Given :
A rectangular page is to contain 36 square inches of print.
The margins on each side are 1 inch.
To Find :
The dimensions of the page such that the least amount of paper is used.
Solution :
Let, length and breadth of paper are x and y respectively.
Area is given by :
Area = xy ....1)
xy = 36 inch²
Now, it is given than the margins on each side is 1 inch.
So, area of paper is :
A = ( x + 2 )( y + 2 )
We want area to be minimum.
Putting value of x from 1 , we get :
A = ( 36/y + 2 )( y + 2 )
Now, differentiating above equation and equating with 0 :
[tex]3 - \dfrac{108}{y^2}=0\\\\y = \pm 6[/tex]
Now, we know dimension cannot be negative.
So, y = 6 and x = 6 .
Therefore, length and breadth are 6 and 6 inch respectively.
The length are breadth is x = 6 and y = 6 inch respectively.
Given;
Each rectangular page is to contain 36 square inches of print.
The margins on each side are 1 inch.
We have to find ;
The dimensions of the page such that the least amount of paper is used.
Therefore,
Let, length and breadth of paper are x and y respectively.
Area is given by :
Area = xy
xy = 36 inch²
Now, it is given than the margins on each side is 1 inch.
So, Area of paper is : A = ( x + 2 )( y + 2 )
We want area to be minimum.
Putting value of x from 1 , we get :
A = ( [tex]\frac{36}{y}[/tex] + 2 )( y + 2 )
Now, Differentiating above equation and equating with 0 :
[tex]3 -\frac{108}{y^{2} } = 0[/tex]
[tex]\frac{3y^{2} - 108 }{y^{2} } = 0[/tex]
[tex]3y^{2} - 108 = 0 \\3y^{2} = 108\\y^{2} = \frac{108}{3} \\y^{2} = 36\\y = 6[/tex]
then; xy = 36
6x = 36
x =[tex]\frac{36}{6}[/tex]
x = 6inches
Now, we know dimension cannot be negative.
So, y = 6 and x = 6 .
Therefore, length and breadth are 6 and 6 inch respectively.
For more information about the Area of dimension click the link given below.
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after allowing 30% discount on the marked price of an article,there is a profit of 10% . if the cost price is 1500 find the marked price
Answer:
2357.14
Step-by-step explanation:
x - .30x = 1500(1.10)
.7x = 1650
x = 2357.14
WILL GIVE BRAINLIEST ! A marble is picked at random.Without putting the first marble back,a second marble is picked at random find the probability that the fist marble picked is green and the second marble is picked red write your result as a percentage
Step-by-step explanation:
The percentage is 1/2 * 2/5 = 1/5 = 20%.
The probability that the first marble picked is green, and the second marble is picked red is 20%
What is probability?A probability is a number that reflects the chance or likelihood that a particular event will occur.
Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.
Given that, there are six marbles in total, 3 are green, 2 are red and one is brown,
we need to find the probability that the first marble picked is green, and the second marble is picked red,
So, P(E) = favorable outcome / total outcome
Therefore, the probability that the first marble picked is green, and the second marble is picked red = 3/6 x 2/5 = 6/30 = 1/5 = 20%
Hence, the probability that the first marble picked is green, and the second marble is picked red is 20%
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if f(x)= 6^2 and g(x)=3 +6(x). What is f(2)
Answer:
I,dont know but use M A T H W A Y it will explain with all the stepp by step and answere
Step-by-step explanation:
HELP!! ASAP!!
Brody drew a scale drawing of a campsite. He used the scale 1 inch : 3 feet. If the actual width of the tent is 6 feet, how wide is the tent in the drawing?
Answer:
the drawing would be 2 inches
Step-by-step explanation:
What are the area and perimeter of square TUVW?
Area=
Perimeter=
Answer:
Area: 196
Perimeter: 56
Step-by-step explanation:
1. Pick a side for both length and height and count the distance between the two coordinates (for example VU and UT)
VU = 14
UT= 14
Also important to note here that you don't even need to count the distance for both because since it's a square, all the sides are the same. Only did this to make it easier to understand the next step.
2. Since it's a square, as I said before, all sides are the same. So, you can go ahead and mark WT and VW as 14 as well.
3. To get the area, use the formula base times height.
14 x 14 = 196
4. For perimeter, simply add up all the sides (or multiply 14 by 4 since all are the same)
14+14+14+14=56
A store donated cases of crayons to a daycare center. Each case holds 24 boxes of crayons; each box holds 8 crayons. How many crayons did the center receive?
Answer:
192
Step-by-step explanation:
Just multiply 24 by 8.
I think thats it tho.
Answer:
I think its 192
Step-by-step explanation:
you just do 24 times 8
which mathematical property is shown here
8+-8=0
1 distributive property
2 inverse property
3 identity property of addition
15 3/8+756-
What is the answer
Answer: 771 3/8
Step-by-step explanation:
15 3/8+756
we can apply the assosiative propery and do 15+756+3/8
so 15+756= 771
so finally you do 771+3/8=771 3/8
In a bag of keys, there are 14 silver keys, 7 black keys, 10 copper keys, and 4 painted keys of various colors. One key is drawn out
at random. What is the probability that the key that is drawn is silver or copper?
Answer:
D. 24/35
Step-by-step explanation:
Step one:
Given
Sample space
14 silver keys,
7 black keys,
10 copper keys, and
4 painted keys of various colors
Sample size= 14+7+10+4= 35
in probability "or" means that we need to add events.
Hence, the probability that the key that is drawn is silver
= 14/35
the probability that the key that is drawn is copper
=10/35
Step two:
The probability that the key that is drawn is silver or copper
14/35+10/35
=14+10/35
24/35
Simplify Negative 3 over 2 ÷ 9 over 6 . (5 points) -4 -1 4 1
Answer:
Step-by-step explanation:
[tex]\frac{3}{2}[/tex] ÷ [tex]\frac{9}{6}[/tex] = [tex]\frac{3}{2}*\frac{6}{9}\\[/tex]
= [tex]\frac{18}{18}[/tex]
= 1
Use KCF method,
Keep the first number.
Change the division to multiplication
Flip the second number
Answer:
sorry dude i need thos points
Step-by-step explanation:
Find the value of r so the line that passes through the pair of points (-4, 8) and (r, 12) has the slope 4/3
.
Answer:
-1
Step-by-step explanation:
4 / (4/3) gives us three, which when added to -4 results in -1
what is x − 2 y − 2 = 0 in slope intercepct form?
Answer:
y=1/2x-1
Step-by-step explanation:
hope this helps
Marie has 11 coins, all of which are quarters and nickels. In all, they're worth $1.15. How many of each kind of coin does Marie have?
Answer:
Step-by-step explanation:
x + y = 11
.25x + .05y = 1.15
25x + 5y = 115
-25x - 25y = -275
-20y = -160
y = 8 nickels
x + 8= 11
x = 3 quarters
3 quarters and 8 nickels
Hurry I need help help
Step-by-step explanation:
C. This system is consistent. It has one solution.
particularly in algebra, a linear or nonlinear system of equations is called consistent
A rectangular pool is 30 1/3 feet long and 12 1/2 feet wide. what is the area of the pool?
Note the 30 and 12 is a whole number
Answer:
381.25 or 381 1/4 feet
Step-by-step explanation:
Area is a rectangle is length times width. so,
30.5*12.5 = 381.25
The local high school is hosting the last soccer game. They charged adults, x, $5 to enter, and $3 for students, y. It cost the school $300 to pay the referees for the game. The school wants to make a profit on the game, and 75 people attended. This is represented by the system:
5x+3y>300
x+y=75
Which of the following points is a solution to the system?
a. (25,70)
b. (30,45)
c. (20,15)
d. (40,35)
Answer:
b.
Step-by-step explanation:
5*30+3*45>300
150+135
30+45=75
Answer:
B)
Step-by-step explanation:
30, 45
Coach Teague is making breakfast for his 6 family members. He is making bacon and omelets. Each omelet needs 3 eggs, how many eggs does he need?
Answer:
18 eggs
Step-by-step explanation:
6 family member has 1 omelet, each omelet needs 3 eggs, 6 x 3 = 18 eggs :D
One third of a number T is equal to 12???
Answer:
1/3×t=12
t=3×12
t=36
Step-by-step explanation:
need thanks for the answer.
13 erasers in your backpack is considered
a what?
Simplify the ratio
30:42
• 5/7
•30/42
• 30 to 42
•7/5
Elizabeth uses 34.95 ounces of granola for 15 servings of trail mix. If each serving contains the same amount of granola, how much granola is in each serving?
Answer:
2.33 ounces
Step-by-step explanation:
Given that:
Ounces of granola used = 34.95 ounces
Number of servings of trail mix = 15 servings
Since each serving contains the same amount of granola :
Amount of granola in each serving :
Ounces of granola used / Number of servings
34.95 / 15
= 2.33 ounces of granola per serving
Write an equation of the line with a slope of 3 and a y-intercept of -7.
Answer:
y=3x-7
Step-by-step explanation:
y=mx+b where m=slope and b=y-intercept
y=3x-7
f(-2) =-2x+11
Evaluate the function
Happy Holidays!
[tex]\large\boxed{f(-2) = 15}[/tex]
f(x) = -2x + 11
Find f(-2) by substituting in -2 for x:
f(-2) = -2(-2) + 11
Simplify:
f(-2) = 4 + 11
f(-2) = 15
A family eats at a restaurant. The bill is $42. The family leaves a tip and spends $49.77.
How much was the tip in dollars?
How much was the tip as a percentage of the bill?
Round your answer to the nearest tenth.
Answer:
Step-by-step explanation:
How much was the tip in dollars? $7.77
How much was the tip as a percentage of the bill? 18.5%
The ratio of North American butterflies to South American butterflies at a butterfly park is 6:2. What is the ratio of North American butterflies to ALL butterflies?
Answer:
6:8
Step-by-step explanation:
From the above question, we are told that:
The ratio of North American butterflies to South American butterflies at a butterfly park is 6:2.
The sum of the proportion = 6 + 2 = 8
The ratio of North American butterflies to ALL butterflies is given as :
6 : 8
Write the following expressions in Standard form
-3•2•a+5(7b)+(12•c•4)
Write an algebraic equation that relates the Profit to the Number of T-Shirts Sold. Use n to represent T-Shirts and p to represent the Profit.
Answer:
y= 3x -5
Step-by-step explanation:
since when x is 0, and y is -5, you know that the y intercept is -5.
look at the table
1x -5 = -2
x= 3
Boom.
LONG LIVE KOREA!
parallel ,perpendicular, neither y=4x+5 and -4x +y=-13
Answer:
here,
slope of line y=4x+5(m1)=-a/b
=4
slope of line -4x+y=-13(m2)=-a/b
4
here m1=m2 so,these are parallel to each other.
BRAINIST & 20 POINTS!!
Answer:
y=2/3x-5
Step-by-step explanation:
First, let's put this equation into slope-intercept form.
2x-3y=24
-3y=-2x+24
y=2/3x-8
For two lines to be parallel, they must have the same slope. Therefore our slope is 2/3.
Now, we must find b. To do that we can plug the y and the x in.
-7=2/3(-3)+b
-7=-2+b
-5=b
y=2/3x-5
Answer:
y = [tex]\frac{2}{3}[/tex]x - 5
Step-by-step explanation:
Points: (-3, -7)
Equation: 2x - 3y = 24
2x - 3y = 24
-3y = -2x + 24
y = [tex]\frac{2}{3}[/tex]x - 8
y = [tex]\frac{2}{3}[/tex]x + b
-7 = [tex]\frac{2}{3}[/tex] ( -3 ) + b
-7 = -2 + b
b = -5
y = [tex]\frac{2}{3}[/tex]x - 5
Marco need to buy some dog food at the nearest store six bags of dog food cost $25.50 how much would Marcos bag of five bags of dog food
Answer:
Five bags of dog food costs $21.25.
Step-by-step explanation:
We can solve using proportions.
[tex] \frac{6 \: bags}{25.50 \: dollars} = \frac{5 \: bags}{x} \\ \\ \frac{127.5}{6} = \frac{6x}{6} \\ \\ 21.25 = x \\ 21.25 \: dollars = x[/tex]