A piece of paper is to display 150, space square inches of text. If there are to be one-inch margins on the sides and the top and a two-inch margin at the bottom, what are the dimensions of the smallest piece of paper that can be used? Choose 1 answer:
Answers
Answer:
[tex]Height = 8.660\ in[/tex]
[tex]Width = 17.321\ in[/tex]
Step-by-step explanation:
Given
[tex]Area= 150in^2[/tex]
[tex]Side\ Margin = 1\ in[/tex]
[tex]Top\ \&\ Bottom\ Margins = 2\ in[/tex]
Required
Determine the smallest dimension to use
To answer this question, I'll make use of the attached figure as a point of reference.
The area of the printed matter is:
[tex]Area = Length * Width[/tex]
[tex]A_1 = H * W[/tex]
Substitute 150 for A1
[tex]150 = H * W[/tex]
Make H the subject
[tex]H = \frac{150}{W}[/tex]
The area of the full paper is:
[tex]Area = Length * Width[/tex]
[tex]A_2 = (W + 2+2) * (H + 1 + 1)[/tex]
[tex]A_2 = (W + 4) * (H + 2)[/tex]
Substitute 150/W for H
[tex]A_2 = (W + 4) * (\frac{150}{W} + 2)[/tex]
Open brackets
[tex]A_2 = W(\frac{150}{W} + 2) + 4(\frac{150}{W} + 2)[/tex]
[tex]A_2 = 150 + 2W + \frac{600}{W} + 8[/tex]
Collect Like Terms
[tex]A_2 =2W + \frac{600}{W} + 8+150[/tex]
[tex]A_2 =2W + \frac{600}{W} + 158[/tex]
Differentiate with respect to w and set the result to 0
[tex]A_2' = 2 - \frac{600}{W^2} + 0[/tex]
[tex]A_2' = 2 - \frac{600}{W^2}[/tex]
Set to 0
[tex]0 = 2 - \frac{600}{W^2}[/tex]
Collect Like Terms
[tex]2 = \frac{600}{W^2}[/tex]
Cross Multiply
[tex]2 * W^2 = 600[/tex]
Make [tex]W^2[/tex] the subject
[tex]W^2 = \frac{600}{2}[/tex]
[tex]W^2 = 300[/tex]
Take positive square root of both sides
[tex]W = 17.321[/tex]
Recall that:
[tex]H = \frac{150}{W}[/tex]
[tex]H = \frac{150}{17.321}[/tex]
[tex]H = 8.660[/tex]
Hence, the smallest dimension of the paper is:
[tex]Height = 8.660\ in[/tex]
[tex]Width = 17.321\ in[/tex]
Answer:
H=18
W=12
Step-by-step explanation:
The question says 1 inch margins on the sides AND the top. And THEN a 2 inch margin ONLY on the bottom.
First, solve for y,
A = xy
150 = xy
150/x = y
If the center dimensions is A and its it equals x*y, then plus the margins, the outer dimensions would just be x+(size of margins) for width and y+(size of margins) for height.
This gives us
Width: x + 2
Height: y + 3
Putting height into terms of x: (Substitute y) = 3 + 150/x
Now, since the area of a rectangle is b*h, the equation is:
(x + 2)(3 + 150/x)
Simplify:
3x + 150 + 6 + 300/x
= 3x + 156 + 300/x
Next, we find the derivative of this and then solve for x.
= 3 - 300/x^2
Solving for x:
0 = 3 - 300/x^2
3 = 300/x^2
3x^2 = 300
x^2 = 100
x = 10
Now that we have x, we plug this into the different equations for height and base:
Base=(10) + 2 = 12
Height=3 + 150/(10) =3+15 = 18
Hope this helps!
Related Questions
PLEASE HELP ASAP!!
After a power failure, the temperature in a freezer increased at an average rate of 3.5 °F per hour. The
total increase was 31.5 °F. Enter and solve an equation to find the number of hours until the power was
restored. Let x represent the number of hours it takes for the temperature to increase to 31.5 °F.
Answers
Answer:
equation: 3.5x=31.5
number of hours: 9
Step-by-step explanation:
31.5/3.5=9
Therefore,
x=9, x=number of hours, number of hours=9
can somebody please help me !
Answers
Answer:
27
Step-by-step explanation:
Christina collected 27 cans.
27 cans plus Zachary's 54 = 81.
Hope this helps!
Plz mark Brainliest!
6 + -4 =
-8 - (-10) =
-7 + 3 =
Answers
-8 -(-10) would be -8 plus 10. 2
-7 plus 3 would be -4
If these don't make sense to you, get a tutor. This is basic math
Step-by-step explanation:
6+ -4=2
-8-(10) = 2
-7 + 3= - 4
PLEASE HELP ME ITS URGENT!!! PLEASEEE IM BEGGING U
Answers
Answer:
The answer would be C.
Step-by-step explanation:
5 * 6 = 30
3(10) * 1 = 30
Hence, your answer would be C.
Answer:
c = 10
Step-by-step explanation:
HELP ME FAST PLEASE!!!!!
Answers
Answer:
the first one
Step-by-step explanation:
kkrkrkrkrkrk
Answer:
(-4,1)
Step-by-step explanation:
Combine the like terms 4x+ 17x + 5y + 19 - 28b + 48y +87a - 24x
Answers
First off, you need to circle every single thing on this expression, including the math symbols. So in order to do that, circle the symbols with the number behind:
19 - 28b -> (19) (-28b)
All of your numbers should end up like this:
(4x) (17x) (5y) (19) (-28b) (48y) (87a) (-24x)
Next, place an addition symbol in between all of them.
4x + 17x + 5y + 19 + (-28b) + 48y + 87a + (-24x)
Then, rearrange the numbers with the same variable (ex. a in “87a” is the variable), and the numbers without a variable as-well.
(4x + 17x + (-24x)) + (5y + 48y) + (19) + (-28b) + 87a
Finally, add all of the variables with the same letter with each other. You also need to add the numbers without one but since 19 is the only number without a variable in this expression you don’t add it to anything.
Your answer should come out to this:
-3x + 53y + 19 + (-28b) + 87a
At Taco Bell, I made a large purchase of 13 items that cost a total of $28.17. If Chicken Burritos cost $1.89 each and a Cheesy Gordita Crunch costs $2.49, determine how many of each that I purchased.
Answers
Answer:
Number of Chicken Burritos purchased=7
Number of Cheesy Gordita Crunch purchased=6
Step-by-step explanation:
Let x be the number of Chicken Burritos and y be the number of Cheesy Gordita Crunch.
Total number items purchased=13
Total cost of 13 items=$28.17
Cost of each Chicken Burritos=$1.89
Cost of each Cheesy Gordita Crunch=$2.49
We have to find number of each items purchased.
According to question
[tex]x+y=13[/tex].....(1)
[tex]1.89x+2.49y=28.17[/tex]...(2)
Equation (1) multiply by 2.49 and then subtract equation (2) from (1)
[tex]0.6x=4.2[/tex]
[tex]x=\frac{4.2}{0.6}[/tex]
x=7
Substitute x=7 in equation (1)
[tex]7+y=13[/tex]
[tex]y=13-7=6[/tex]
Number of Chicken Burritos purchased=7
Number of Cheesy Gordita Crunch purchased=6
Solve for the indicated measure for each of the following.
Answers
Answer:
x = 55°
Step-by-step explanation:
gcgjcgjcgcjgcjgjgccgjgcjcjgjgcjgcgjcgjc
is (3,4) a solution to the linear equation y=4x-8? Yes or No?
Answers
Answer:
Yes
Step-by-step explanation:
To find if the point (3,4) a solution to the linear equation y=4x-8 you need to substitute (3,4) into y=4x-8
(x,y)
(3,4)
x=3 and y=4
Subistute:
4=4(3)-8
4=12-8
4=4 which is correct so the answer is yes (3,4) is a solution for y=4x-8
To find 40% of 75, Priya calculates 25⋅75 . Complete the statement about whether her calculation gives the correct value for 40% of 75. Her calculation is , 1 of 4. Select Choice because 25 and 40% are , 2 of 4. Select Choice . b. If x represents a number, complete the statement about whether 25⋅x always represents 40% of that number. , 3 of 4. Select Choice because 25 are 40% are 4 of 4. Select Choice .
