Answer:
Step-by-step explanation:
If Martha needs 28 strawberries for every 4 smoothies she makes, then she needs 7 strawberries per smoothie.
Function A is represented by y = 4x – 3. Function B is a linear function that passes through the points shown in the table. x –1 1 3 5 y 0 4 8 12 What is the rate of change of function A? What is the rate of change of function B? Which function has a greater rate of change? Select ... Select ...
Therefore , the solution of the given problem of function comes out to be Since 4 > 2, function A has a greater rate of change than function B.
Describe Function.The mathematics curriculum covers the study of numbers or rather their variations as well as in our environment, buildings, and both actual and imagined locations. A function presents a graph representation of the relationship between input and output quantities. A function, expression simply, is a collection of sources that, when combined, result in particular outputs by each input. There is a locale, territory, or range assigned to each job.
Here,
The rate of change of a linear function is the slope of the line.
Function A is y = 4x - 3, so the rate of change (slope) is 4.
To find the rate of change of function B, we can calculate the slope of the line passing through the points given in the table. Using the two points (1,4) and (5,12), we get:
slope = (change in y) / (change in x) = (12-4) / (5-1) = 2
So the rate of change of function B is 2.
Since 4 > 2, function A has a greater rate of change than function B.
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In a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse.
If a = 5.7 meters and c = 9.6 meters, what is b? If necessary, round to the nearest tenth.
Solving the provided question, we can say by Pythagorean theorem b = [tex]\sqrt{a^2 + b^2}[/tex] = [tex]\sqrt{32.49 + 92.16}[/tex] = 11.231meters
what is Pythagorean theorem?The Pythagorean Theorem, sometimes known as the Pythagorean Theorem, is the basic Euclidean geometry relationship between a right triangle's three sides. According to this rule, the area of a square with the hypotenuse side equals the sum of the areas of squares with the other two sides. The Pythagorean Theorem, often known as the generic algebraic notation a2 + b2 = c2, states that the square that crosses the hypotenuse of a right triangle opposite the right angle equals the sum of the squares that span the sides of a right triangle.
By Pythagorean theorem
a = 5.7 meters and c = 9.6
b = [tex]\sqrt{a^2 + b^2}[/tex]
b = [tex]\sqrt{32.49 + 92.16}[/tex]
b = [tex]\sqrt{124.65}[/tex]
b = 11.231meters
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A scientist evaluated the local deer population. The scientist found that there were 110 juveniles and 90 adults in the local population. What percentage of the deer were juveniles?
Answer:
55%
Step-by-step explanation:
To find the percentage of juveniles in the local deer population, we need to calculate the proportion of juveniles in the total population and convert it to a percentage.
First, find the total number of deer in the population by adding the number of juveniles and adults:
110 juveniles + 90 adults = 200 deer
Next, divide the number of juveniles by the total number of deer and multiply by 100 to convert to a percentage:
110 juveniles / 200 deer * 100 = 55%
Therefore, 55% of the local deer population were juveniles.
Two houses are 1.5 inches apart on a map. The actual distance between the houses is 10.8 miles. What is the scale of the map?
Answer:
I inch = 7.2 miles
Step-by-step explanation:
Proportion method is applied:
1.5 inches on a map = 10.8 miles of actual distance
∴ 1 inches on the map = x miles of the actual distance
Cross-multiplication is applied:
(1.5 inches)(x miles) = (1 inch)(10.8 miles)
x needs to be isolated and made the subject of the equation:
x miles = [tex]\frac{(1 inch)(10.8 miles)}{1,5 inches}[/tex]
Inches in the numerator and denominator will cancel eachother out:
x miles = [tex]\frac{10.8 miles}{1.5}[/tex]
x miles = 7.2 miles
∴ Scale on the map:
1 inch = 7.2 miles
6.6 Midpoints and Bisectors
(6.6.4 Apply the concept of midpoint to solve real-life problems)
55. SCAVENGER HUNT Pablo is going to ask Bianca to prom by sending her on a scavenger hunt. At the end of the scavenger hunt, Pablo will be standing halfway between the gazebo and the ice cream shop in town. Where should Pablo stand?
