(4+√5)/(√5 -2) rationalize the denominator and simplify

If the temperature dropped at a constant rate, it would have dropped 4°C per hour. This can be calculated by taking the difference in temperature (24°C) and dividing it by the number of hours that passed (4 hours).

Answer:

-3

Step-by-step explanation:

I Think :D

Answer:

\(\pm24\)

Step-by-step explanation:

To find the geometric mean of two numbers, you find their product and then take the square root of that product:

\(GM=\sqrt{16*36}=\sqrt{576}=\pm24\)

Answer:

Step-by-step explanation:

Im not all the way sure, but I think it would be 1.8.

11+2 = 13

24/ 13 = 1.84...

rounded, 1.8

Answer:

The answer is 2.

Step-by-step explanation:

11 × 2 = 22

22 + 2 = 24

Therefore, 2 is the answer.

Answer:

16.5

Percentage Calculator: 33 is what percent of 200? = 16.5.

Answer:

39 pages

Step-by-step explanation:

If 13 pages are read in 1/3 of an hour, we need to multiply 13 by 3 to get the number of pages read in 1 hour. 13*3 = 39 pages

Answer:

1/14

Step-by-step explanation:

The ratio is 5:70. The fraction form of that is 5/70. To get the lowest terms, I divided both numbers by 5. So it is 1/14

Answer: -1/3

Step-by-step explanation: To solve the equation -18t - 6 = 0, we need to isolate the variable t on one side of the equation.

First, we add 6 to both sides of the equation to get:

-18t = 6

Then, we divide both sides by -18 to get:

t = -6/18

Simplifying -6/18 by dividing both the numerator and denominator by 6, we get:

t = -1/3

Therefore, the solution to the equation -18t - 6 = 0 is t = -1/3.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

The final expression of -16\(x^{8}\) / -8\(x^{9}\) is 2/x.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

-16\(x^{8}\) / -8\(x^{9}\)

= (-16/-8)\(x^{8 - 9}\)

= 2 \(x^{-1}\)

= 2/x

Thus,

The final expression of -16\(x^{8}\) / -8\(x^{9}\) is 2/x.

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Explanation

Given the equation;

Using a graphing calculator, the graph of the circle becomes;

Answer:

The confidence interval based on the given values (x = 45, n = 96, Confidence level = 95%.

The confidence level (95%), sample size (n = 96), and sample mean (x = 45), we can calculate the margin of error and the confidence interval. Here's how:

1. Margin of Error:

The margin of error represents the maximum expected difference between the true population parameter and the sample estimate. It depends on the confidence level and the standard deviation (which we don't have in this case).

Since the standard deviation is unknown, we can use the t-distribution to estimate it. With a sample size of n = 96, the degrees of freedom are (n - 1) = 95. Considering a 95% confidence level, the critical value for a two-tailed test is approximately 1.984 (referencing a t-distribution table or calculator).

The margin of error (E) can be calculated using the following formula:

E = critical value * (standard deviation / sqrt(n))

However, since we don't have the standard deviation, we can't compute the margin of error in this case.

2. Confidence Interval:

The confidence interval represents a range of values within which the true population parameter is likely to fall.

The confidence interval can be calculated using the formula:

CI = x ± (critical value * standard deviation / sqrt(n))

The confidence interval based on the given values (x = 45, n = 96, confidence level = 95%.

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Answer:

x^2 + 10x +21

Step-by-step explanation:

Your multiplying the Squares together and then adding them

Blue Square : x*x= x^2

Pink  Square : x*7= 7x

Green Square: x*3= 3x

Orange Square: 3*7= 21

Now we add all the squares together to get the total area.

x^2+7x+3x+21

x^2+ 10x +21

The range of data set 1 is 4

The range of data set 2 is 4.

A line plot is a graph that is made up of a number line and check marks above the number line. The check mark above the number represents the frequency of the number in the data set. For example, if the number 3 on the number line has 2 checkmarks above it, it means 3 has a frequency of 2.

The range is the difference between the highest number in a dataset and the smallest number in the dataset. Range is a measure of variation.

