You are working for the company Trinity Mathematical Concepts are
asked for create the following logo for the company. If each vertices of the triangle are the centers of the circles, what is the area of the shaded region?
Your answer will be in terms of "x", where "x" is the radius of the circles.
Answers
Answer:
[tex](2\pi -3\sqrt{3})x^2/4[/tex]Step-by-step explanation:
The sides of the triangle in the middle are equal to x so tis is equilateral triangle.
Its interior angle is 60°.
Each shaded part is the area of 60° segment of circle with the radius x.
The area of each segment is the difference between 60° sector and the area of triangle.
[tex]A_{segment}=A_{sector}-A_{triangle}[/tex]Area of sector
[tex]A_{sector} = (60/360)*\pi r^2=(1/6)\pi x^2[/tex]Area of triangle
[tex]A_{triangle}=(\sqrt{3}/4)a^2= (\sqrt{3}/4)x^2[/tex]The shaded area is
[tex]A = 3((1/6)\pi x^2 - (\sqrt{3} /4)x^2)=((1/2)\pi -3\sqrt{3} /4)x^2=(2\pi -3\sqrt{3})x^2/4[/tex]Related Questions
The expression (2x - 1) (x + 3) - (x + 1) (2x - 3) simplify
Answers
[tex](2x - 1) (x + 3) - (x + 1) (2x - 3) \\\\=(2x^2+6x -x -3)-(2x^2-3x +2x -3)\\\\=(2x^2 +5x -3)-(2x^2-x -3)\\\\=2x^2+5x -3 -2x^2+x+3\\\\=6x[/tex]
An auditorium has rows of seats with a seats in each row Kayla
knows there are at least 70 seats but fewer than 156 seats in the
auditorium. How many rows of seats can there be in the auditorium
Use Exercises 1-a to answer the question
1. Explain how you would find the least possible number of rowe
in the auditorium
2. How would you find all the possible numbers of rows, without
having to check if & is a factor of every number between
70 and 1507
3. Name all the possible numbers of rows in the auditorium,
Answers
Step-by-step explanation:
Note: there is a typo, 'a' should be '8'The number of seats in each row is 8 and the total number of seats is between 70 and 150.
Let x be the number of rows, then we have the inequality:
70 ≤ 8x < 156Divide all sides by 8 to get:
70/8 ≤ x < 156/89 ≤ x ≤ 19 (taking closest integers)So the number of rows is between 9 and 19 both inclusive.
All possible number of rows
9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19Answer:
1. 9 rows
2. see below
3. 9, 10, 11, 12, 13, 14, 15, 16, 17, 18
Step-by-step explanation:
Please note that I believe there are typing errors in the question and that the given information should be:
8 seats in each rowAt least 70 seatsLess than 150 seatsQuestion 1
To determine the least possible number of rows in the auditorium, divide the least number of seats by the number of seats in a row:
⇒ 70 ÷ 8 = 8.75
As the answer is a decimal, round it up to the nearest whole number.
Therefore, the least possible number of rows in the auditorium is 9 rows.
Question 2
Find the greatest number of rows by dividing the greatest number of seats by the number of seats in a row:
⇒ 150 ÷ 8 = 18.75
As there should be fewer than 150 seats we cannot round the number up (as this would make there be more than 150 seats), so instead must round it down to 18.
Therefore, the greatest number of rows in the auditorium is 18 rows.
Question 3
As we have found the least number of rows in question 1 and the greatest number of rows in question 2, all we need to do is list all the numbers between (and including) these numbers.
Therefore, all the possible numbers of rows in the auditorium are:
9, 10, 11, 12, 13, 14, 15, 16, 17, 18
In this unit, you’re working with a variety of methods for solving quadratic equations. Which method do you prefer over the others? Describe the method in your own words, and give an example of a quadratic equation that could be solved with this method. Show and explain the steps for solving the equation.
Answers
Answer:
I believe using the formula is the best method.
