A rectangular poster is to contain 578 square inches of print. The margins at the top and bottom of the poster are to be 2 inches, and the margins on the left and right are to be 1 inch. What should the dimensions of the poster be so that the least amount of poster is used?
Answers
Answer:
19 by 38
Step-by-step explanation:
The area of the poster, A=xy
Margin at both up and bottom is 2inches, at the right and left is 1 inch
Then we can say
(x-4)(y-2)= 578
Let us make y subject of the formula
(y-2)= 578/(x-4)
y=[ 578/(x-4)] + 2
If we substitute into the area A equation we have
A= x { [ 578/(x-4)] + 2}
A= 2x + (578x)/(x - 4)
If we differentiate we have
A'(x)= [2+578(x-4)+578x ]/ (x-4)^2
=[ 2(x-4)^2 + 578(x -4) + 578x ] / (x-4)^2
=[ 2(x^2 - 8x +16) + 578(x-4) + 578x ] /(x-4)^2
If we simplify this we have
=[ 2x^2 -16x +32+578x -578x - 2312]/ (x-4)^2
=( 2x^2 -16x - 2312) / (x-4)^2
At A'(x)= 0
= ( x^2 - 8x - 2312) / (x-4)^ =0
If we divide through by 2 we have
x^2 - 8x - 1156= 0
Solving the quadratic eqn( CHECK THE ATTACHMENT)
X= 38 or -30 then we choose the positive one, then x= 38
Then from area of the poster
A= (x-4)(y-2)= 578
Substitute 38 as value of x
(38-4)(y-2)= 578
34(y-2)=578
34y-68=578
34y=646
y=19
Hence dimensions of the poster is 19 by 38
CHECK THE ATTACHMENT FOR QUADRATIC SOLUTION
Related Questions
What is the correct answer?!
HELP FAST!
Answers
Answer:6.66
Step-by-step explanation:
I’m pretty sure its infinite if not just putt that answer
Answer: 84 r4
Step-by-step explanation:
I think that is correct.
What is h(p)=(p3+4p2-2) in distributive property
Answers
h
p
=
p
3
+
4
p
2
−
2
Step 1: Divide both sides by p.
h
p
p
=
p
3
+
4
p
2
−
2
p
h
=
p
3
+
4
p
2
−
2
p
Answer:
h
=
p
3
+
4
p
2
−
2
p
Jason claims he has finished reading 25% of his book. If his book has 200 pages, how many pages has he read?
Answers
Answer:
Jason has read 50 pages.
Step-by-step explanation:
25% of 200 = 50
Remember "of" means multiply so you multiply 25% to 200
25% x 200
Convert 25% into a decimal
0.25 x 200 = 50
So Jason has read 50 pages.
−5(3x − 39) = 2(x − 3) − 3
Answers
Answer:
x=12
Step-by-step explanation:
I don’t know the answer! Please help
Answers
Answer:
3x=4x-24, x=24, RST=72
I will be doing more 100 point free questions
I need the answers to these questions ASAP, thank you in advance!
Answers
Answer:
1. sliver's gym
2. sliver's gym
3. fitness planet
4. fitness:345 to sliver: 185
Step-by-step explanation:
1. with zero months
fitness planet cost is C = 22(0)+15= 15
sliver's gym cost is C = 15(0)+5= 5
2. sliver's gym because the rate of change is slower than fitness, resulting in you paying less for monthly memberships
3. Fitness planet because the rate of change is higher meaning that you will pay more for the monthly memberships.
4. Fitness planet C = 22(12)+15 = 345
Sliver's gym C = 15(12)+15 = 185
bus a leaves every 30 mins
bus b leaves every 20 mins
at 10 am both buses leave the station together
work out the next time they will leave at the same time
Answers
Answer:
Step-by-step explanation:
Find the LCM of 30 & 20
30 = 2 * 5 * 3
20 = 2 * 2 * 5
LCM = 2 * 3 * 2 * 5 = 60
60 minutes = 1 hour
So, again at 10am both will leave at the same time
Answer:
11 am.
Step-by-step explanation:
That would be the LCM of 20 and 30 which is 60 minutes.
So the nexrt time will be 10.00 + 60 mins
= 11.00 am.
Rewrite y= 16X+64 +3 to make it easy to graph using a translation. Describe the graph.
Answers
Answer:
C
Step-by-step explanation:
Which shows the numbers Nine-tenths, 0.3, 0.8, Five-tenths, and Two-tenths in order from least to greatest?
0.3, Five-tenths, Nine-tenths, Two-tenths, 0.8
Two-tenths, 0.3, Five-tenths, 0.8, Nine-tenths
Five-tenths, Two-tenths, 0.3, 0.8, Nine-tenths
Nine-tenths, 0.8, Five-tenths, 0.3, Two-tenths
Answers
Answer:
Step-by-step explanation:
Let's express all the given numbers as decimals:
nine tenths- 0.9
0.3
0.8
five tenths- 0.5
two tenths- 0.2
Ordering them from least to greatest:
two tenths, 0.3, five tenths, 0.8, nine tenths
Answer:
B is your answer
Step-by-step explanation:
At Carly's Pancake House there are 39 dirty coffee mugs and 21 clean coffee mugs. What
percentage of the coffee mugs at the pancake house are dirty?
Answers
Answer:
65%
Step-by-step explanation:
What you need to do is add both the clean and the dirty mugs together to get a total amount of mugs (60) and then divide 39 by 60 because you are dividing the mugs that you want to find the percentage of by the total amount of mugs. The equation would look like this:
39/60=0.65
therefore, the answer is 65%
Find the slope of 6x – 3y = 5
Answers
Answer:
slope is 2
Step-by-step explanation:
simplify this equation so that you can get to "y ="
your equation is: 6x - 3y = 5
start by subtracting 6x from both sides: -3y = -6x - 5
then divide both sides by -3 to isolate y: y = 2x - 5/3
so now we can clearly see that the slope is 2, since that is what is right next to x
please help me out!!! i have to pass this test
Answers
Answer: 126!
Step-by-step explanation: I subtracted 180-54, because a triangle should always equal 180.
PLEASE HELP DUE IN 6 MINS!!!!!!!!!!!!!!!!!!!!!
Box of nails: $3.80
Box of screws:$5.25
Claw Hammer:$12.95
Electric Drill:$42.50
a.Write two expressions to represent the total cost of 3 boxes of nails, 2 boxes of screws, 2 hammers, and 1 electric drill.
b.What is the total cost of the items purchased?
Answers
Answer:
Step-by-step explanation:
a. 3n+2s+2h+1x=42.50
b. 90.3
How do you find the run between two points? Can the rise be negative? Explain
Answers
Answer:
Step-by-step explanation:
To find run between two points, you will use the x-values.
For example, (2,3) and (4,5).
Your equation for slope is m=[tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]
To find the run of these two numbers, you will subtract the second x value from the first x value.
Your answer would be 2 for the run.
It is possible for the rise to be negative if the y value of the point is greater in the first point than the second.
Example:
points (2,8) and (5,1)
1 - 8 would equal -7.
Solve the equation by completing the square.
x^2+18x=7
please show me how to also. :)
Answers
Answer:
x=-2[tex]\sqrt{x} 22 -9[/tex]
Step-by-step explanation:
what does x + 16 equal when x means 7?
Answers
Answer:23
Step-by-step explanation:
If R is the midpoint of TS, TR = 5x - 12, and RS = 3x + 8, find TS.
Answers
Answer:
5x -12 = 3x +8 (set the two = each other because they are the same length)
2x- 12= 8 (subtract 3x from both sides)
2x = 20 (add 12 to both sides)
x=10 (what x= for both expressions)
5(10) -12 (plug it into the first one to see what the length is and to see they're =
50 - 12 ( I already multiplied, now subtract)
38 (what the length of TR is)
3(10) +8 (plug it in again but into the other expression)
30+8 (multiply and add)
38 (the two have the same answer, so the x-value is correct.)
38+38= 76 (add the lengths of RS and TR and you get the length of TS)
Step-by-step explanation:
I hope this helps :)
Applying the segment addition theorem, the value of TS is: 76
Given:
TR = 5x - 12
RS = 3x + 8
If T is the midpoint of TS, therefore we would have the following equation:
TR = RS
Plug in the expressions5x - 12 = 3x + 8
Add like terms together5x - 3x = 12 + 8
2x = 20
Divide both sides by 2x = 10
TS = TR + RS (segment addition theorem)
SubstituteTS = 5x - 12 + 3x + 8
Plug in the value of xTS = 5(10) - 12 + 3(10) + 8
TS = 50 - 12 + 30 + 8
TS = 76
Learn more about segment addition theorem on:
https://brainly.com/question/1397818
The minute hand of a clock in a clock tower has a length of 36 inches.
If a butterfly landed on the extreme tip of the minute hand at exactly 12:00 noon and rode the minute hand until 12:45 p.m., how far did the butterfly ride along the arc traced by the minute hand?
Answers
45 i guessStep-by-step explanation:
Sara makes and sells bracelets. She bought material for $28.50 and used it all to make 15 bracelets. Sara used the equation 15 x minus 28.50 = 99 to determine x, the amount she should charge for each bracelet to make a profit of $99. How much should each bracelet cost? $4.70 $6.60 $8.50 $13.75
Answers
Each bracelet should cost $8.50. Replace x with 8.50, 15(8.50)-28.50=99
hope this helps :)
Answer:
the answer is c, 8.50
Step-by-step explanation:
Factor with the distributive property (no variables)
90+27=
Answers
Your answer is 9(10 + 3)
Tell me if you need an explanation
pleasee help!! im confused
Answers
Answer:
28k + 68
Step-by-step explanation:
7(8 + 4k) + 12
first, you use the distributive property on the parentheses
56 + 28k + 12
then you add like term, 56 + 12 = 68
68 + 28k
numbers with variables go first
28k + 68
Kylie is creating a scale drawing of her bedroom. The actual length of her bodis 75 inches fi inch on her drawing represents 2 feel how long should her bed
be in the drawing?
Answers
Answer:
77 feet
Step-by-step explanation:
What is the solution to the following system of equations?
4x + 2y = 6
x − y = 3
A. (2, 1)
B. (−2, −1)
C. (2, 4)
D. (2, −1)
Answers
What is the difference?
7-3=
A. 3
B. 4.
O c. 5
OD. 10
O E. 11
Answers
hope this helped
A new pair of boots is priced at $123.75, plus 6% sales tax. What is the total cost of the boots?
Answers
Answer:
131.18
Step-by-step explanation:
What is the LCF of 60 and 10 ?
Answers
Do you mean LCM
If you just want to know what is the least common multiple of 10 and 60, it is 60
Answer:
the lowest common factor is 5
Step-by-step explanation
5 can go into both 60 and 10, and thats the lowest that can go into both numbers because 5 times 2 is equal to 10 and 5 times 12 is equal to 60. hope this helps :)
3x-4 or = to 7
plz help
Answers
Answer:
3 + 4 = 7 which is true.
Step-by-step explanation:
Whenever you have an equation with a plain variable (that is, no exponent included), there is only one number that will work when substituted for x.
To solve it, you have to "undo" what is done to the variable. You also go in the reverse order of operations, so you do the addition/subtract first, then multiplication/division.
You also have to do the same to both sides, kind of like keeping a balance scale in balance.
In this case, we subtract 4 from both sides first:
3x + 4 -4 = 7 - 4
The + 4 - 4 cancel each other out, so you get:
3x = 3
3x means "3 times x" so you divide by 3 to undo it. I will use the / to indicate division:
3x / 3 = 3 /3
so 1x = 1.
Since 1x is "1 times x" it is the same as x by itself, so:
x=1
AND, if we substitute 1 back into the original equation (the asterisk stands for multiply):
3 * 1 + 4 = 7
3 * 1 is 3, so:
3 + 4 = 7 which is true.
1 is the only number that works.
Hope this helped.
In a recent survey 5/8 of the Siamese cat said that they didn't mind having a lap up water from a bowl but another 3/16 admitted they would have preferred to use a straw instead of 39 of the Siamese cats gave one of these two answers how many were surveyed in total make sure your answer is fully reduced
Answers
Answer:
48 Siamese cats were surveyed
Step-by-step explanation:
Let x represent the total number of surveyed Siamese cats.
Since 5/8 of the Siamese cat said that they didn't mind having a lap up water from a bowl , hence:
Number of cats who lapped = (5/8)x
Also, 3/16 admitted they would have preferred to use a straw:
Number of cats who used straw = (3/16)x
Taking into consideration that 39 of the Siamese cats gave one of those two answers:
(5/8)x + (3/16)x = 39
(13 / 16)x = 39
x = 39 * 16 / 13
x = 48
48 Siamese cats were surveyed
Hey I need help ASAP!
Identify the function shown in this graph
Answers
Answer:
The answer is B.
y=-5x + 3
Step-by-step explanation:
Hope this helps
Emma used 1/7 of a liter of milk to make 1/3 of a jug of tea. How much milk, in liters, is required to fill the jug?
Answers
Answer:
Step-by-step explanation:
Well....if 1/7 liters of milk makes 1/6 of a jug
Then six times this must be a full jug....so
6*(1/7) =
6/7 liters of milk required
i hope this helps you happy holidays let me know if you need more information
Answer:
6/7
Step-by-step explanation: