The perimeter of the rectangle is the sum of its dimensions
The dimensions that minimize the perimeter are [tex]\mathbf{10\sqrt{10 },10\sqrt{10 }}[/tex]
The area is given as:
[tex]\mathbf{A = 1000}[/tex]
Let the dimension be x and y.
So, we have:
[tex]\mathbf{A = xy = 1000}[/tex]
Make x the subject
[tex]\mathbf{x = \frac{1000}{y}}[/tex]
The perimeter is calculated as:
[tex]\mathbf{P = 2(x + y)}[/tex]
Substitute [tex]\mathbf{x = \frac{1000}{y}}[/tex]
[tex]\mathbf{P = 2(\frac{1000}{y} + y)}[/tex]
Expand
[tex]\mathbf{P = \frac{2000}{y} + 2y}[/tex]
Differentiate
[tex]\mathbf{P' = -\frac{2000}{y^2} + 2}[/tex]
Set to 0
[tex]\mathbf{ -\frac{2000}{y^2} + 2 = 0}[/tex]
Rewrite as:
[tex]\mathbf{ -\frac{2000}{y^2} = -2}[/tex]
Divide both sides by -1
[tex]\mathbf{\frac{2000}{y^2} = 2}[/tex]
Multiply y^2
[tex]\mathbf{2000 = 2y^2}[/tex]
Divide by 2
[tex]\mathbf{1000 = y^2}[/tex]
Take square roots of both sides
[tex]\mathbf{y = \sqrt{1000 }}[/tex]
[tex]\mathbf{y = 10\sqrt{10 }}[/tex]
Substitute [tex]\mathbf{y = \sqrt{1000 }}[/tex] in [tex]\mathbf{x = \frac{1000}{y}}[/tex]
[tex]\mathbf{x = \frac{1000}{\sqrt{1000}}}[/tex]
[tex]\mathbf{x = \sqrt{1000}}[/tex]
[tex]\mathbf{x = 10\sqrt{10 }}[/tex]
Hence, the dimensions that minimize the perimeter are [tex]\mathbf{10\sqrt{10 },10\sqrt{10 }}[/tex]
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Crafts Unlimited sells ribbon by the foot. Serena needs ribbon
for an art project. The cost of the ribbon is 5 feet for $3.00.
Feet of Ribbon 1 5 10 15
Cost (in dollars) $3.00
a. Complete this ratio chart based on the information provided.
b. How many feet of ribbon can Serena buy for $12.00?
c. If Serena needs 17 feet of ribbon, how much will she pay?
How do you know?
The completed ratio chart is provided below:
Feet of Ribbon 1 5 10 15
Cost $0.60 $3 $6 $9
The amount Serena would get if she has $12 is 20 yards.
The amount Serena would pay if she wants 17 feet of the ribbon is $10.20.
The first step is to determine the unit cost of a ribbon.
Unit cost of a ribbon = $3 / 5 = $0.60
The cost of 10 feet of the ribbon = $0.60 x 10 = $6
The cost of 15 feet of the ribbon = $0.60 x 15 = $9
The feet of ribbon Serena can buy if she has $12 = $12 / $0.60 = 20 yards.
The cost of 17 feet of the ribbon = $0.60 x 17 = $10.20
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What is the value of w?
Answer:
w= -2. Solve for w: (w-5) (w+2) = w^2-4. Expand out terms of the left hand side: w^2-3 w-10 = w^2-4. Subtract w^2-4 from both sides
Step-by-step explanation:
Given m\parallel nm∥n, find the value of x. n m (8x+19)° 59°
Which expression can be placed on the right side of the equals sign to form an equation. 2+33=
Answer:
7x.
Step-by-step explanation:
2 + 33 = 7x
35 = 7x
Solution is x = 5.
Answer: 5² + 4
Step-by-step explanation:
Select the table of values that you would use to graph f(x) = 3x2 – 4.
