Answers
Answer:
7.30
Step-by-step explanation:
number 13 is simple subtraction.
Related Questions
Triangle PQR is rotated 180 degrees clockwise about the origin to produce the image Triangle P’Q’R’. Which of the following statements is TRUE abóyate Triangle P’Q’R’.
Answers
Answer:
Step-by-step explanation:
We get triangle PQR by plotting the point P (1, 4), Q (3, 1), R (2, -1) on the graph paper when rotated through 180° about the origin. The new position of the point is: P (1, 4) → P' (-1, -4) Q (3, 1) → Q' (-3, -1) R (2, -1) → R' (-2, 1) Thus, the new position of ∆PQR is ∆P’Q’R’.
There is a 25% chance that a vowel is drawn from a bag of random letter tiles. what is the probability of drawing a vowel, placing it back in the bag, and then drawing a consonant
Answers
The probability of drawing a vowel, placing it back in the bag, and then drawing a consonant is 0.1875 or 18.75%.
Calculating the probability
The probability of drawing a vowel from the bag of random letter tiles is 25%. Since the tile is replaced after drawing, the probability of drawing a vowel on the second draw is also 25%.
The probability of drawing a vowel and then a consonant can be calculated by multiplying the probabilities of each event:
P(vowel and consonant) = P(vowel) x P(consonant)
= 0.25 x 0.75
= 0.1875
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20. The volume of a large crate is 84 yd³. It is 23 yd wide and 4 yd high. What is the length of the crate?
Answers
Volume = length x width x height
We are given that the volume of the crate is 84 yd³, the width is 23 yd, and the height is 4 yd. Substituting these values into the formula, we get:
84 = length x 23 x 4
To solve for the length, we can divide both sides by 23 x 4:
84 ÷ (23 x 4) = length
Simplifying the left side of the equation, we get:
84 ÷ (23 x 4) = 0.913043478
Therefore, the length of the crate is approximately 0.913043478 times the width, or:
Length ≈ 0.913043478 x 23 yd = 21 yd (rounded to the nearest whole number)
Therefore, the length of the crate is approximately 21 yards.
If you horizontally…
Answers
Check the picture below.
so following the template below, a shift 2 units to the left, means C=2
[tex]G(x)=\sqrt{x+2}[/tex]
Hello, I am confused on how to answer this question.
Answers
Answer: x=14
Step-by-step explanation:
cb=10.
ac=14
The value of X will be 14.
This is a simple mathematics problem that can be solved by using ratios.
Given, AC : BC : AB = 7 : 5 : 8
AC = X ; BC = 10 ; AB = X + 2
AC/ BC = X/ 10 = 7/5 (Ratios can also be represented as fractions)
X/10 = 7/5
On Transposing,
5X = 70
X = 70/5
X = 14
Alternatively,
BC/AB = 5/8 = 10/ (X + 2)
5/8 = 10/ (X + 2)
On Transposing,
80 = 5X + 10
5X = 70
X = 14
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If P(A)=0.3, P(B)=0.2 and P(A∩B)=0.2 determine the following probabilities:
(a) P(A')
(b) P(A∪B)
(c) P(A'∩B)
(d) P(A∩B')
(e) P[(A∪B)']
Answers
The probabilities are as follows:
(a) P(A')= 0.7
(b) P(A∪B) = 0.3
(c) P(A'∩B) = 0
(d) P(A∩B') = 0.1
(e) P[(A∪B)'] = 0.7
What is probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.
(a) P(A') = 1 - P(A) = 1 - 0.3 = 0.7
(b) P(A∪B) = P(A) + P(B) - P(A∩B) = 0.3 + 0.2 - 0.2 = 0.3
(c) P(A'∩B) = P(B) - P(A∩B) = 0.2 - 0.2 = 0
(d) P(A∩B') = P(A) - P(A∩B) = 0.3 - 0.2 = 0.1
(e) P[(A∪B)'] = 1 - P(A∪B) = 1 - 0.3 = 0.7
Note: P(A) represents the probability of event A occurring, P(B) represents the probability of event B occurring, and P(A∩B) represents the probability of both events A and B occurring simultaneously. The symbol '∪' represents the union of two events, and the symbol '∩' represents the intersection of two events. The complement of an event A is represented by A'.