Answers
Answer:
See Explanation
Step-by-step explanation:
See comment for correct presentation of the question
Given
[tex]Expression = 40\% * 75[/tex]
[tex]Priya = \frac{2}{5} * 75[/tex]
Required
Is Priya correct?
We start by simplifying the expression.
[tex]Expression = 40\% * 75[/tex]
Express 40% as fraction
[tex]Expression = \frac{40}{100} * 75[/tex]
Simplify fraction: Divide numerator and denominator by 20
[tex]Expression = \frac{40/20}{100/20} * 75[/tex]
[tex]Expression = \frac{2}{5} * 75[/tex]
By comparing:
[tex]Expression = \frac{2}{5} * 75[/tex]
and
[tex]Priya = \frac{2}{5} * 75[/tex]
We can conclude that Priya is correct because:
[tex]40\% = \frac{2}{5}[/tex]
Find the slope of the line.
Answers
Answer:
In technical terms, the slope of the line is the change in y over the change in x. But I just like to think of it as rise over run. To find the slope of the line, pick two points on the line
PLEASE HELP ILL MAKE YOU BRAINLEST
A small particle has a mass of approximately 0.00000043 grams. How would this number be expressed in scientific notation? Select one: O A. 4.30 x 10-7 O B. 4.30 x 10-6 O C. 4.30 x 107 O D. 4.30 X 106
Answers
Answer:
1. 4.3x10^-7
2. the picture is cut off
Combine like terms and write an equivalent expression
with the fewest number of terms.
3x + 5x – 1
Can someone help me?
Answers
Answer:
8 + -1 here you go hope this helps
Which detail in text number one do you better understand because of details in the text number two
Answers
order these fractions from least to greatest
5/12, 5/7, 5/8
Answers
I NEED HELP ASAP!!! I'LL GIVE BRAINLIEST FOR THE CORRECT ANSWER!!!
Answers
Answer:
-x 7
Step-by-step explanation:
Pls help!! ASAP!!!! I WILL GIVE YOU BRAINLIEST! I NEED A EXPLANATION FOR THIS QUESTION
Answers
Answer:
A system of equations are two or more equations that has to be valid at the same time. It means that the variables of one equation can be substitute in the other equation.
For example we have y=5x−8 and we can substitute this value of y in the other equation
4x+3y=33
4x+3(5x−8)=33 we can solve now for x
4x+15x−24=33
19x=33+24
19x=57
x=5719=3.
y can be obtained from the first equation
y=5x−8
y=5⋅3−8=15−8=7
Then x=3 and y=7.
Step-by-step explanation:
Answer:
x = 3
y = 7
Step-by-step explanation:
y = 5x - 8 ---------------(I)
4x + 3y = 33 ------------(II)
Substitute y = 5x - 8 in equation (II)
4x + 3 (5x - 8) = 33
4x + 3*5x - 8*3 = 33
4x + 15x - 24 = 33 {Combine like terms}
19x - 24 = 33 {Add 24 to both sides}
19x = 33 + 24
19x = 57 {Divide both sides by 19}
x = 57/19
x = 3
Substitute x = 3 in equation (I)
y = 5*3 - 8
y = 15 - 8
y = 7
PLZ HURRY!!!!
Michael has 4 pairs of boots, 10 pairs of basketball sneakers, 6 pairs of Vans, and 4 pairs of flip flops. What percent of Michael's shoes are Vans?
Answers
Answer:
25%
Step-by-step explanation:
6/24 = 0.25 = 25%
Urgentttt Workkk help
Answers
Answer:
3, 15
Step-by-step explanation:
1/10 of a unit also just means dividing by 10. 1/2 is just dividing by 2. Hope this helped!
Answer:
1/10= 3
1/2=15
Step-by-step explanation:
If the whole unit is 30, then one tenth of it would be three (3x10=30) and one half of it would be 15 (2x15=30)
Solve for X
1) 8(1 + 5x) + 5 = 13 + 5x
Answers
Answer:
X=0
Step-by-step explanation:
[tex]8(1 \times 5x) + 5 = 13 + 5x \\ 8 + 40x + 5 = 13 + 5x \\ 40x + 13 = 13 + 5x \\ 40x - 5x = 13 - 13 \\ 35x = 0 \\ x = 35 \times 0 \\ x = 0[/tex]
The solution to the equation is x = 0.
Here, we have,
Let's solve the equation step by step:
Distribute the 8 to the terms inside the parentheses:
8 + 40x + 5 = 13 + 5x
Combine like terms on both sides of the equation:
40x + 13 = 5x + 13
Subtract 5x from both sides to isolate the variable terms on one side:
40x - 5x + 13 = 5x - 5x + 13
Simplifying:
35x + 13 = 13
Subtract 13 from both sides to isolate the variable term:
35x + 13 - 13 = 13 - 13
Simplifying:
35x = 0
Divide both sides of the equation by 35 to solve for x:
35x/35 = 0/35
Simplifying:
x = 0
Therefore, the solution to the equation is x = 0.
To learn more on equation click:
https://brainly.com/question/14468218
#SPJ6
Solve the equation 0.5x = 16 for x using the division property of equality.
x =
Answers
Answer:
32
Step-by-step explanation:
got it right on edge
The pentagon shown has 5 equal sides. The side lengths are represented by the expression 9k+4. What is the perimeter?
Answers
Answer:
5(9k+4)
45k+20
Step-by-step explanation:
You could add all the sides together or use distributive property and multiply the one side length by 5
Simplify:
20x + 27y + 38y + 29x
Answers
Answer:
49x +65y
Step-by-step explanation:
add like terms
what is the meaning of altitude?
Answers
Answer:
1.
a settled way of thinking or feeling about something
Answer:
Altitude or height is a distance measurement, usually in the vertical or "up" direction, between a reference datum and a point or object. The exact definition and reference datum varies according to the context.
Step-by-step explanation:
Find the sum. Write the answer in its simplest form. -7.1+(-5.63)
Answers
Answer:
-12.73
Step-by-step explanation:
since you are adding a negative, it is the same as subtracting. subtract -7.1 from -5.63 to get -12.73. hope this helps
Anexo 5
Martes 26 do Brero de 2021
Instrucciones del planteamiento y relacionals columnas, para ello encuentra el recuadro con la
tracción equivalente
Circo JONN
El circo JOMI, ha hecho una gira alrededor de todo el continente
Americano
El tiempo de gira se repartió de la siguiente manera, la cuarta
parte del circo estará en Argentina, 4/32 partes en Brasil, una
octava parte en Venezuela, la dieciseisava parte en Bolivia, 5/32
portes en Cuba, 8/32 partes en México y el resto en Guatemala
2
8
Partes del tiempo se
32 presentó en México
32
10
32
Partes del tiempo se
presentó en Cuba
64
2
La dieciseisava parte la
invirtió en Bolivia.
8
1
4 Partes del tiempo se
32 presentó en Brasil
8
2
1 Partes del tiempo se
32 presentó en Guatemala
64
2
Una octava parte del
tiempo estuvo en Venezuela.
16
Answers
A forest covers 52000 acres. A survey finds that 0.4% of the forest is old-growth trees. How many acres of old-growth trees are there?
Answers
Given:
Total forest area = 52000 acres
Area of old growth trees in the forest = 0.4%
To find:
The area of old growth trees.
Solution:
We have,
Total forest area = 52000 acres
Area of old growth trees in the forest = 0.4%
Area of old growth trees is
[tex]Area=0.4\% \text{ of total forest area}[/tex]
[tex]Area=\dfrac{0.4}{100}\times 52000[/tex]
[tex]Area=0.4\times 520[/tex]
[tex]Area=208[/tex]
Therefore, the area of old growth trees is 208 acres.
What is the sum of 1/8+5/15+3/8
Answers
Answer:
pls give me brainliest
Step-by-step explanation:
0.83333333333
Answer:
5/6
Step-by-step explanation:
(x ^ 3 - 13x ^ 2 + 40x + 18)/(x - 3) pls solve this
Answers
Step-by-step explanation:
tu lo que pusiste es falso
Which of the following shapes are used to compose this figure?
a
3 cm
triangle
trapezoid
circle
parallelogram
Answers
triangle trapezoidis the answer