The midpoint is given by the coordinates M ( 6 , 7.5 )
What is the midpoint of two points?The midpoint of a line segment is a point that lies halfway between 2 points. The midpoint is the same distance from each endpoint.
Measure the distance between the two end points, and divide by 2.
Let A ( x₁ , y₁ ) be the first point
Let B ( x₂ , y₂ ) be the second point
The midpoint between A and B is M ( a , b ) where
a = ( x₁ + x₂ )/2
b = ( y₁ + y₂ ) / 2
Given data ,
Let the midpoint of gazebo and the ice cream shop in town be M ( a , b )
Now , the equation will be
The coordinates of the point Gazebo = G ( 10 , 12 )
The coordinates of the point Ice Cream = C ( 2 , 3 )
Now , midpoint between A and B is M ( a , b ) where
a = ( x₁ + x₂ )/2
b = ( y₁ + y₂ ) / 2
Substituting the values in the equation , we get
a = ( 10 + 2 ) / 2
a = 12 / 2
a = 6
b = ( 12 + 3 ) / 2
b = 15 / 2
b = 7.5
So , the coordinates of the midpoint is M ( 6 , 7.5 )
Hence , the midpoint is M ( 6 , 7.5 )
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a negative x a negative =
A teacher randomly chooses a two-person leadership team from a group of four qualified students. Three of the students, Sandra, Marta, and Jane, are girls. The fourth student, Franklin, is a boy.
Using the sample space of possible outcomes listed below, where each student is represented by the first letter of his or her name, answer each of the following questions.
What is P(A)P, left parenthesis, A, right parenthesis, the probability that the first student is a boy?
Answer: The sample space of possible outcomes is:
{SM, SJ, MJ, MS, JS, JM}.
There are 6 possible outcomes in the sample space, and 1 of these outcomes results in the first student being a boy (Franklin, represented by "F").
Therefore, the probability of the first student being a boy is P(A) = 1/6.
Step-by-step explanation:
kate works 8 hours a day at minimum wage Monday through Friday. Find her gross pay for one week
Before any taxes, deductions, and other adjustments, she earns $98.40 per week.
What is gross pay?Gross pay refers to the total amount of money an employee earns before any deductions or taxes are taken out. It is the total amount of money earned by an employee for the hours worked, including any overtime or bonuses.
here, we have,
To calculate Talia's gross pay for a week, we need to know how many hours she works per day and her pay rate.
You've provided that information:
Talia works 6 hours per day on Fridays and Saturdays each week.
Her pay rate is $8.20 per hour.
First, we need to find out how many hours she works a week. As she works 6 hours on Friday and 6 hours on Saturday, the total hours she works in a week is 6 hours/day x 2 days/week = 12 hours/week.
Next, we need to multiply her hourly rate by the number of hours she works per week to find her gross pay. Her pay rate is $8.20/hour and she works 12 hours/week, so her gross pay is:
$8.20/hour x 12 hours/week = $98.40/week
So, Talia's gross pay for a week is $98.40.
Therefore, before any taxes, deductions, and other adjustments, she earns $98.40 per week.
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Suppose that Y1 and Y2 are independent, standard normal random variables. Find the density function of U = Y1^2 +Y2^2.
The cumulative distribution function (CDF) of U is also well known and is given by:
F(u) = 1 - [tex]e^{(-u/2)}[/tex] × γ(1/2, u/2)
where γ is the lower incomplete gamma function.
What is the chi-squared distribution?
The chi-squared distribution is a continuous probability distribution that is widely used in statistics and other fields.
The random variable U = Y1^2 + Y2^2 has a well-known distribution called the chi-squared distribution with two degrees of freedom. The density function of U is given by:
[tex]f(u) = (1 / (2 \times \pi)) \times e^{(-u/2)} \times (u/2)^{(1/2 - 1)}[/tex]
where e is the base of the natural logarithm and π is the mathematical constant pi. This distribution has a positive support on the interval [0, +∞).
