A rope 18 feet long is cut into two pieces. one piece is used to form a circle and the other used to form a square. find a function representing the area of both square and circle as a function of the length of one side of the square.
Answers
f(x)=x^2 + (4x^2 -18x +81)/pi
Related Questions
HELP Please THANKS (;
Answers
2x+2x-8=16
4x-8=16
4x=24
x=6
y=6-4
y=2
Answer is C
Sarah decides to take her six-year-old son to the circus the price for the child ticket is $4.75 dollars Less in the price for the adult ticket if you represent their price for the child ticket using the variable X how would you write the algebraic expression for an adult ticket price?
Answers
It would be : A=X+4.75
Or. X= A-4.75
If one honey bee makes 1/2 teaspoon of honey during its lifetime, how many honey bees are needed to make 1/2 teaspoon of honey
Answers
1 bee makes 1/2 teaspoon of honey
How many honey bees are needed to make 1/2 teaspoon if honey?
The answer is 1? I'm assuming you wrote the question wrong?
Show that the equation is not an identity by finding a value of x for which both sides are defined but not equal. cos x - cos x sinx = cos3 x
Answers
Answer:
The answer is pi/4
Step-by-step explanation:
You substitute each x for "pi/4", you will see that the equation is incorrect, the two values are no longer equal.
The equation is not an identity. Value of x = nπ, where n∈I , I → set of integers, for which both sides are defined but not equal.
What are the trigonometric identities?Equations using trigonometric functions that hold true for all possible values of the variables are known as trigonometric identities.
We have the equation,
cos x - (cos x) (sin x) = cos³x
Simplifying,
cos x [ 1 - (sin x) ] = cos²x (cos x)
1 - sinx = cos²x
1 - sinx = 1 - sin²x
1 - sinx = 1² - sin²x
1 - sinx = (1 - sinx)(1 +sinx)
1 = 1 + sinx
sinx = 0
x = nπ, where n∈I , I → set of integers.
It is not an identity equation.
cos x - (cos x) (sin x) ≠ cos³x
Therefore, both sides are defined but not equal.
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Find the area of the square.
Answers
Where s is the side length of the square.
[tex]A = 4^2[/tex]
A = 16
So, the area of the square is 16 square units.
If tan y = 3 over y and cos x = y over z what is the value of sin x??
A. sin x = 3/z
B. sin x = 3y
C. sin x = z/3
D. sin x = 3z
Answers
Answer: (A) sin x° = 3/z
Step-by-step explanation: i couldnt find it anywhere else but i figured it out and dont worry i got it right on the quiz
Let f(x) = 2x − 6. Solve f−1(x) when x = 2. (1 point) explanation please! algebra 2 makes no sense to me!
Answers
and if f⁻¹(a)=b then f(b)=a
this is helpful for our problem
alright
the problem is
find f⁻¹(2)
ok
f⁻¹(2)=?
look familiar?
if f⁻¹(2)=? then f(?)=2
easy now
so
solve for x such that f(x)=2
2=2x-6
8=2x
4=x
so te value is 4
f⁻¹(2)=4
given that (6 3) is on the graph of f(x) find the corresponding point for the function f(-1/2x)
Answers
Answer:
this answer is wrong on plato, trust me
Step-by-step explanation:
We need to find the corresponding y-coordinate for x = -3. Unfortunately, since we don't have additional information about the function f(x), we cannot determine the value of f(-3) and provide the corresponding point.
To find the corresponding point for the function f(-1/2x) when (6, 3) is on the graph of f(x), we need to substitute the x-coordinate of (6, 3) into the function -1/2x and determine the resulting y-coordinate.
Given that (6, 3) is on the graph of f(x), it means that f(6) = 3.
Now let's substitute -1/2x into the function:
f(-1/2x) = f(-1/2 * 6) = f(-3)
Therefore, we need to find the corresponding y-coordinate for x = -3. Unfortunately, since we don't have additional information about the function f(x), we cannot determine the value of f(-3) and provide the corresponding point.
In summary, without more information about the function f(x), we cannot find the corresponding point for the function f(-1/2x) when (6, 3) is on the graph of f(x).
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A license plate comprised of 3 letters followed by 3 numbers is to be chosen (repetition is allowed). If the first letter cannot be a "Z", how many different ways can this occur? In your answer, include the set up and calculations for the license plate.
Answers
25(26)26(10)10(10)
16,900,000
a hot air balloon holds 3,249 cubic meters kf helium. the density of the helium is 0.1785 kilograms per cubic meter. how many kilograms of helium does the balloon contain, round to the nearest tenth of a kilogram?
