NEED HELP ASAP AS SOON AS POSSIBLE, WILL GIVE 69 POINTS
A city park commission received a donation of playground equipment from a parents' organization. The area of the playground needs to be 256 square yards for the children to use it safely. The playground will be rectangular.
The city will also put a fence around the playground. The perimeter, P, of the fence includes the gates. To save money, the city wants the least perimeter of fencing for the area of 256 square yards.
Jovana was trying to find a formula for that perimeter with one side 8 yards longer than the other side using the area. In which step did she make a mistake?
Step 1:
Step 2:
Step 3:
Step 4:
Step 5:
Step 6:
Step 7:
Explain her mistake. What is the correct formula?
Answers
Answer:
Explanation
Jovana needs to solve the equation x(x+8) = 256 for x
To do so, first distribute and get everything to one side
x*(x+8) = 256
x*x+x*8 = 256
x^2+8x = 256
x^2+8x-256 = 0
Now use the quadratic formula (a = 1, b = 8, c = -256)
x=−b±b2−4ac/√2a
x=−(8)±82−4(1)(−256)/√2(1)
x=−8±1088/√2
x≈−8±32.98485/2
x≈−8+32.98485/2 or x≈−8−32.98485/2
x≈24.98485/2 or x≈−40.98483/2
x≈12.49242 or x≈−20.49242
Another approach is to graph x^2+8x-256 and locate the roots as shown below
wwwdotdesmosdotcom/calculator/0miqroxamw
which leads to the same approximate solutions
Ignore the negative solution because a negative length or width makes no sense.
So the only practical x value is roughly 12.49242
If x = 12.49242, then
x+8 = 12.49242+8 = 20.49242
Therefore
Width = W = 12.49242
Length = L = 20.49242
which are approximate
The perimeter is approximately
P = 2*(L+W)
P = 2*(20.49242+12.49242)
P = 65.96968
Side Note:
A = L*W = 20.49242*12.49242 = 255.9999174564
which is fairly close to 256
Related Questions
What is the slope of the line that passes through the points (-3,5) and (6,-1)?
Answers
Answer:
C.
[tex]slope = \frac{( - 1 - 5)}{6 - ( - 3)} \\ = \frac{ - 6}{9} \\ = - \frac{2}{ 3} [/tex]
Interpret the numbers and variables in the following questions.
9.
A colony of bacteria doubles in number every hour. The expression 250.2 gives the numb
bacteria after h hours. What does tthe constant 250 in the expression represent?
he constant 250 in the expression represent?
Answers
Answer:
The input for the method is a continuous function f, an interval [a, b], and the function values f(a) and f(b). The function values are of opposite sign (there is at least one zero crossing within the interval). Each iteration performs these steps: Calculate c, the midpoint of the interval, c = a + b2.
Step-by-step explanation:
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The maximum number of students in a classroom
is 26. If there are 16 students signed up for the
art class, how many more students can join the
class without exceeding the maximum?
Answers
Answer:
10 students
Step-by-step explanation:
The maximum number is 26 and 16 have already signed up so in order to know how many can join without exceeding the maximum. You subtract 16 from 26. which then leaves you with 10
wats the answer of 1 2/5 ÷14/15
Answers
Answer:
2/5 ÷-14/15
2/5×-15/14
-3/7 is ur answer
Answer:
3/2 = 1 1/2 or 1.5
Step-by-step explanation:
1 2/5 ÷ 14/15
= 7/5 ÷ 14/15
= 7/5 × 15/14
= 3/2 = 1 1/2 or 1.5
Which is an equation of the line with
slope that contains the point (6, 4)?
Answers
Answer:
y=x-2
Step-by-step explanation:
x=6 and y=4, so simplest equation is y=x-2
You can have infinity lines with the point (6,4). Another example is [tex]y=\frac{1}{2} x+1[/tex]
Twelve apples were cut in thirds. How many pieces of apples are there now?
Answers
Answer:
36
Step-by-step explanation:
12*3=36
multiply 12 x 3. each apple is cut into groups of three so you now have twelve groups of 3 which is just multiplication. you can draw this out and count by hand
Rita is spending more time at home to study and practice math. Her efforts are finally paying off. On her first assessment she scored 58 points, then she scores 63 and 68 on her next two assessments. If her scores continued to increase at the same rate, on which assessments will she be scoring above 85? Select all that apply.
Answers
Answer:
7th
Step-by-step explanation:
63 - 58 = 5
68-63 = 5
She is adding 5 points each time
a1 = 58
d = 5
a2 = 63
a3 = 68
a4 = 58+5 = 73
a5 = 73+5 = 78
a6 = 78+5 = 83
a7 = 83+5 = 88
This is the first assessment greater then 85, so the 7th assessment
A pool has two inlet pumps A and B. If pump A alone is open, it takes 12 hours to fill the pool with water. If pump B alone is open, it takes 18 hours to fill the pool with water. If the pool needs to be filled in 10 hours, what is the least amount of time (in hours) both pumps need to be open?
Answers
Answer:
The least amount of time (in hours) both pumps need to be open is 3 hours.
Step-by-step explanation:
According to the Question,
Given That, A pool has two inlet pumps A and B. If pump A alone is open, it takes 12 hours to fill the pool with water. If pump B alone is open, it takes 18 hours to fill the pool with water.Let the Capacity of the Pool is 36Litre.
Thus, If pump A alone is open, it takes 12 hours to fill the pool with water. thus the Efficiency of Pipe A is 3 ltr/hour.And, If pump B alone is open, it takes 18 hours to fill the pool with water. thus the Efficiency of Pipe B is 2 ltr/hour.If the pool needs to be filled in 10 hours the least amount of time (in hours) both pumps need to be open is 3 hours.
Note:- if 3 hour both pipe open so 3 x (5) = 15 ltr Pool is Filled.
Now For Remaining 7 hour Pipe A with Efficiency 3 ltr/hour is open alone to fill the pool Remaining 7 x 3 = 21 ltr . Total 21+15 = 36ltr .
balance the following redox reaction by ion electron method.
I2+ HNO3 = HI03+ NO2+ H20
Answers
Answer:
BRO I DONT KNOW SORY I NEED POINTS
Step-by-step explanation:
Minke earned $100 working for h hours in a resuarant. He earns $10 an hour, and recieved $30 in tips. Write an equation using this information.
Answers
Answer:
10h + 30 = 100
Step-by-step explanation:
10h + 30 = 100
Answer:
140$
Step-by-step explanation:
So Mike earned 100$ right. So he earns 10$. And got 30$ by Tips The answer is 140$ I hope it helps :)
Solve the system of equations. Simplify your answer. Write the solution as an
ordered pair. *
2p+59 = 1
5p + 139 = 2
Answers
Answer:
(-29,-27.4)
Step-by-step explanation:
2p+59=1
-59 -59
2p=-58
/2 /2
p=-29
5p+139=2
-139 -139
5p=-137
/5 /5
p=-27.4
1) You are eating 3/4 cup of ice cream, 1/8 cup of chocolate syrup, and one sixteenths cup of cherries. How many (total) cups is your dessert?
Answers
Answer:
3/4=ice cream
1/8=chocolate syrup
1/16=cherries
Total=3/4+1/8+1/16
[tex]\frac{3X4}{4X4} +\frac{1X2}{8X2} + \frac{1X1}{16X1} \\\frac{12+2+1}{16} = \frac{15}{6}[/tex]
Total cups =15/6=2.5 cups.
Hoped this helped!
fine measure of each angle indicated
Answers
3) 160° 14) 111°
Suppose you roll a cube 30 times, what is a to describe the theoretical of rolling a 1, 4, 6, 7 Please help me!
Answers
Answer:
[tex]Pr(x) = \frac{1}{6}[/tex]
Step-by-step explanation:
Given
[tex]n = 30[/tex] --- number of rolls
Required
The theoretical probability of rolling: (a) 1 (b) 4 (c) 6 (d) 7
Assume the cube is 6 sided.
The sample space is:
[tex]S = \{1,2,3,4,5,6\}[/tex]
And the probability of each is:
[tex]Pr(x) = \frac{1}{6}[/tex]
Irrespective of the number of rolls, the theoretical probability of (a). (b), (c) and (d) is:
[tex]Pr(x) = \frac{1}{6}[/tex]
Help me down below
PLEASE
Answers
Answer:
there is one more zero
Step-by-step explanation:
now it's 8 million rather than 800 thousand.
Please help 50 points!
Simplify the expressed
Answers
Answer:
Step-by-step explanation:
[tex]\frac{x^{2} -x-12}{x+4} * \frac{2x^{2}-32 }{x^{2} -8x+16}[/tex] rewrite as multiplication
[tex]\frac{x^{2} +3x-4x-12}{x+4} * \frac{2(x^{2}-16) }{x^{2} -8x+16}[/tex] look to factor
[tex]\frac{x(x+3)-4(x+3)}{x+4} * \frac{2(x-4)(x+4) }{(x-4)^{2}}[/tex] , difference of 2 squares and perfect square
[tex]\frac{(x+3)(x-4)}{x+4} * \frac{2(x-4)(x+4) }{(x-4)^{2}}[/tex], finish factoring and simplify
2(x+3)
pls help ill give brainleiesr
Answers
Answer:
<1 and <3 are vertical angles
Step-by-step explanation:
Vertical angles are formed from the same lines are share a vertex. They are opposite from each other
<1 and <3 are vertical angles
<2 and <4 are vertical angles
Answer:
[tex]{\Huge{\underline{\underline{\textbf{\textsf{Answer}}}}}}[/tex]
Vertical angles are formed from the same lines are share a vertex. They are opposite from each other
● <1 and <3 are vertical angles● <2 and <4 are vertical anglesWhat are the coefficients in the problem 7a + 5b =c
a and b
5 and c
a,b,and c
7 and 5
Answers
Answer:
7 and 5
Step-by-step explanation:
they have variables with them
Answer:
D
Step-by-step explanation:
Need quick help with this math
Answers
Answer:
Eleanor and Harold
Step-by-step explanation:
The decimal [tex]0.13\overline{7}[/tex] consists of the sum of two terminating decimals and one non-terminating decimal:
[tex]0.13\overline{7}=0.1+0.03+0.00\overline{7}[/tex]
Therefore, we have:
[tex]0.13\overline{7}=\frac{1}{10}+\frac{3}{100}+\frac{7}{900},\\\\0.13\overline{7}=\frac{10}{100}+\frac{3}{100}+\frac{7}{900},\\\\0.13\overline{7}=\frac{13}{100}+\frac{7}{900}=\frac{117}{900}+\frac{7}{900}=\boxed{\frac{124}{900}}[/tex]
Hector's answer is equivalent but not simplified. However, they are both technically correct.
The length of the ladder that will run from the ground to the door of the tree house is nine feet. The plan recommends that the rungs of the ladder be spaced at 8-inch intervals. The first and last rung should be 6 inches from the respective ends. How many rungs will the tree house ladder have?
Answers
Answer:
13 Rungs
Step-by-step explanation:
According to the Question,
Given, The length of the ladder that will run from the ground to the door of the treehouse is 9 feet ( 9 × 12 = 108 inches).The plan recommends that the rungs of the ladder be spaced at 8-inch intervals.
And, The first and last rung should be 6 inches from the respective ends.Thus, the rungs Cover on 108 -(6+6) = 96 inches with 8-inch gaping between each rung.
Therefore, the Total Rungs on the treehouse ladders have (96/8)+1 ⇒ 13 Ladders.Find the average of 40.6, 10, 0.7, and 120.02
Answers
Answer:
42.83
Step-by-step explanation:
add all the numbers and divide by how many their are
wahat is 3556+55432
plaease fast
Answers
Answer:
58988
Step-by-step explanation:
3556+55432
=58988
Chin was shown the graph of a line that contained point (1, 7). He wrote f(x) = 4x + 3 to correctly represent the line. Which of these equations could represent the same line?
y – 7 = 3(x – 1)
y – 1 = 3(x – 7)
y – 7 = 4(x – 1)
y – 1 = 4(x – 7)
Answers
The equation that represents the same line containing point (1, 7) is as follows:
y - 7 = 4(x - 1)
Slope intercept form equation:y - y₁ = m(x - x₁)where
m = slope
The graph of the line contains (1, 7) .He represent the line correctly as f(x) = 4x + 3.
The equation that represent the same line is as follows:
Using the model:
y = mx + b
Therefore,
m = 4
Finally , the equation is as follows:
y - 7 = 4(x - 1)learn more on linear equation: https://brainly.com/question/2409163?referrer=searchResults
Work out the surface area of this cylinder.
Height=25
Diameter=12
Answers
help pls no brainlist if not
Answers
PLEASE HELP MEEEEEEEEEEEEE
Answers
Answer: 20 ft
Step-by-step explanation:
The mirror is set away from the flagpole on the same scale set away from her.
The distance she stand's away from the mirror is 1/4 of the length of the distance between the mirror and the flag pole because she's 1/4 of the flagpole's size.
This means her size x4 is the size for the flag pole. This checks out because 12x4=48
So to find the height we must do 5x4
5x4=20
17/18 dived by 2/4 as a reduced fraction
Answers
Answer:
1 8/9
Step-by-step explanation:
Hope you enjoy :)
please answer thissssss
Answers
Answer:
A? oof not sure
Step-by-step explanation:
I dont know
Help. Direct answers pls
Answers
Answer:
a₄ = 256
Step-by-step explanation:
Using the given definition , then
a₂ = a₁² = 2² = 4
a₃ = a₂² = 4² = 16
a₄ = a₃² = 16² = 256
Answer:
256
Step-by-step explanation:
a₁ = 2
a₂ = (a₁)² = 2 ² = 4
a₃ = (a₂)² = 4² = 16
a₄ = (a₃)² = 16² = 256
Alejandra correctly wrote the equation y-3=1/5 (x-10) to represent a line that her teacher sketched. The teacher then changed the line so it had a slope of 2, but still went through the same point. Which equation should Alejandra write to represent the new line?
Answers
Answer:
y-3=2(x-10)
Step-by-step explanation:
y-3=2(x-10)
