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
What is the slope of the line that passes through the points(1,6) and (13,2)?
Answers
Answer:
[tex]\boxed{\sf{-\dfrac{2}{3} }}[/tex]Step-by-step explanation:
Use a slope formula.
Slope formula:
[tex]\Longrightarrow: \sf{\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{RISE}{RUN} }[/tex]
y2=2
y1=6
x2=13
x1=1
Rewrite the problem.
[tex]\sf{\dfrac{2-6}{13-1}=\dfrac{-8}{12}=\dfrac{-8\div4}{12\div4}=\dfrac{-2}{3}=\boxed{\sf{-\dfrac{2}{3}}}[/tex]
Therefore, the slope is -2/3, which is our answer.I hope this helps you! Let me know if my answer is wrong or not.
Three 3-digit numbers are formed using the digits 1 through 9 exactly once each. The hundreds digit of the first number is 1. The tens digit of the second number is 8. The units digit of the third number is 5. The ratio of the first number to the second number to the third number is 1:3:5, respectively. What is the sum of the three numbers?
Answers
Answer:
1161
Step-by-step explanation:
We can solve this using what we know about multiples of 3 and 5. Multiplying the first number by 3 will give the value ...
1?? × 3 = 38? . . . . where ? is an unknown digit
The two least significant digits in the first number must be ones that give 80-something when multiplied by 3. They will be between 80/3 = 26 2/3 and 90/3 = 30. The requirement that the least significant digit be odd* means the choices are 27 or 29.
When the first number is 127, its triple is 381. The 1 in the least significant digit is disallowed by the requirement that the 9 digits of these numbers be unique. (127 already has 1 as its most-significant digit.)
So, the first number is 129, making the second number be 3×129 = 387, and the third number be 5×129 = 645.
The numbers have the ratios ...
129 : 387 : 645 = 1 : 3 : 5 . . . . . . . as required.
We note that the digits 1–9 are used exactly once each, as required.
The sum of the numbers is 1161.
_____
* Only odd numbers will give a product that ends in 5 when they are multiplied by 5. The requirement that the third number have a ones digit of 5 means the ones digit of the first number must be odd.
6|-5| - 3(2/3) + 7(-8)=
-88
-16
-28
Answers
Answer:
-28
Step-by-step explanation:
6|-5| - 3(2/3) + 7(-8)=
30 -2 -56
30 -58 = -28
P(x) = 4x^3 - 6x^2 + ax – 2. Find a If P(3) = 2.
Answers
[tex]P(x)=4x^3-6x^2+ax-2\\\\P(3)=2\\\\\implies 4\cdot 3^3-6 \cdot 3^2 +3a-2=2\\\\\implies 108-54-4 +3a=0\\\\\implies 50+3a=0\\\\\implies a = -\dfrac{50}3[/tex]
Answer:
The value of a = -16.6.... or -16.7
Step-by-step explanation:
Given :
P(3) = 2
P(x) = 4x^3 - 6x^2 + ax – 2
=> 2 = 4(3)³ - 6(3)² + a(3) -2
=> 2 = 4(27) - 6(9) +3a - 2
=> 2+2 = 108 - 54 +3a
=> 4 = 54 + 3a
=> 4-54 = 3a
=> -50 = 3a
=> -50/3 = a
=> a = -16.6.... or -16.7
Albert had a goal of saving $80. He saved 115% of his goal. How much money did Albert save
Answers
Answer:
$92
Step-by-step explanation:
PLEASE HELP BRAINLIEST AND 10 POINTS
A sculptor is planning to order a cylinder of composite stone to sculpt a full-sized person. The figure will be 6 feet tall, and 2’ at the longest diameter. The composite stone weighs 50 pounds per cubic foot. About how much will the smallest cylinder weigh that the sculptor can order to make his statue?
Answers
47 lbs
hope this helps
6. The ancient Babylonians were writing fractions in 1800 BCE. But they did not have a concept of zero until about 1489 years later. In what year did the Babylonians develop the concept of zero
Answers
Answer:
I think it was the third century b.c. If not then I am sorry.
In a class, 60% of the students are boys and the rest are girls. If the number of boys is 30, how many students are there?
Answers
50 total students
20 girlsExplanation:
total students: 100%
----------------
60% → 301% → 30/601% → 0.5100% → (0.5 * 100)100% → 50number of girls:
total students - number of boys 50 - 3020)The diameter of a cylinder is 7 yards. The height
is 12 yards. What is the volume, in terms of T and
to the nearest cubic yard, of the cylinder?
Answers
Answer: 462 yards ^3
Step-by-step explanation:
The equation for the volume of a cylinder is πr^2h
the diameter is 7 yards and the radius is just half the diameter so the radius is 3.5
the height is 12 yards
so π(3.5)^2(12) = 461.814120078 yards ^3
On Saturday, Mark sold 2 7/8 gallons of lemonade. On the same day, Regan sold 2/3 as much lemonade as Mark. How much lemonade, in gallons, did Regan sell? Help
Answers
Answer:
Step-by-step explanation:
The total amount of lemonade Regan sells is 69/16 gallons and this can be determined by using the arithmetic operations.
Given :
Mark sold 2 7/8 gallons of lemonade.
Regan sold 2/3 as much lemonade as Mark.
The following steps can be used in order to determine the total amount of lemonade Regan sells:
Step 1 - The arithmetic operations can be used in order to determine the total amount of lemonade Regan sells.
Step 2 - According to the given data, Mark sold 23/8 gallons of lemonade.
Step 3 - Let the total amount of lemonade Regan sells be 'x'.
Step 4 - So, the value of 'x' can be calculated as:
x = 23/8 × 3/2
x = 63/16
The total amount of lemonade Regan sells is 69/16 gallons.
how to solve (3p⁴ + 2q⁴)²
Answers
Answer:
9p⁸ + 12p⁴q⁴ + 4q⁸
Step-by-step explanation:
(3p⁴ + 2q⁴)² ⇒ The square of (3p⁴ + 2q⁴)
Squares are such bases that multiply itself two times.
⇒ (3p⁴ + 2q⁴)(3p⁴ + 2q⁴)
Simplifying the expression using (a + b)(a + b) = (a x a) + (ab) + (ab) + (b²)
⇒ (9p⁸ + 6p⁴q⁴ + 6p⁴q⁴ + 4q⁸)
⇒ (9p⁸ + 12p⁴q⁴ + 4q⁸) = 9p⁸ + 12p⁴q⁴ + 4q⁸
We know the identity
(a+b)²=a²+b²+2abSo
[tex]\\ \rm\Rrightarrow (3p^4+2q^4)^2[/tex]
[tex]\\ \rm\Rrightarrow (3p^4)^2+(2q^4)^2+2(3p^4)(2q^4)[/tex]
[tex]\\ \rm\Rrightarrow 9p^8+4q^8+12p^4q^4[/tex]
Done
Which graph would be produced by k*f(x) if f(x)=x squared k
x= -1/2
Answers
Answer:The square below represents one whole.
What percent is represented by the shaded area?
Step-by-step explanation:
Virgil opened an account with a deposit of $815.
. The bank pays 5% interest compounded annually on this account.
• Virgil makes no additional deposits or withdrawals.
How much interest will the account have earned after 6.5 years?
Answers
Answer:
$304.15
Step-by-step explanation:
The amount of interest earned can be found from the formula ...
I = P((1 +r)^t -1)
I = $815((1 +0.05)^6.5 -1) ≈ $815(0.373189) ≈ $304.15
Virgil's account will have earned about $304.15 in interest in 6.5 years.
The side lengths of three triangles are shown in the table. Which of the triangles is a right triangle? Select all that apply. Triangle Side Lengths | 610 810 1 || 7 7 13 ||| 313 413 513 A. Triangle I B. Triangle II C. Triangle III D. None of the above E. All of the above
Answers
To identify whether or not a triangle is a right triangle, it must satisfy the pythagorean theorem : [tex]a^{2}+ b^{2} =c^{2}[/tex] (where a;b;c represent the 3 sides, and c being the hypotenuse)
Replace the lengths :
Triangle 1 : [tex]1^{2} + 610^{2} \neq 810^{2}[/tex] (not right triangle, also does not satisfy the triangle inequality, so not a real triangle)
Triangle 2 : [tex]7^{2} + 7^{2} \neq 13^{2}[/tex] (not right triangle)
Triangle 3 : [tex]313^{2} + 413^{2} \neq 513^{2}[/tex] (not right triangle)
So, correct answer is D
Write the following in scientific notation
Answers
Answer:
3.25 x 10^-4
Step-by-step explanation: mark brainliest
Write the absolute value equations in the form |x-b|=c (where b is a number and c can be either a number or an expression) that have the following solution sets. Two solutions: x=2, x=14
Answers
Answer:
|x - 8| = 6
Step-by-step explanation:
|x - b| = c
⇒ (x - b)² = c²
Given:
x = 2x = 14Substitute the values of x into (x - b)² = c²:
(2 - b)² = c²
(14 - b)² = c²
Equate and solve for b:
(2 - b)² = (14 - b)²
⇒ 4 - 4b + b² = 196 - 28b + b²
⇒ 4 - 4b = 196 - 28b
⇒ 24b = 192
⇒ b = 8
Substitute b = 8 into the equations to find c:
x = 2 ⇒ |2 - 8| = 6
x = 14 ⇒ |14 - 8| = 6
Therefore, c = 6
Final equation: |x - 8| = 6
Given the definitions of f(x) and g(x) below, find the value of (g•x)(1).
=
f(x) = 3x2 + 2x - 3
g(x) = -x + 4
Answers
Step-by-step explanation:
f(x) = 3x2+2x-3
g(x) = -x+4
(g.f)(x) = g[3x2+2x-3]
= -(3x2+2x-3)+4
= -3x2-2x+3
(g.f)(1) = -3(1)2-2(1)+3
= -3-2+3
= -2
manatees are large, gentle, slow-moving sea creatures found along the coast of florida. many manatees are injured or killed by boats. here is a scatterplot showing the relationship between the number of boats registered in florida (in thlusands) and the number of manatees killed by boats for the years 1977 to 2015. is r>0 or r<0? closer to r=0 or r=+- 1? explain your reasoing
Answers
Using correlation coefficients, it is found that the value of r is greater than 0 and close to 1, as the scatter-plot is increasing linearly.
What is a correlation coefficient?It is an index that measures correlation between two variables, assuming values between -1 and 1.If it is positive, the relation is positive, that is, they are direct proportional. If it is negative, they are inverse proportional.If the absolute value of the correlation coefficient is greater than 0.6, the relationship is strong.Researching the problem on the internet, it is found that the relation is modeled by an increasing scatter-plot, hence r > 0. There are very few points in which there are oscillations, which indicate a strong relationship, hence r is closer to 1.
More can be learned about correlation coefficients at https://brainly.com/question/25815006
#SPJ1
A. ((4 × 5) – 15) ÷ (2 + 22 – 1) =
((4 × 5) – 15) ÷ (2 + 22 – 1) =
B. 4 × (– 3 + (42 – 13)) + 8 ÷ (6 + 2) =
4 × (– 3 + (42 – 13)) + 8 ÷ (6 + 2) =
Answers
Answer:
A. 8 1/4 - 3 2/5 - (2 1/3 - 1/4) = 83/30 = 2 23/30 ≅ 2.7666667
B. 5
The table displays the scores of students on a recent exam. Find the mean of the
scores to the nearest 10th.
Score Number of Students
65
1
70
6
75
2
80
9
85
3
90
1
95
6
100
8
Answers
Answer:
85.3
Step-by-step explanation:
The Total number of students = 36. Add all the values but don't forget how much of that value there is. so for the score of 70, you would multiply that by 6 because that's how much students got it.
To buy an article marked Rs. 20,000, we get a discount of 15% and have to pay the value added tax (VAT) at the rate of 13%. How much value added tax amount we have to pay to buy that article ?