Hello Please help.
The the table of values that you would use to graph [tex]f(x) = 3x^{2} -4[/tex] is option "B"
What is point on graph?A point is the basic relationship displayed on a graph. Each point is defined by a pair of numbers containing two coordinates. A coordinate is one of a set of numbers used to identify the location of a point on a graph.
According to the question
Points on graph for equation :
[tex]f(x) = 3x^{2} -4.[/tex]
Now,
Table of points on graph
x y
-2 8
-1 -1
0 -4
1 -1
2 8
Hence, The the table of values that you would use to graph [tex]f(x) = 3x^{2} -4[/tex] is option "B" .
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A rectangular photograph has an area of 48 square inches. If the width of the photograph is 8 inches less than its height, find the dimensions of the photograph
The height of the photograph is
Answer:
H= 12, W=4
Step-by-step explanation:
let H = height
let H-8 = width
We know that the area of the rectangle is A = H*W
now we substitute the statements we have made:
H(H-8) = 48
H^2 - 8H - 48 = 0
Simplify:
(H-12)(H+4) = 0
So now we have 2 options H = -4 or H = 12, having a -ve number as height does not make sense so we use 12.
We know that width is H-8 so now we do 12-8 which is 4.
Therefore width is 4 and height is 12.
1
Write the equation
for this line in
slope-intercept form.
y = -2x + [?]
4-3-4-1
34
op
A 4
B. 2
C -2
D. -12
Answer:
A, -4 is the answer
Step-by-step explanation:
it intersects there
You buy a $266,000 home.with. a.down payment of 21%. Find the amount of the down payment and the mortgage amount.
down payment mortgage amount
Harold and his brother collected 2019 cans a 1-year period. Each boy collected the same number of cans. About how many cans did each boy collect? Explain how you found your answer.
Answer:
1008.5 cans
Step-by-step explanation:
2019/2=1008.5
if you wanted per day, 1008.5/365=2017/730
Evaluate.
12⋅(1/4+1/3)power 2 +23 help ASAP
Answer:
325/12
Step-by-step explanation:
12(1/4 + 1/3)² + 23
12(7/12)² + 23
12(49/144) + 23
49/12 + 23
325/12 = 27 1/12 = 27.08333333
Lol pls hurry!!
I need this asap
Answer: 2, D
Step-by-step explanation: f=-2, so 4x-2 would give -8 add 10 would give 2 as it is for the negative
what is the equation of this line in slope-intercept form
Answer:
y=3/5x+3 i think
Step-by-step explanation:
3 is the y intercept, and to find the slope its rise over run so 3 up and 5 to the side, i hope this helps!!
plz help asap plzz plllzzzzz
1
4
3
Time (h)
2
.
3
Cars
Washed
6
9
12
a. Proportional?
b. Equation:
C. Number of hours:
3. Cars washed:
Step-by-step explanation:
Proportional = time/cars washed
= 1/3
no. of hours= 90hours
cars washed = 30 cars washed
1. A cylindrical jar has a radius of 5 inches and a height of 9 inches. The jar is filled with marbles that have a volume of 20 in3. Use 3.14 for pi. Show work. Complete sentences.
a. What is the volume of the jar?
b. How many whole marbles can fit in the jar?
who ever gets the right answer will get brainliest ;)
Answer:
a. Volume = π15.02 9.0=6361.73
b. I am very sorry, I don't know
Step-by-step explanation:
WHAT DOES EXPONENT C MEAN LETS SAY A NUMBER IS IN PARANTHESIS AND WITHIN THAT PARENTHESIS THERES A C AS AN EXPONENT WHAT DOES THAT MEAN
Answer:
It means that the number is raised to the power of c. For example, if it is (2^3), the answer would be 8.
Step-by-step explanation:
What is the period of the trigonometric function f(t) = 3sin()?
A) 2 pi
B) 3 pi
C) 4 pi
D) pi / 2
Problem 1
Each scholar in fifth grade participates in one of the three extracurricular activities: sports,
chess, or art.
2/5 of the fifth grade scholars participate in sports
1/4 of the fifth grade scholars participate in chess
What fraction of the fifth grade scholars participate in art?
Answer:
7/20 participate in art.
Answer:
7/20 hcjauwauhfehhfieafuewaueiwavibiurbviubwibvebaiubj
plz help its so confusing
Answer:
20, 4
Step-by-step explanation:
Let's assume total number of students registered is n
Last week n/4 people are absent
so people present are n - n/4 = 3n/4
Today after return of Jen 1/5 n are absent
so people present are n - n/5 = 4n/5
which is also equal to last week present people + 1 (Jen)
= 3n/4 + 1
= (3n + 4) / 4
so (3n + 4) / 4 = 4n/5
=> 3n + 4 = 4n/5 * 4
=> (3n + 4) * 5 = 16n
=> 15n + 20 = 16n
=> 20 = n
=> n = 20
So total students registered for class is 20
today no of people absent = n/5 = 20/5 = 4
Which set of ordered pairs lies along the same vertical line?
Answer:
All ordered pairs with the same x value
Step-by-step explanation:
A vertical line can be represented by the equation x=k for some value k. So any pair with x value equal to k satisfies the equation and is thus in the set
8.5x-y= 16
O -y= 5x + 16
O x=5y-16
O y= 5x +16
O y= 5x- 16
Answer:
y = 5x - 16
Step-by-step explanation:
1. To solve this question, we must convert 5x - y = 16 into slope-intercept form (y = mx + b).
2. (Solving for y)
Step 1: Subtract 5x from both sides.
[tex]5x - y - 5x = 16 - 5x[/tex] [tex]-y = -5x +16[/tex]Step 2: Divide both sides by -1.
[tex]\frac{-y}{-1} =\frac{-5x+16}{-1}[/tex] [tex]y = 5x - 16[/tex]Therefore, the answer is y = 5x - 16.
Pls help this is timed and I don’t understand
Answer:
178
Step-by-step explanation:
All right!!
Line l is parellel to line m.
So if r is 91 then we can infer that s helps it make a 180 degree angle/straight line.
So 180 - 91 = 89
s = 89
If the two lines are parallel then s = u because of inner angles/outer angles stuff.
If s=u then u = 89 as well.
And because of vertical angles, t =u so t = 89.
Now the question asks to find t + u, so t + u = 89 + 89 = 178
Hope that helps!!
100 Points
Emily wants to buy turquoise stones on her trip to New Mexico to give to at least 4 of her friends. The gift shop sells small stones for $4 and large stones for $6, and Emily has no more than $30 to spend.
Write and graph a system of Linear Equations and write two possible solutions.
Answer:
Step-by-step explanation:
what is she going to buy? Small stones or big stones? if its small stones then she can buy 7 small stones. If its big stones then she can buy 5 big stones.
If 3 bananas cost of 50 cents, how many bananas can be bought for 20 dollars?
Answer:
120 bananas
Step-by-step explanation:
$20 = 2000 cents
Create a proportion:
Cross multiply, then divide: 3 × 2000 = 6000, 6000 ÷ 50 = 120
So, you can buy 120 bananas for $20
hope this helps
sara buys two bags of chips and three boxes of pretzels for $ 85. He then buys another bag of chips and two more boxes of pretzels for $ 50. Find the cost of each bag of chips and each box of pretzels.
Answer:
Chips= $20 Pretzel=$15
Step-by-step explanation:
Sara bought 2 Chips + 3 Pretzels = $85
(Extra) 1 Chips + 2 Pretzels = $50
Pretzels are twice as much as chips so above ^^ Can be expressed
as Pretzel (15) + Pretzel (15) + Chips(20) = $50
Now lets go back to the first line Putting in the new prices
Chips(20) + Chips(20) + Pretzel(15) + Pretzel(15) = Pretzel(15) = $85
A satellite orbits the Earth with an elliptical orbit modeled by x squared over 47 million three hundred thirty four thousand four hundred plus y squared over forty three million nine hundred fifty six thousand nine hundred equals 1 comma where the distances are measured in km. The Earth shares the same center as the orbit. If the radius of the Earth is 6,370 km, what is the maximum distance between the satellite and the Earth?
6,880 km
6,630 km
510 km
260 km
An elliptical of the satellite in the field of astrodynamics is known as a
Kepler orbit.
The distance between the satellite and the Earth is; 510 km.
Reasons:
The function that represents the elliptical orbit of the satellite is presented
as follows;
[tex]\dfrac{x^2}{47,334,400} + \dfrac{y^2}{43,956,900} = 1[/tex]
The radius of the Earth, R = 6,370 km.
The equation of an ellipse is presented as follows;
[tex]\mathbf{\dfrac{(x - h)^2}{a^2} + \dfrac{(y - k)^2}{b^2}} = 1[/tex]
Where, in a horizontal ellipse;
a = The major axis (the longer axis), which gives the maximum distance
between the satellite and Earth.
b = The minor axis (the shorter axis)
By comparison, we get;
a² = 47,334,400 km²
Therefore;
a = √(47,334,400 km²) = 6,880 km.
The distance between the satellite and the surface of the Earth, d, is given
as follows;
d = a - R
Which gives;
d = 6,880 km - 6,370 km = 510 km
Distance between the satellite and the surface of the Earth, d = 510 km.
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Answer:510 KM
Step-by-step explanation:
To mail a letter to Vienna, Austria the post office charges a flat rate of $8.00 and an additional $0.50 for every ounce the letter weighs. The cost of mailing a letter is determined by the equation y=0.50x+8.00, where y is the cost of the postage and x is the weight of the letter in ounces.
Step 2 of 2 : Use the graph to estimate to the nearest quarter of a dollar ($0.25) the cost to send a letter that weighs 3 ounces.
Answer:
It will cost 38 quarters
Step-by-step explanation:
y = 0.50x + 8.00
y = 0.5(3) + 8.00
y = 1.5 + 8.00
y = $9.50
$9.50/.25
38 quarters
Hope this is the answer you are looking for.
The table shows a proportional relationship between x and y what is the unit rate of y per x ( 4, 5 , 6 , 7 ) (8 , 10 , 12 , 14 ) ?
Answer:
6
Step-by-step explanation:
A study found that 85% of sports business executives surveyed believed that sponsor development of ________ in new venues will be a benefit of top-tier sponsorships in coming years.
you have to estimate
Answer:
75,388
Step-by-step explanation:
Long Multiplication form
[tex]\mathrm{Mutliply\:the\:bold\:numbers}[/tex]
[tex]\frac{\begin{matrix}\space\space&8&0&\textbf{2}\\ \times \:&\space\space&9&\textbf{4}\end{matrix}}{\begin{matrix}\space\space&\space\space&\space\space&8\end{matrix}}[/tex]
[tex]\frac{\begin{matrix}\space\space&8&\textbf{0}&2\\ \times \:&\space\space&9&\textbf{4}\end{matrix}}{\begin{matrix}\space\space&\space\space&0&8\end{matrix}}[/tex]
[tex]\mathrm{Multiply}\\\\8\cdot \:4=32[/tex]
[tex]\mathrm{Carry\:}3\mathrm{\:to\:the\:column\:on\:the\:left\:and\:write\:}2\mathrm{\:in\:the\:result\:line}[/tex]
[tex]\frac{\begin{matrix}\space\space&3&\space\space&\space\space&\space\space\\ \space\space&\space\space&\textbf{8}&0&2\\ \times \:&\space\space&\space\space&9&\textbf{4}\end{matrix}}{\begin{matrix}\space\space&\space\space&2&0&8\end{matrix}}[/tex]
[tex]\mathrm{Add\:the\:carried\:digit,\:}3\mathrm{,\:to\:the\:result}[/tex]
[tex]\frac{\begin{matrix}\space\space&3&\space\space&\space\space&\space\space\\ \space\space&\space\space&8&0&2\\ \times \:&\space\space&\space\space&9&4\end{matrix}}{\begin{matrix}\space\space&3&2&0&8\end{matrix}}[/tex]
[tex]\mathrm{Multiply\:the\:top\:number\:by\:the\:bolded\:digit\:of\:the\:bottom\:number}[/tex]
[tex]\frac{\begin{matrix}\space\space&\space\space&\textbf{8}&\textbf{0}&\textbf{2}\\ \space\space&\times \:&\space\space&\textbf{9}&4\end{matrix}}{\begin{matrix}\space\space&3&2&0&8\end{matrix}}[/tex]
[tex]\mathrm{Mutliply\:the\:bold\:numbers}:\quad \:2\cdot \:9=18[/tex]
[tex]\mathrm{Carry\:}1\mathrm{\:to\:the\:column\:on\:the\:left\:and\:write\:}8\mathrm{\:in\:the\:result\:line}[/tex]
[tex]\frac{\begin{matrix}\space\space&\space\space&\space\space&1&\space\space\\ \space\space&\space\space&8&0&\textbf{2}\\ \space\space&\times \:&\space\space&\textbf{9}&4\end{matrix}}{\begin{matrix}\space\space&3&2&0&8\\ \space\space&\space\space&\space\space&8&\space\space\end{matrix}}[/tex]
[tex]\mathrm{Add\:the\:carried\:number\:to\:the\:multiplication}:\quad \:1+0\cdot \:9=1[/tex]
[tex]\frac{\begin{matrix}\space\space&\space\space&\space\space&\textbf{1}&\space\space\\ \space\space&\space\space&8&\textbf{0}&2\\ \space\space&\times \:&\space\space&\textbf{9}&4\end{matrix}}{\begin{matrix}\space\space&3&2&0&8\\ \space\space&\space\space&1&8&\space\space\end{matrix}}[/tex]
[tex]\mathrm{Mutliply\:the\:bold\:numbers}:\quad \:8\cdot \:9=72[/tex]
[tex]\mathrm{Carry\:}7\mathrm{\:to\:the\:column\:on\:the\:left\:and\:write\:}2\mathrm{\:in\:the\:result\:line}[/tex]
[tex]\frac{\begin{matrix}\space\space&7&\space\space&1&\space\space\\ \space\space&\space\space&\textbf{8}&0&2\\ \times \:&\space\space&\space\space&\textbf{9}&4\end{matrix}}{\begin{matrix}\space\space&3&2&0&8\\ \space\space&2&1&8&\space\space\end{matrix}}[/tex]
[tex]\mathrm{Add\:the\:carried\:digit,\:}7\mathrm{,\:to\:the\:result}[/tex]
[tex]\frac{\begin{matrix}\space\space&7&\space\space&1&\space\space\\ \space\space&\space\space&8&0&2\\ \times \:&\space\space&\space\space&9&4\end{matrix}}{\begin{matrix}\space\space&3&2&0&8\\ 7&2&1&8&\space\space\end{matrix}}[/tex]
[tex]\mathrm{Add\:the\:rows\:to\:get\:the\:answer.\:\:\:Fill\:in\:trailing\:zeros\:\:(not\:required)}[/tex]
[tex]\frac{\begin{matrix}\space\space&\space\space&8&0&2\\ \space\space&\times \:&\space\space&9&4\end{matrix}}{\begin{matrix}0&3&2&0&8\\ 7&2&1&8&0\end{matrix}}[/tex] [tex]=75,388[/tex]
See Image for the addition: