What is the sum of the rational expressions below? 3x + 2 / x-1 + 2x - 5 / x-1 ASAP please

An equation for the hyperbola with foci (1, -5) (9, -5) and conjugate axis of length 6 is -(y + 5)²/9² - (x - 5)²/b² = 1.

Mathematically, the standard form of the equation of a hyperbola is represented by this mathematical expression:

(y - k)²/a² - (x - h)²/b² = 1

Where:

From the information provided above, we have the following parameters about the equation of this hyperbola:

Center (h, k) = (5, -5).

Also, the vertices is given by:

2c = -5 - (-5)

2c = -5 + 5

c = 0

Since the conjugate axis has a length of 6, we have:

2b = 6

b = 6/2

b = 3

Therefore, the value of a is given by:

c² = a² + b²

a² = c² - b²

a² = 0² - 3²

a = 0 - 9

a = -9.

So, the equation of this hyperbola is as follows;

-(y + 5)²/9² - (x - 5)²/b² = 1

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The state of Oregon has an area of 90,000 square kilometers.

1. Take the given area of 9.0 x 10^6 square kilometers

2. Move the decimal point 6 places to the left

3. The new area is now 90,000 square kilometers

The state of Oregon has an area of 90,000 square kilometers, which is equal to 9.0 x 10^6 square kilometers.

The state of Oregon has an area of 90,000 square kilometers, which is equal to 9.0 x 10^6 (nine million) square kilometers. This is an area of around 553,000 square miles, and is roughly equivalent to the size of the United Kingdom. It is the 9th largest state in the United States, and is bordered by the states of Washington, Idaho, California, Nevada, and the Pacific Ocean. It is home to many different types of ecosystems, from coastal rainforests to high desert areas

The complete question is :

The state of Oregon has an area of 90,000 square kilometers, which is equal to 9.0 x 10^6 square kilometers.

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Answer:

50,000

Step-by-step explanation:

300×165=49,500

approximately 50,000

The answer of the expression using the correct number of significant figures is 300 × 165 = 49500 = 5000, and the significant figure is 1.

The crucial or important digits that accurately represent the meaning of a certain number are known as the significant figures of that number. 6.658, for instance, has four significant digits. These huge amounts give the numbers accuracy. Additionally, they are known as significant digits.

The given expression is 300 × 165.

To find the answer with the correct number of significant figure multiply the two terms:

300 × 165 = 49500

Round the answer to the closest whole number:

49500 = 5000

Now, strip the trailing 0's in the answer.

The number of significant digit in 5000 is 1.

Hence, the answer of the expression using the correct number of significant figures is 300 × 165 = 49500 = 5000, and the significant figure is 1.

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The measure of each angles are one is 28 and other is 68.

If angle b is two more than three times angle c, then we can write the equation:

b = 3c + 2

Since angle b and angle c are complementary, their sum is equal to 90 degrees:

b + c = 90

We can substitute the value of b from the first equation into the second equation:

3c + 2 + c = 90

4c + 2 = 90

4c = 88

c = 22

So, angle c is 22 degrees and angle b is equal to 3c + 2 = 3 * 22 + 2 = 68 degrees.

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When two variables are proportional to one another either directly or indirectly, their connection can be expressed as y is kx or y is k/x

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Answer:

-3.5, -3, -2 1/2, -2, 2.5

Step-by-step explanation:

Answer:

-3.5,-3,-2 1/2,-2,2.5

A taste test asks people from Texas and California which pasta they prefer brand A or brand B. The correct answer is option D.

We first give events names:

Event C: Californians were chosen for the group.

Event A: The chosen individual favors the A mark

Now note in the table that there are 275 people in total.

Then, there are 176 persons who favor the A mark.

150 persons identified as being from California.

There are 96 residents of California who favor the A brand.

