a) find that x = 140/2 = 70.
b) side length [tex]x[/tex] the maximum area that the playground can have is x = 70
c) The maximum area that the playground can have is 980 square meters
How to find the area of playground?a. The playground is a rectangle, and the perimeter of a rectangle is given by 2(l + w) = 2x. The given information is that the perimeter is 280 meters, so we can set up the equation 2x = 280. Solving for x, we find that x = 140/2 = 70.
Now that we know the perimeter, we can find the area of the playground by using the formula A = lw. Since the perimeter is fixed at 280 meters, we can express the area of the playground as a function of x:
A(x) = lw = (x/2)(280 - x) = 140x - x^2
b. To find the side length x that gives the maximum area, we need to take the derivative of the area function and set it to zero.
A'(x) = 140 - 2x = 0
x = 70
c. Plugging x = 70 back into the area function, we get:
A(x) = 140x - x^2 = 140 * 70 - 70^2 = 140 * 70 - 4900 = 980.
The maximum area that the playground can have is 980 square meters.
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i seriously need help fast
Answer:
y=2/3x+3
Step-by-step explanation:
(0,3) is the y intercept
2/3 is the slope
Please help with this
answer
x(x + 2)(x + 3)
Step-by-step explanation:
x ^ 3 + 5x ^ 2 + 6x
>
x(x ^ 2 + 5x + 6)
x(x ^ 2 + 2x + 3x + 6)
x((x ^ 2 + 2x) + (3x + 6))
x(x(x + 2) + 3(x + 2))
x(x + 2)(x + 3)
Please Help me ASAP!!!!!!
Answer:
root of √81 = 9
100 -9 +3 = 94 so you mark right one
An element with a mass of 300 grams decays by 5.4% per minute. To the nearest tenth of a minute, how long will it be until there is 110 elements remaking
The period of time it will take for the element to remain 110 grams would be = 11.7mins
What is decay reaction?A decay reaction is defined as the type of reaction whereby the a substance disintegrates to form new smaller substances.
The mass of the element = 300g
The percentage that decays per minute = 5.4% of 300g.
That is;
= 5.4/100 ×300
= 1620/100
= 16.20g
The difference between the given mass = 300 - 110 = 190g
if 1 minute = 16.20
X minutes = 190
X = 190/16.20
X = 11.7mins.
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6 less than the quotient of 32 and a number y
Answer: y = 3/16
Step-by-step explanation:
32/y-6 =
32y = 6
jackson pays 24.00 for 4 pounds of grapes. How many will he pay for 10 pounds of grapes?
Please explain and solve! I would appreciate it :) I’ll give brainly.
Answer: 60
Step-by-step explanation:
$24÷4lbs=$6 per lb
6×10=60
LAST ONE PLEASE HELP
Answer:
0.01
Step-by-step explanation:
if there are five boys who get a b and one gets pick it would be 0.01
Solve the inequality both algebraically and graphically. Draw a number line graph of the solution and give interval notatic
5(x-9) 3x
>
3
7
- 20
The solution as an inequality is x2
105
26
(Type an inequality. Simplify your answer. Use integers or fractions for any numbers in the expression.)
105
The solution in interval notation is
26
(Type your answer in interval notation. Use integers or fractions for any numbers in the expression.)
Choose the correct graph of the solution below.
OA. H
4
,00
5
OB. +
-5
The solution is Option H.
The inequality equation is x ≥ ( -105/26 ) and the interval notation is given by x ⊆ [ -105/26 , ∝ )
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
( 5/3 ) ( x - 9 ) ≥ ( 3/7 )x - 20
On simplifying the equation , we get
( 5x - 45 ) / 3 ≥ ( 3x - 140 ) / 7
Cross multiply the denominators on both sides of the equation , we get
35x - 315 ≥ 9x - 420
Adding 315 on both sides of the equation , we get
35x ≥ 9x - 105
Subtracting 9x on both sides of the equation , we get
26x ≥ -105
Divide by 26 on both sides of the equation , we get
x ≥ -( 105/26 )
Hence , the inequality equation is x ≥ -( 105/26 )
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Frank is selling magazine subscriptions. He keeps 16% of the cost of each subscription he sells
as his commission. How many dollar's worth of subscriptions must he sell to earn $125?
O $2000
O $781.25
O $200
O $78.13
scammers have created an account in your name or taken over your account.
How can I cancel magazine subscriptions that I did not request?If you did not order the magazine, just mail or phone the magazine firm to inform them that you did not order it and do not wish to continue receiving it.Contact information is generally found inside the magazine.
According to a poll, 42% of consumers are still paying for a service they no longer utilize. Many of these occur as a result of being attracted by a free trial for an internet streaming service or a monthly subscription service for clothing or personal items, and then failing to cancel it when the trial period expires.
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Find the simple interest on a loan of $24,000 for 8 months at 6.5%. Be sure to show all your work and include units! Hint: Use the formula I=PRT
The simple interest on a loan of $24,000 for 8 months at 6.5% is $12480
What is Simple interest ?
simple interest can be defined as the ratio of product of principal amount , rate , time and hundred .
Given,
To find the simple interest on a loan of $24,000 for 8 months at 6.5%.
So here,
P = 24000
T = 8
R = 6.5
So, we know that
simple interest = P*T*R / 100
= 24000*8*6.5 / 100
= 24 * 8 * 65 / 1
= 12480
Therefore, The simple interest on a loan of $24,000 for 8 months at 6.5% is $12480 .
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OMG IM DYING HELPP MEE
Answer:
A. 1 + (-6) = -5
Step-by-step explanation:
Assuming the starting point is 1, we know the arrow is pointing left to the other point which shows it's going down 6 on the graph. This means we are subtracting 6 from the starting point. The only option subtracting 6 is A.
Select Is a Function or Is not a Function to correctly classify each relation. Is a Function Is not a Function
{(2,2),(4,4),(6,6),(8,8)}
{(0,3),(3,5),(5,6),(8,4)}
{(1,2),(3,3),(4,8),(6,3)}
{(3,4),(5,2),(5,6),(7,3)}
The classification of the ordered pairs as functions and not functions are as follows;
{(2, 2), (4, 4), (6, 6), (8, 8)} is a function
{(0, 3), (3, 5), (5, 6), (8, 4)} is a function
{(1, 2), (3, 3), (4, 8), (6, 3)} is a function
{(3, 4), (5, 2), (5, 6), (7, 3)} is not a function
What is a function?A function is a rule, law or definition that maps the elements of a set of values known as the input, to the elements of a set of values known as the output, such that each element of the input element is mapped to exactly one output element.
The values in each of the set of ordered pairs can be arranged into an input and output set as follows;
{(2, 2), (4, 4), (6, 6), (8, 8)}
Input [tex]{}[/tex] Output
2 [tex]{}[/tex] ⇒ 2
4 [tex]{}[/tex] ⇒ 4
6 [tex]{}[/tex] ⇒ 6
8 [tex]{}[/tex] ⇒ 8
In the above mapping, each input is mapped to exactly (only) one value of the output, such that the relationship is a function.
{(0, 3), (3, 5), (5, 6), (8, 4)}
Input [tex]{}[/tex] Output
0 [tex]{}[/tex] ⇒ 3
3 [tex]{}[/tex] ⇒ 5
5 [tex]{}[/tex] ⇒ 6
8 [tex]{}[/tex] ⇒ 4
In the above mapping, each input is mapped to exactly (only) one value of the output, such that the relationship is a function.
{(1, 2), (3, 3), (4, 8), (6, 3)}
Input [tex]{}[/tex] Output
1 [tex]{}[/tex] ⇒ 2
3 [tex]{}[/tex] ⇒ 3
4 [tex]{}[/tex] ⇒ 8
6 [tex]{}[/tex] ⇒ 3
In the above mapping, each input is mapped to exactly (only) one value of the output, such that the relationship is a function.
{(3, 4), (5, 2), (5, 6), (7, 3)}
Input [tex]{}[/tex] Output
3 [tex]{}[/tex] ⇒ 4
5 [tex]{}[/tex] ⇒ 2
5 [tex]{}[/tex] ⇒ 6
7 [tex]{}[/tex] ⇒ 3
In the above mapping, the input value of 5 has two output values of 2 and 6, therefore, the input, 5 maps to two values of the output, 2 and 6, which indicates that the relationship is not a function
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Anyone have the code?
Every 30 seconds, it produces a six-digit number that is unique. You won't have to wait a little while for a text message when using the app.
An authentication code with six digits—how can I acquire one?Every 30 seconds, it produces a six-digit number that is unique. You won't have to wait a little while for a text message when using the app. Every 30 seconds, it produces a six-digit number that is unique. You won't have to wait a little while for a text message when using the app.Every 30 seconds, it produces a six-digit number that is unique. You won't have to wait a little while for a text message when using the app .Every 30 seconds, it produces a six-digit number that is unique. You won't have to wait a little while for a text message when using the app. Every 30 seconds, it produces a six-digit number that is unique. You won't have to wait a little while for a text message when using the app.Every 30 seconds, it produces a six-digit number that is unique. You won't have to wait a little while for a text message when using the app .To learn more about code refer to:
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What’s the length of ac
Answer: 24
Step-by-step explanation: alright since AC = x+ 19, x+19 is equal to 2x+9+x. This means :
x+19 = 3x+9
subtract 19 from both sides:
x = 3x-10
now subtract 3x on both sides:
-2x = -10
Multiply by -1 on both sides:
2x = 10
x=5
Now we just add 19 to 5 to get 24
Which event would have a sample of space of S equals g b
A. Flipping a fair, two sided coin
B.Rolling a six die
C. Flipping a two sided coin with one green and the other side blue
D. choosing a tile from a pair of tiles one with the letter a one with the letter B
Flipping a two-sided coin with one side green and the other side blue is the correct answer for the given sample space. So, option C is correct answer.
What is a sample space?
A sample space is a set of potential results from a random experiment. The letter "S" is used to denote the sample space. Events are the subset of possible experiment results. Depending on the experiment, a sample area could contain a variety of results.
Given that, a sample space of S = {g, b}.
In the sample space there two outcome, one is g other is b.
Therefore, option C is the correct answer.
Hence, Flipping a two sided coin with one green and the other side blue is true.
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Answer: C: Flipping a two-sided coin with one side green and the other side blue
Step-by-step explanation:
I need help with this question please
The fraction 31/72 = (1 × 31)/(1 × 72) = 31/72
5/8 = (9 × 5)/(9 × 8) = 45/72
How do you find which fraction is larger?As you saw, if two or more fractions have the same denominator, you can compare them by looking at their numerators. As you can see below, 3/4 is larger than 1/4. The larger the numerator, the larger the fractionWhen fractions have the same denominators , they are ordered by the size of their numerators:The fraction with the smallest numerator is the smallest fraction.The fraction with the greatest numerator is the greatest fraction.Fractions can be arranged in ascending or descending order.The fraction with the bigger numerator is the larger fraction.And you can see very clearly that 1/3 covers more of the whole, it's a larger fraction of the whole than 1/5 is. So 1/3 is greater than 1/5To learn more about fraction refers to:
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The Student Council is having an election for its executive board, which consists of 3 positions—president, vice president, and secretary. If there are 9 members on the Student Council, how many different possibilities are there for selecting an executive board?
362,880
729
504
84
There are 504 possibilities are there for selecting an executive board.
What is permutation?The number of possible arrangements for a given set is calculated mathematically, and this process is known as permutation. Simply said, a permutation is a term that refers to a variety of possible arrangements or orders. With permutations, the arrangement's sequence is important.
Given the number of positions for executive board = 3
total members = 9
The problem is a permutation problem trying to select 3 from 9 where order matters.
a permutation is given by
ⁿpₓ = n!/(n - x)!
n = 9, x = 3
⁹P₃ = 9!/(9 - 3)!
⁹P₃ = (9*8*7*6!)/6!
⁹P₃ = 9*8*7
⁹P₃ = 504
Hence there are 504 possibilities.
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2. On average, Shawnte drinks ½ of a 6 ounce glass of water in % hour. How much water does she drink in an hour?
At the same rate, the amount of water that she drinks in an hour will be 4.5 ounce.
What is the rate of change?
The rate of change is the change of a quantity over 1 unit of another quantity.
Most of the time the rate of change is the change with respect to time.
For example the speed 3meter/second.
As per the given,
On average shown drinks 1/2 of a 6-ounce glass of water for 2/3 hour.
Amount that Shawnte drinks = 1/2 of 6 ounces = 3 ounces
3 ounces for 2/3 hour
Per hour = 3 x 3/2 = 9/2 = 4.5 ounce
Hence "At the same rate, the amount of water that she drinks in an hour will be 4.5 ounce.".
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After a 75% reduction, you purchase a new clothes dryer on sale for $140.
What was the original price of the clothes dryer?
The original price was?
Answer:
245
Step-by-step explanation:
140 x 1.75 = 245
Hannah has a $1,600 balance on Credit Card #2. She wants to pay off her balance on this card within 12 months. If she keeps paying $114 each month, how long will she need to pay her balance?
A.
10 months
B.
11 months
C.
14 months
D.
18 months
Answer:
To find out how long Hannah will need to pay her balance, we need to divide the balance by the monthly payment amount and then round up to the nearest whole number.
1600 (balance) / 114 (monthly payment) = 14 months.
So the answer is C, 14 months.
It's important to note that this is an estimate, and Hannah may end up paying off the balance sooner or later depending on interest rates, fees, or any changes to her monthly payments.
Step-by-step explanation:
Through calculations, Kelsey and Jack estimated the diameter of the fountain in the park.
A drawing of two students and their approximations is shown. Jack: the square root of two hundred feet. Kelsey: fifteen and four tenths feet.
If the actual length is 15 feet, which student’s estimate is more accurate? Explain your reasoning.
Select the answers from the drop-down lists to complete the sentence.
200−−−√≈
, so
estimate is more accurate.
Kelsey's estimate is more accurate.
What is fraction?An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.
Given:
Kelsey and Jack estimated the diameter of the fountain in the park.
Jack interpreted the diameter: square root of two hundred feet.
Jack : √200 = 14.14
Kelsey: fifteen and four tenths feet.
Kelsey : 15[tex]\frac{4}{10}[/tex] = 154/10. = 15.4 feet.
Thew actual length of the diameter is 15 feet.
Kelsey's estimation is closest to actual length.
Therefore, Kelsey's estimation is closest to actual length.
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Graph the first two inequalities you solved in question 2.
These two linear inequalities will coincide as shown in graph.
What are linear inequalities?
In mathematics, inequality denotes a mathematical expression in which neither side is equal. In Math, an inequality occurs when a connection produces a non-equal comparison between two expressions or two integers. The equal sign "=" in the phrase is substituted by any of the inequality symbols, such as greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤), or not equal to symbol (≠).
In mathematics, there are three types of inequalities: polynomial inequalities, rational inequalities, and absolute value inequalities.
Hence,
The graph for these linear inequalities will be made as shown in image and both will coincide.
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how do i show the work
Answer:
x = 30
Step-by-step explanation:
answer please time value of money
The amount that you need to save to be able to buy the car in four years time, given the interest rate is RM55, 480.20
How to find the amount to be saved ?The amount to be saved every year is an annuity because it is a certain amount and the price of the car would therefore be the future value of the annuity.
The amount to be saved therefore is:
250, 000 = Savings x Future value interest factor of annuity, 8 %, 4 years
250, 000 = Savings x 4.506112
Savings = 250, 000 / 4.506112
Savings = 55, 480.20
The amount to save is RM55, 480.20
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HELPPP ME PRECAL CLASS
the answer is g(x)= (x+6).
What is function?Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.
here, we have,
from the given , we get,
f(x)=x^4
and, f(g(x))= (x+6)^4
hence, the answer is g(x)= (x+6).
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You and a friend go to Tacos Galore for lunch. You order three soft tacos and three burritos and your total bill is $12. Your friend's bill is $10 for four soft tacos and two burritos. How much do soft tacos cost? How much do burritos cost?
A deli has two platters of sandwiches. The first platter costs $37 and you get 2 turkey sandwiches and 3 ham sandwiches. The other platter costs $38 and you get 3 turkey sandwiches and 2 ham sandwiches. Let x represent the cost of each turkey sandwich and y represent the cost of each ham sandwich. What is the system of linear equations for the given scenario? What is the cost of each sandwich?
We can rewrite the expression in two possible ways as -
f{x} = {- x - 17}/{3} and f{x} = - {x + 17}/{3}
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is the expression as -
f{x} = - {1/3}x - {17/3}
We can rewrite the expression in two possible ways as -
f{x} = {- x - 17}/{3}
and
f{x} = - {x + 17}/{3}
Therefore, we can rewrite the expression in two possible ways as -
f{x} = {- x - 17}/{3} and f{x} = - {x + 17}/{3}
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f f(x) = 3x2 + 1 and g(x) = 1 – x, what is the value of (f – g
The value of the function operation f - g(x) is 3x² + x
What is Function OperationsFunction operations refer to mathematical operations that can be performed on functions, such as addition, subtraction, multiplication, and composition.
Addition and subtraction of functions:
A function can be added or subtracted with another function if both of them have the same domain. The result is a new function with the same domain as the original functions.
Multiplication of functions:
Two functions can be multiplied together to create a new function. The result is a new function whose value at each point in the domain is the product of the original functions' values at that point.
Composition of functions:
Function composition is the application of one function to the result of another function. The result is a new function that is the composition of the original functions. It is represented by (f ∘ g) (x) = f(g(x)) where f and g are the functions being composed.
In this problem, we have two functions which are;
f(x) = 3x² + 1g(x) = 1 - xThe value of (f - g)(x) = 3x² + x
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26)
(1+2x)
45°
27)
SO
Bring the variable terms to one side of the equation and the constant terms to the other side using the addition and subtraction properties of equality.
what is equation based on related angle?
Angles Formulas at the center of a circle can be expressed as, Central angle, θ = (Arc length × 360º)/(2πr) degrees or Central angle, θ = Arc length/r radians, where r is the radius of the circle.Related Angles are the pair of angles that are related to each other. For each pair of related angles, there is a particular name given to them. These angles are related to each other based on some specific conditions. Two angles are said to be related if they satisfy certain criteria.A linear relationship (or linear association) is a statistical term used to describe a straight-line relationship between two variables. Linear relationships can be expressed either in a graphical format or as a mathematical equation of the form y = mx + b.To learn more about equation refers to:
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is the variable w in this equation the amount of money left over
$100−w=$36
Answer:
yeah “w” would just be 100-36 which is 64.