Using the Babylonian method, [tex]\( \sqrt{5} = 2.236}[/tex]. This method involves iteratively averaging and recalculating until the calculated value stabilizes to the desired accuracy.
To demonstrate the Babylonian method for finding the approximate value of [tex]\( \sqrt{5} \)[/tex]
A. In order to determine [tex]\( \sqrt{5} \)[/tex], let [tex]\( G_1 = 2 \)[/tex], a number whose square is close to [tex]5.[/tex]
B. Calculate [tex]\( \frac{5}{G_1} = \frac{5}{2} = 2.5 \)[/tex], which is not equal to [tex]\( G_1 \)[/tex], so further action is necessary. Average [tex]\( 2 \)[/tex] and [tex]\( G_1 \)[/tex] to find [tex]\( G_2 = \frac{2 + 2}{2} = 2.25 \). \( \frac{5}{G_2} = \frac{5}{2.25} = 2.222 \)[/tex], which is not equal to [tex]\( G_2 \)[/tex], so further action is necessary.
C. Average [tex]\( 2.25 \)[/tex] and [tex]\( G_2 \)[/tex] to find [tex]\( G_3 = \frac{2.25 + 2.222}{2} = 2.236 \). \( \frac{5}{G_3} = \frac{5}{2.236} = 2.237 \)[/tex], which is equal to [tex]\( G_3 \)[/tex]. That means [tex]\( \sqrt{5} \)[/tex] is approximately [tex]\( 2.236 \).[/tex]
The complete Question is
The ancient Babylonians developed a method for calculating nonperfect squares by 1700 BCE. Complete the statements to demonstrate how to use this method to find the approximate value of .
A. In order to determine , let G1 = 2, a number whose square is close to 5.
B. 5 ÷ G1 = , which is not equal to G1, so further action is necessary. Average 2 and G1 to find G2 = 2.25. 5 ÷ G2 ≈ (rounded to the nearest thousandth), which is not equal to G2, so further action is necessary.
C. Average 2.25 and G2 to find G3 = 2.236. 5 ÷ G3 ≈ (rounded to the nearest thousandth), which is equal to G3. That means is approximately 2.236.
(ab - 9)(ab + 8) Please help
Divide a six-sided polygon into triangles to find the sum of its interior angles.
A.360 degrees
B. 900 degrees
C. 1080 degrees.
D. 720 degrees
What’s 100-((10x7)+(5x7-5)
Answer:
the answer 60
Step-by-step explanation:
First I did 10x7 which equals 70, Second I did 5x7 which equals 35 and then subtracted 5 to get 30, Third I did 100-70 to get 30 and than I did 30+30 to get 60.
State whether the relationship between the variables in the table is a direct variation, an inverse variation, or neither. If it is a direct or inverse variation, write a function to model it.
x=3,9,13,20
y=9,27,39,60
I know it's direct but how do I write a function model to it?,
The variation is a direct variation, and the function to model it is y = 3x
From the table, we can see that:
The y values are calculated by multiplying the corresponding x values by 3
Take for instance;
When x = 3, y = 9
When x = 9, y = 27
Using the above pattern, the function to model the table is y = 3x
Read more about direct variations at:
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Answer:
B. Neither
Step-by-step explanation:
The hypotenuse of a right triangle is 6 inches. if one of the legs is 2 inches, find the degree measure of each angle
Answer:
(square root) 30
Step-by-step explanation:
I don't know if that's right I'm taking this test right now it might be wrong sorry if its wrong lol
Describe the trend in the scatter plot.
not enough information because the trend line is unclear
positive correlation
no correlation
negative correlation
Answer:
No correlation.
Step-by-step explanation:
A Scatter (XY) Plot has points that show the relationship between two variables.
Scatter plots use a collection of points placed using Cartesian coordinates to show values of two variables. By showing a variable on each axis, it can be detected if there is a relationship or correlation between the two variables.
Several types of correlation can be interpreted through the patterns shown in the scatter diagrams. These are: positive (values increase together), negative (one value decreases as the other increases), null (no correlation).
In the case presented, it can be clearly seen that the variables have no correlation, because the trend is not that the points form a straight line, but that there is too much dispersion.
So, the answer is:
No correlation.
Hope this helps!
-21 - 7x = 8x + 24 How do you solve this?
what is the factored form of 3c²+24c+48 ?
Hurry please I need the answer right away soo send me math work answers my friend said it's 42? Is it right
The area of a rectangle is 10r (squared) − 11r − 6. The width is 2r − 3. What is the length?
The length of the rectangle whose area is (10r² − 11r − 6) and the width is (2r−3) is (5r+2).
What is a rectangle?A parallelogram in which adjacent sides are perpendicular to each other is called a rectangle. A rectangle is always a parallelogram and a quadrilateral but reverse statement may or may not be true.
Area of rectangel = Length × Width
Given that the area of a rectangle is 10r² − 11r − 6, while the width is 2r − 3. Therefore, it can be writen as,
[tex]\text{Area = Length}\times\text{Width}\\\\10r^2 - 11r - 6 = \text{Length} \times (2r - 3)\\\\\text{Length} = \dfrac{10r^2 - 11r - 6}{2r-3}\\\\\text{Length} = 5r+2[/tex]
Hence, the length of the rectangle is (5r+2).
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Jake is in the stands at a football game with his girlfriend Diane. He decides that he needs to ask Diane a serious question, so he brings her to a quiet lounge in the stadium complex. What type of context has Jake changed?
A. the cultural context
B. the social-psychological context
C. the temporal context,
Jake has shifted the (B) social-psychological context by moving to a quieter, more private space in the stadium to ask Diane a serious question, which changes the norms and atmosphere to match the situation's gravity.
Jake has changed the social-psychological context by moving from the stands to a quiet lounge. The social-psychological dimension of context includes status relationships among participants, roles, norms of the society or group, and the overall atmosphere like friendliness, formality, or gravity of the situation. By choosing to ask Diane a serious question in a quieter, more private environment, Jake is altering the norms and atmosphere to better suit the gravity of the conversation he intends to have, thus changing the social-psychological context.
I will fan and medal!!! PLEASE
A gray-scale digital camera with 1,000,000 pixels takes a picture (the picture is made of 1,000,000 parts and each part has a certain amount of gray). A histogram is made where the data is the amount of gray in each of these parts. The histogram looks bell-shaped with a mean of 125 gray levels and a standard deviation of 15.
How many pixels are brighter than 163 gray levels?
5000
10,000
160,000
50,000
To find the number of pixels brighter than 163 gray levels in a digital camera histogram, calculate the Z-score and use it to determine the percentage of values above that score, resulting in 160,000 pixels.
A gray-scale digital camera with 1,000,000 pixels has a histogram with a mean of 125 and standard deviation of 15 gray levels. To find the number of pixels brighter than 163 gray levels, first calculate the Z-score for 163: Z = (163 - 125) / 15. Then, use a Z-table or calculator to find the percentage of values above this Z-score, which corresponds to the number of pixels brighter than 163.
The answer to the question is 160,000 pixels brighter than 163 gray levels.
The main tank at an aquarium is a cylinder with a diameter of 203 ft and a height of 4 ft. What is its approximate volume? Use 3.14 for π. a. 129,400 ft3 b. 79,830 ft3 c. 236,560 ft3 d. 32,366 ft3
Answer: [tex]a.\ 129,400\ ft^3[/tex]
Step-by-step explanation:
The volume of a cylinder is given by:-
[tex]\text{Volume}=\pi r^2h[/tex]
Given: The diameter of cylinder = 203 ft.
Then the radius of the cylinder =[tex]\dfrac{203}{2}[/tex] ft.
The height of the cylinder = 4 ft.
Now, The volume of cylinder :will be -
[tex]\text{Volume}=(3.14)(\dfrac{203}{2})^2(4)=\\\\\Rightarrow\text{Volume}=129,396.26\approx129,400\ ft^3[/tex]
MEDAL
True or false
The coefficient of x^k y^n-k in the expansion of (x+y)^n equals (n-k / k),
Answer: the answer is FALSE. Just took this on a p e x
Step-by-step explanation:
PLEASE HELPME QUICKLY QUICK
How many solutions does the equation sin(4x)=1/2 have on the interval (0,2pi)?
Answer:
2 solutions
Step-by-step explanation:
Given the equation sin(4x)=1/2, to know the total number of solutions that the equation has within the interval (0,2π), we will need to solve for x first.
sin(4x)=1/2
4x = arcsin1/2
4x = 30°
x = 30/4
x1 = 7.5° (This angle lies in the first quadrant)
Since sine is positive in the second quadrant as well and the angle in the second quadrant is (180°-theta) where theta is 7.5°, therefore;
x2 = 180-7.5°
x2 = 172.5°
Therefore 7.5° and 172.5° are the two solutions of x that falls within the range (0,2π)
Please help! How many ways can a cook arrange 7 or 10 spice jars on a spice rack?
A. 720
B. 604,800
C. 5,040
D. 120
Please help with this one question thanks!