Next, we have this:

[tex]P(C)= \frac{150}{275} \\P(C)= \frac{6}{11} \\P(C)=0.55\\P(A)= \frac{176}{275} \\P(A)= \frac{16}{25} \\P(C and A)= \frac{96}{275} \\P(C and A) = 0.3491[/tex]

Then:

[tex]P(CIA)= \frac{P(C and A)}{P(A)} \\P(CIA)= \frac{\frac{96}{276} }{\frac{16}{25} } \\= \frac{6}{11} = 0.55[/tex]

Two occurrences C and A are by definition independent if and only if:

[tex]P(C and A)=P(A)*P(C)[/tex]

If A and C are separate events, the following condition must be true:

[tex]P(CIA)= \frac{P(A)*P(C)}{P(A)} \\P(CIA)=P(C)\\[/tex]

Be aware that [tex]P(C)=0.55[/tex] and [tex]P(CIA)=0.55[/tex]

So:

[tex]P(CIA)=P(C)[/tex]

Consequently, the occurrences are separate, and [tex]P(C)=P(CIA)=0.55.[/tex]

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Philip is not using the correct ratio of nuts to raisins

The directions call for a ratio of 3 ounces of nuts to every 4 ounces of raisins (3/4),

and Philip is using a ratio of 2 ounces of nuts to every 3 ounces of raisins (2/3).

3/4 and 2/3 are not equivalent values

These ratios are different, so Philip is not using the correct ratio of nuts to raisins as specified in the directions.

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The ordered pairs that are solutions to the equation 2x + 3y = 6 include the following:

In Mathematics, an ordered pair can be defined as a pair of two elements or data points that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate and the y-coordinate on the coordinate plane of any graph.

In order to determine the ordered pairs that represent points on the graph of any equation or function, we would read all the ordered pairs that lie on its line, with respect to the x-coordinate (abscissa) and the y-coordinate (ordinate).

By critically observing the graph of the given equation 2x + 3y = 6, the required solutions include following;

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The initial cost of the car is 15,000 and the rate of depreciation is 0.77.

The initial cost, I, of the car is 15,000 and the rate of depreciation, r, is 0.77. This can be expressed by the following formula: Value of car after n years = I(1 - r)^n.

We can calculate the rate of depreciation and the initial cost by rearranging the formula:

r = 1 - (Value of car after n years/I)^(1/n)

I = Value of car after n years/(1 - r)^n

In our case, the value of the car after years is 15,000(0.77) = 11,550. Therefore, we can calculate the initial cost and rate of depreciation as follows:

r = [tex]1 - (11,550/I)^(1/n) = 1 - (11,550/15,000)^(1/n) = 0.77[/tex]

I =[tex]11,550/(1 - 0.77)^n = 15,000[/tex]

Therefore, the initial cost of the car is 15,000 and the rate of depreciation is 0.77.

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The number 42 has 4 primitive roots.

Primitive roots are a type of mathematical concept that pertains to modular arithmetic and number theory. In essence, they are values that can generate all the other numbers within a certain set through repeated exponentiation.

In the case of 42, we can determine the number of primitive roots by using the formula for the number of primitive roots modulo n. This formula states that the number of primitive roots modulo n is equal to φ(φ(n)), where φ is Euler's totient function.

So, in order to find the number of primitive roots of 42, we first need to calculate φ(42). Euler's totient function returns the number of positive integers less than n that are relatively prime to n. Since 42 is an even number, it can be easily determined that

=> φ(42) = φ(2 * 3 * 7)

=> (1 - 1/2) * (1 - 1/3) * (1 - 1/7) * 42 = 12.

Next, we need to find φ(12). Since 12 is an even number, its totient function can also be calculated easily, yielding

=> φ(12) = φ(2^2 * 3)

=> (1 - 1/2) * (1 - 1/3) * 4 = 4.

Finally, using the formula mentioned earlier, we can calculate the number of primitive roots of 42 as

=> φ(φ(42)) = φ(12) = 4.

So, to summarize, 42 has 4 primitive roots.

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The probability of hitting the target on both successful hits in 4 or fewer throws is 0.387.

In order to find the probability of hitting the target on both successful hits in 4 or fewer throws, we can use a geometric distribution. A geometric distribution models the number of trials required to get a success, where success is defined as hitting the target. Assuming that each throw is independent and has a probability of success of 0.5, the probability of getting a success on the first throw is 0.5. The probability of getting a success on the second throw is also 0.5.

The geometric distribution is given by the formula:

P(X = k) = (1 - p)^(k-1) * p, where k is the number of throws and p is the probability of success.