Range = highest number - lowest number

The range of data set 1 = 7 - 3 =  4

The range of data set 2 : 7 - 3 =  4

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Answer:  1/4

Step-by-step explanation:

If there are  6 black markers and they are a total combination of 24 difference colored markers.  

The  the fraction will be 6/24  which reduces to 1/4

Answer:

Largo = 62m

Ancho = 54m

Step-by-step explanation:

\(P=232m\\ b=(x+8)\\ h=x\)

\(P=2(h+b)\\ P=2(x+(x+8))\\ P=2(2x+8)\\ P=4x+16\)        →         \(4x+16=232\\ 4x=232-16\\ 4x=216\\ x=\frac{216}{4}\)

\(b=54m\)              \(x=54m\)

\(b=x+8=(54)+8\)

\(b=62m\)

Answer: - 21/16 = 15/16 (simplified)

= - 1.3125 convert decimal to fraction

= - 13125/10000

= - 21/16 = 15/16  (simplified)

Answer: There is no slope.

Step-by-step explanation:

First, we use the slope-intercept form to find out the slope. The slope-intercept form formula is : m = y2 - y1 / x2 - x1.

m = (27 - 2) / (9 - 9)

m = 25 / 0

m = undefined

This isn't a positive, nor negative slope, rather a slope called "undefined". (Think of every slope as a hill for your skateboard, if it's easier to remember.) And since the x is 0, x is stagnant, making the y and number that doesn't move from the x-coordinates. So, The entered points belong to a vertical line. There is no slope.

Hope this helps.

During the morning rush hour, there are 6,400 junior and high school students, 3,400 adults, and 5,800 senior citizens riding the subway.

Let's assume the number of junior and high school students riding the subway during the morning rush hour is J, the number of adults is A, and the number of senior citizens is S.

From the given information, we can set up a system of equations based on the number of riders and the revenue generated.

Equation 1: J + A + S = 15,600 (total number of riders)

Equation 2: 1.04J + 2.20A + 1.04S = 32,464 (revenue equation with original ticket prices)

Equation 3: 1.24J + 2.60A + 1.04S = 38,264 (revenue equation with new ticket prices)

We can start by subtracting Equation 2 from Equation 3 to eliminate the J and S terms:

0.2J + 0.4A = 3,800

Next, we can multiply Equation 1 by 0.2 and subtract it from the above equation to eliminate the J term:

0.4A - 0.2J - 0.2A = 3,800 - 3,120

0.2A = 680

A = 680 / 0.2 = 3,400

Now, we can substitute the value of A back into Equation 1 to find the values of J and S:

J + 3,400 + S = 15,600

J + S = 15,600 - 3,400

J + S = 12,200

We have two equations with two variables (J + S = 12,200 and 1.04J + 1.04S = 12,264). By solving these equations simultaneously, we find J = 6,400 and S = 5,800.

Therefore, during the morning rush hour, there are 6,400 junior and high school students, 3,400 adults, and 5,800 senior citizens riding the subway.

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To find the number of subway riders in each category, we set up a system of equations based on the total number of passengers and the total revenue. Solving this system will give us the number of junior and high school students, adults, and senior citizens. The number of riders doesn't change with the increase of ticket prices.

To solve this problem, we set up a system of equations based on the information given in the question.

Let's denote the number of junior and high school students as J, adults as A, and senior citizens as S. We know that there's total of 15,600 passengers, so:

J + A + S = 15,600

We also know that the total revenue was $32,464. Given the ticket prices for each group, we can write:

$1.04J + $2.20A + $1.04S = $32,464

Solving this system of equations (possibly with the help of a calculator or computer software), we can find the number of riders in each category.

The number of riders for each category would only change if the number of riders changes, not the price of the tickets, so when the prices increase, the number of riders remains the same.

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The amount of the 12 grams sample of gold-195m having a half-life of 30.5 s that would remain after 41 s is 4.726 g

n = t / t½

n = 41 / 30.5

n = 82/61

N = N₀ / 2ⁿ

N = 12 / 2^(82/61)

N = 4.726 g

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The algorithm justifies the answer of 3/5 as the fraction each person gets.

Representation of the fractions on the second row:

From what you described, two of the loaves were divided into thirds.

