Answers
Answer:
1) x = 50 m
2) Max area = 22500 m²
3) Max area of each pen = 1500 m²
4) y = 150 m
5) dimensions of pen are 50m and 30m
6) Graph is attached
Step-by-step explanation:
Area of a rectangle is length × width
Let length be y and let width be x
Thus;
A = xy
Fencing material is 600m
Thus,perimeter = 600
Perimeter is; P = 6(length) + 2(width)
Thus;
600 = 6x + 2y
y = (600 - 6x)/2
y = 300 - 3x
Thus,
A = x(300 - 3x)
A = -3x² + 300x
We can see that the coefficient of x² is negative. This means that the parabola will open downward and has a maximum value at the vertex.
The vertex formula is;
x = -b/2a
a = -3
b = 300
Thus;
x = -300/(2 × -3)
x = 50 m
Since y = 300 - 3x, then;
y = 300 - 3(50)
y = 150 m
Maximum area of entire garden = xy = 50 × 150 = 7500 m²
There are 5 pens, thus;
Max area of each pen = max area of entire garden/5 = 7500/5
Max area of each pen = 1500 m²
Dimensions of each pen will be;
x and y/5
>> x = 50 m and y/5 = 150/5 = 30m
Related Questions
Jamal is x years old. His mother is 28 years older than Jamal. Jamal's uncle is two times older than Jamal's mother. Write and simplify an expression that represents Jamal's uncle age in years
Answers
Given: Jamal is x years old.
⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━
And, his mother is 28 years older than Jamal.
Then, age of Jamal's mother is = (x + 28)
⠀⠀⠀
Jamal's uncle is two times older than Jamal's mother.⠀⠀⠀
[tex]:\implies\sf Jamal's\: uncle\:age = (Jamal's mother age)\\\\\\ :\implies\sf Jamal's\: uncle\:age = 2(x + 28)\\\\\\ :\implies{\underline{\boxed{\pmb{\frak{\purple{Jamal's\: uncle\:age = 2x + 56}}}}}}\:\bigstar\\\\[/tex]
[tex]\therefore\:{\underline{\sf{Hence,\:the\:expression\:that\: represents\: Jamal's\: uncle \:age\:is\: {\pmb{2x + 36}}.}}}[/tex]
30 men can do a piece of work in 40 days . How long will it take to complete the work if 5 men are reduced? (Ans - 48 days ) Do step by step
Answers
Answer:
48 days
Step-by-step explanation:
Given that :
30 men can ado a piece of work in 40 days
Assume they work at the same rate, then we it means that ;
1 man will take (30 * 40) = 1200 days to finish the work
Reducing 5 men, means we now have (30 - 5) = 25 men
If ;
1 man takes 1200
25 men will take ;
1200 / 25
= 48 days
Can someone help me plzzz and thank you
Answers
Answer:
(0.5,-6)
Step-by-step explanation:
mid point=(x1+x2)/2
=(-3+4)/2
= 1/2
=0.5
midpoint=(y1+y2)/2
=(-9+(-3))/2
=(-9-3)/2
=--12/2
=-6
what are prime factors of 90
Answers
Answer:
2×3×3×5
Step-by-step explanation:
2×
[tex]{3}^{2} [/tex]
×5
Look at the question below
Answers
Answer:
y=6x is the answer
Step-by-step explanation:
Answer: y=6x
Step-by-step explanation:
12= (6) 2
24=(6) 4
36=(6) 6
48= (6) 8
So 6 is the correct.
Could someone help? please the deadline is in 20 min!!!
Answers
Answer:
7.$95 8. $112.50
Step-by-step explanation:
7.
50 divided by 100 is 0.5, then times by 90 is 45.
45 plus 50 is 95.
8.
$150/4=$37.50
$150-$37.50=$112.50
NUMBER THEORY The ratio of two less than a number to six more than that
number is 2 to 3. Which of the following numbers is it?
A8
B 18
C 22
D 24
Answers
Answer:
B 18.
Step-by-step explanation:
(n - 2) /(n + 6) = 2/3 Cross multiply:
2n + 12 = 3n - 6
18 = n.
The exponential function), whose graph is given below, can be written as h(x) = a•b^x.
Complete the equation for h(x).
Answers
Answer:
Step-by-step explanation:
h(x)=a*b^x
it passes through (0,6) and (1,4)
6=a*b^0
6=a*1
a=6
h(x)=6*b^x
4=6*b^1
b=4/6=2/3
[tex]h(x)=6*(\frac{2}{3} )^x[/tex]
Can someone please help me with math
Answers
Answer:
B. Y=2x+3
Step-by-step explanation:
I am not sure if you want the top one to be answered. However, The answer to the bottom one is B.