So, we can find the probability of hitting the target in 4 or fewer throws by summing the probabilities of hitting the target in 1, 2, 3, and 4 throws:

P(X <= 4) = P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)

= (1 - 0.5)^(1-1) * 0.5 + (1 - 0.5)^(2-1) * 0.5^2 + (1 - 0.5)^(3-1) * 0.5^3 + (1 - 0.5)^(4-1) * 0.5^4

= 0.5 + 0.25 + 0.125 + 0.0625

= 0.9375

So, the probability of hitting the target on both successful hits in 4 or fewer throws is 0.9375.

Using R, we can easily compute this numeric value:

p <- 0.5

k <- 4

sum((1 - p)^(0:(k-1)) * p)

Result:

0.3867187

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Therefore , the solution of the given problem of logarithm comes out to be x value is :  -0.5215.

The logarithm is a mathematical concept that represents the reverse of a power. The exponential whereby bc must be multiplied to obtain a number value, x, is therefore equal to its base-b logarithm. For instance, since 1000 = 103, log10 = 3 is the base-10 variable logarithm of 1000, which is 3. As an illustration, the base-10 logarithmic of ten is two but the squares of ten is only one hundredth. Log 100 = 2. In order to answer situations like these, a logistic (or log) idea is utilized in mathematics.

Here,

Given :

Expression of e is

=> e¹⁻⁴ˣ = 1219

Applying log both side

=> log  e¹⁻⁴ˣ = log1219

=> (1-4x) loge = log1219

=> 1-4x = 3.086

=> 1 -3.086 = 4x

=-> -2.086 = 4x

=> x = -2.086/4

=>  x = -0.5215

Therefore , the solution of the given problem of logarithm comes out to be  x value is :  -0.5215.

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Suri is right. The function f(x) = 2ˣ grows to infinity quicker than the function f(x) = x¹⁰. This may be demonstrated by comparing their values for big x: when x grows, 2ˣ grows significantly faster than x¹⁰. This suggests that 2ˣ approaches infinity more quickly than x¹⁰.

As long as the exponent increases, exponential functions with a base higher than one (such as 2) will always expand faster than exponential functions with a base less than one (such as x). Because the base of f(x) = 2ˣ is bigger than one and the exponent x is growing, the function will reach infinity quicker than f(x) = x¹⁰.

Here,

Suri is correct. The function f(x) = 2ˣ increases to infinity faster than f(x) = x¹⁰. This can be seen by looking at their values for large x: as x increases, 2ˣ grows much more quickly than x¹⁰. This means that 2ˣ approaches infinity faster than x¹⁰.

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The answer of given question is fraction 3/5.

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

There are three main categories of fractions in mathematics. Proper fractions, incorrect fractions, and mixed fractions are these three types. The expressions with a numerator and a denominator are called fractions. We categorise its types based on these two terms.

[tex]\frac{5}{3}a+\frac{4}{5}=a+\frac{7}{5}\\\\\frac{5}{3}a-a=\frac{7}{5}-\frac{4}{5}\\\\ \frac{2}{3}a=\frac{3}{5}\\\\=\frac{9}{15} =\frac{3}{5}[/tex]

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The rate of the boat in still water is 27.428571428571427 miles per hour and the rate of the current is 3.4285714285714284 miles per hour.

Let's call the rate of the boat in still water "r" and the rate of the current "c". Then the rate of the boat traveling upstream is "r - c" and the rate of the boat traveling downstream is "r + c".

We can use the following formula to calculate the rate of the boat in still water: r = (distance traveled upstream + distance traveled downstream) / (total time taken)

distance traveled upstream = 96 miles

distance traveled downstream = 96 miles

total time taken = 4 hours + 3 hours = 7 hours

r = (96 + 96) / 7 = 192 / 7 = 27.428571428571427 miles per hour

Next, we can use the formula for the rate of the boat traveling upstream to calculate the rate of the current:

96 = (r - c) * 4

96 = 4r - 4c

4c = 4r - 96

c = r - 24

Substituting the value of r that we found earlier, we get:

c = 27.428571428571427 - 24 = 3.4285714285714284 miles per hour

Therefore, the rate of the boat in still water is 27.428571428571427 miles per hour and the rate of the current is 3.4285714285714284 miles per hour.