This means each person receives one third, and there is one third remaining. Then, this remaining third from the second loaf was further divided into fifths.

Therefore, each person receives one fifth from this remaining third.

So, the representation of the fractions on the second row would be:

Each person receives 1/3 (one third) from the two loaves.

Each person receives 1/5 (one fifth) from the remaining third.

Algorithm/Abstract strategy to justify the 3/5 found as the answer:

To find the final answer of 3/5, we can follow the steps you provided:

Divide two loaves into thirds, giving each person 1/3.

Divide the remaining third from the second loaf into fifths, giving each person 1/5.

Combining the fractions, each person has 1/3 + 1/5.

To add these fractions, we need to find a common denominator. In this case, the least common multiple (LCM) of 3 and 5 is 15. We can convert 1/3 and 1/5 to have a denominator of 15:

1/3 = 5/15 (multiplying numerator and denominator by 5)

1/5 = 3/15 (multiplying numerator and denominator by 3)

Now, we can add the fractions:

5/15 + 3/15 = 8/15

Therefore, each person receives 8/15 of a loaf.

Simplifying this fraction, we get 3/5.

Hence, the algorithm justifies the answer of 3/5 as the fraction each person gets.

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Chandler ended up 8 feet below sea level. The negative sign indicates that his final position is below sea level. This means that he has descended further into the lake compared to the starting point on the cliff.

Chandler started on the cliff at 32 feet above sea level. When he jumped for 40 feet, we need to determine the final position in relation to sea level.

Since Chandler jumped down, the distance below sea level will be calculated as a negative value. To find how far below sea level Chandler ended up, we subtract the jump distance (40 feet) from the starting height (32 feet above sea level):

32 feet - 40 feet = -8 feet

It's important to note that negative values are used here to represent the direction and magnitude of Chandler's descent relative to sea level

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Answer:

-8 feet

Step-by-step explanation:

Answer:

Step-by-step explanation:

You want the center, radius, and equations in standard form and general form for the circle shown in the graph.

The center is the point marked. Its coordinates are ...

  (x, y) = (2, -1)

The radius is the distance from the center to any point on the circle. It is usually convenient to read the radius on a graph by considering points on the same horizontal or vertical line as the center of the circle.

Here, the circle passes through point (6, -1), so the radius is 6 -2 = 4.

The radius is 4 units.

The standard form equation for a circle with center (h, k) and radius r is ...

  (x -h)² +(y -k)² = r²

For center (2, -1) and radius 4, this is ...

  (x -2)² +(y +1)² = 16 . . . . standard form equation

The general form of a polynomial equation is f(x, y) = 0, with the terms listed in lexicographical order by decreasing degree. This is found from the standard form by expanding it, combining terms, and arranging them in the required order:

  (x -2)² +(y +1)² = 16 . . . . . standard form

  x² -4x +4 +y² +2y +1 -16 = 0 . . . . . eliminate parentheses, subtract 16

  x² +y² -4x +2y -11 = 0 . . . . general form equation

The solution to the inequality is x >= -2 for inequality 3x-5≥-11

The given inequality is 3x-5≥-11

Three times of x greater than or equal to minus eleven

x is the variable

3x - 5≥ -11:

Adding 5 to both sides, we get:

3x ≥ -6

Dividing both sides by 3, we get:

solution is  x≥-2

Therefore, the solution to the inequality is x >= -2.

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Answer:

if the terms are approaching zero then it is convergent.

Therefore the stated series is convergent

Step-by-step explanation:

Answer:

12 + 7 = 19

19 + 10 = 29

answear = 29

Answer:

divide 8 by 4.16

Step-by-step explanation:

Answer:

52 cents

Step-by-step explanation:

Answer:

49

Step-by-step explanation:

Answer:

The answer is 49 :)

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The inverse of a graph flips the x and y coordinates for the points.  If you look at A one point that you see graphed is (-4, -1), its inverse would be (-1,-4).  You see that point on the other line.  Another point would be (-2,1), so the inverse would be (1,-2)  You see both of these points on the two different lines.  

You do not find the same relationships for graphs B and C.