclusion are reach.

Therefore Scenario A: Counties in eastern Iowa that received either an above typical or below typical rainfall in a given year are compared in terms of corn production - observational study.

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The required solution of the given inequality 2x < 8 is x < 4.

The relation between two expressions that are not equal, employing a sign such as ≠ ‘not equal to’, > ‘greater than’, or < ‘less than’.

Given:

The given  inequality is

2x < 8

According to given question we have

Write inequality

2x < 8

Divide both sides by 2 we get,

x < 4

Therefore, the required solution of the given inequality 2x < 8 is x < 4.

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Answer:

C

Step-by-step explanation:

Answer: No Solution

Step-by-step explanation:

There is no solution.

A set of equations with the same slopes and different y-intercepts have no solution.

The yard is an English unit of length in both the British imperial and US customary systems of measurement equalling 3 feet or 36 inches.

Since 1959, it has been precisely standardised to 0.9144 metres per international agreement. The word "yard" comes from the Old English word "gerd," "gyrd," etc., which was used for measuring sticks, staves, and branches.

The term first appears in the late 7th-century regulations of Ine of Wessex  where "yard of land" refers to the yardland, an ancient English tax assessment unit equivalent to one-fourth of a hide.

Around the same time, it was substituted for a branch moved by the wind in the Lindisfarne Gospels description of the messengers from John the Baptist in the Gospel of Matthew. In addition to the yardland, surveying lengths of 15 feet (4.6 m) or 16.5 feet were also referred to as "yards" in Old and Middle English (5.0 m).

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Answer:The correct statement among the given options is:

StartFraction 1 inch Over 2.54 centimeters EndFraction = StartFraction 7 inches Over 17.68 centimeters EndFraction SO 1 is the answer.

Answer:

(x,y) = (-1/4, -5/4)

Step-by-step explanation:

To solve the system of equations using the substitution method, we can start by solving one equation for one variable in terms of the other. Let's start by isolating y in the first equation:

y = -3x - 2

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

6x - 2(-3x - 2) = 1

Simplifying this, we get:

6x + 6x + 4 = 1

12x + 4 = 1

12x = -3

x = -3/12 = -1/4

Now we can substitute this value of x back into the first equation to solve for y:

y = -3(-1/4) - 2 = 3/4 - 2 = -5/4

So the solution of this system of equations is (x,y) = (-1/4, -5/4)

You can check this solution by substitute these values back into the original equation and check that both are correct.

Tell me if this helped :)

Answer:

( - [tex]\frac{1}{4}[/tex], [tex]\frac{-5}{4}[/tex] )

Step-by-step explanation:

Substitute -3x - 2 for y

6x - 2y = 1

6x -2(-3x - 2) = 1

6x + 6x + 4 = 1  Combine like terms

12x + 4 = 1  Subtract 4 from both sides

12x + 4 - 4 = 1 - 4

12x = -3  Divide both sides both sides by 12

[tex]\frac{12x}{12}[/tex] = [tex]\frac{-3}{12}[/tex]

x = - [tex]\frac{1}{4}[/tex]

Substitute - [tex]\frac{1}{4}[/tex] for x to solve for y

y = -3x - 2

y = (-3)[tex]\frac{-1}{4}[/tex] - 2

y =[tex]\frac{3}{4}[/tex] - 2

y = [tex]\frac{3}{4}[/tex] - [tex]\frac{8}{4}[/tex]

y = [tex]\frac{-5}{4}[/tex]

Answer:

parallel

Step-by-step explanation:

solve for the second equation so y is by itself

y=-2x+3

their slopes are the same so they're parallel

Answer:

357

Step-by-step explanation:



The circumference of a circle with a given diameter of 15 inches is equal to 15pi which is equal to 47.12 inches.

The circumference of a circle is the distance around the edge of the circle.

The formula for calculating the circumference of a circle is given by,

C = 2πr = πd

Where C is the circumference, π is a mathematical constant approximately equal to 3.14, and r is the radius of the circle and d is the diameter.

It is also known as the perimeter of the circle.

In the question above, we're given,

Diameter of the circle (d ) = 15 inches.

So, using the formula for the circumference of the circle,

Circumference (c) = π d

                              = π * 15

                              = 47.12 inches

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Answer: x = -2

Step-by-step explanation: Divide each side by factors that do not contain the variable to isolate it.

The values of x for which f(x) = g(x) - 2 are given as follows:

x = 1 and x = 2.

The functions for this problem are defined as follows:

The equation is given as follows:

f(x) = g(x) - 2.

Replacing the values, we have that:

x² - 2x - 1 = x - 1 - 2

x² - 2x - 1 = x - 3

x² - 3x + 2 = 0.

We can factor the equation as follows:

(x - 2)(x - 1) = 0.

Hence the solutions are obtained as follows:

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Answer:

Every 10 seconds is 1 gallon

19/6 * 3+2, expression is equivalent to 19÷6•3+2

Expressions that are equivalent do the same thing even when they have distinct appearances.

When we enter the same value(s) for the variable, two algebraic expressions that are equivalent have the same value (s).

We may be given equations with algebraic expressions on both sides in some situations.

The two expressions on either side of the equation must be comparable in order for the equation to hold true for all values of the variable. F

Hence, 19/6 * 3+2, expression is equivalent to 19÷6•3+2

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