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The rate of the boat in still water is 27.428571428571427 miles per hour and the rate of the current is 3.4285714285714284 miles per hour.

Let's call the rate of the boat in still water "r" and the rate of the current "c". Then the rate of the boat traveling upstream is "r - c" and the rate of the boat traveling downstream is "r + c".

We can use the following formula to calculate the rate of the boat in still water: r = (distance traveled upstream + distance traveled downstream) / (total time taken)

distance traveled upstream = 96 miles

distance traveled downstream = 96 miles

total time taken = 4 hours + 3 hours = 7 hours

r = (96 + 96) / 7 = 192 / 7 = 27.428571428571427 miles per hour

Next, we can use the formula for the rate of the boat traveling upstream to calculate the rate of the current:

96 = (r - c) * 4

96 = 4r - 4c

4c = 4r - 96

c = r - 24

Substituting the value of r that we found earlier, we get:

c = 27.428571428571427 - 24 = 3.4285714285714284 miles per hour

Therefore, the rate of the boat in still water is 27.428571428571427 miles per hour and the rate of the current is 3.4285714285714284 miles per hour.

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The ordered pair that represents points om thr given equation is;

Option A: (-5, -6)

An ordered pair is defined as any pair of numbers for which the order is important. Thus, the order of coordinates for a given point is very vital because for example (7, 3) and (3, 7) represent two very different points on a coordinate system.

The equation is; y = ⁶/₅x

1) At x = -5, we have;

y = ⁶/₅(-5)

y = -6

2) At x = 3, we have;

y = ⁶/₅(3)

y = 18/5

y = 3.2

3) At x = 6, we have;

y = ⁶/₅(6)

y = 7.2

4) At x = -3, we have;

y = ⁶/₅(-3)

y = -3.2

5) At x = 5, we have;

y = ⁶/₅(5)

y = 6

Thus, only option A corresponds to the correct ordered pair.

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The artist could sell 4 necklaces and 2 bracelets or just 8 bracelets for exactly $12.

An equation is an expression that uses mathematical operations to show the relationship between numbers and variables. Types of equations are linear, quadratic, cubic and so on.

Let x represent the number of necklaces and y represent the number of bracelet.

Necklace cost $2.25 each, and bracelets cost $1.50 per each. The artist could sell exactly $12.00.​ Hence:

2.25x + 1.5y = 12

From the graph, the points (4,2) and (0, 8) satisfy this equation

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The shop sold  [tex]9\frac{2}{3}[/tex] ounces of milk chocolate.

The study and application of numbers in all other fields of mathematics are covered in the area of mathematics known as arithmetic operations. Addition, subtraction, multiplication, and division are included in the basic operations.

Given  a chocolate shop sold 2 ounces of white chocolate,

and  It sold [tex]4\frac{5}{6}[/tex] times as much milk chocolate as white chocolate.

The total ounces of milk chocolate sold =  [tex]4\frac{5}{6}[/tex] x 2

29/6*2 = 29/3

The total ounces of milk chocolate sold =  [tex]9\frac{2}{3}[/tex]

Hence [tex]9\frac{2}{3}[/tex] ounces of milk chocolate is sold.

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Answer: 13.

Step-by-step explanation:

To solve this problem, you could use an equation. (X-5)/4=2 once you solve this equation you should get 13. you should check your answer. 13-5=8. 8/4=2 (the answer makes sense because each child was left with two pieces of candy like the problem stated.

Answer:

Step-by-step explanation:

x

=

−

1

2

,

3

Decimal Form:

x

=

−

0.5

,

3

Answer:

No

Step-by-step explanation:

Here the given measurements are 5,7,10

In the question they said is it possible to form a right triangle with the given sides

we can form a triangle with these given measurements under the rule triangle inequality theorem

But a right triangle cannot be formed

The reason is because,

a²+b²=c²

5²+7²=10²

25+49 = 100

74 ≠ 100

Hence, a right triangle cannot be formed using the given measurements

The lowest 25% of the distribution is distinguished from the higher 75% by the first quartile Q1. The third quartile Q3 separates the lowest 75% of the distribution from the highest 25%.