The cumulative distribution function (CDF) of U is also well known and is given by:
F(u) = 1 - [tex]e^{(-u/2)}[/tex] × γ(1/2, u/2)
where γ is the lower incomplete gamma function.
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Solve, for 0 ≤ x < 360°, the equation
5 sinx - 5 cosx = 2
In response to the query, x is equal to 60°, 120°, 240°, and 300°. These four options are the answer to the equation.
What does equation mean in its entirety?A mathematical equation is a statement that two amount or values are equal, such as 6 x 4 = 12 x 2. 2. A noun that counts. An equation is applied when several or more factors must be considered jointly in order to understand or explain the whole situation.
This equation can be solved using the trigonometric identity:
[tex]sinx = \sqrt{ (1 - cos^2x)}[/tex]
This identity can be used as a substitution in the equation:
5 sinx - 5 cosx = 2
5 [tex]\sqrt{(1 - cos^2x) }[/tex] - 5 cosx = 2
5 sqrt[tex](1 - cos^2x)[/tex]) = 7 + 5 cosx
Squaring both sides:
25([tex]1 - cos^2x[/tex]) = 49 + 70 cosx + 25 [tex]cos^2x[/tex]
25 - 25 [tex]cos^2x[/tex] = 49 + 70 cosx + 25 [tex]cos^2x[/tex]
0 = 74 + 45 cosx
45 cosx = -74
cosx = -74/45 = -2/3
The inverted cosine function can be used to determine that x = cos-1(-2/3). x must be within the range of 0° to 360°, hence x must be 300°.
5 sin - 5 cos - 5(-1/2) = 5 sqrt(3)/2 + 5/2 = 2 + 2.5 = 2.5
Since the left side of the equation is not equal to 2, x = 300° is not a solution to the equation.
We can repeat this process for the other solutions to the equation:
x = 60°, x = 120°, x = 240°, and x = 300°
These are the four solutions to the equation for 0° <= x < 360°.
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Jessie is baking a cake and uses 1/2 of the 4
pound bag of flour. How many pounds of
flour did Jessie use to bake her cake?
Answer: 2 pounds of flour
Step-by-step explanation:
1/2 of four is two,
4 * 1/2 = 2
Answer:
Jessie used 1/2 of the 4-pound bag of flour, so she used 1/2 * 4 pounds = 2 pounds of flour to bake her cake.
All things algebra unit 5 homework 10 systems of inequalities
Note that a system of two linear inequalities in two variables is made up of at least two inequalities in the same variables.
What are systems of inequalities used for?Consider the following scenarios: highway speed restrictions, minimum credit card payments, the quantity of text messages you may send each month from your cell phone, and the time it will take to commute from home to school.
All of these may be expressed mathematically as inequalities. A linear inequality's solution is the ordered pair that is a resolution to all inequalities in the system, and the graph of the linear inequality is the graph of all system solutions.
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what is the geometric progression of; 1+3+6+9+12...
Answer:
Addition with the number 3.
Next numbers will be 15, 18, 21,...
Use the general slicing mothod to find the volume of the following solid. The solid with a semicircular base of radius 16 whose cross section is perpendicular to the base and parallel to the diameter are squares. Place the semicircle on the xy-plane so that its diameter is on the x-axis and it is centered on the y-axis. Set up the integral that gives the volume of the solid. Use increasing limits of integration.
[tex]V= [0,16] \int\limits {4y^2 \sqrt{(256 - y^2)} } \, dy[/tex] would be the integral that gives the volume of the solid.
What is Disk method of integration?
Disc integration is a method for estimating the volume of a solid of revolution of a solid-state material when integrating along an axis "parallel" to the axis of revolution in integral calculus.
