The function that gives the area (A) of the garden in terms of the width (x) is A(x) = x × (35 - x)
The domain of the function would be: 0 ≤ x ≤ 35
To find the function that gives the area of the garden, let's start by understanding the problem. Patricia wants to enclose a rectangular garden with a total of 70 feet of fencing material. This means that the sum of all sides of the rectangular garden (perimeter) should be equal to 70 feet.
For a rectangular garden, the perimeter is given by the formula:
Perimeter = 2 × (length + width)
In this case, since one of the sides is the width (x) and the other side is the length, the formula becomes:
70 = 2 × (x + length)
Solving for the length:
x + length = 70 / 2
length = 35 - x
Now, the area of a rectangle is given by the formula:
Area = length × width
Substitute the expression for the length:
Area = (35 - x) × x
Now, you have a function that gives the area (A) of the garden in terms of the width (x):
A(x) = x × (35 - x)
The domain of this function is the range of valid values for x. Since x represents the width of the garden, it should be a positive value. Also, the width cannot exceed 35 (since the length is 35 - x). So, the domain of the function is:
0 ≤ x ≤ 35
This means that the width (x) can take any value between 0 and 35 feet, inclusive, within the context of the problem.
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Final answer:
To find the area of the garden, we need to relate the width and length of the garden to the amount of fencing material. The function that gives the area of the rectangular garden is A = x(35 - x). The domain of the function is 0 ≤ x ≤ 35.
Explanation:
To find the function that gives the area of the rectangular garden, we need to relate the width and length of the garden to the amount of fencing material. Since the garden has four sides, two sides of length x and two sides of length y, we have the equation 2x + 2y = 70. Solving for y, we get y = 35 - x. The area of a rectangle is given by the formula A = x * y. Substituting y = 35 - x, we get A = x(35 - x) = 35x - x^2.
The domain of the function f(x) = 35x - x^2 is determined by the values of x that make sense in the context of the problem. In this case, the width cannot be negative and it cannot be greater than 35 (since the length cannot be negative or greater than 35 either).
Therefore, the domain of the function is 0 ≤ x ≤ 35.
The area of a triangle is 27 square feet its height is three times the length of its base find the height and base of the triangle
An ant is roughly 10 superscript negative 3 meters in length and the average human roughly one meter. how many times longer is a human than an ant?
Stan wants to make a rectangular garden. he has 34 ft of fencing to put around the perimeter. if the length is to be 5 ft more than the width, find the dimensions of the planned garden.
Using the concept of perimeter and given conditions, the planned garden's dimensions should be 6 feet by 11 feet with a total perimeter coverage of 34 feet.
Explanation:The problem can be solved by using the concept of perimeter in mathematics. The perimeter of a rectangle is the sum of all its sides, and given that Stan has 34 ft of fencing, this can be translated to a formula: 2*(length + width) = 34ft.
From the question, we also know that the length of the fence is 5 ft more than the width. This can also be translated into an equation: length = width + 5.
By substituting this into the earlier equation, we can find the width: 2*(width + width + 5) = 34, which simplifies to 4*width + 10 = 34. Solving this gives us width = 6 ft.
Substitute width = 6 ft into the length equation to get length = width + 5 = 6 + 5 = 11 ft. Therefore, the dimensions of the planned garden are 6 ft by 11 ft.
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what is the solution to the inequality 2n+5 > 1
The solution to the inequality 2n + 5 > 1 is n > -2 after isolating the variable n and simplifying the equation.
Explanation:The solution to the inequality 2n + 5 > 1 involves some basic algebra. First, we should isolate the variable, n, on one side of the inequality. This is accomplished by subtracting 5 from both sides of the inequality which gives us: 2n > 1 - 5.
Simplifying the right side gives us 2n > -4. Then, we need to divide every term by 2 which gives us n > -4/2. Simplifying further, we find that the solution to the inequality 2n + 5 > 1 is n > -2.
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Noah wants to put $1,000 in a savings account with a 1.5% annual interest rate. How much more money will he have after one year if it is compounded monthly versus no compounding
A:$0.10
B:$15.00
C:$1015.00
D:$1015.10
if f(x)=-6x+12, then f^-1(x)=
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What is the relationship between 8.76×106 and 8.76×102 ?
Select from the drop-down menus to correctly complete the statement.
8.76×10^6 is ___ times ___ than 8.76×10^2 .
1) 1000, 10,000, 100,000, or 1,000,000.
2) Greater or Less.
10^6 = 1,000,000
10^2 = 100
1,000,000 / 100 = 10,000
so 8.76x10^6 is 10,000 times greater than
2 angles, angle A and angle B, form a linear pair. Angle B is an obtuse angle. What type of angle is angle A
t - yc = b solve for c (literal equations)
Hey!