Step-by-step explanation:
If I am able to remember the formula this becomes the easiest method in my opinion. It is very simple and anyone can do it if the know basic algebrA.
Cuánto es 5000000 dividido en 87
porfa con la operación
Answers
Answer:
it equals 57,471
Step-by-step explanation:
5000000÷87=57,471
PLEASE HELP ME TO FIND THE VALUE OF X AND Y
Answers
Answer:
x=85/5
x= 17
y=95/5
y=19
Step-by-step explanation:
vertically opp angles are equal
Answer:
vertical angles here make an X
1. 5y and 95 are vertical
2. 5x and 85 are vertical
3. x = 17
4. y = 19
.
Step-by-step explanation:
angles MPL and NPO are equal
5x = 85
x = 17
angles MPN and LPO are equal
5y = 95
y = 19
for f(x)=4x+2, what value of x makes f(x)=-14
Answers
Hey there,
f(x) = 4x + 2
what value of x makes f(x) = -14?
Answer :x = -4 ✅
Explanations:f(x) = 4x + 2
>> We want f(x) to be equal to -14:
4x + 2 = -14
>> Substract 2 from both sides :
4x + 2 - 2 = -14 - 2
4x = -16
>> Divide both sides by 4:
4x/4 = -16/4
x = -4
✅
Have a good day ;)
Answer:
x = -4
Step-by-step explanation:
Given:
f(x) = 4x + 2If the value of f(x) is -14,
⇒ 4x + 2 = -14 [f(x) = 4x - 2 and -14]
To simplify the equation, we need to isolate the variable completely. Start out by subtracting 2 both sides. This will isolate "x" and the cooeficient of x.
⇒ 4x = -14 - 2⇒ 4x = -16Then, divide 4 both sides to isolate the cooeficient of x on one side and a constant on the other side. The constant will be the value of x.
⇒ 4x/4 = -16/4⇒ x = -4Thus, -4 is the value of x that makes f(x) equivalent to -14
question number 4 please help
Answers
Answer:
The correct answe is H , if yu sub the x value in each of the equations yu should get y
Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex]
m = the slopeb = the y-intercept (the value of y when x=0)To find the slope of a line (m):
Find the coordinates of two points that fall on the linePlug them into the following formula:[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex] where [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are the coordinates of the pointsTo find the y-intercept of a line (b):
Plug the slope into [tex]y=mx+b[/tex]Plug in one of the pointsSolve for bSolving the Question
We're given a set of coordinates for this linear relation.
First, solve for the slope.
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
⇒ Plug in any two points that fall on the line (in this case we used (-2,-7) and (2,1)):
[tex]m=\dfrac{1-(-7)}{2-(-2)}\\\\m=\dfrac{1+7}{2+2}\\\\m=\dfrac{8}{4}\\\\m=2[/tex]
Therefore, the slope of the line is 2. Plug this into [tex]y=mx+b[/tex]:
[tex]y=2x+b[/tex]
Now, let's solve for the y-intercept (b)
[tex]y=2x+b[/tex]
Plug in any of the given points:
[tex]1=2(2)+b\\1=4+b\\b=-3[/tex]
Therefore, the y-intercept of the line is 3. Plug this back into [tex]y=2x+b[/tex]:
[tex]y=2x-3[/tex]
Answer[tex]y=2x-3[/tex]
At an assembly 7 out of the first 10 students who entered the gym were carrying a backpack. Based on this information, if 70 students were at the assembly, how many students could be expected to be carrying a backpack?
Record your answer and fill in the bubbles on your answer document. Be sure to use the correct place value.
Answers
Answer:
Step-by-step explanation:
49
What is the range of the given function?
{(-2, 0), (-4, -3), (2, -9), (0, 5), (-5, 7)}
{x | x = -5, -4, -2, 0, 2}
{y l y = -9, -3, 0, 5, 7}
O (x | x = -9, -5, -4, -3, -2, 0, 2, 5, 7}
O tyl y = -9, -5, -4, -3, -2, 0, 2, 5, 7}
Answers
Answer:
{-9, -3, 0, 5, 7}
Step-by-step explanation:
Well, you already have the relation of the function. The domain of a function are its x coordinates and the range are all the y coordinates:
0, -3, -9, 5, 7
We write them in ascending order:
-9, -3, 0, 5, 7
And this way we get the range
It is important to check if the coordinates you are given can form a function. In this case they do, but in other cases they might not.
If you have coordinates where for example there are two equal values of x but the y is different in both, for example (1, 2) and (1, 5), this cannot be a function because y can be on two possible destinations for the same value of x.
Help please! I keep going down on ixl and I’ve been trying to do this ixl since yesterday so ima post a lot of these.
Answers
u can add lines to split the figure into a triangle and two rectangles.
Area of the figure
= (12x15)/2 + 6x4 + 2x5
=124 yd^2
pls help me to answer this
Own words*
Answers
Answer:
I hope it will help you.
Step-by-step explanation:
Dear Teacher
Your way of setting up with math makes it easier to learn.
There's few lines for you. I hope you like it
An Awesome Math
Teacher Is Hard To Find
Difficult To Part With,
And IMPOSSIBLE To Forget.
MATH may not teach us how to ADD love or SUBTRACT hate but it gives us hope that EVERY PROBLEM has a SOLUTION.
An airplane flies with a constant speed
of 820 miles per hour. How far can it
travel in 3 1/2 hours?
Answers
2870 miles
D= s x t
= 820 x 3.5
=2870
Hope this helps!
The Molina family's pancake recipe uses 2 teaspoons of baking powder for every 1 3 of a teaspoon of salt. How much baking powder would they need if they used 1 teaspoon of salt?
Answers
Answer: 7
Step-by-step explanation:
help please 4(2x-1)+3=8x+1
Answers
Use the distributive property:-
4(2x-1)
8x-4
8x-4+3=8x+1
8x-8x-4+3=1
8x-8x-1=1
0-1=1
-1=1
Wait, what? -1 is equal to 1?
Hence, the equation has no solutions.
Hope it helps :)
The volume of a sphere is 29307 cubic centimeters. What is the radius of the sphere?
Round to the nearest whole number.
Answers
Answer:
19 cubic centimeters
Step-by-step explanation:
The equation for the volume of a sphere is [tex](4/3)\pi r^3[/tex].
We can setup the equation as [tex]29307 = \frac{4}{3}\pi r^3[/tex].
Now we need to isolate the r^3. Divide both sides by 4/3 and pi, which leaves [tex]\frac{29307}{(4/3) \pi } =r^3[/tex]
Now we take the cube root of both sides to have a single r on the right side. This comes out to equal 19 cm^3
whats 50% of 1/2 of a mile
Answers
Answer:
0.25 or 1/4
Step-by-step explanation:
hope this helps
Answer:
Step-by-step explanation:
Half of half a mile is one quarter mile: (1/2)(1/2) = 1/4
4. Sebastian's lemonade recipe uses 4 cups
of water and 1 cup of lemon concentrate.
What is the percentage of the lemonade
recipe that is lemon concentrate,
Answers
1/5 = 0.2
0.2 = 20%
At a restaurant, 8 plates are accidentally broken each day for a week (7 days). What number represents the change in the number of plates the restaurant has?
Answers
solve pls brainliest
Answers
Answer:
w = 2/7
Step-by-step explanation:
You do 8 divided by 4 over 7, which is 2/7.
Write a rational expression with denominator (x - 3)(x + 2) that is equivalent to 3x-1/x+2
Answers
Answer:
(x-3)(3x-1)/((x-3)(x+2))
Step-by-step explanation:
An equivalent fraction is formed by multiplying or dividing numerator and denominator by the same factor.
__
To get the desired denominator, the given denominator must be multiplied by (x-3). To get the desired numerator of the equivalent fraction, the numerator must also be multiplied by (x-3).
[tex]\dfrac{3x-1}{x+2}=\boxed{\dfrac{(x-3)(3x-1)}{(x-3)(x+2)}=\dfrac{3x^2-10x+3}{x^2-x-6}}[/tex]
find the measures of m and n
Answers
Answer:
m=3 n=6
Step-by-step explanation:
top diagonals are congruent
9 = 3m
solve for m
m = 3
bottom diagonals are congruent
m + 8 = 2n -1
plug in 3 for m
3 + 8 = 2n -1
solve for n
11 +1 = 2n
12 = 2n
n=6
Find the slope of the line that passes through the points (-1, 2),
(0, 5). Show work
Answers
To find the slope:
⇒ must know the slope's formula
⇒ [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
⇒ [tex](x_{1} ,y_{1} )[/tex] and [tex](x_{2} ,y_{2} )[/tex] are any points on the line
⇒ we use (-1,2) and (0,5) since they are the only points that we
know that are on the line
[tex](x_{1} ,y_{1} )[/tex]: (-1,2)[tex](x_{2} ,y_{2}[/tex]): (0,5)Let's solve:
[tex]Slope = \frac{5-2}{0--1} =\frac{3}{1}[/tex]
Slope is 3
Hope that helps!
Write the proportion. do not include units in the answer.
60feet is to 100feet as 12feet is to 20feet.
Answers
Answer:
(60/100) = (12/20)
Step-by-step explanation:
If A = 49 degrees, a = 32,
and b = 28, find c.
Round to the nearest tenth.
Answers
Answer:
please can you resend the question clearly maybe with a diagram
Can someone help me with this easy math problem.
Answers
It's a geometric sequence
common ratio=r=84/21=4First term 1.3125Formula:&
[tex]\\ \sf\longrightarrow a(n)[/tex]
[tex]\\ \sf\longrightarrow ar^{n-1}[/tex]
[tex]\\ \sf\longrightarrow 1.3125(4)^{n-1}[/tex]
whats 2+7
a. 14
b. 19
c.88383838837
Answers
Answer:
9
Step-by-step explanation:
Was this a joke or something
If the mean absolute deviation is a really
large number, then what does that mean about
the data set?
Answers
Answer:
The data is more spread out so their is a greater variability in the data.
Step-by-step explanation:
The Mean absolute deviation is large, then the data is more spread out and there is greater variability in the data.
What is mean absolute deviation?Mean absolute deviation is "collected data set is the average of absolute deviations from the center point of the data set".
According to the question,
Formula for Mean absolute deviation = summation of ( absolute value of xₙ - x⁻ divided by number of data values), where ' xₙ' is the input data values and 'x⁻ ' is mean of the given data values .
When the mean absolute deviation is large number then the data spread out more and the variability is greater in data.
Hence, the Mean absolute deviation is large then there is greater variability in the data.
Learn more about Mean absolute deviation here
https://brainly.com/question/4364130
#SPJ2
Solve the math problem
Answers
Answer:
a no association b non liner c liner d liner
Answer:
A) No association
B) Nonlinear
C) Linear
D) Nonlinear
Step-by-step explanation:
Linear Relationship: A linear relationship is one in which the scatter plot resembles a straight line. When one variable increases, the other variable increases or decreases proportionally.
Nonlinear Relationship: A nonlinear relationship is one in which the scatter plot does not resemble a straight line. It could resemble a curve or it could not resemble anything at all. A proportional increase or decrease in one variable does not result in a proportional rise or decrease in the other variable.
No Association: a graph of data showing discrete (individual) points of data that are not connected.
Using these definitions we can conclude whether the graphs are linear, nonlinear, or no association.
Question 3:
Solve for e.
m=-2e+c/3
Answers
Answer:
5
Step-by-step explanation:
You want to paint the four walls in your
bedroom. Each wall is 9
feet tall by 12 feet
wide. What is the total
area