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Given the figure below .find X and Y to three significant digits.Write your answer in the answer box provided below
Answers
Check the picture below.
Make sure your calculator is in Degree mode.
[tex]\cos(25^o )=\cfrac{\stackrel{adjacent}{x}}{\underset{hypotenuse}{12}}\implies 12\cos(25^o)=x\implies \boxed{10.876\approx x} \\\\[-0.35em] ~\dotfill\\\\ \sin(25^o )=\cfrac{\stackrel{opposite}{z}}{\underset{hypotenuse}{12}}\implies 12\sin(25^o)=z \\\\[-0.35em] ~\dotfill\\\\ \sin(50^o )=\cfrac{\stackrel{opposite}{z}}{\underset{hypotenuse}{y}}\implies y=\cfrac{z}{\sin(50^o)}\implies y=\cfrac{12\sin(25^o)}{\sin(50^o)}\implies \boxed{y\approx 6.62}[/tex]
Which is NOT the same as asking:
What is the logarithm of 1,296 if the base is 6?
Answers
Reason: log=exponent, so whenever you see a log, that means you’re solving for an exponent.
Matt can save $225 per month that he puts into a savings
account earning 5% annual interest. How much will he have
saved after 2 years?
Answers
Answer:
FV ≈ $5,673.56
Step-by-step explanation:
To calculate the total amount that Matt will have saved after 2 years of saving $225 per month at an annual interest rate of 5%, we can use the formula for the future value of an annuity:
FV = P * (((1 + r/12)^(n*12) - 1) / (r/12))
where:
FV is the future value of the annuity
P is the periodic payment (in this case, $225 per month)
r is the interest rate per year (in this case, 5%)
n is the number of years (in this case, 2)
Substituting the given values, we get:
FV = $225 * (((1 + 0.05/12)^(2*12) - 1) / (0.05/12))
Using a calculator, we get:
FV ≈ $5,673.56
Therefore, after 2 years of saving $225 per month at an annual interest rate of 5%, Matt will have saved approximately $5,673.56.
how can you tell if a quotient is less than 1'.
Answers
Answer:
Step-by-step explanation:
Okay so when a smaller number is divided by a larger number, the quotient is less than 1. Hope this helps Bye sisters slay.
^4√p7
in exponential form.
Answers
Answer:1111
Step-by-step explanation:
. (Adapted from Terence Blows, Northern Arizona University.) Classify as in Exercise 6 but for the following circumstances. a. The amount of caffeine in the bloodstream decreases by 50% every 5 hours or so after stopping drinking coffee. b. The amount of trash in a landfill increases by 350 tons per week. c. The amount of alcohol in the bloodstream decreases by 10 grams (the amount in a standard drink) per hour after stopping drinking. d. Your age increases every day.
Answers
The statements are classified as Exponential decay and Linear growth.
What are the classification of the statements?
a. Exponential decay: The amount of caffeine in the bloodstream decreases by 50% every 5 hours, which indicates an exponential decay process where the quantity decreases at a constant percentage rate over time.
b. Linear growth: The amount of trash in a landfill increases by 350 tons per week, which indicates a linear growth process where the quantity increases by a constant amount over time.
c. Exponential decay: The amount of alcohol in the bloodstream decreases by 10 grams (the amount in a standard drink) per hour after stopping drinking, which indicates an exponential decay process where the quantity decreases at a constant percentage rate over time.
d. Linear growth: Your age increases every day, which indicates a linear growth process where the quantity (age) increases by a constant amount (1 day) over time.