Answers
Mass = Density x Volume
Mass = 0.1785 kg / m^3 x 3249 m^3
Mass = 579.9465 kg
Therefore, the mass of helium gas in the hot air balloon would be about 579.9 kg.
Use the drop-down menus to complete each statement to show why √65 is between 12 and 18.
Answers
Answer:
12 < 6√5 < 18
Step-by-step explanation:
It has been given in the question 4 < 5 < 9 and we have to show 6√5 is between 12 and 18.
For box number 1.
4 < 5 < 9 ⇒ √4 < √5 < √9
For the box number 2.
√4 < √5 < √9 ⇒ 2 < √5 < 3
For the box number 3.
we multiply the inequality by 6.
6×(2 < √5 < 3) ⇒ 6×2 < 6×√5 < 6×3
Therefore final answer is 6×2 < 6×√5 < 6×3 ⇒ 12 < 6√5 < 18
The square root of 65 (√65) falls between 8 and 9, as these are the square roots of the closest perfect square numbers (64 and 81 respectively). The range of 12 to 18 provided in the question seems incorrect.
Explanation:The student's question is referring to the mathematical concept of square roots of numbers. The square root of a number is a value which, when multiplied by itself, yields the original number. In the case of √65, we need to locate it between two perfect square numbers, which are 64 (8^2) and 81(9^2). As a result, √65 should fall between 8 and 9.
However, the interval of 12 and 18 as stated in the question seems to be a mistake, as they are not the correct boundaries for the value of √65. Please verify the numbers in your question.
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The sum of three numbers is 91 . the third number is 2 times the first. the first number is 9 more than the second. what are the numbers?
Answers
First number = 9 + x
Third number = 2(9 + x) = 18 + 2x
Sum of the numbers = 91
9 + x + x + 18 + 2x = 91
4x + 27 = 91
4x = 64
x = 16
Thus,
The first number is 25. The second number is 16. The third number is 50.
A parent rewards a child with 50 cents for each correctly solved mathematics problem and fines the child 30 cents for each incorrectly solved problem. if the child nets $22.00 after 100 problems. how many problems were solved correctly?
Answers
x = correct answer
y = incorrect answer
0.50x-0.30(100-x)=22.00
0.50x-30.00+0.30x=22.00
0.80x=22.00+30.00
0.80x=52.00
x=52.00/0.80
x= 65
y=100-65 = 35
0.5x65 = 32.50
35*0.30=10.5
32.5-10.5 = 22
there were 65 correct answers
Answer:
65 problems were solved correctly, 35 incorrecly.
Step-by-step explanation:
1. Data:
Total answers= 100
50 cent = $0.50 for each correct answer
-30 cent = -$0.30 for each incorrect answer
Net reward= $22.00
2. Define Variables:
x= Correct answers
y= Incorrect answers
3. Formulate the Equations
Total number of answers (Eq 1)
[tex]x+y=100\\y=100-x[/tex]
Net reward (Eq 2)
[tex]0.50*x-0.30*y=22.00[/tex]
4. Solve by replaccing the Eq 1 in Eq 2 as follows:
[tex]0.50*x-0.30*y=22.00\\0.50*x-0.30*(100-x)=22.00[/tex]
5. Apply distrivutive property and operate:
[tex]0.50x-(0.30*100)+(0.30*x)=22.00\\0.50x-30.00+0.30x=22.00[/tex]
6. Separate numbers and variables on each side of the equation and solve
[tex]0.50x+0.30x=22.00+30.00\\0.80x=52.00[/tex]
7. Solve x
[tex]x=\frac{52.00}{0.8} \\x=65[/tex]
Now you know that correct answers are equal to 65
8. Find Incorrect Answers with Eq 1.
[tex]y=100-x\\y=100-65\\y=35[/tex]
Now you know that incorrect answers are equal to 35
9. Answer
65 problems were solved correctly, 35 incorrecly.
John's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs John $4.70 per pound, and type B coffee costs $5.90 per pound. This month, John made 181 pounds of the blend, for a total cost of $967.10 . How many pounds of type A coffee did he use?
Answers
A +B = 181
A=181-B
4.70A+5.90B= 967.10
4.70(181-B) +5.90B =967.10
850.70-4.70B+5.90B=967.10
850.70+1.2B =967.10
1.2B=116.40
B =116.40/1.2 = 97
A=181-97 = 84 pounds of type A coffee
How can I do this with the function (x+2)/x-3
Create a rational function with a linear binomial in both the numerator and denominator.
Part 1. Graph your function using technology. Include the horizontal and vertical asymptotes and the x- and y-intercepts on your graph. Label the asymptotes and intercepts.
