A string 60 inches long is to be laid out on a tabletop to make a rectangle of perimeter 60 inches. Write the width of
the rectangle as 15 + x inches. What is an expression for its length? What is an expression for its area? What value
for x gives an area of the largest possible value? Describe the shape of the rectangle for this special value of x.
Answers
Answer:
Okay
Step-by-step explanation:
Hope this helps
Enjoy ur day
a) An expression for its length will be (15 - x) inches.
b) An expression for the area of rectangle will be (225 - x²) inch².
c) At x = 0 the rectangle has maximum area.
d) The shape of a rectangle will be square at x = 0.
What is Perimeter of a rectangle?
The perimeter of a rectangle with length L and width W is defined as;
Perimeter = 2 (L + W)
Given that;
Total length of string = 60 inches
Perimeter of rectangle = 60 inches.
Now,
a) When the width of rectangle is 15 + x inches.
Then, Expression for its length is calculated as;
Perimeter of rectangle = 2 ( length + width)
60 = 2 ( length + (15 + x) )
Divide by 2,
30 = Length + 15 + x
Length = 30 - 15 - x
Length = 15 - x
So, An expression for its length will be (15 - x) inches.
b) Length of rectangle = (15 - x) inches
Width of rectangle = 15 + x inches
Then, Area of rectangle = Length x width
Area of rectangle = (15 - x) × (15 + x)
Area of rectangle = 15² - x²
Area of rectangle = 225 - x²
Thus, An expression for the area of rectangle will be (225 - x²) inch².
c) When all sides of a rectangle is equal to each then, the area of a rectangle is maximum.
So, We can formulate,
Length = width
15 - x = 15 + x
2x = 15 - 15
2x = 0
x = 0
Hence, At x = 0 the rectangle has maximum area.
d) When x = 0,
Then, The sides of a rectangle are equal.
This imply that the shape of a rectangle will be square.
Therefore,
a) An expression for its length will be (15 - x) inches.
b) An expression for the area of rectangle will be (225 - x²) inch².
c) At x = 0 the rectangle has maximum area.
d) The shape of a rectangle will be square at x = 0.
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Related Questions
r(x)=2square root of x S(x)= square root of x (rs)(4)=
Answers
Answer:
[tex](rs)(4) = 8[/tex]
Step-by-step explanation:
Given
[tex]r(x) = 2\sqrt{x[/tex]
[tex]s(x) = \sqrt x[/tex]
Required
Determine [tex](rs)(4)[/tex]
In functions:
[tex](fg)(x) = f(x) * g(x)[/tex]
This implies that:
[tex](rs)(x) = r(x) * s(x)[/tex]
Substitute values for r(x) and s(x)
[tex](rs)(x) = 2\sqrt{x} * \sqrt{x}[/tex]
[tex](rs)(x) = 2(\sqrt{x})^2[/tex]
[tex](rs)(x) = 2x[/tex]
Substitute 4 for x
[tex](rs)(4) = 2 * 4[/tex]
[tex](rs)(4) = 8[/tex]
The formula for the velocity of an object is v=d/t, where v is the velocity of an object, dis the distance traveled, and t is the time elapsed, while the distance is traveled. If you had only this formula to work with, what should your first step be in determining how long it takes for light to reach Earth from the Sun? What additional information do you need to calculate this?
Answers
Answer:
To know the distance between the sun and the earth you need isolate d of the equation:
[tex]v = \frac{d}{t} \\ d = vt[/tex]
and the additional information needed is the velocity of light and the time elapsed to be in the earth
The function f(t) represents the cost to connect to the Internet at an online gaming store. It is a function of t, the time
in minutes spent on the Internet.
O
$0 0<30
f(t) = $5 30 < 1 S 90
$ 10 > 90
Which statement is true about the Internet connection cost?
It costs $5 per hour to connect to the Internet at the gaming store.
The first half hour is free, and then it costs $5 per minute to connect to the Internet.
It costs $10 for each 90 minutes spent connected to the Internet at the gaming store.
Any amount of time over an hour and a half would cost $10.
Save and Exit
Next
Submit
Mark this and return
no
Answers
Answer:the answer is D Any amount of time over an hour and a half would cost $10
Step-by-step explanation:
How many solutions does the equation have? 2(x+3)=2x+6
Answers
Answer:
Infinitely Many Solutions
Step-by-step explanation:
Subtract 6 from both sides of the equation
2
A large lemonade container at a party holds 9 liters of lemonade. About how many gallons of lemonade does the container hold? ( 1 liter=0.264 gallon )
Answers
it will be 2.4 gallons
PLEASE ANSWER ASAP FOR BRAINLEST WITH WORK!!!!!!!!!!!!!!!
Answers
Answer:
The answer is 43 because 600/14 = 42.8571429 rounded to the nearest whole number is 43.
Step-by-step explanation:
Jake created a scale drawing of an airplane. In the scale drawing, the length of the airplane was 15 inches. The length of the actual airplane is 75 feet. What scale did Jake use to create the scale drawing of the airplane? A. 1 inch represents 15 foot A. 1 inch represents 1 over 5.... , foot, B. 1 inch represents 5 feet B. , 1 inch represents 5 feet, , , C. 5 inches represents 1 foot C. , 5 inches represents 1 foot , D. 5 inches represents 15 foot
Answers
Answer:
B. 1 inch represents 5 feet.
Step-by-step explanation:
15 X 5= 75
josie buys a scoop of dried cranberries and a scoop of dried bananas to make trail mix. The dried cranberries weight 8.5 ounces and cost $0.30 per ounce. The dried bananas weigh 10.5 ounces and cost $0.20 per ounce. How much does josie spend on the dried food
Answers
Answer:yes
Step-by-step explanation:
In ΔVWX, v = 98 inches, w = 95 inches and x=26 inches. Find the measure of ∠X to the nearest 10th of a degree.
Answers
Answer:
15.4
Step-by-step explanation:
cos A = b^2 + c^2 - a^2 / 2bc
cos X = 98^2 + 95^2 - 26^2 / 2(98) (95)
cos X = 17953 / 18620
cos X = 0.964
X = cos^-1 (0.964) = 15.38 = 15.4
Lisa bought bottles of soda for $2.50 each and a large pizza for $17. The total cost was $27. How many bottles of soda did Lisa buy?
A.
4
B.
3
C.
10
D.
6
Answers
Answer:
a
Step-by-step explanation:
27-17= 10$ 2.5 goes into 10 4 times
Trina had 50 eggs. After using some of her eggs to make 12 batches of brownies, she has 14 eggs remaining. How many eggs did Trina use in one batch of brownies?
Answers
Step-by-step explanation:
eggs used : 50-12= 38 eggs
[tex] \frac{38 \: eggs}{12 \: batches} = 3.1667eggs \: per \: batch[/tex]
Find the approximate area of the shaded region below, consisting of a right triangle with a circle cut out of it.
Use 3.14 as an approximation for π .
Answers
Answer:
1,254 sqaure ft
Step-by-step explanation:
Use the radius of the circle, 202=10, to find the area of the circle: A=πr2=π(10)2=π⋅100≈3.14⋅100=314square meters. The area of the triangle is: A=12b⋅h=12⋅56⋅56=12⋅3,136=1,568 The area of the shaded region equals the area of the triangle minus the area of the circle. This is approximately 1,568-314=1,254 square meters.
The area of the shaded region is 1,254 square ft, consisting of a right triangle with a circle cut out of it.
What is the area of the circle?The area of the circle is equal to the product of the square of the radius of the circle and pi.
A = πr²
where 'r' is the radius of the circle
Use the radius of the circle, 20/2 =10, to find the area of the circle:
A = πr²= π(10)² = π⋅100 ≈ 3.14⋅100 = 314 square meters.
The area of the triangle is:
A=12b⋅h = 12⋅56⋅56 = 12⋅3,136 = 1,568
The area of the shaded region equals the area of the triangle and subtracts the area of the circle.
This is approximately 1,568 - 314 = 1,254 square meters.
Hence, the correct answer would be an option (B).
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he points in the table lie on a line. What is the slope?
Answers
Slope formula (y2-y1)/(x2-x1)
solve for c
c+d=15
3c+2d=36
WILL MARK BRAINLIEST AND MANY POINTS PLS ANSWER
Answers
6+9=15
3(6)+2(9)=36
18 + 18 = 37
c = 15 - d ( get c by itself first)
3(15 - d) + 2d = 36 (replace c with 15 + d)
45 - 3d + 2d = 36 (distribute)
45 - d = 36 (combine like terms)
-d = -9
d = 9
Madison is making a cleaning solution by mixing a multi-surface cleaner with water in the
ratio of 2 to 11. How many pints of the
cleaner and water does she need to make 39 pints of solution?
Cleaner:
Answers
Answer:
Im pretty sure its 33 and 6
Step-by-step explanation:
Answer:
Step-by-step explanation:
Set up a proportion
2/13 = x / 39 Cross multiply
13*x = 2 * 39 Combine the right
13x = 78 Divide by 13
x = 78/13
x = 6
Why pick 13? Because the total must come to 39. You will make a mistake if you use 11 rather than 13. You must include the cleaner in the denominator. Very tricky question.
So the final answer is
Cleaner: 6
Water: 39 - 6 = 33 pints of water.
Very few of your classmates will get this if they are not in chemistry. You might even be told your answer is incorrect. It isn't.
Please help thank you
Answers
Answer:
B
Step-by-step explanation:
Increasing trials promotes the chance of reaching theoretical.
9.66 rounded to 1 decimal place
Answers
Answer:
9.7
Step-by-step explanation:
When rounding 9.66 to one decimal place we use One Decimal Place Rule #2. Therefore, the answer to "What is 9.66 rounded to 1 decimal place?" is:
your answer would be 9.7
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If BD bisects ∠ABC, find each value
Answers
Answer:
x=14
y=10
AD=19
CD=19
Step-by-step explanation:
x:
5x-6=64
+6 +6
5x=70
x=14
y:
3y-11=y+9
+11 +11
3y=y+20
-y -y
2y=20
y=10
AD:
3y-11
3(10)-11
30-11
19
CD:
y+9
(10)+9
19
The sum of the enterior angles of any triangle is equal to:
Answers
Answer:
is equal to 180°
I hope it's helps you
Two trains leave the station at the same time, one heading east and the other west. The eastbound train travels at 75 miles per hour. The westbound train travels at 85 miles per hour. How long will it take for the two trains to be 384 miles apart?
Do not do any rounding.
Answers
Let the time = x
Distance = Speed x time
One train is 75x, the other train 85x
Add together to equal total distance:
75x + 85x = 384
Simplify:
160x = 384
Divide both sides by 160:
x = 384 / 160
x = 2.4 hours
*8th grade math*
1.6(1 + 0.5n) - 3, 2 = 1.1(n - 6.8)
please answer with work
Answers
Answer:
67
Step-by-step explanation:
__
Answer: 5.4945...
Step-by-step explanation:
1.6 (1 + 0.5n) − 3 , 2 = 1.1 (n − 6.8)
Rewrite the equation as 1.1 (n − 6.8) = 2.
1.1 (n − 6.8) = 2
Divide each term by 1.1 and simplify.
Divide each term in 1.1 (n − 6.8) = 2 by 1.1.
1.1 (n − 6.8)/1.1 = 2/1.1
Cancel the common factor of 1.1.
n − 6.8 = 2/1.1
Divide 2 by 1.1.
n − 6.8 = 1.81...
Move all terms not containing n to the right side of the equation.
Add 6.8 to both sides of the equation.
n = 1.81... + 6.8
Add 1.81... and 6.8.
n = 8.618...
Replace the variable n with 8.618... in the expression.
1.6 (1 + 0.5 (8.618...)) − 3
Simplify each term.
Multiply 0.5 by 8.618...
1.6 (1 + 4.309...) − 3
Add 1 and 4.309...
1.6 ⋅ 5.309... − 3
Multiply 1.6 by 5.309...
8.4945... − 3
Subtract 3 from 8.4945...
5.4945...
Graph
y + 4 = 2/5 (x − 3)
Answers
Answer:
Y= 2/5x - 23
Step-by-step explanation:
Firstly:
Move the 1/5 to the other side of the equation
So
5(y+4) =2(x-3)
Secondly:
Expand the brackets
5y +20 = 2x-3
Thirdly:
Solve
5y= 2x - 3-20
5y=2x-23. (Divide by five both sides)
Y= 2/5 x - 23 (Straight line graph)
To plot the graph:
First create a table of values
For x coordinates and y coordinates
Put the points in the graph and match
The price of a 7-minute phone call is $1.05. What is the price of a 19-minute phone call
Answers
Answer:
19.95
Step-by-step explanation:
if you take 1.05 times it by 19 you get your answer
The list of ordered pairs is a function. which of the following to be the missing ordered pair? (12,6) (3,1) (2,-2) (5,10) (-8, -4) (___,___)
Answers
Answer:
D
Step-by-step explanation:
the awnser is D
Answer:
8,8
Step-by-step explanation:
so if x +3y =1 how do i plug it in to -x +2y =4
-x +3y=1-x
3y/3=1-x/3
y=1/3 - x/3
y=-1/3x +1/3
Then I have to plug x into the y= the fractions confuse me
Answers
If x + 3y = 1, then x = 1 - 3y.
Then in the second equation, replace x with 1 - 3y :
-x + 2y = 4
- (1 - 3y) + 2y = 4
-1 + 3y + 2y = 4
-1 + 5y = 4
5y = 5
y = 1 → x = -2
since x = 1 - 3•1 = 1 - 3 = -2.
Alternatively, you can instead solve for y in the first equation, so that if x + 3y = 1, you get
x + 3y = 1
3y = 1 - x
y = (1 - x)/3
Then replace y in the second equation:
-x + 2y = 4
-x + 2 ((1 - x)/3) = 4
-x + 2/3 (1 - x) = 4
Multiply both sides by 3 to get rid of the fraction:
-3x + 2 (1 - x) = 12
-3x + 2 - 2x = 12
-5x + 2 = 12
-5x = 10
x = -2 → y = 1
since y = (1 - (-2))/3 = (1 + 2)/3 = 3/3 = 1.
help me please!!!!!!
Answers
==========================================================
Explanation:
Recall that sine is the ratio of opposite over hypotenuse.
For angle C, the opposite side is AB = 24 as this leg is furthest as possible from angle C. The hypotenuse is always opposite the 90 degree angle.
So,
sin(angle) = opposite/hypotenuse
sin(C) = AB/AC
sin(C) = 24/40
sin(C) = (8*3)/(8*5)
sin(C) = 3/5
If you want to find the measure of angle C, then you apply the arcsine rule to both sides. Inverse sine is the same as arcsine.
Answer:
Step-by-step explanation:
Solution
Here,
H=40
P=32
B=24
Now,
sinC=p/h
=32/40
=4/5
Where, 4 is perpendicular and 5 is hypotenuse.
Hope it helped you.
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Answers
The Jones family want to enclose the garden with a fence. To the nearest foot (round to the nearest whole number), how much fencing will they need to buy?
Answers
Answer:
hey hun, I think u need to give us more information on the question. Is that the full question ??
Solve for x: -3x + 3 < 6 (2 points)
a
x>-1
..
x <-3
Od
x>-3
Answers
Answer:
System of Linear equations. To find the quadratic functions f(x) = ax^2 + bx + c whose graphs contain the points (1,0) and (3,0) we can evaluate f at 1
Step-by-step explanation:
Answer:
Step-by-step explanation:
Here you go mate
Step 1
-3x+3<6 Equation/Question
Step 2
-3x+3<6 Simplify
-3x<3
Step 3
-3x<3 Divide
Answer
x>-1
Hope this helps
Solve It! Suppose that you want to create two identical wings for a model airplane. You draw one wing on a large sheet of tracing paper, fold it along the dashed line, and then tract the first wing. How do you know that the two wings are identical?
Answers
Answer:
you copied the other line
Step-by-step explanation:
you drew over the other line and it should be exact
Answer:
Hope this helps ! (OwO)/
Step-by-step explanation:
A line is formed when the paper is flod. Because of this, this helps the paper give an even form so there won't be any troubles. And if, the paper is uneven then the paper plane will be clusmy and fly in a corner. Brainlist? ʕ·ᴥ·ʔ