A farmer has 300 ft of fencing with which to enclose a rectangular pen next to a barn. The barn itself will be used as one of the sides of the enclosed area.
What is the maximum area that can be enclosed by the fencing?
Enter your answer in the box.
ft²
Answers
.. y = x(300 -x)/2
This describes a downward opening parabola with zeros at x=0 and x=300. The vertex (maximum) will be found at the value of x that is halfway between those, x = 150.
For that value of x, the pen area is
.. y = 150(300 -150)/2 = 150^2/2 = 11,250 . . . . . square feet.
Answer:
11250ft2
Step-by-step explanation:
i took the test to make sure the other guy was right
Related Questions
Place the indicated product in the proper location on the grid. -4x 3 y 2 (7xy 4 )
Answers
Answer:
-28x^4y^6
Step-by-step explanation:
Given are two terms as
[tex]-4x^3y^2[/tex] and
[tex]7xy^4[/tex]
To find the product
we group like terms and find their product
Here we have -4 and 7 for coefficients : Product =-28
x terms are x^3 and x hence product = x^(1+3) =x^4
y terms are y^2 and y^4 hence product = y^(2+4) = y^6
Hence product is
[tex]-28x^4y^6[/tex]
Which law would you use to simply the expression 3^10/3^4
Answers
3^10/3^4
= 3^(10 - 4)
= 3^6
= 729
(50 points worth ) A rectangular prism fish tank a length of 5 1/2 in., a width of 7 in., and a height of 2 1/2 in. Use this to answer questions (a) and (b) below.
A) What’s the volume of this fish tank? Show all work and express your answer as a mixed number in its most simplified form!
B) Could this fish tank hold 100 in³ of water? Answer yes or no, then explain why in one or more sentences.
Answers
By definition we have that the volume of a rectangular prism is given by:
V = (w) * (l) * (h)
Where,
w: width
l: long
h: height
We then have to replace the values:
V = (7) * (5.5) * (2.5)
V = 96.25 in ^ 3
Equivalently:
V = 96 1/4 in ^ 3
B) Could this fish tank hold 100 in³ of water? Answer yes or no, then explain why in one or more sentences.
No, this fish tank could not hold 100 in³ of water.
This is because the prism volume (part A) is less than 100 in ^ 3.
In other words;
96 1/4 in ^ 3 <100 in ^ 3
PLEASE HELP
Describe the graph of y=1/2x-10 -3 compared to the graph of y=1/x
Answers
Answer: The graphs are attached.
Step-by-step explanation: We are to describe the graph of the function [tex]y=\dfrac{1}{2x-10}-3[/tex] compared to the graph of the function [tex]y=\dfrac{1}{x}.[/tex]
The graphs of both the functions are shown in the attached figure.
We can see that the graph of the function [tex]y=\dfrac{1}{2x-10}-3[/tex] is stretched by a factor of 0.5, shifted 5 units to the right and 3 units downwards as compared to the graph of the function [tex]y=\dfrac{1}{x}.[/tex]
Answer:
The graph of [tex]y=\frac{1}{2x-10}-3[/tex] is the graph of [tex]y=\frac{1}{x}[/tex] stretched vertically, shifted right by 10 unit and shifted 3 unit down.
Step-by-step explanation:
Given : The graph of [tex]y=\frac{1}{2x-10}-3[/tex] compared to the graph of [tex]y=\frac{1}{x}[/tex]
To find : Describe the comparison of the graphs.
Solution :
Let the parent function be[tex]y_1=\frac{1}{x}[/tex]
Transformed function [tex]y_2=\frac{1}{2x-10}-3[/tex]
Vertically Stretch:
If y =f(x) , then y= a f(x) gives a vertical stretch if a> 1.
Multiplying the parent function by 2 means you are stretching it vertically,
i,e [tex]y_1=\frac{1}{x} \rightarrow \text{Vertically stretch by 2} \rightarrow \frac{1}{2x} [/tex]
Shifting right :
f(x)→f(x-b), graph is transformed by b unit
Subtracting 10 means you are moving it right by 10 units
[tex]y_1=\frac{1}{2x} \rightarrow \text{Shifted right by 10 units} \rightarrow y_1=\frac{1}{2x-10}[/tex]
Shifting down :
f(x)→f(x)-b , graph is transformed by b unit
Subtracting 3 means you are moving it down by 3 units
[tex]y_1=\frac{1}{2x-10} \rightarrow \text{Shifted down by 3 units} \rightarrow y_1=\frac{1}{2x-10}-3=y_2[/tex]
Refer the attached figure below.
The graph of [tex]y=\frac{1}{2x-10}-3[/tex] is the graph of [tex]y=\frac{1}{x}[/tex] stretched vertically, shifted right by 10 unit and shifted 3 unit down.
A line Segment is part of a line that is bounded by two distinct end points. True or False?
Answers
The part of a line that connects two points.
It has definite end points.
Adding the word "segment" is important, because a line normally extends in both directions without end.
A diagram of line segment is attached with the solution .
11. The polygons are similar, but not necessarily drawn to scale. Find the values of x and y.
Answers
ABCD ~ NMPO. Note it's important to match up the corresponding angles.
For similar triangles, the ratio of corresponding sides is the same.
So the ratio of AB to NM equals the ratio of BC to MP.
AB/NM = BC/MP
(y - 1) / 6 = 5/3
Solve for y.
Use the same process to find x.
CD/PO = BC/MP
Could use some help!
Answers
[6, ∞) , x >= 6 so
answer is D. last one
6<= x < ∞
Jason's insurance company pays 80% of the cost of an ambulance ride, after he pays a $200 deductible. The ambulance ride costs $1200. How much would Jason pay for an ambulance ride?
A. $200B. $240C. $400D. $440
Answers
That's 1200 - 200 = 1000.
The insurance pays 80% of 1000. Percent means "out of 100" (per means "for every" and "cent" means 100 --> think CENTury...100 years). So 80% means 80 out of 100. That is, [tex] \frac{80}{100} [/tex]. To find 80% of 1000 we multiply: [tex] (\frac{80}{100})( 1000) = \frac{80000}{100}=800 [/tex]
If decimals are more your thing then represent 80% as .80 and multiply (1000)(.80) = 800.
Now, that's what the insurance pays. So out of that $1,000 the insurance pays $800 leaving Jason with a bill of $200 plus the deductible (another $200). That means Jason pays $400.
Answer:
400
Step-by-step explanation:
Find the values of x for which f(x) = g(x). (Enter your answers as a comma-separated list.) f(x) = x2, g(x) = x + 20
Answers
function f(x) = x²
function g(x) = x + 20
Solution:
Substitute f(x) with x² and substitute g(x) with (x + 20)
f(x) = g(x)
x² = x + 20
Move all terms to the left side. After moving, the positive ones become negative.
x² = x + 20
x² - x - 20 = 0
I break -x into -5x + 4x
x² - x - 20 = 0
x² - 5x + 4x - 20 = 0
Factorize x² - 5x
x² - 5x + 4x - 20 = 0
x(x - 5) + 4x - 20 = 0
Now factorize 4x - 20
x(x - 5) + 4x - 20 = 0
x(x - 5) + 4(x - 5) = 0
Separate (x - 5) from all terms using distributive property, the remaining one is (x + 4)
x(x - 5) + 4(x - 5) = 0
(x - 5)(x + 4) = 0
The solution
x - 5 = 0
x = 5
or
x + 4 = 0
x = -4
f(x) and g(x) will be both equal if the value of x is either 5 or -4
[4 - (3c - 1)][6 - ( 3c - 1)]
Answers
A cylindrical candle has a height of 11 cm and a diameter of 10 cm.
what is the volume of the candle, rounded to the nearest whole number?
Answers
The answer is 864 cm³
A circle is inscribed inside a square as shown. If graphed on the coordinate plane, the coordinates of the center of the circle would be (2, 5) and the coordinates of one other point on the circle would be (5,2). Find the area of the square. A) 12 2 B) 18 C) 24 2 D) 72
Answers
.
The formula for area of a circle is A = (pi) x r^2
3.14 x 5 x 5 = 78.5
therefore the area of the square must be larger than 78.5 and 72 is your only option.
D would be ur closest answer
im not 100% sure this is what i would pick
Two angles are ____ when they have a common vertex and a common side and don’t overlap.
Answers
Complete the tasks to subtract the polynomials vertically. (1.3t3 + 0.4t2 – 24t) – (0.6t2 + 8 – 18t) What is the additive inverse of the polynomial being subtracted? –0.6t2 + (–8) + (–18t) –0.6t2 + (–8) + 18t –0.6t2 + 8 – 18t 0.6t2 + (–8) + 18t
Answers
Final answer:
The additive inverse of the polynomial [tex](0.6t^2 + 8 - 18t)[/tex]being subtracted is [tex]-0.6t^2 - 8 + 18t.[/tex] This involves changing the sign of each term in the polynomial.
Explanation:
The additive inverse of a polynomial is obtained by changing the sign of each term in the polynomial. Given the polynomial to be subtracted ( [tex]0.6t^2 + 8 - 18t)[/tex], its additive inverse is found by changing the sign of each term, resulting in [tex]-0.6t^2 - 8 + 18t.[/tex] This operation flips the signs, preparing the polynomial for the subtraction process without altering its magnitude but reversing its direction on the number line.
A local restaurant advertises that the mode cost of their most popular meals is $8. If the costs of their most popular meals are $7, $8, $8, $12, $13, $15, $17, $18, and $20, which word or phrase best describes this kind of advertising?
Answers
What is the area of this figure?
Answers
2. First Triangle (on top) AREA: 7 * 2 * 1/2 = 7
3. Rectangle (middle) AREA: 7 * 4 = 28
4. Second Triangle (on bottom) AREA: 7 * 2 * 1/2 = 7
5. All together: 7 + 28 + 7 = 14 + 28 = 42
Will bought 3 college textbooks. One cost $32, one cost $46, and one cost $39. What is the average price of his books? What statement correctly calculates the average
Answers
117 / 3 = $39 ( average price)
The average price of the textbooks Will bought is $39, calculated by adding the individual prices and dividing by the number of books.
To calculate the average price of the textbooks Will bought, we simply sum up the costs of the three textbooks and divide by the number of textbooks. Let's do the math:
Add the cost of the textbooks: $32 + $46 + $39 = $117.Divide the total cost by the number of books: $117 / 3 = $39.The average price of the textbooks is $39.
a ladder leans against a wall and reaches a point 35 feet up the wall.The base of the ladder is 7 feet from the wall.To the nearest tenth of a foot, what is the length of the ladder
Answers
[tex]a^2+b^2=c^2[/tex]
[tex]c = \sqrt{a^2+b^2} [/tex]
Plug in values:
[tex]c = \sqrt{35^2+7^2}= \sqrt{1274} = 35.69[/tex]
Rounded to the nearest foot, is, 35.69ft.
Evaluate the expression for y = -7.
2y = __
Answers
Answer:
2y=-14
Step-by-step explanation:
If y=-7 and you multiply y by 2, you do the same thing to both sides and get -7 × 2 = -14
A book is in the shape of a right rectangular prism. It measures 8 1/2 inches tall, 7 inches wide, and 2 1/2 inches thick. What is the volume of the book? 47 1/2 in³ 80 1/2 in³ 148 3/4 in³ 179 1/2 in³
Answers
The formula for volume of a rectangular prism is:
V = lwh
Let's convert the dimensions to decimals, and then use the formula to solve.
8 1/2 = 8.5 as a decimal.
7 = 7 as a decimal.
2 1/2 = 2.5 as a decimal.
Multiply:
V = 8.5 × 7 × 2.5
V = 59.5 × 2.5
V = 148.75
148.75 = 148 3/4 as a fraction because if you convert 3/4 to a decimal by dividing the numerator by the denominator, it equals 0.75.
ANSWER:
The volume of the book is 148 3/4 inches cubed.
L = 8.5
W = 7
H = 2.5
V = 8.5 * 7 * 2.5
V = 148. 75 = 148 3/4
Alice, Bob, Farhana, and Jamal went out for pizza. When the bill came, they decided to split the check. Alice figured out what she owed by multiplying the bill by 0.25. Bob figured his share by finding 30% of the total. Farhana figured out her amount by dividing the total by 3. To determine what he owed, Jamal found 12% of the total. Who paid the most money?
Answers
Alice paid $35
Bob paid $42
Farhana paid about $46.67
Jamal paid $16.80
Your answer is Farhana, any number that you pick as your total, you will end up with the same results, Farhana being the most.
Hope this helped!
~xox Melis
In the scenario where a pizza bill is split between Alice, Bob, Farhana, and Jamal, Farhana ends up paying the most since she covers approximately 33.33% of the total bill.
Explanation:The question asks about Alice, Bob, Farhana, and Jamal splitting a pizza bill and figuring out who paid the most. Alice paid 25% (0.25) of the total bill, Bob paid 30% (0.30), Farhana paid a third which is approximately 33.33% (1/3), and Jamal paid 12% (0.12). Given these percentages, it is clear that Farhana paid the most for the pizza because 33.33% is the largest percentage amongst all. Therefore, irrespective of the total bill amount, Farhana ended up paying the highest portion.
Learn more about Percentage Distribution here:https://brainly.com/question/37916906
#SPJ2
The system of equations below has no solution 2/3x+5/2y=15 4x+15y=12 which equation could represent a linear combination of the system
Answers
we have
(2/3)x+(5/2)y=15 equation (I)
4x+15y=12 equation (2)
multiplying equation (1) by 6
6(2/3)x+6(5/2)y=6(15)--------------------- > 4x+15y=90 equation (3)
Subtracting equation (3) from equation (2) gives
4x+15y=90
4x+15y=12
-----------------
0x+0y=78------------ > 0=78
Therefore, a system of linear equation that has no solution results on two unequal numbers in both sides of the equation.
the answer is the option B) 0=26
Answer:
B.)0=26
Step-by-step explanation: Keep it simple
can someone answer this ?
A circle has a circumference of 1pi
what is the diameter if the circle
Answers
πD = 1π
D = 1π/π
D = 1
the length of the diameter is 1 unit
Given that lines a and b are parallel and that m∠8 = 108°, find m∠3.
Answers
Answer:
The answer would be 72
Find an equation of the line perpendicular to the graph of 14x-7y=4 that passes through the point at (2,-9)
Answers
Plugging into our slope- point formula, where y1=(-9), x1=2, and m=(-1/2), then:
y-(-9)=(-1/2)(x-2)
y+9=(-1/2)x+1
y=(-1/2)x-8
Hope this helps!
Answer:
The correct answer is D) y= -1/2x-8.
Step-by-step explanation:
Edge 2021.
Find two consecutive whole numbers that 76 lies between
Answers
Solve
8x^2+5=35
Round to the nearest hundredth.
The solutions are
___ and ___
Thanks! I need help with this one.