Part 2. Show all work to identify the vertical asymptote, the x-intercepts, and the y-intercept.
Answers
[tex]f(x) = \frac{x+2}{x-3} [/tex]
Part 1
The horizontal asymptote is obtained by either long division or synthetic division. It may be obtained also as
[tex]f(x)= \frac{x-3+5}{x-3} = \frac{x-3}{x-3} + \frac{5}{x-3} =1+ \frac{5}{x-3} [/tex]
Therefore the horizontal asymptote is
y = 1.
The vertical asymptote occurs when the denominator is zero because the function becomes undefined. Set x-3 = 0 to obtain
x = 3.
Therefore a vertical asymptote occurs at x = 3.
The x-intercept occurs when f(x) = y = 0. Set f(x)=0 to obtain
[tex] \frac{x+2}{x-3} =0[/tex]
For x≠3, obtain
x+2=0 => x = -2
The x-intercept is x = -2.
The y-intercept occurs when x=0. Set x=0 in f(x) to obtain
[tex]f(0)= \frac{0+2}{0-3} =- \frac{2}{3} [/tex]
The y-intercept is
y = -2/3
Part 2
The graph of the function is shown below. It identifies the horizontal and vertical asymptotes, the x-intercept, and the y-intercept.
How many different 1010-letter permutations can be formed from 88 identical h's and two identical t's?
Answers
A permutation of these letters is simply an arrangement in a row.
For example:
h h h t h h t h h h
or
h t h h h h h h t h
The number of arrangements is equal to the number of pairs of positions we fix for t, the rest of the positions are filled with h:
these positions are :
(1, 2), (1, 3), (1,4)..... (1, 10)
(2, 3), (2,4)..... (2, 10)
(3,4).... (3,10)
(9,10)
so the 1st position combined with any of the remaining 9
the 2 position combined with any of the remaining 8
...
the 9th position combined with the remaining 1
this makes 9+8+7+6+5+4+3+2+1=45 positions to place the 2 t's.
Remark: the number of positions for the 2 t's could also have been calculated by C(10, 2)=10!/(8!2!)=(10*9)/2=45
Answer: 45
Find the value of cos θ for the angle shown. A line is drawn from the origin through the point four comma negative square root of thirty-three. The angle theta is given as the measurement from the positive x axis counterclockwise to the line.
cos θ = seven-fourthscos θ = square root of thirty-three divided by four
cos θ = four-sevenths
cos θ = square root of thirty-three divided by seven
Answers
Answer
Cos θ = 4/7
Explanation
The angle θ is in the 3rd quadrant. So, it is positive.
cos θ = adjacent / hypotenuse
hypotenuse = √(4² + (√33)²)
= √(16 + 33)
= √47
= 7
Cos θ = 4/7
Answer:
Step-by-step explanation:
cos 0= 4/7
reason: i took the test
equations that look different but have the same solution are said to be
a. equivalent
b. expressions
c. equals
d. similar
e. radical
Answers
A. Equivalent - equivalent equations may not look exactly the same on face value. But they are equivalent because they have the same exact solution.
B. Expressions - expression is a general term for equations that are formed from word problems
C. Equal - equal equations are the exact duplicate of each other
D. Similar - this term is only used on geometric shapes to tell that the two shapes have a fixed ratio of their similar sides or angles
E. Radical - radical equations are those involving fractions
Therefore, from their descriptions, the answer is A.
A right triangle has a side with length 12 in and a hypotenuse with length 20 in. find the length of the second leg (in inches). (round to the nearest hundredth if needed)
Answers
x² = b² - a²
x² = (20)² - (12)² = 256
x = 16 in
if a circle is inscribed in a triangle, the center of the circle is called the _____ of the triangle.
A. radius
B. incenter
C. circumcenter
Answers
Hope I could help.
Answer:
The correct answer to the following question will be Option B (Incenter).
Step-by-step explanation:
The middle of the circle which is carved in a triangle is the triangle incenter, the point where the triangle angle bisectors cross.
There are following steps to construct an inscribed circle in a triangle are as follows:
Step 1: Create the incenter.
Step 2: Construct a line that passes through incenter, perpendicular to one side of the triangle. The segment which connects the incenter with the triangle intersection point and the perpendicular line is the circle radius.
Step 3: Build a centered circle at the incenter with radius spotted in step 2.
In a group of students 25% are enrolled in physics, 23% in sociology, 17% in chemistry, 14% in political science, 12% in anthropology, and 9% in math. you are going to select an individual from the group of students. the probability of event a is equivalent to the probability that you select someone who studies social science (sociology, political science and anthropology) or physics. what is the probability of the event a’s complement?