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It costs $350 to spend 4 nights at the Econo Motel. It costs $475 to spend 6 nights at the Bluebird Inn. Which of these statements is true?
Answers
Answer: A
Step-by-step explanation: The bluebird Inn is more expensive per night because 475 is greater than 350.
Spring Basketball Tournament Expenses and Income Guidelines:
1. A permit for the event is required and costs $75.60. It takes 8 hours to run a tournament for 8 teams.
2. Each player will be charged a $32 entry fee.
3. There will be exactly 8 players on each team.
4. The rent for a gym in a high school is $62.50 an hour.
5. A caretaker must be present for a Saturday permit and earns $56 an hour.
Will your Spring Basketball Tournament fundraiser make money? What adjustments might you make to this tournament to ensure that it is more profitable? Show your work and explain your thinking below.
Answers
Expenses:
- Permit: $75.60
- Gym rental for 8 hours: $62.50/hour x 8 hours = $500
- Caretaker for 8 hours on a Saturday: $56/hour x 8 hours = $448
Total expenses: $1,023.60
Income:
- Entry fee per player: $32 x 8 players = $256 per team
- Total income for 8 teams: $256 x 8 teams = $2,048
Total income: $2,048
Profit (income minus expenses): $2,048 - $1,023.60 = $1,024.40
Based on these calculations, the Spring Basketball Tournament is projected to make a profit of $1,024.40.
To ensure that the tournament is more profitable, some adjustments that can be made include:
- Increase the entry fee per player or per team
- Invite more teams to participate
- Consider alternative and potentially cheaper locations for the tournament
- Explore sponsorship opportunities to potentially offset costs
- Encourage participants to bring their own food and drinks instead of providing it at the tournament
Overall, it is important to closely analyze expenses and income to determine the profitability of any fundraising event and make necessary adjustments to ensure success.
1. All numbered streets runs parallel to each other. Both 3rd and 4th Streets are intersected by King Ave. as shown:
(a) Suppose a car is traveling east on 4th Street and turns onto King Avenue heading northeast. What is the measure of the angle created by the car's turning? Explain your answer.
(b) Suppose a car is traveling southwest on King Avenue and turns left onto 3rd Street. What is the measure of the angle created by the car's turning? Explain your answer.
(c) Suppose a car is traveling northeast on King Avenue and turns right onto 3rd Street. What is the measure of the angle created by the car's turning? Explain your answer.
Answers
When the car travels east on 4th Street and turns onto King Avenue heading northeast, the angle created by the car's turning is a 45-degree angle.
When the car travels southwest on King Avenue and turns left onto 3rd Street, the angle created by the car's turning is a 135-degree angle.
When the car travels northeast on King Avenue and turns right onto 3rd Street, the angle created by the car's turning is a 45-degree angle.
How to get the Angle?(a) When the car travels east on 4th Street and turns onto King Avenue heading northeast, the angle created by the car's turning is a 45-degree angle. This is because the intersection of 4th Street and King Avenue creates a right angle, and the car turns northeast, creating another 45-degree angle with the horizontal 4th Street.
(b) When the car travels southwest on King Avenue and turns left onto 3rd Street, the angle created by the car's turning is a 135-degree angle. This is because the intersection of King Avenue and 3rd Street creates a right angle, and the car turns left, creating an additional 90-degree angle. Therefore, the total angle is 90 degrees + 45 degrees = 135 degrees.
(c) When the car travels northeast on King Avenue and turns right onto 3rd Street, the angle created by the car's turning is a 45-degree angle. This is because the intersection of King Avenue and 3rd Street creates a right angle, and the car turns right, creating another 45-degree angle with the horizontal 3rd Street.
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This pattern follows the rule add 2. What is another feature of this pattern? (4 points) An image of a pattern. Term one has one dot, term two has three dots, term three has five dots, term four has seven dots. a The terms appear even, odd, even, odd. b All the terms are even. c Two terms are even, then two terms are odd. d All the terms are odd.
Answers
The correct answer is c: Two terms are even, then two terms are odd. This pattern follows the rule of adding 2, so each successive term is an even number followed by an odd number.
Number is a mathematical object used to count, measure and represent a quantity. It is used to symbolize a numerical quantity or value, and is used in various ways in mathematics, science, engineering, finance and other fields. Numbers are also used to represent relationships between objects, such as the number of sides in a triangle or the number of students in a classroom.
This alternating pattern of even and odd terms is a feature of the pattern, with two terms being even followed by two terms being odd. This pattern continues as the terms increase, with the even terms adding 2 and the odd terms adding 2 as well. This pattern is a good way to remember a sequence of numbers and can be used to help understand patterns in mathematics.
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In ΔHIJ, h = 33 cm, i = 61 cm and j=39 cm. Find the area of ΔHIJ to the nearest square centimeter.
Answers
Thus, the area of ΔHIJ using the Heron's formula is found as 580.47 square centimeter.
Explain about the Heron's formula:Heron of Alexandria (c. 62 ce) is credited with developing the Heron's formula, which determines the area of a triangle in regards of the lengths of its sides. If the side lengths are represented by the symbols a, b, and c: √s(s - a)(s - b)(s - c)
where s = half the perimeter,
s = (a + b + c)/2.
given data:
In ΔHIJ,
h = 33 cm, i = 61 cm and j =39 cm.semi -perimeter s = (i + j + h) / 2
s = (33 + 61 + 39) / 2
s = 66.5
Now,
s - h = 66.5 - 33 = 33.5
s - i = 66.5 - 61 = 5.5
s - j = 66.5 - 39 = 27.5
area of ΔHIJ = √s(s - h)(s - i)(s - j)
area of ΔHIJ = √66.5*33.5*5.5*27.5
area of ΔHIJ = √336947.1875
area of ΔHIJ = 580.47
Thus, the area of ΔHIJ using the Heron's formula is found as 580.47 square centimeter.
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i have 60 square feet of paper to wrap a box in the shape of a right rectangular prism the height of the box is 1 2/3 feet the width is 4 feet and the length is 5 1/2 feet what percent of the box will remain unwrapped if i use all the paper i has available
Answers
The percent of the box that will remain unwrapped by the 60 square feet of paper is about 20.70%
What is a percentage?A percentage is a proportion of a number expressed as fraction of a 100
The dimensions in mixed fractions can be expressed as follows;
Height of the box = 1 2/3 feet = 5/3 feet
Width of the box = 4 feet
Length of the box = 5 1/2 feet = 11/2 feet
Surface area of the box, A = 2 × (5/3) × 4 + 2 × 4 × 11/2 + 2 × (5/3) × 11/2 = 227/3 = 75 2/3 square inches
The percent of the box that will remain unwrapped is therefore;
Percentage = 60/(227/3) × 100 ≈ 79.3%
The percentage of the box that will remain unwrapped is about (100 - 79.3)% = 20.70%
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3. How many ways can you line up 7 books on a shelf?
Answers
Answer:
There are 5040 different ways to arrange the 7 books on a shelf.------------------------------
Use the formula for permutations:
n! = n × (n - 1) × (n - 2) × ... × 1, where n is the number of objects and ! denotes a factorial.The number of objects is n = 7 books.
Calculate the factorial:
7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5040Brenda is fishing from a small boat. Her fishing hook is 12 feet below her, and a fish is swimming at the same depth as the hook, 16 feet away. How far away is Brenda from the fish?
Answers
Answer:
We can use the Pythagorean theorem to solve this problem. Let's call the distance Brenda is away from the fish "x". Then, we have a right triangle with legs of length 12 and x, and a hypotenuse of length 16. So:
x^2 + 12^2 = 16^2
Simplifying:
x^2 + 144 = 256
x^2 = 112
Taking the square root of both sides:
x ≈ 10.6 feet
Therefore, Brenda is approximately 10.6 feet away from the fish.
coordinate plane with points at A 0 comma 2 and B 2 comma 0 intersected by line f Dilate line f by a scale factor of one half with the center of dilation at the origin to create line f′. Where are points A′ and B′ located after dilation, and how are lines f and f′ related? The locations of A′ and B′ are A′ (0, 2) and B′ (0, 0); lines f and f′ intersect at point A. The locations of A′ and B′ are A′ (0, 1) and B′ (1, 0); lines f and f′ are parallel. The locations of A′ and B′ are A′ (0, 0) and B′ (2, 0); lines f and f′ intersect at point B. The locations of A′ and B′ are A′ (0, 2) and B′ (2, 0); lines f and f′ are the same line.
Answers
The answer of the given question based on the graph is , The locations of A′ and B′ are A′ (0, 1) and B′ (1, 0); lines f and f′ are parallel.
What is Scale factor?A scale factor is a number that scales, or multiplies, a quantity by some factor. It is used in mathematics to describe the relationship between corresponding measurements of two similar figures, such as triangles or rectangles.
To dilate line f by scale factor of one half with center of dilation at origin, we multiply coordinates of each point on line f by 1/2.
The equation of line f can be found by using the points A and B:
slope of line f = (0 - 2)/(2 - 0) = -1
y-intercept of line f = 2
Therefore, the equation of line f is y = -x + 2.
To find the coordinates of A' and B' after dilation, we can apply the dilation factor to each point:
A' = (0, 2)*1/2 =(0, 1)
B' = (2, 0)*1/2 =(1, 0)
So A' is located at (0, 1) and B' is located at (1, 0) after dilation.
Now let's analyze the relationship between lines f and f'. The dilation was centered at the origin, so the origin is a fixed point of the dilation. This means that the point where lines f and f' intersect must be the origin.
If we plug in x = 0 into the equation of line f, we get y = 2. This means that point A is located at (0, 2) and intersects with line f at y = 2. After dilation, point A' is located at (0, 1), which means that lines f and f' intersect at point A.
To determine the relationship between lines f and f', we can compare their equations. The equation of f' can be found by using the points A' and B':
slope of f' = (0 - 1)/(1 - 0) = -1
y-intercept of f' = 0
Therefore, the equation of f' is y = -x.
Comparing the equations of f and f', we can see that they have the same slope of -1, which means they are parallel. Therefore, the correct answer is: The locations of A′ and B′ are A′ (0, 1) and B′ (1, 0); lines f and f′ are parallel.
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A student attempted to solve the system 5x + 2y = 10 and 10x + 2y = 1 by graphing. The graph and the conclusion are
below. What can you say about the student's work?
y
-10x + 2y = 1
5x + 2y = 10
The soluion is ().
O The solution is incorrect because the student did not correctly identify the intersection.
O The solution is correct and the lines are graphed correctly.
O The solution is correct, but the lines were graphed incorrectly.
O The solution is incorrect because the lines are not graphed correctly.
Answers
Answer:
Option A: The solution is incorrect because the student did not correctly identify the intersection.
Step-by-step explanation:
Solve by elimination method.
5x + 2y = 10; -10x + 2y = 1
Multiply the second equation by -1, then add the equations together.
(5x + 2y = 10)
-1 (-10x + 2y = 1)
Forms:
5x + 2y = 10
10x - 2y = -1
Add these equations to eliminate y.
15x = 9
Then solve 15x = 9 for x:
15x = 9
15/15 = 9/15 (Divide both sides by 15)
x = 3/5
Now that we've found x let's plug it back in to solve for y.
Write down the original equation:
5x + 2y = 10
Substitute 3/5 for x in:
5x + 2y = 10:
5(3/4)+2y=10
2y+3=10
2y+3-3=10+-3
2y=7
2y/2 = 7/2
y = 7/2
x = 3/5 and y = 7/2.
Comparing the identified answers to the one found by the students, it can be concluded that Option A: The solution is incorrect because the student did not correctly identify the intersection.
Question 1 of 10 What is the area, measured in square centimeters, of the green shape pictured below? Do not include units in your answer. Icm 1cm Answer here
Answers
21 is the area, measured in square centimeters, of the green shape pictured below.
What is square?
Square, in geometry, a plane figure with four equal sides and four right (90°) angles. A square is a special kind of rectangle (an equilateral one) and a special kind of parallelogram (an equilateral and equiangular one).
the area of a parallelogram, we can split this shape up into a rectangle and two right triangles.
The rectangle:
The rectangle has dimensions of 4 by 3 centimeters therefore the area would be 4*3=12 cm squared
two right triangles:
The area of a triangle is 1/2 base * height, but since there are two triangles it would just be the base times the height. The base is 3 cm and the height is 3 so 3*3=9
Next, we add the two areas together: 12+9 = 21
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Find the area of a shaded region
Answers
Answer:
40 cm²
Step-by-step explanation:
you have to multiply the top of the triangle by the base(40) which is 80 then you divide by two since it's a triangle then you get 40 again since your finding the area you have to put the 2 above the cm
The table below shows the numbers of two to five bedroom houses in the Belmont Neighborhood. What is the mean number of bedrooms in a house in this neighborhood?
Number of bedrooms Frequency
2 7
3 35
4 56
5 27
Answers
The mean number of bedrooms in a house in this neighborhood will be: 3.824.
How to determine the mean number of bedroomsIn order to find the mean number of bedrooms in a house in the Belmont Neighborhood, we need to calculate the weighted mean by multiplying each number of bedrooms by their respective frequency.
Next, we will add the products, and then divide by the total frequency. So we can start as follows:
(2 * 7) + (3 * 35) + (4 * 56) + (5 * 27) = 14 + 105 + 224 + 135 = 478
Total frequency = 7 + 35 + 56 + 27 = 125
Therefore, the mean number of bedrooms = 478 / 125 approximately 3.824
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4. This number line
number of minutes Diane read
week for 3 weeks.
0
200
100
300
How many minutes did she read after
the first week?
minutes
After the second week?
After the third week?
minutes
minutes
How many minutes did she read each
week? Explain how you know.
5. Diane reads the same number of minutes
each week. How many minutes does
she read after 4 weeks? After 5 weeks?
Skip count on the number line above to
find the answers.
After 4 weeks:
After 5 weeks:
minutes
minutes
Answers
4) Dane read an average of 400 minutes per week. 5) Diane will have read 2000 minutes after 5 weeks.
How to determine how many minutes did she read each week4) The number "0200100300" represents the number of minutes Diane read each week for 3 weeks. To find out how many minutes she read after the first week, we simply look at the first digit, which is "0." This means that Diane did not read any minutes during the first week.
To find out how many minutes she read after the second week, we add the digits in the first two positions, which are "02." This gives us a total of 2 x 60 = 120 minutes.
To find out how many minutes she read after the third week, we add the digits in the first three positions, which are "020." This gives us a total of 20 x 60 = 1200 minutes.
To find out how many minutes she read each week, we simply divide the total number of minutes by the number of weeks, which is 3. So Diane read a total of 1200 minutes in 3 weeks, which means she read an average of 400 minutes per week.
5) If Diane reads the same number of minutes each week, then she will read that same number of minutes after 4 weeks and after 5 weeks. To find out how many minutes she reads after 4 weeks, we can skip count by the same number repeatedly: 400, 800, 1200, 1600. So Diane will have read 1600 minutes after 4 weeks.
Similarly, to find out how many minutes she reads after 5 weeks, we can skip count again by the same number repeatedly: 400, 800, 1200, 1600, 2000. So Diane will have read 2000 minutes after 5 weeks.
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Chef Lori uses 1 1/4 cup of milk for every 3/4 cup of broth in her soup recipe. This recipe will feed 4 people. Lori is making soup for a banquet that will feed 120 people. How many gallons of milk and broth combined does she need.
Answers
Answer: To make soup for 4 people, Lori needs 1 1/4 cups of milk for every 3/4 cup of broth. Therefore, the ratio of milk to broth is:
(1 1/4 cups milk) / (3/4 cup broth) = (5/4 cups milk) / (3/4 cups broth) = (5/3) cups milk per cup of broth
To make soup for 120 people, Lori needs to multiply the ratio by 30 (120/4) to get the total amount of milk and broth needed:
(5/3 cups milk per cup of broth) * 30 = 50 cups of milk per 30 cups of broth
To convert cups to gallons, we divide by 16 (since there are 16 cups in a gallon):
50/16 = 3.125 gallons of milk
30/16 = 1.875 gallons of broth
Therefore, Lori needs a total of 3.125 + 1.875 = 5 gallons of milk and broth combined.
Step-by-step explanation:
Can someone help me with this problem, and explain how to solve it?
Answers
Thus, the height of flagpole from the ground is found as 23.34 feet.
Explain about the angle of elevation:The measurement of the angle between a person's eyes' line of sight to anything above and the horizontal line is known as the angle of elevation.
The movement of the observer's eyes determines the elevation angle. The angle of elevation is the angle formed by the line of sight and the horizontal line when a viewer is looking up at an object.
Given data:
height of boy = 5 ftDistance of boy from flagpole = 30 ft angle of elevation = 35 degreesLet the height of pole above the boy be 'h'feet.Using the trigonometric ratios in the right triangle ABE.
tan 35 = h / 30
h = 30* tan(35)
h = 18.34
Height of flagpole = 18.34 + 5 = 23.34 feet
Thus, the height of the flagpole from the ground is found as 23.34 feet.
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FIND THR CIRCUMFERENCE OF A CD THAT HAS A RADIUS OF 6 CENTIMETERS
___cm
Answers
Answer:
Hm
Step-by-step explanation:
The formula to find the circumference of a circle is:
Circumference = 2πr
Where "r" is the radius of the circle, and "π" (pi) is a mathematical constant approximately equal to 3.14.
Substituting the given value of radius, we get:
Circumference = 2 x π x 6
Circumference = 12π
Circumference ≈ 37.7 cm (rounded to one decimal place)
Therefore, the circumference of a CD that has a radius of 6 centimeters is approximately 37.7 cm.
Landon and Maria are meeting at the library to work on their history project. Maria walks 9 blocks east and 3 blocks north to get to the library from her house. Landon walks 5 blocks south and 7 blocks west to get to the library from his house. The map below shows the location of the library and Landon's and Maria's houses. To the nearest block, how far is Landon's house from Maria's house if Maria could walk in a straight line?
Answers
To the nearest block, Landon's house is at distance of 12 blocks away from Maria's house if Maria could walk in a straight line.
What is Pythagoras theorem?A basic mathematical theorem relating to the sides of a right-angled triangle is known as Pythagoras' theorem. The square of the length of the hypotenuse, the side that faces the right angle, is said to be equal to the sum of the squares of the lengths of the other two sides, known as the legs, in a right triangle.
This can be written in mathematical notation as:
c² = a² + b²
where c is the length of the hypotenuse, and a and b are the lengths of the legs of the right triangle.
In this case, we can consider the straight line between Maria's house and Landon's house as the hypotenuse of a right triangle, with the distances they walked as the other two sides. We can use the distance formula to find the lengths of those sides:
Distance walked by Maria = √(9² + 3²) = √90 ≈ 9.49 blocks
Distance walked by Landon = √(5² + 7²) = √74 ≈ 8.60 blocks
Now we can use the Pythagorean theorem to find the distance between their houses:
Distance between houses = √(9.49² + 8.60²) ≈ 12.46 blocks
To know more about Pythagoras' theorem, visit:
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