Answers
[tex]8 {x}^{2} + 5 = 35[/tex]
[tex] {8x}^{2} = 30[/tex]
[tex] {x}^{2} = 3 \frac{3}{4} [/tex]
[tex]x = ( \sqrt{3.75} ) \: \: \: \: \: x = - ( \sqrt{3.75} )[/tex]
[tex]x = 1.94 \: \: \: \: x = - 1.94[/tex]
Answer:
The solutions are [tex]1.94[/tex] and [tex]-1.94[/tex]
Step-by-step explanation:
we have
[tex]8x^{2} +5=35[/tex]
Solve for x
Subtract [tex]5[/tex] both sides
[tex]8x^{2} +5-5=35-5[/tex]
[tex]8x^{2}=30[/tex]
Divide by [tex]8[/tex] both sides
[tex]8x^{2}/8=30/8[/tex]
[tex]x^{2}=15/4[/tex]
Take square root both sides
[tex]x=(+/-)\sqrt{\frac{15}{4}} \\ \\x1=\frac{\sqrt{15}}{2}=1.94\\ \\x2=-\frac{\sqrt{15}}{2}=-1.94[/tex]
The solutions are [tex]1.94[/tex] and [tex]-1.94[/tex]
In which of the following circles are the values of the area and circumference the same? Approximate Π as 3.14.
a circle with a radius of 2 feet
a circle with a diameter of 2 feet
a circle with a radius of 4 feet
a circle with a diameter of 1 foot
Answers
[tex]A = \pi r^2[/tex]
and
[tex]C=2\pi r[/tex]
so:
[tex]A=C\\\\\pi r^2=2\pi r\qquad|:\pi\\\\r^2=2r\qquad|:r\\\\\boxed{r=2}[/tex]
It is true when radius = 2 units, so correct answer is:
A) a circle with a radius of 2 feet.
Answer:
Circle with a radius of 2 feet
Step-by-step explanation:
The cost of attendance at State College is $19,500 for the first year. Devise a periodic savings plan that will allow you to make small deposits for 5 years at a simple interest rate of 1.5% and save enough to pay for the first year at the college. 15 points!@!!
Answers
[tex]A=P*(1+r*t)[/tex]
Where:
A= total accumulated amount (principal + interest)
P= principal
r= yearly percentage rate
t= number of years
We need to save $19500 for the first year at a college. This is the amount we will have at the account after five years. In our case this is A.
Principal is the amount we need to put into savings to get the total amount needed. In our case this is P.
Yearly percentage rate is the percentage by which our savings increase at the end of a year. In our case this is r.
t is number of years that we are holding our money on the bank account.
To solve this problem we will assume that we are putting same amount each month on the bank account.
We are given:
A=$19500
P=?
r=1.5%
t=5 years
First step is to transform r into decimal number:
[tex]r= \frac{1.5}{100} =0.015[/tex]
Now we get back to our formula and we solve it for P:
[tex]A=P*(1+r*t) \\ P= \frac{A}{1+r*t} [/tex]
We insert numbers and we get our principal:
[tex]P= \frac{19500}{1+0.015*5} \\ P=18139.53[/tex]
We need to put $18139.53 into savings to get required amount after 5 years or 5*12=60months. Assuming that we put same amount each month into savings we need to put
[tex]18139.53 / 60 = 302.33[/tex]
This is our solution for this problem. This is closest to the amount we would need to put in real life. In real life we would earn interest onto interest and our monthly amount would be smaller.
What is the order of 5 x 10^4, 7 x 10^-5, 3 x 10^-9, 8 x 10^4 from least to greatest?
Answers
The numbers 5 x 10⁴, 7 x 10⁻⁵, 3 x 10⁻⁹, and 8 x 10⁴ ordered from least to greatest are 3 x 10⁻⁹, 7 x 10⁻⁵, 5 x 10⁴, and 8 x 10⁴.
The order of the numbers 5 x 10⁴, 7 x 10⁻⁵, 3 x 10⁻⁹, and 8 x 10⁴ from least to greatest is as follows:
3 x 10⁻⁹7 x 10⁻⁵5 x 10⁴8 x 10⁴Here, the least number is 3 x 10⁻⁹ because it has the smallest exponent indicating the smallest value.
The greatest number is 8 x 10⁴, which has the highest exponent denoting the largest value.