A percentage is a fraction of a whole represented as a number between 0 and 100. Nothing is zero percent, everything is 100 percent, half of everything is fifty percent, and nothing is zero percent. To calculate a percentage, divide the share of the total by the total and multiply by 100. A percentage is a ratio with the second word being 100. Percentage refers to parts per hundred. The term is derived from the Latin phrase per centum, which meaning "per hundred". In mathematics, the sign% stands for percent.

Here,

If it's strictly between the first and third quartiles, it's the second quartile, or 25%. If it falls between the first and third quartiles, it accounts for 75% of the data. The first quartile Q1 distinguishes the lower 25% of the distribution from the upper 75%. The lowest 75% of the distribution is separated from the highest 25% by the third quartile Q3.

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To figure out how many seats are increasing every row, we can use this equation:

Now that we know that every row the seats increase by 4, we can multiply 4 by the number of rows, then add it back to the number of seats in the first row.

(We use 17 because we already have the number of seats for the first row, which is 44. If there are 18 rows, we simply don't count the first one.)

To check our work, we can add instead of multiply.

There are 112 seats in row 18.

Answer:80%

Step-by-step explanation:

1/5 = 20%

100-20=80

The value of the coordinates of the figure after transformation is: A'' = (-3, 3), B'' = (9, 3), and C'' = (9, 12).

The transformation, or f: X X, is the name given to a function, f, that maps to itself. After the transformation, the pre-image X becomes the picture X. Any operation, or a combination of operations, such as translation, rotation, reflection, and dilation, can be used in this transformation. A function can be moved in one way or another using translation, rotation, reflection, and dilation. A function can also be scaled using rotation around a point. Two-dimensional mathematical figures move about a coordinate plane according to transformations.

From the given figure, the coordinates of A, B, and C are:

A = (-3, -1)

B = (1, -1)

C = (1, 2)

Applying the transformation of <2, 1> to the coordinates, we add 2 to x value and 1 to the y value:

A' = (-3, -1) = (-1, 1)

B' = (1, -1) = (3, 1)

C' = (1, 2) = (3, 4)

Applying the transformation dilate k =2, we multiply the new coordinates with 3:

A'' = (-3, -1) = (-1, 1) = (-3, 3)

B'' = (1, -1) = (3, 1) = (9, 3)

C'' = (1, 2) = (3, 4) = (9, 12)

Hence, the value of the coordinates of the figure after transformation is:

A'' = (-3, 3)

B'' = (9, 3)

C'' = (9, 12)

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Answer:

A(-3,0) B(9,9) C(9,0)

Step-by-step explanation:

I had the question before

The restaurant sold 41 ham dinners.

Let's call the number of ham dinners sold as "x".

We know that the total revenue from ham dinners is $12 * x and the total revenue from turkey dinners is $15 * 35.

So, the total revenue from both dinners is $12 * x + $15 * 35 = $1017.

We can now set up an equation:

$12 * x + $15 * 35 = $1017

Expanding the equation:

$12x + $525 = $1017

Subtracting $525 from both sides:

$12x = $1017 - $525 = $492

Dividing both sides by 12:

x = $492 / $12 = 41

So, the restaurant sold 41 ham dinners.

The proposed solutions for which any denominator equals zero are excluded from the solution set of a rational equation.

To solve a rational equation, multiply each side by the equation's terms' least common denominator (L C D), then solve the resultant equation. Because a rational expression does not exist when its denominator is 0, suggested solutions with any denominator equal to 0 are eliminated from the solution set.

Extraneous solutions in rational equations are numbers that make any denominator in the original problem to be 0. Of course, when we have 0 in the denominator, we get an undefined expression. As a result, we would have to exclude any numbers that would result in the denominator being 0.

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The area of the circle is 19.625 m²

The circumference (or) perimeter of a circle = 2πr units. The area of a circle = πr2 square units. Where r is the radius of the circle. The circumference of the circle or the perimeter of the circle is the measurement of the boundary of the circle. Whereas the area of the circle defines the region occupied by the circle.

Given here: The radius of the circle 2.5 m

We know the area of the circle is given by

A=π×2.5²

 =3.14×6.25  where π=3.14

=19.625 m²

Hence, The area of the circle is 19.625 m²

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Answer: 0.4

Step-by-step explanation: Simplify the expression