Answers
Answer:
Based on the given conditions, formulate:: 13%×20000×(1−15%)
Calculate the sum or difference: 0.13×20000×0.85
Calculate the product or quotient: 2210
The expression 2(x2 - 4) – (x2 - 8x + 12) is equivalent to
-
A.
x2 - 8x + 4
B.
x2 + 8x - 4
С.
x2
- 8x + 20
D.
x2 + 8x - 20
Answers
Answer:
D
Step-by-step explanation:
write a function that represents the number of emergency responses professionals in the town in terms of the towns total population
Answers
The exponential growth function will be: y = 4000(1 + 0.04)⁴
How to solve Exponential growth unctions?An exponential equation is an equation with exponents where the exponent (or) a part of the exponent is a variable.
We are given;,
Initial population = 4000
Rate of increase = 4%
Let current population be p.
Let number of years passed be t.
Thus, the exponential growth function will be:
y = 4000(1 + 0.04)⁴
Complete question is;
A town has a current population of 4,000. The population increased 4 percent per year for the past four years, Emergency response professionals make up 3 percent of the town's population.
Part A
Write a function that represents the population (p) of the town in terms of the number of years (1) for the last four years.
Read more about Exponential Growth Functions at; https://brainly.com/question/27161222
#SPJ1
Answer:
number of emergency response professionals = 3% of population
e = 0.03p
e is a function of p
e(p) = 0.03p
Step-by-step explanation:
edumentum
Hussain and sam are sharing money in the ratio of 2:5 sam got 70p how much money were they sharing in total
Answers
Answer:
if 5=70
2=?
cross multiply=28
add 70+28=98
Step-by-step explanation:
2. Find the slope of this line.
Answers
Answer:
Answered below
Step-by-step explanation:
Slope = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
You need 2 coordinates from your graph as long as the line you have is completely straight. You have 2 points it is (0,3) & (8,0)
So your y2 is 0
y1 is 3
So your x2 is 8
x1 is 0
Plug in and solve (keep in mind you should be expecting a negative slope since your line is sloping downwards as you advance to the right.
m = (0-3)/(8-0)
m = -3/8
m = slope = -3/8x = -0.375x
Slope is given as a number followed by value x
Plsss answer as fast as possible! IMPORTANT
Answers
Step-by-step explanation:
Attached picture might help you out
If a florist uses 10 red roses in a bouquet , how many white roses did she use?
Answers
Answer:
2 white roses.
A dozen is 12.
12-10 red roses = 2 white roses
Step-by-step explanation:
Answer:
she used 2 white rose
Step-by-step explanation:
12 is a dozen so 12-10 is 2 white roses
Hope this helps :)
Select all the systems of equations that have exactly one solution.
Option 1. y = 4x - 1 and y = -4x + 7 Option 2. y = 3x + 1 and y = 2x + 1
Option 3. y = x + 2 and y = x + 7 Option 4. 2x + 2y = 20 and 3x + 3y = 30
Option 5. x + y = 40 and x + y = 90
Answers
Answer:
Option one and option 2
Step-by-step explanation:
Only ones that have 1 solution, option 3 and 5 have no solution, option 4 has infinetly many.
18. Without solving the radical equation VX + 5 + 9 = 0, how could you tell that it has no real solution?
Answers
Answer:
Has two unkown variables
Step-by-step explanation:
When there is only one equation provided with two unknown variables, it is difficult to solve for the unknown variables
The most simplified version of this equation would be VX = -14
More information would be needed to solve
what is equivalent to 8x-12y+32
Answers
Answer:
C. 16(0.5x - 0.75y + 2) = 8x - 12y + 32
Step-by-step explanation:
Answer:
Yeah I got the answer
Step-by-step explanation:
C option is correct
We will have to take common like this
. 16(0.5x - 0.75y + 2) = 8x - 12y + 32
PLEASE MARK ME BRAINLIEST IF MY ANSWER IS CORRECT PLEASE