You have 20 shirts in your closet. 4 blue, 7 red, 3 green and 6 black. You pick one without looking. What is the probability that you pick a blue or black shirt?
Please help ASAP! 16 points
Three-fourths of an inch on a map equals 750 miles. what would one inch equal?
One inch on the map is equal to 1000 miles.
Explanation:To find what one inch would equal on the map, we can set up a proportion using the given information. We know that three-fourths of an inch on the map equals 750 miles. Therefore, the proportion would be: 3/4 inch = 750 miles. To find what one inch would equal, we can cross multiply and solve for the missing value:
3/4 inch * 1 inch = 750 miles * 1 inch
Simplifying, we get: 3/4 = 750 miles * 1 inch
Dividing both sides by 3/4, we get: 1 inch = (750 miles * 1 inch) / (3/4)
Simplifying further, we find that one inch on the map is equal to 1000 miles.
Please help with 2 questions thank you.
The value of x is
PLEASE ANSWER FAST IM IN THE MIDDLE OF A TEST
sam decides to build a square garden if the area of the other garden is 9x^2 -24x +16 square feet what is the length of one side of the garden
One gallon of paint usually covers about 350 square feet. How many square feet will 2.5 gallons cover? Show your work, including labeling your answer with the appropriate units of measure.
Unit rate is the quantity of an amount of something at a rate of one of another quantity.
If 1 gallon covers 350 square feet.
2.5 gallons will cover 875 square feet.
What is a unit rate?It is the quantity of an amount of something at a rate of one of another quantity.
Example:
A man can walk 8 miles in 2 hour
In one hour, the man can walk for 4 miles
We have,
One gallon covers 350 square feet.
This can be written as:
1 gallon = 350 square feet
Multiply both sides by 2.5.
2.5 x 1 gallon = 2.5 x 350 square feet
2.5 gallons = 875 square feet
Thus,
If 1 gallon covers 350 square feet.
2.5 gallons will cover 875 square feet.
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What is a possible value for the missing term of the Geometric sequence. 50_450
Answer: The missing term of the Geometric sequence can be 150.
Step-by-step explanation:
Let the missing number is x,
Hence, the G.P. will,
50, x, 450
Since, the consecutive element of G.P. are in same ratio,
[tex]\implies \frac{x}{50}= \frac{450}{x}[/tex]
[tex]\implies x^2 = 50\times 450 = 22500[/tex]
[tex]\implies x = 150[/tex]
Thus, the missing term of the Geometric sequence can be 150.
The Smiths were just approved for a 25 year mortgage at an 11% fixed rate. If they had not filed bankruptcy in the past, they could have gotten a rate of 7%. If their loan amount is $128,000, how much more per month will the Smiths be paying for their mortgage as a result of their bankruptcy? a. $349.86 b. $125,840.78 c. $904.68 d. $235.09
Which inequality represents the following sentence?
Twelve fewer than a number is at least 18.
12 + x ≤ 18
x – 12 ≥ 18 (This one correct?)
12 – x ≥ 18
x – 12 < 18,
Answer:
B) x - 12 ≥ 18.
Step-by-step explanation:
Given : Twelve fewer than a number is at least 18.
To find : Which inequality represents the following sentence?.
Solution : We have given
Twelve fewer than a number is at least 18.
Let the number be x .
According to question :
Twelve is less than a number x .
x - 12 ( negative sign used for fewer).
x - 12 ≥ 18.
Here we used greater than equal to sign because x- 12 is at least 18 mean is must be 18 or greater than 18.
Then equation become x - 12 ≥ 18.
Therefore, B) x - 12 ≥ 18.
HELP! Two lines intersect at a point, forming ∠1 , ∠2 , ∠3 , and ∠4 .
∠1 and ∠3 are vertical angles.
∠2 and ∠4 are vertical angles.
m∠1=70°
What is the measure of ∠2 ?
triangle abc is an isosceles right triangle. what is the measure of a base angle
Answer:
The measure of the base angle = 45°
Step-by-step explanation:
For better explanation of the solution see the attached figure of the diagram :
Given : An isosceles right triangle ABC
To find : Measure of the base angle
Solution :
Since, The triangle is right angle triangle.
⇒ m∠B = 90°
Also, ΔABC is an isosceles triangle
So, AB = BC
Now, Angles opposite to equal sides are equal
⇒ m∠A = m∠C
Now, Using Angles sum property of a triangle
⇒ m∠A + m∠B + m∠C = 180°
⇒ m∠C + 90° + m∠C = 180°
⇒ 2m∠C = 180° - 90°
⇒ 2m∠C = 90°
⇒ m∠C = 45°
Hence, The measure of the base angle = 45°