The volume of the solid can be found using the disk method of integration. In this method, we consider thin slices of the solid perpendicular to the x-axis, each of which is a disk with a square cross-section.
The volume of each slice is equal to the product of the area of its cross-section and its thickness, which is equal to the difference in x-coordinates between the top and bottom of the slice.
Let's call the top-right corner of the square cross-section (x, y, z). We k[tex]x^2 + y^2 = 256[/tex]
And we also know that the side length of the square is equal to 2y. So, the area of the cross-section is equal to [tex](2y)^2 = 4y^2.[/tex] The volume of the slice is equal to [tex]4y^2 dx.[/tex]
Since the semicircle is centered at the origin, the value of y ranges from 0 to 16.
The value of x ranges from 0 to the square root of [tex]256 - y^2.[/tex]Using these ranges, the volume of the solid can be calculated as follows:
[tex]V=\int\limits {[0,16] 4y^2 \sqrt{(256 - y^2)} } \, dy\\V= [0,16] \int\limits {4y^2 \sqrt{(256 - y^2)} } \, dy[/tex]
This is the integral that gives the volume of the solid.
Therefore, [tex]V= [0,16] \int\limits {4y^2 \sqrt{(256 - y^2)} } \, dy[/tex] would be the integral that gives the volume of the solid.
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An automobile manufacturer can produce up to 300 cars per day. The profit made from the sale of these vehicles can be modelled by the function p(x) = -x²+ 350x-6600 where p(x) is the profit in thousand Rupees and x is the number of automobiles made and sold. Answer the following questions based on this
model:
(i) When no cars are produce what is a profit/loss?
(ii) What is the break even point? (Zero profit point is called break even)?
(iii) What is the profit/loss if 400 cars are produced?
i) The profit/loss when no cars are produced is a loss of 6600 Rupees.
II) The break even point is at 20 cars
III) The profit/loss if 400 cars are produced is; a loss of 13400Rupees.
How to solve Profit functions?(i) When no cars are produced, x = 0.
Thus, plugging this value into the function p(x) = -x² + 350x - 6600, we have;
p(0) = -0² + 350(0) - 6600 = -6600.
Therefore, the profit/loss when no cars are produced is a loss of 6600 thousand Rupees.
(ii) The break-even point is the point at which the profit is zero, i.e., p(x) = 0. Setting p(x) = 0 and solving for x, we find that;
-x² + 350x - 6600 = 0
x = 20
Therefore, the break-even point is x = 20 cars. T
(iii) If 400 cars are produced, the profit can be found by plugging this value into the function p(x) = -x² + 350x - 6600.
We find that p(400) = -400² + 350(400) - 6600
= -160000 + 140000 + 6600 = -13400. Therefore, the profit/loss if 400 cars are produced is a loss of 13400 Rupees.
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I really need help with these questions pls?
Answer:
Top one is 3/8
Middle is 4/7
Bottom is 1/3
Step-by-step explanation:
what are some services offered by the banks and credit unions
Step-by-step explanation:
mortgages, lines of credit, checking and savings accounts, auto loans and the convenience of electronic banking and Automated Teller Machines (ATMs)
Step-by-step explanation:
Banks and credit unions offer a variety of financial services, including:
Checking and savings accounts
Personal loans
Mortgages
Credit cards
Investment products (e.g. mutual funds, individual retirement accounts (IRAs))
Foreign currency exchange
Online and mobile banking
Wire transfers
Automated teller machines (ATMs)
Insurance products (e.g. life, auto, homeowners)
Wealth management services
Small business banking services.
Note that the exact services offered may vary depending on the institution.
Solve the equation for the specified variable.
M = F/a
a=
Answer:
A=F/M
Step-by-step explanation:
m=f/a ......,,, cross product
f= ma......,..., both sides divided by m
then the answer is a=f/m
suppose that x is a discrete random variable that takes integer values from 1 to 100 (both inclusive), and has cumulative distribution function (cdf)
The probability that the discrete random variable x takes a value less than or equal to 50 is 0.50, since F(50) = 50/100 = 0.50.
F(x) = x/100
Then, the probability that x takes a value less than or equal to 50 is 0.50, since
F(50) = 50/100 = 0.50
The cumulative distribution function (CDF) of a random variable is a function that gives the probability that the random variable is less than or equal to a certain value. In this case, the CDF of the random variable x is given by F(x) = x/100.
Therefore, to find the probability that x takes a value less than or equal to 50, we simply need to evaluate the CDF at x = 50. This is done by substituting 50 into the CDF, which gives us F(50) = 50/100 = 0.50. This means that the probability that x takes a value less than or equal to 50 is 0.50.
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Three classes ordered lunch from a restaurant. In one class 5/6 of the children ordered hamburger, In the other class 2/4 ordered hot days. 1/2 of the other class ordered chicken wings. what is the total number of children that ordered Sandwiches ?
The total number of children that ordered Sandwiches is 1 5/6
What is the total number of children that ordered SandwichesFrom the question, we have the following parameters that can be used in our computation:
Class 1 = 5/6 Hamburger
Class 2 = 2/4 Hot days
Class 3 = 1/2 Chicken wings
So, the total number of children that ordered Sandwiches is
Total = 5/6 + 2/4 + 1/2
Evaluate
Total = 1 5/6
Hence, 1 5/6 of the three classes ordered sandwiches
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Let P(x) = 3x³ - 7x² + 3x-4 and Q(x) = 2x³ - 6x² - 15. Add the polynomials functions, as indicated below.
(P+Q)(x)
(P+Q)(x) = (Simplify your answer. Do not factor.)
K
The addition of the polynomial P(x) and Q(x) is 5x³ - 13 x² + 3x - 19.
What is Polynomial?A polynomial is a mathematical equation that solely uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are sometimes known as indeterminates in mathematics.
Given:
P(x) = 3x³ - 7x² + 3x-4 and Q(x) = 2x³ - 6x² - 15.
Now, adding the both Polynomials
P(x) + Q(x)
= 3x³ - 7x² + 3x-4 + 2x³ - 6x² - 15.
Now, solving the like terms
= 3x³ + 2x³ - 7x² - 6x² +3x -4 -15
= (3+ 2) x³ + (-7-6) x² +3x -4 - 15
= 5x³ - 13 x² + 3x - 19
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If the public debt in 2006 was 6,783,231,062,743.62 and the budget for 2007 was in deficit by 595,821,633,586.70 what was the public debt in 2007?
Answer: The public debt in 2007 would be 6,783,231,062,743.62 + 595,821,633,586.70 = 7,379,052,696,330.32
Step-by-step explanation:
Find the equation of the line with slope 14 and y-intercept (0,−1).
Answer:
y = 14x - 1
Step-by-step explanation:
By equation of the line, we mean the slope intercept form equation [tex]y=mx+b[/tex] where m is the slope and b is the y intercept. As a result, we are given the slope and the y intercept in the problem. So we can use this to write our equation
[tex]y=14x-1[/tex]
Hope this helps!
6.9.4 Journal: Similar circles6.9.4 Journal: Similar Circles
Journal
Geometry Sem 1
Points Possible:20
Name:
Date:
Scenario: Prove That All Circles Are Similar
Instructions
View the video found on page 1 of this Journal activity.
Using the information provided in the video, answer the questions below.
Show your work for all calculations.
The Students' Conjectures:The two students have different methods for proving that all circles are similar.