Answers
The probabilities of selecting students studying a certain subject are as follows
P(physics)=25/100
P(chemistry)=17/100
P(maths)=9/100
P(sociology)=23/100
P(political sciences)=14/100
P(anthropology)=12/100
since all the sets are disjoint, that is there are no common elements, and since all the students in consideration are enrolled in one these 6 subjects:
P(physics)+P(chemistry)+P(maths)+P(sociology)+P(political sciences)
+P(anthropology)=1
P(a)=P(sociology)+P(political sciences)+P(anthropology)+P(physics)
thus
P(a')=1-P(a)=P(chemistry)+P(maths)=17/100+9/100=26/100=0.26
Answer: 0.26
The probability of event A's complement, which signifies selecting a student not studying social science or physics, is 26%.
The probability of selecting someone who studies social science (sociology, political science, and anthropology) or physics is the sum of the individual probabilities for those subjects: 23% (sociology) + 14% (political science) + 12% (anthropology) + 25% (physics) = 74%. To find the probability of the event A's complement, which is selecting a student not studying any of these subjects, we subtract the probability of event A from 100%: 100% - 74% = 26%. Therefore, the probability of selecting a student not enrolled in any of the mentioned social science subjects or physics is 26%.
The gold leaf on your necklace is 0.000045 of an inch thick. How do you write 0.000045 in scientific notation?
Answers
= 000.0045 / 100
= 0000.045 / 1 000
= 00000.45 / 10 000
= 000004.5 / 100 000 = 4.5 * 10^(-5)
That is in scientific notation
I hope that helps
The camera melissa wanted for her birthday is on sale at 27%off the usual price. theamount of the discount is $99.90.what was the original price of the camera?$nothing
Answers
divide the discount by the percentage off
so:
99.90/0.27 = 370
the original price was 370 dollars
You are taking a multiple-choice test that has 10 questions. each of the questions has four answer choices, with one correct answer per question. if you select one of these four choices for each question and leave nothing blank, in how many ways can you answer the questions?
Answers
which situation involving raul's Bank account would be modeled by a positive number?
A.Raul deposited his paycheck.
B.Raul wrote a check to his grandmother
C.Raul withdrew cash from an ATM
D.Raul paid for groceries with his debit card.
Answers
positive means add
so it would be a deposit into the account
so A is the correct answer
- The reason it's 'A' is because when you deposit your paycheck, you are depositing money.
It can't be any of your 3 other answers though, here's why: When you write a check, that takes money from your account. When you take money from the ATM, that takes the money straight from the account. Paying for groceries also takes money from your bank account.
What is the fifth term in the expansion of (3x - 3y)7?
__ x3y4
Answers
so 5th term of (3x - 3y)^7 = 7C4 * (3x)^(7-4) (-3y)^4 (NOTE r = 4)
= 35 * 27x^3 * 81y^4
= 76545 x^4y^3
Answer:
76545
Step-by-step explanation:
got it write on edge :)
In a plane, line N is parallel to line O, Line O is parallel to P, and line L is perpendicular to line N. Which must be true?
A) N||L
B) N||P
C) L||O
D) P||L
Answers
Answer:
The correct answer is option B) N || P
Step-by-step explanation:
N || P.
As it is given, in a plane, line N is parallel to line O, Line O is parallel to P, and line L is perpendicular to line N.
Since, N is parallel to O, and O is parallel to P, then N must be parallel to P.
So, option B is correct.
Solve 3x2 + 2x + 7 = 0. Round solutions to the nearest hundredth. (5 points)
x ≈ −1.90 and x ≈ 1.23
x ≈ −1.23 and x ≈ 1.90
x ≈ −0.44 and x ≈ −3.56
No real solutions
Answers
D = b² - 4ac = 2² - 4*3*7 = 4 - 84 = -80
D < 0 ⇒ No real solutions
Answer:
The answer is No Solutions Look Below
Step-by-step explanation:
Charmaine pays $848 for landscaping rocks for a project. The cost per pound is 32 cents. How many pounds did she purchase?
Answers
You need to find the number of pounds
So, do 848/0.32
You get 2650
Charmaine purchased 2,650 pounds of rocks
hope this helps:)
Answer:
D
Step-by-step explanation:
the question is............
Answers
A(8,4.6)=(8*4.6^2)/(4tan22.5)
A(8,4.6)=42.32/tan22.5 m (exact)
A(8, 4.6)≈102.17 m^2 (to nearest hundredth of a square meter)