Hope this helps...
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Like equations with the same variable on both sides...
We want to get c by itself...
T - yc = b [Subtract T from both sides]
-yc = b - T [divide -y from both sides]
c = -(b - T)/y
So...
The answer is: c = -(b - T)/y
Which is true? A 11.949 > 12.000 B 14.887 < 14.097 C 17.0010 > 17.0100 D 19.0929 < 19.7893
(01.04) jorge was tracking the decreasing temperature in the morning. at 7
a.m., it was 65 degrees fahrenheit. at 9
a.m., it was 55 degrees fahrenheit. if jorge made the function f(x) = −5x + 100, what would the −5 represent? (1 point) the temperature at midnight the length of time he recorded for the total change in degrees the rate at which the temperature was decreasing
Find a number whose product with 9 is the same as its sum with 56
Final answer:
The requested number is 7, which when multiplied by 9 or added to 56, gives the same result of 63.
Explanation:
To find a number whose product with 9 is the same as its sum with 56, we set up the equation x * 9 = x + 56. Solving for x, we first distribute the 9 to the x, resulting in 9x = x + 56. Next, we subtract x from both sides to get 8x = 56. Finally, we divide both sides by 8 to find that x = 7. Hence, 7 is the number we are looking for, as 7 * 9 = 63 and 7 + 56 = 63, confirming that the product and the sum yield the same result.
Lola takes the train from Paris to Nice. The distance between the two cities is about 921,000 meters. If the train travels at a speed of 307 kilometers per hour, how long will it take Lola to travel from Paris to Nice
Answer: It will take 1.75 minutes to travel from Paris to Nice.
Step-by-step explanation:
Since we have given that
Distance between the two cities = 921,000 meters
Since we know that
1 km = 1000 meters
[tex]1\ m=\dfrac{1}{1000}\ km\\\\921000\ m=\dfrac{921000}{1000}\ km=921\ km[/tex]
Speed at which the train travels = 307 km/hr
As we know the formula for time taken:
[tex]Time=\dfrac{Distance}{Speed}=\dfrac{921}{307}=0.029\ hours\\\\Time=0.029\times 60=1.75\ minutes[/tex]
Hence, it will take 1.75 minutes to travel from Paris to Nice.
PLEASE HELP Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x
f(x) = (x+3)/4
g(x) = 4x - 3
How to you find the cotangent of 5(pi)/6?
Write a real world description to fit the expression -59/5
A debt of $59 dollars owed by five (5) ladies and will also be divided among them. They borrow $59 dollars to buy the materials for their science project because 3 out of 5 ladies do not have money to spend to their science project.
Order feet,inches,miles,yards from most precise to least precise
The measurement 5.22 cm has three significant figures which means that
Gabrielle is 14 years older than Mikhail. The sum of their ages is 96 . What is Mikhail's age?
Please help. Determine the domain of the inverse function and find the inverse function.
Cynthia besch wants to buy a rug for a room that is 1313 ft wide and 2222 ft long. she wants to leave a uniform strip of floor around the rug. she can afford to buy 112112 square feet of carpeting. what dimensions should the rug have?
Solve the Quetion and times 50 equals 5000 explain your solution
What is the length of y on this circle
8 units
12 units
10 units
18 units
How would I do this?
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choose the correct word to complete the following sentance: a natural number is (always, sometimes, never) a whole number
Nina can ride her bike 63,360 feet in 3,400 seconds, and Sophia can ride her bike 10 miles in 1 hour. What is Nina's rate in miles per hour if there are 5,280 feet in a mile?
Which girl bikes faster?
3400/60 = 56.6666 minutes/60 = 0.94 hours
63360/5280 = 12 miles
12/0.94 = 12.76 miles per hour for Nina
Nina is faster
During the month of February, Fabulous Feet Shoe Mart sold 30 pairs of red loafers. After an ad campaign to boost sales, they sold 39 pairs in March. Find the percent of increase in sales.
35%
30%
23%
18%
Solve for c.
a(c + b)=d
A. c = d + ab / a
B. c = d − ab/b
C. c = d − ab/a
D. c = ab − d/a
Solve for b.
d = 3a + 3b
A. b = 3a−d/3
B. b = d−3a/3
C. b = d − 3a
D. b = d − 3a/ a
The formula for a trapezoid relates the area A, the two bases, a and b, and the height, h.
A = h(a+b)/2
Solve for b.
b=2A−a/h
b=Ah/2 − a
b=2A/h − a
b=2A/h + a
The formula for the perimeter of a rectangle is P = 2(l+w).
Solve for l.
l = 2P − w
l = p−w/2
l = P/2 + w
l = p/2 − w
Answer:
Here is your answer for K12 AZVA:
c = d − a b / a
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