A rectangle has a perimeter of 100 inches, and
one side has length x. Express the area of the
rectangle as a function of x.
Use the function in part a to find the dimensions of the rectangle with permitter 100 inches and the largest possible area
Answer:
a. A = 50x - x² b. length = 25 inches and width = 25 inches and the maximum area is 625 in²
Step-by-step explanation:
a. The perimeter of a rectangle P = 2(L + W) where L = length and W = width. Now, given that P = 100 inches and W = x, substituting these into the equation, we have
P = 2(L + W)
100 = 2(L + x)
dividing both sides by 2, we have
100/2 = L + x
50 = L + x
making L subject of the formula, we have
L = 50 - x
Now, the are of a rectangle A = LW. Substituting the values of L and W, we have
A = LW
A = (50 - x)x
A = 50x - x²
b. To find the largest possible area of rectangle with perimeter 100 inches, we differentiate A and equate it to zero to find the value of x that maximizes A.
So, dA/dx = d(50x - x²)/dx
dA/dx = d50x/dx - dx²/dx
dA/dx = 50 - 2x
dA/dx = 0 ⇒ 50 - 2x = 0
50 = 2x
dividing both sides by 2, we have
x = 50/2
x = 25
To find it this gives maximum value for A, we differentiate A twice.
d²A/dx² = d(50 - 2x)/dx
d²A/dx² = d50/dx - d2x/dx
d²A/dx² = -2
Since d²A/dx² = -2 < 0, so x = 25 gives maximum value for the area, A.
Since W = x = 25 in and L = 50 - x. So, L = 50 - 25 = 25 in
So, the maximum area A = LW = Lx = 25 in × 25 in = 625 in²
The dimension with perimeter 100 inches that give maximum area are length = 25 inches and width = 25 inches and the maximum area is 625 in²
What is the definition of a number trick? (Math)
Answer:
How does the number trick work?
Trick 1: Think of a number
Pick a whole number between 1 and 10.
Add 2.
Multiply by 2.
Subtract 2.
Divide by 2.
Subtract your original number.
Everyone's final answer will be 1.
Step-by-step explanation:
The Number 5 Trick. Ask somebody to think of a number and keep it secret. Then ask that person to double the secret number and then multiply by 5. Ask for the total. Whatever the total is, knock off the last digit and you will have the secret number the person mentally chose at the start.
LEMMEBE HONEST
I HAVE NO IDEAAAA
“Think-of-a-number” tricks
These tricks come in two types: Think of a number (but don't tell me), do some arithmetic with that number, and I can predict your result. Think of a number, do some arithmetic, tell me your result, and I can instantly say what number you started with.
Hope this helps!
Sending U good luck!
Riding an elevator down 3 floors
Answer:
And, then what? rp?
Step-by-step explanation:
Answer: Elevators wer invented in 1880 by Elisha Otis's . They could carry cargo and people to higher floors. Now we see them everywhere, in places such as hospital, schools, malls, and even some houses.
Angl is a square. The equation of line NG is Y= 1/2 X - 6. Find the equation of line LG in slope intercept form given that the coordinates of L are (-5,1)
Answer: y=-2x-9
Step-by-step explanation:
If ANGL is a square, then NG and LG are adjacent sides.
Adjacent sides are perpendicular. [Each angle is 90°]
The equation of line NG is [tex]Y=\dfrac12 X-6[/tex].
By comparing it to equation in slope intercept form y=mx+c ( where , m= slope , c=y-interecpt)
slope =[tex]\dfrac12[/tex]
Let slope of LG be n, then
[tex]n\times \dfrac{1}{2}=-1[/tex] [Product of slopes of two perpendicular line =-1]
[tex]\Rightarrow n=-2[/tex]
Equation of a line passes through (a,b) and have slope m is given by :-
[tex](y-b)=m(x-a)[/tex]
Equation of LG :
[tex](y-1)=-2(x-(-5))\\\\\Rightarrow\ y-1=-2x-10\\\\\Rightarrow\ y=-2x-9[/tex] [In intercept form]
can someone help me pls?
Answer: yes it has gone down 1/5th because the answer would be 27 and that is a lot lower than the other numbers.
Step-by-step explanation:
162 minus 135 = 27
Please help me.......
Answer:
x=206
Step-by-step explanation:
the area of rectangle is x^2-3x+2. Find a possible length and width of the rectangle.
Answer:
x - 2 and x - 1 can be possible length and width of the rectangle.
Step-by-step explanation:
Area = x² - 3x + 2
◇◇◇◇◇◇◇◇◇◇◇◇◇◇◇◇◇◇◇
To find possible length and width we can factorize the above expression.
◇◇◇◇◇◇◇◇◇◇◇◇◇◇◇◇◇◇◇◇
x² - 3x + 2 ( 2 = -1 × -2 )
x² - x - 2x + 2 ( 3 = -1 + -2 )
x(x - 1) + -2(x - 1)
(x - 2) (x - 1)
◇◇◇◇◇◇◇◇◇◇◇◇◇◇◇◇◇◇◇◇
x - 2 and x - 1 can be possible length and width of the rectangle.
_________________________________
#teamtrees#WAP
How do you figure this out? I am having a hard time. The variables x and y are related to proportionally. When x = 8, y = 20. Find y when x = 80.
When x = 80, y
Answer:
200
Step-by-step explanation:
(80×20)/8
y is equal to 200
7(x + 4) = -21 what is x in this problem?
Answer:
-7
Step-by-step explanation:
7x+28=-21
7x=-49
x=-7
Write 178/48
as a percent.
Answer:
370.83%
Step-by-step explanation:
Divide them, and then multiply by a hundred.
Sam wrote on the board counting numbers from 12 to 111:12, 13, 14, ..., 110, 111. How many digits did Sam write?
Answer: Sam wrote 99 digits
Step-by-step explanation: Take the highest number minus the lowest number and that his how many numbers are between 12 and 111.
Solve and Graph the System of Linear Equations
1) 3 X + 2 Y = 4
X + 2 Y = -4
Answer:
y=-4
x=-12
Step-by-step explanation:
Set up the system
Then you have to cancel out a variable
Then you solve for the remaining variable
Then plug in to find other variable
I'm sorry if that's confusing:/
Write the equation 2x - 3y= 6 in slope-intercept form.
y=2/3 x+3
y=2/3 x-2
Y=3/2 x+3
Can someone help me please
Solve for
9
19
17
None of the above
Other:
Answer:
none of the above,
Step-by-step explanation:
The answer would be seven because the angle they're looking for is complementary, meaning that the angles would have to equal 90 degrees.
1. add up angles given
2. subtract what you get from that by 90
A pizza place charges a flat fee for each pizza and a delivery fee. One customer buys 3 pizzas and pays $41. Another pays $29 for two pizzas.
Write a linear function for this situation (use p for the number of pizzas).
Answer:
Step-by-step explanation:
p=12x+5
Please answer this, I’m a bit confused...
Will ran the diagonal distance across a square field measuring 40 yards on each side. James ran the diagonal distance across a rectangular field with a length of 25 yards and a width of 35 yards. Who ran a longer distance, and how much longer did he run?
Answer: The distance across a rectangular field is longer distance.
So, Perimeter of rectangle would be 120 yards.
Diagonal of square would be 56.56 yards.
Mel can walk 1 mile in 18 minutes. If she stays at the same rate, how far can she walk in 45 minutes?
Answer:
2.5 miles
Step-by-step explanation:
45 ÷ 18 = 2.5 miles
PS: please mark as brainliest! I hope this answer helps!
Mel can walk 2.5 miles in 45 minutes. All you have to do is 45/18. Remember this for the future, it will help in high school.
(ANSWER PLZ! BRAINLIEST) When you graph a proportional relationship explain what happens.
Answer:
The best way to show and explain direct proportional relationships is by graphing two sets of related quantities. If the relation is proportional, the graph will form a straight line that passes through the origin.
Step-by-step explanation:
Answer:
when you graph and proportional the graph will form a straight line that passes through the origin
Step-by-step explanation:
PLEASE DO NOT TELL ME THE ANSWER! Please just tell me how I can find the answer. Thank you!
Answer:
You have to find the equivalent fraction of 7/2.
Step-by-step explanation:
Steps to find an equivalent fraction:
You can make equivalent fractions by multiplying or dividing both top and bottom by the same amount. You only multiply or divide, never add or subtract, to get an equivalent fraction. Only divide when the top and bottom stay as whole numbers.
Answer:
[tex]\frac{70}{20}[/tex]
Step-by-step explanation:
Answer this question in your head: Which of the options has a numerator and denominator that are proportional to the given fraction?Let's look at the choices (I will explain in the steps below)First option: The numerator is increased by ×5, but the denominator is increased by ×4, so it is not the answer.Second option: The numerator is increased by ×10 and the denominator is increased by ×10, so it is the answer.Therefore, 70/20 is the answerI hope this helps!
Write an algebraic equation that models the following statement.
Twice the sum of 'x' and '4' is six less than the quotient of 'q' and '9'.
Symplify the expession 71 2/3% helppp
Answer:
0.71(6)
Step-by-step explanation:
the ending of "6" is forever.
Apply the distributive property to create an equivalent expression.
(6m -7) x 4 can someone pls answer fastt.
Answer:
24m-28
Step-by-step explanation:
We have to multiply each term inside the parenthesis by 4, so we get the result
solve the system by substitution -x+3y=15
y=2x
Answer:
(3,6)
Step-by-step explanation:
Larry shaded this area model to show an expression.
A model with 6 rows of 5 orange squares and 6 rows of 7 blue squares.
Which expressions did Larry model?
Check all that apply.
5(7)
30 + 42
6 + (5)(7)
6(5 + 7)
(6)(5) + (6)(7)
Answer:
The answers are B,D,E
Step-by-step explanation:
Answer:
bde
Step-by-step explanation:
Find the slope of the line that goes through the points (9,-13) and (7,3).
hi
You have two points A ( X;Y) and B ( X ; Y)
slope is : ( Yb -Ya) / (Xb -Xa )
(3 - (-13) ) / ( 7 - 9) = (3 +13) / -2 = 16/-2 = - 16/2 = -8
slope is -8
Answer:
-8
Step-by-step explanation:
The slope formula is as follows:
m = y2 - y1 / x2 - x2
You would first plug in the points into the formula, and this is what you would get:
m = 3 - (-13) / 7 - 9
From there, because of additive inverse, the negative signs would become + signs.
m = 3 + 13 / 7 - 9
You would now add/subtract.
m = 16 / -2
And lastly, you would simplify.
m = 8/-1
8/-1 is the same thing as a slope of -8.
can u help me solve 8-3(7-4y) i know the answer i just need to kown how i got the answer
the ratio the ratio of two numbers is 5:6 . find the sum of two numbers is 55. find the number
Answer:
25 and 30
Step-by-step explanation:
Given the ratio of 2 numbers is 5 : 6 = 5x : 6x ( x is a multiplier ), then
5x + 6x = 55, that is
11x = 55 ( divide both sides by 11 )
x = 5
Thus
5x = 5 × 5 = 25
6x = 6 × 5 = 30
Then the 2 numbers are 25 and 30
Xavier can paint the average house in 4 hours, while Mohamad can do it in 12 hours. Find the number of hours, $$, that it would take to paint a house if they both worked together.
Answer:
3 hours
Step-by-step explanation:
Xavier can paint the average house in 4 hours
This means that in 1 hour, Xavier paints 1/4 of the house
Mohamad can do it in 12 hours
That means in 1 hour, Mohamad paints 1/12 of the house
Hence,
Together the amount of the house they can paint in 1 hour is
1/4 + 1/12
The Least common denominator is 12
(3 × 1 + 1 × 1)/1#
= 3 + 1/12
= 4/12
= 1/3
Together they can paint 1/3 of the house
The number of hours, that it would take to paint a house if they both worked together is
= 1/3 = 1
Cross Multiply
= 3 × 1
= 3 hours
Calcula x para que sean ciertas las igualdades siguientes:
a. 3x = 243
b. 53 = x
c. x 2 = 64
d. 2x = 128
e. 9x = 729
f. 10x =10.000
Ayuda