Hope this Helps,
-Jay
guys what does integer mean in mathematicians , plss help i kind of forgot✌
Answers
Answer:
Integer is a whole number; a number that is not a fraction.
Step-by-step explanation:
Match each shape with its corresponding formula for area.
1. the line which divides a figure into two congruent mirror images
rotational symmetry
2. property where a figure can be folded along a line to create two congruent mirror images
line symmetry
3. property where a figure can be rotated less than 360° and still look the same
line of symmetry
Answers
Answer:
1- line of symmetry
2- line symmetry
3- rotational symmetry
Step-by-step explanation:
im pretty sure because i just did this unit :]
5 pts
A 65 inch TV is 65 inches across the diagonal. If the length of
the TV is 57.1 inches wide, how tall is it?
Answers
Answer:
a number
Step-by-step explanation:
Write the equation of the circle with a center of (-5, 3) and a radius of 4.
A
(x + 5)2 + (y - 3)2 = 4
B
(x - 5)2 + (y + 3)2 = 4
(X - 5)2 + (y + 3)2 = 16
D
(x + 5)2 + (y - 3)2 = 16
Answers
Answer:
C
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
Here (h, k ) = (- 5, 3 ) and r = 4 , then
(x - (- 5))² + (y - 3)² = 4² , that is
(x + 5)² + (y - 3)² = 16 → D
State the best term for the given figure in the diagram
1.) F
2.) FE
B
13.) HG
4.) DB
5.) C
6.) BE
7.) DB
8.) AG
Note: Be able to define and draw a picture all all terms used in Chapter 10
In questions 9-10, BC is a radius of OC and AB is a tangent to OC.
Find the value of x
9.)
10.)
96
100
32
Q
56
The points K and M are points of tangency. Find the value(s) of x
11.)
12.)
K
K
3x - 10
4x + 7
.L
17
7x - 8
M M
Page
1 / 5
- +
Answers
Answer:
i dont understand what the question means
Step-by-step explanation:
Which sport has the smallest median height?
Answers
Answer:
baseball
Step-by-step explanation:
Answer:
baseball
Step-by-step explanation:
Look at the graph for baseball. Notice how the median, represented by the vertical line inside the box, is the one farthest to the left of center. This makes it the smallest median height (about 72.5 inches).
Write the equation of the graphed line.
Answers
Answer:
y = 1/4x+2
Step-by-step explanation:
y = mx+b where m is the slope and b is the y-intercept.
y = (-1/4)x+2
The volume of the Hawk’s refrigerator is 30 × 68 × 28.5 cubic inches.
The volume of the Lopez’s refrigerator is (30 × 68 × 28.5) + 16 cubic inches.
Without doing any calculations, which statement describes how the volume of
the Hawk’s refrigerator compares to the Lopez’s refrigerator?
A.
The volume of the Hawk's refrigerator is 16 cubic inches greater than the volume of the Lopez's refrigerator.
B.
The volume of the Hawk's refrigerator is 16 times less than the volume of the Lopez's refrigerator.
C.
The volume of the Hawk's refrigerator is 16 times greater than the volume of the Lopez's refrigerator.
D.
The volume of the Hawk's refrigerator is 16 cubic inches less than the volume of the Lopez's refrigerator.
Answers
Answer:D
Step-by-step explanation:
The correct statement that describes how the volume of the Hawk's refrigerator compares to the Lopez's refrigerator is: Option D.
D. The volume of the Hawk's refrigerator is 16 cubic inches less than the volume of the Lopez's refrigerator.
From the given information, we get,
The volume of the Hawk's refrigerator is given as 30 × 68 × 28.5 cubic inches.
The volume of the Lopez's refrigerator is given as (30 × 68 × 28.5) + 16 cubic inches.
We can see that the volume of the Lopez's refrigerator is obtained by adding 16 cubic inches to the volume of the Hawk's refrigerator.
Since 16 cubic inches are being added to the Hawk's refrigerator to get the Lopez's refrigerator, the volume of the Hawk's refrigerator must be 16 cubic inches less than the volume of the Lopez's refrigerator.
So, option D, "The volume of the Hawk's refrigerator is 16 cubic inches less than the volume of the Lopez's refrigerator," is the correct statement.
To learn more on volume click :
brainly.com/question/1578538
#SPJ6
Can somebody plz help answer these questions correctly (only if u done this before) thx :3
WILL MARK BRAINLIEST WHOEVER ANSWER THESE FIRST :DDD
Answers
Answer:
Shown Below
Step-by-step explanation:
WPT = 90
WPV = 30
VPT = 60
VPS = 90
RPS = 60
WPS = 120
QPS = 150
PLEASEE HELPPP!!! I APPRECIATE ITTTT
Answers
Answer:
this is about a 45 degree angle
Step-by-step explanation:
Triangle ABC is dilated using D as the center of dilation with a scale factor of 1/3
Answers
Answer:
The middle also 9 -8 = 1
Step-by-step explanation:
what are the coordinates of the vertex of the graph or table is it a maximum or minimum
Answers
Answer:
I'm pretty sure the answer is D.!
(1 point) A certain magical substance that is used to make solid magical spheres costs $800 per cubic foot. The power of a magical sphere depends on its surface area, and a magical sphere can be sold for $70 per square foot of surface area. If you are manufacturing such a sphere, what size should you make them to maximize your profit per sphere
Answers
Answer:
The answer is "[tex]r=0.175 \ ft[/tex]"
Step-by-step explanation:
using formula:
[tex]\to \text{profit = revenue-cost}[/tex]
[tex]\to revenue = 70 \times 4\pi r^2 = 280\pi r^2\\\\\to cost = 800 \times \frac{4}{3} \pi r^3 = \frac{3200}{3} \pi r^3[/tex]
so,
[tex]\to profit (p)= 280\pi r^2 - \frac{3200}{3} \pi r^3\\\\\text{max profit when}\\\\\to 560 \pi r-3200 \pi r^2=0[/tex]
[tex]\to \pi r(560 -3200r)=0\\\\ \to (560 -3200r)=0\\\\\to 3200r=560\\\\\to r=\frac{560}{3200}\\\\\to r=\frac{56}{320}\\\\\to r=\frac{7}{40}\\\\\to r=0.175 \ ft[/tex]
The box-and-whisker plot represents the heights (in meters) of the tallest buildings in Chicago.
a. What percent of the buildings are no taller than 345 meters?
About ____
percent of the buildings are no taller than 345 meters.
Answers
Answer:
75%
Step-by-step explanation:
The answer is 75% because each point/dot, represents 25% of the data. Below 345 meters are 3 points, therefore 3 * 25% = 75%.
Approximately 75% of the buildings are no taller than 345 meters for the box-and-whisker plot.
What is the box and whisker plot?A box and whisker plot (also known as a box plot) depicts a five-number summary of a set of data: lowest, lower quartile, median, upper quartile, and maximum.
The box-and-whisker plot represents the heights (in meters) of the tallest buildings in Chicago.
We can see that all three of the data points that are less than or equal to 345 meters are included in the lower half of the box-and-whisker plot, which represents the range from the minimum to the median height.
This means 3 × 25% = 75%.
So, we can estimate that approximately 50% of the buildings are no taller than 345 meters.
To learn more about the box and whisker plot click here:
https://brainly.com/question/2742784
#SPJ2
Some rational numbers are negative? True or false.
By the way:Give a reason why it is true or false
Answers
Step-by-step explanation:
True
As long as the denominator isn't zero and can be expressed as a fraction with two non zero intergers., the number would be rational
Which of the following binomials is a factor of 22 + 7 −9 ?
A. − 3
B. + 1
C. 2 − 3
D. 2 + 9
Answers
There are 240 calories in 5 ounces of a type of ice cream. How many calories are in 8 ounces of that ice cream?
Answers
Answer:
384 calories in 8 ounces of that ice cream
Step-by-step explanation:
240/5= 48
1 ounze of ice cream has 48 calories
48x8= 384
find the amount of sap maple syrup producer would have cod from each tree if the total amount (5gallons) was redistributed equally among the trees
Answers
Answer: hi
Step-by-step explanation:
Answer:
1/4
Step-by-step explanation:
hope is helps <3
3. Julissa's rose garden is in the shape of a trapezoid with a height of 35 feet. The bases of
the garden measure 50 feet and 32 feet. What is the area of Julissa's rose garden? *
C. 1,435 square feet
A. 58.5 square feet
B: 1,360 square feet
D. 2,870 square feet
Answers
Answer:
Step-by-step explanation:
i dont nkoe
express the area of the entire rectangle.
Answers
Answer:
Step-by-step explanation:
What is the unit rate from 1 1/4 cups of milk in 15 brownies
Answers
Answer:
12
Step-by-step explanation:
divide 15 by 1.25 because 1 1/4 in decimals is 1.25