1. Complete the table to summarize each student's conjecture about how to solve the problem. (2 points: 1 point for each row of the chart)
Classmate Conjecture
John
Teresa
Evaluate the Conjectures:
2. Intuitively, does it make sense that all circles are similar? Why or why not? (1 point)
Construct the Circles:
3. Draw two circles with the same center. Label the radius of the smaller circle r1 and the radius of the larger circle r2. Use the diagram you have drawn for questions 3 – 10. (2 points)
4. In your diagram in question 3, draw an isosceles right triangle inscribed inside the smaller circle. Label this triangle ABC. (1 point)
5. What do you know about the hypotenuse of △ABC? (2 points)
6. In your diagram in question 3, extend the hypotenuse of △ABC so that it creates the hypotenuse of a right triangle inscribed in the larger circle. Add point Y to the larger circle so it is equidistant from X and Z. Then complete isosceles triangle XYZ. (1 point)
7. What do you know about the hypotenuse of △XYZ? (2 points)
8. How does △ABC compare with △XYZ? Explain your reasoning. (2 points)
9. Use the fact that △ABC ≈ △XYZ to show that the ratio of the radii is a constant. (2 points)
Making a Decision
10. Who was right, Teresa or John? (1 point)
Further Exploration:
11. What is the circumference of the circle that circumscribes a triangle with side lengths 3, 4, and 5? (4 points)
Transcript: Similar Circles
The video begins with a young woman talking in front of a blank screen.
Audio:
I'm Teresa. My friend John and I need to prove that all circles are similar. It seems obvious, right?! Of course they're similar, they’re all circles!
[Many circles of different sizes and colors pop up onto the screen.]
Um, this is making me a little dizzy.
[The circles disappear.]
But we do need to prove that all circles are mathematically similar.
Here’s the way John looks at it: Remember what we learned about similar triangles?
[Two triangles appear on the screen. One is small and the other is large.]
We can take one triangle, and move it on top of another triangle.
[The small triangle is placed on top of the large triangle.]
Then, we dilate it to show that they are similar. Like that.
[The small triangle is dilated to the size of the large triangle.]
John says we can do the same thing with circles.
[Two circles appear on the screen. One is small and the other is large.]
Take any two circles, and move them so that they have the same center.
[The small circle is moved on top of the large circle.]
Then, you can dilate or contract the circles until they are the same size.
[The small circle is dilated to the size of the large circle.]
Taa-daa! The circles are similar. I have another way to prove it.
[Two triangles appear on the screen. The small triangle has sides of length 2, 2, and 3 and the large triangle has sides of length 6, 6, and 9.]
We also know that triangles are similar if all of their corresponding sides have the same ratio.
[The corresponding sides of the triangle are highlighted. On-screen text: 2 over 6 equals 2 over 6 which equals 3 over 9 which equals 1 over 3 Similar!]
Well, the same idea should also work with circles.
[Two circles appear on the screen. One circle is small and the other circle is large.]
If the corresponding parts of two circles have the same ratio, then the circles must be similar. And lucky for us, everything about a circle can be described with its radius!
[Beneath the small circle is written "equals r sub 1." Inside the large circle is written "equals r sub 2." On-screen text: Diameter equals 2r, Circumference equals 2pi r, and Area equals pi r squared.]
So, if the radii of these circles have a constant ratio, then the circles are similar.
[On-screen text: If r sub 1 over r sub 2 equals k, a constant, then the circles are similar.]
What's more, I think I can prove all this by using inscribed triangles. But I need your help.
[A triangle is inscribed in each of the circles using the diameter of the circles as their bases.]
Can we actually use inscribed right triangles to show that all circles are similar?
Step-by-step explanation:
Classmate Conjecture
John | All circles are similar if they have the same center and can be dilated or contracted to the same size.
Teresa | All circles are similar if their corresponding radii have a constant ratio.
Evaluate the Conjectures:
2. Yes, it makes intuitive sense that all circles are similar because they all have the same shape and form.
Construct the Circles:
3. [Diagram not provided]
[Diagram not provided]
The hypotenuse of △ABC is the diameter of the smaller circle.
[Diagram not provided]
The hypotenuse of △XYZ is the diameter of the larger circle.
The two triangles, △ABC and △XYZ, are similar because they are both isosceles right triangles with the same angle measures.
The ratio of the lengths of their sides are equal, therefore the ratio of their radii is a constant.
