Answer:
The dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches
Step-by-step explanation:
We have that:
[tex]Area = 128[/tex]
Let the dimension of the paper be x and y;
Such that:
[tex]Length = x[/tex]
[tex]Width = y[/tex]
So:
[tex]Area = x * y[/tex]
Substitute 128 for Area
[tex]128 = x * y[/tex]
Make x the subject
[tex]x = \frac{128}{y}[/tex]
When 1 inch margin is at top and bottom
The length becomes:
[tex]Length = x + 1 + 1[/tex]
[tex]Length = x + 2[/tex]
When 2 inch margin is at both sides
The width becomes:
[tex]Width = y + 2 + 2[/tex]
[tex]Width = y + 4[/tex]
The New Area (A) is then calculated as:
[tex]A = (x + 2) * (y + 4)[/tex]
Substitute [tex]\frac{128}{y}[/tex] for x
[tex]A = (\frac{128}{y} + 2) * (y + 4)[/tex]
Open Brackets
[tex]A = 128 + \frac{512}{y} + 2y + 8[/tex]
Collect Like Terms
[tex]A = \frac{512}{y} + 2y + 8+128[/tex]
[tex]A = \frac{512}{y} + 2y + 136[/tex]
[tex]A= 512y^{-1} + 2y + 136[/tex]
To calculate the smallest possible value of y, we have to apply calculus.
Different A with respect to y
[tex]A' = -512y^{-2} + 2[/tex]
Set
[tex]A' = 0[/tex]
This gives:
[tex]0 = -512y^{-2} + 2[/tex]
Collect Like Terms
[tex]512y^{-2} = 2[/tex]
Multiply through by [tex]y^2[/tex]
[tex]y^2 * 512y^{-2} = 2 * y^2[/tex]
[tex]512 = 2y^2[/tex]
Divide through by 2
[tex]256=y^2[/tex]
Take square roots of both sides
[tex]\sqrt{256=y^2[/tex]
[tex]16=y[/tex]
[tex]y = 16[/tex]
Recall that:
[tex]x = \frac{128}{y}[/tex]
[tex]x = \frac{128}{16}[/tex]
[tex]x = 8[/tex]
Recall that the new dimensions are:
[tex]Length = x + 2[/tex]
[tex]Width = y + 4[/tex]
So:
[tex]Length = 8 + 2[/tex]
[tex]Length = 10[/tex]
[tex]Width = 16 + 4[/tex]
[tex]Width = 20[/tex]
To double-check;
Differentiate A'
[tex]A' = -512y^{-2} + 2[/tex]
[tex]A" = -2 * -512y^{-3}[/tex]
[tex]A" = 1024y^{-3}[/tex]
[tex]A" = \frac{1024}{y^3}[/tex]
The above value is:
[tex]A" = \frac{1024}{y^3} > 0[/tex]
This means that the calculated values are at minimum.
Hence, the dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches
60% of 89 is what number?
Answer:
53.4
Step-by-step explanation:
Simplify: 3(x + 2 = 5).WILL GIVE BRAINLIEST!!!!
Answer:
the answer is -1/3
Step-by-step explanation:
Question
Solve the equation. Enter the answer in radical form, and then use a calculator to approximate the
solution to two decimal places, if necessary. Use a graphing calculator to graph the related function to
check your answer.
5x2 - 16 = 29
The solutions are x =
and x-
Answer:
solving the equation [tex]5x^2 - 16 = 29[/tex] we get the solution: [tex]\mathbf{x=3,x=-3}[/tex]
Step-by-step explanation:
We need to solve the equation [tex]5x^2 - 16 = 29[/tex]
We need to solve the equation to find the value of x.
We can solve this equation using simple DMAS rule.
We are given:
[tex]5x^2 - 16 = 29[/tex]
Add 16 on both sides
[tex]5x^2 - 16+16 = 29+16\\5x^2=45[/tex]
Now, divide both sides by 5
[tex]\frac{5x^2}{5}=\frac{45}{5} \\x^2=9[/tex]
Now, we know that [tex]\sqrt{x^2}=\pm x[/tex]
Taking square root on both sides.
[tex]\sqrt{x^2}=\sqrt{9}\\x=\pm3[/tex]
So, we get values of x:
[tex]x=3, x=-3[/tex]
Therefore, solving the equation [tex]5x^2 - 16 = 29[/tex] we get the solution: [tex]\mathbf{x=3,x=-3}[/tex]
Can anyone help me with this Midterm Advanced Algebra problem. (DONT ANSWER IF YOUR NOT SURE)
Answer:
y = -1/2x + 13/2
Step-by-step explanation:
The slope of a line that is perpendicular to a line will be a negative reciprocal. When you rewrite 2x-7=8 into slope-intercept form, you get y=2x-8. The negative reciprocal of the slope 2x is -1/2x. There is only one option with this slope. If you're still not sure then you can use a graphing calculator to check this. An online one would be desmos
more of my math lesson plz help guyssss
Tim bought a washing machine for a total of $651 with tax included. What was the price of the washing machine before tax if Tim lives in an area with an 8.5% sales tax rate?
Answer:
The washing machine cost $600 before tax
Step-by-step explanation:
Percentages
The washing machine cost $651 including a tax of 8.5%.
If x was the cost of the washing machine before tax, then the tax was:
x*8.5/100 = 0.085x
It was added to the original price:
x + 0.085x = 1.085x
That is the final price, thus
1.085x=$651
Solving:
x = $651/1.085
x = $600
The washing machine cost $600 before tax
259 Students go on a field trip. There are 19 vehicles, some vans and some buses.
7 students can fit in a van, and 25 students can fit in a bus.
how many buses were there?
how many vans were there?
-5x + 4y = 3
x = 2y - 15
solve for x and y
I'm failing please send help
Answer:
Let's solve for x.
−5x + 4y = 3
Step 1: Add -4y to both sides.
−5x + 4y+ −4y =3+ −4y
−5x = −4y +3
Step 2: Divide both sides by -5.
-5x divided by 5 = -4y+3 divided by -5
x=4/5y + −3/5
Step-by-step explanation:
Express 2 19/250 as decimals.pls fast
2.076
2+19/250= 2.076
HELP ANSWER X FOR THIS ISOSCELES TRIANGLE THANK YOU
Answer:
Step-by-step explanation:
Remark
The point about the question is that the two sides are marked as equal.
Equation
3x + 5 = 5x + 1 Subtract 3x from both sides
Solution
3x - 3x + 5 = 5x - 3x + 1 Combine like terms
5 = 2x + 1 Subtract 1 from each side
5-1 = 2x +1 - 1 Combine
4 = 2x Divide by 2
4/2 = 2x/2
x = 2
A 13ft ladder is leaning against a wall when its base starts ti slide away from the wall. By the time its base is 12 feet from the wall, the base is moving at the rate of 5ft/sec. How fast is the top of the ladder sliding down the wall?
Given :
A 13ft ladder is leaning against a wall when its base starts ti slide away from the wall.
By the time its base is 12 feet from the wall, the base is moving at the rate of 5ft/sec.
To Find :
How fast is the top of the ladder sliding down the wall.
Solution :
By, Pythagoras theorem, distance of ladder from horizontal to wall is 5 feet.
Now, [tex]x^2 + y^2 = 13^2[/tex]
Differentiating both sides, we get :
[tex]2x\dfrac{dx}{dt}+2y\dfrac{dy}{dt}=0\\\\(2\times 12\times 5) + (2\times 5 \times \dfrac{dy}{dt})=0\\\\\dfrac{dy}{dt}= -12 \ feet/sec[/tex]
please help me I dont want to do it and I am on a timed thing
Answer:
-1
Step-by-step explanation:
Answer:
-1
Step-by-step explanation:
-5 -15 = -20
-20+4 = -16
-16+15 = -1
Therefore, -5-15+4+15 = -1
One letter was selected at random from words SAN ANTONIO what is the probability that the selected letter was either an A or an N?
Answer:
the posibility for both of these answers are 5/10 or a 5 in ten chance that it would be a or n because in this there is 5 or these letters
Step-by-step explanation:
The entrance to our school has a height of 10.5 feet. There are approximately 30.5 centimeters in 1 foot. What is the height of the entrance in centimeters?
Answer:
320.25 centimeters
Step-by-step explanation:
you multiply 10.5 * 30.5
the question is in the picture
Answer:
It seems you forgot to add the picture.....
If you put it in the comments i will try to solve it...
Stay safe and have a Merry Christmas!!!!!!! :D
Please help need answer now!!
Answer:
b i think
Step-by-step explanation:
Lima beans $2.13 for 2 lb
Answer:
i think its $1.07 per pound.
Step-by-step explanation:
is it yes or no??........
Answer:
No
Step-by-step explanation:
It's not proportional because the unit rate for each hour isn't the same.
A local coffee house donates 2 pounds of
gourmet coffee beans to be sold at a local
fundraiser. The people running the fundraiser
decide to package and sell the coffee beans
in pound packages. How many pound
packages can they make
Answer:
They can make 2
Step-by-step explanation:
The coffee shop donated 2lbs, and if they package it in 1lb bags, 2/1=2
563/84 show how u solved
Answer:
u just have to divide
put the numbers in a calculator and the answer is 6.70238095238
Step-by-step explanation:
hope this helps
Answer:
you can't divide it
if u do then its
6.70238095238095238095.............................
6 r 59
Step-by-step explanation:
ok ok um so
multiples of 84:
84
168
252
336
420
504
588
we take 504
563-504 = 59
504/84 = 6
so 6 r 59
(10 points) only answer section b plz
Beckett purchased a diamond ring for $14,000. The value of the ring increases 2.1% every year
Answer:
14,000+2.1%(0.021)x
Step-by-step explanation:
x is how many years
HELPPPPPPP ............ please.
Answer:
B) 1/3
Step-by-step explanation:
Add up all the marbles
5 + 6 + 3 + 4 = 18 marbles
Make a fraction of the red marbles out of all the marbles
6/18
Simplify the fraction
1/3
Answer:
b
Step-by-step explanation:
chances of drawing a red is 6/18
6/18=1/3, so its B
help im confusion......
Answer:
Line J
Step-by-step explanation:
It is sloping downwards. It starts in the top left and end at the bottom right, so it it the only negative one
Answer:
Line J
Step-by-step explanation:
Its the only one descending downwards, while the other two are going up in a positive direction.
Hope this helps (:
Solve the inequality − 3 x + 6 > 15
Answer:
The Answer to your question is x<-7 Hope This could Help
Step-by-step explanation:
Answer:
x<−3
Step-by-step explanation:
Let's solve your inequality step-by-step.
−3x+6>15
Step 1: Subtract 6 from both sides.
−3x+6−6>15−6
−3x>9
Step 2: Divide both sides by -3.
−3x/−3>9/−3
pls mark as brainliest
Help me please!
How much can the Owen family expect to pay per year for tuition to a private college?
A)$22,568
B)$23.068
C)$24.618
D)$25.458
Please help the question is in the photo
Answer:
SSS or SAS
Step-by-step explanation:
Pls help someone my brain is about to explode
Answer:
It has to be the third option.
Happy to help :)
Factor 72x−18xy
Find the Factor of 72x-18xy
Answer:
4x and (1-y)
Step-by-step explanation:
4x(1-y)
this is my answer
The factors of the expression are 18x and 4-y
Given the expression 72x - 18xy
Find the factor of each term:
72x = 18 * 4 * x
18xy = 18 * x * y
Since 18x is common to both terms, hence the factored form is expressed as:
72x - 18xy = 18x (4 - y)
The factors of the expression are 18x and 4-y
Learn more on factors here: https://brainly.com/question/24539261
132
Corresponding Angle
Vertical Angle
Alternate Interior Angle
Alternate Exterior Angle