Making a Decision:
10. Both John and Teresa were right as all circles are similar if they have the same center and can be dilated or contracted to the same size (John's method) and also if their corresponding radii have a constant ratio (Teresa's method).
Further Exploration:
11. The circumference of the circle that circumscribes a triangle with side lengths 3, 4, and 5 can be found using the Pythagorean theorem to find the diameter of the circle, which is equal to the sum of the lengths of the three sides. The diameter is equal to 5, so the circumference is equal to 2 * pi * (5 / 2) = 5 * pi
Please provide all information when asking a question
Shannon put some money in her savings account. After 6 months, she earned $10.50 in interest. If the interest rate was 7%, how much money did Shannon put in her account?
The amount of money put by Shannon in her account is $300.
What is simple interest?Simple interest is a way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific amount of time.
Contrary to compound interest, where we add the interest of one year's principal to the next year's principal to calculate interest, the principal amount in simple interest remains constant.
Given that Shannon put some money in her savings account. After 6 months, she earned $10.50 in interest. If the interest rate was 7%,
The amount will be calculated as:-
SI = ( P x R x T ) / 100
10.50 = ( P x 7 x 1 ) ( 2 x 100 )
P = ( 10.50 x 2 x 100 ) / ( 7 )
P = $300
Therefore, $300 has been deposited into Shannon's account.
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What is the answer to x in this equation 4x+4=12?
Answer:
x=2
Step-by-step explanation:
4x+4=12
-4 -4
_______
4x=8
_____
4 4
x=2
given the parallelagram below, micheal writes triangle abc
Michael writes, "Triangle ABC is congruent to triangle CDA'',
if the segment AC ≅ AC.
What is congruent?In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.
Given the parallelogram below,
Michael writes, "Triangle ABC is congruent to triangle CDA''.
By the parallelogram property:
AB ≅ CD
BC ≅ AD.
If triangle ABC is congruent to triangle CDA,
then the segment AC ≅ AC.
Therefore, the segment AC ≅ AC.
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circular cake is 12 inches in diameter and 4 inches high. The side and top of the cake are to be covered with icing. To the nearest square inch, what is the area that needs to be iced?
The area needed to be iced is 263.76 inches².
How to find the area of the cake that will be iced?The circular cake is 12 inches in diameter and 4 inches high. The side and top of the cake are to be covered with icing. The area of the cake that will be iced can be found as follows;
The area to to be iced is the top and the lateral area.
Therefore,
area to be iced = πr² + 2πrh
area to be iced = πr(r + 2h)
Therefore,
r = 12 / 2 = 6 inches
h = 4 inches
Hence,
area to be iced = 6π(6 + 2(4))
area to be iced = 6π(14)
area to be iced = 84π
area to be iced = 263.76 inches²
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Which choices if multiplied by √36
would result in an irrational number answer?
Responses
A 3.454545...
B −52
C √9/16
D 2.828427...
E √18
The choices if multiplied by √36 would result in an irrational number are
3.454545... and 2.828427... the correct options are A and D.
What are natural numbers, rational numbers, integers and irrational numbers?
Natural numbers are: 1, 2, 3, ....
Integer numbers are: ...., -2, -1, 0, 1, 2, ... (so it includes positive and negative natural number, and 0 )
Rational numbers are numbers which can be written in the form of \dfrac{a}{b} where a and b are integers. Example: 1/2, 3.5 (which is writable as 7/5) etc.
Irrational numbers are those real numbers which are not rational numbers.
Know that all natural numbers are integers, all integers are rational numbers. That means, natural numbers are not irrational.
Given;
The number is multiplied by √36
√36=6
3.454545*6=20.72727
-5*6=-30
3/4*6=9/2
2.828427*6=16.970562
√18*6= 6√18
Therefore, the irrational numbers will be 3.454545... and 2.828427...
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Which term does not belong?
term
coefficient
constant
slope
Answer:
not sure but slope doesn't belong
Step-by-step explanation: