Among all rectangles that have a perimeter of 156, find the dimensions of the one whose area is largest. write your answers as fractions reduced to lowest terms.
The dimensions of the one whose area is largest is 39 by 39
The formula for calculating the perimeter of a rectangle is expressed as:
P = 2(L + W)
L is the length of the rectangle
W is the width
Given that the perimeter is 156, hence;
2(L + W) = 156
2L + 2W = 156
L + W = 78
W = 78 - L
The area of the rectangle is expressed as:
A = LW
A = L(78-L)
A = 78L - L^2
To get the dimensions of the one whose area is largest, dA/dL = 0
dA/dL = 78 - 2L
0 = 78 - 2L
2L = 78
L = 78/2
L = 39
Recall that 2(L+W) = 156
2(39 + W) = 156
39 + W = 78
W = 78 - 39
W = 39
Hence the dimensions of the one whose area is largest is 39 by 39
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Which property justifies this statement?
If 4x=20, then x=5.
How is angle a related to angle d?
A) vertical angles
B) alternate interior angles
C) alternate exterior angles
D) corresponding angles
Answer: Option 'A' is correct.
Step-by-step explanation:
since we have given a line AB and CD such that AB║CD,
And a transversal say 'l' cut the two parallel lines
And we know that when a transversal cuts two parallel lines we get linear pair and corresponding angles
But relation between angle 'a' and angle 'd' is vertically opposite angles.
So, Option 'A' is correct.
I need help asap
the triangles below are congruent. which of the following statements are true
A. a~=d
B. b~=e
C. ab~=de
D. bc~=df
Sergio is S years old. Which expression shows how old will he be 7 years from now?
A. 7s
B. 7-s
C. s+7
D. 7s+7
Juan used the expression 16 – 9 – 12 + 22 to find his profit for days 2 and 3. He rewrote the expression as 16 + (–9) + (–12) + 22. Juan can use the associative and commutative properties to rewrite the expression again. Explain why he had to use the additive inverse before he could use these properties.
Answer:
Associative property and commutative property true for addition, not true for subtraction.
Step-by-step explanation:
Associative property and commutative property true for addition.
i) a + (b + c) = (a + b) + c ---> Associative property of addition
ii) a + b = b + a --> commutative property of addition.
These properties not true for subtraction.
That's the reason Juan used additive inverse before applying these property.
Hope this will helpful.
Thank you.
[tex]\bold{ a + (b + c) = (a + b) + c } \to[/tex] Associative property of addition
[tex]\bold{a + b = b + a } \to[/tex] commutative property of addition.
As we show above both the property used for the addition and no used for the subtraction, that is why before applying the property Juan applied reverse additives.Learn more:
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How can sums and differences of cubes be identified for factoring?
Consider the terms pyramid, line, square, and triangle. The term ____is not defined in Euclidean geometry.
During a sale,Susan grody paid $155 for a clothes dryer.The price paid reflects a 75% discount off the original price. Determine what is the original price of the dryer.
The original price of the dryer would be; 38.75 dollars.
How to calculate the unit price of something?Unit means 'single entity, the fundamental constructing block. Usually, it is 1 in mathematics and science. Thus, the unit price of something is the price of 1 thing.
Given that Susan grody paid $155 for a clothes dryer.
The price paid by her reflects a 75% discount off the original price.
Required the original price of the dryer.
Thus,
100 - 75 = 25%
Therefore,
155 x 25%
155 x 0.25 = 38.75
Hence, the original price of the dryer would be; 38.75 dollars.
Learn more about unit prices here:
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A rectangle has an area of 16 ft2. every dimension is multiplied by a scale factor, and the new rectangle has an area of 64 ft2. what was the scale factor?
How to factor this:
6x² + 7x - 5
Please give an explanation on how you did it
(See attachment please)
What postulate can be used to prove that △ADC≅△CBA ?
The graph of which of the following equations contains the points (2, 3) and (3, 2)? y = x - 1
y = 5 - x
y= 7 - 2x
Konnor wants to burn 250 calories while exercising for 45 minutes at the gym. on the treadmill, he can burn 6 cal/min. on the stationary bike, he can burn 5 cal/min. if t represents the number of minutes on the treadmill and b represents the number of minutes on the stationary bike, which expression represents the number of calories that konnor can burn on the stationary bike?
Given that b is the number of calories that can be burned using the stationary bike, and the burning rate is 5 cal / min, therefore:
b = 5 t
where t is the time spent on the stationary bike
Answer:
B=5t
Step-by-step explanation:
Davis knows that the area of his square shaped bag is 81 ft sq. What is the length of any side of the bag
What does y and z equal. I already got x
A club with 19 members is to choose three officers president vice president and security secretary treasurer. If each office is to be held by one person and no person can hold more than one office in how many ways can those offices be filled
If rectangle DEFG is dilated by a scale factor of 1/2 with a dilation center of (0, 0), what will be the coordinates of point F'?
Claire's cousin is now 3 times as old as Claire. in 10 years, her cousin will be twice as old as claire. how old is Claire now?
Claire is currently 10 years old.
Explanation:Let's assume that Claire's age is x.
According to the given information, Claire's cousin is now 3 times as old as Claire. This can be represented as Cousin's age = 3x.
In 10 years, Cousin's age will be twice as old as Claire's age. So, we can write the equation:
(3x + 10) = 2(x + 10)
Simplifying the equation:
3x + 10 = 2x + 20
Subtracting 2x from both sides:
x + 10 = 20
Subtracting 10 from both sides:
x = 10
Therefore, Claire is currently 10 years old.
FREE POINTS HELPPP HELPPP WILL GIVE BRAINLEST AND THANKS EASY PLEASE HELP ME
The exponential function in the graph shows the population of Greeville in the years since 2010. What real-world information is given by the point (6, 2707)?
options:
The population in 2006
The population in 2010
The population in 2016
The year in which the population is twice the population in 2010
The measure of an angle is forty-four times the measure of a supplementary angle. what is the measure of each angle?
if y equals -12 when x equals 9 find y when x equals negative 4
A dentist is making identical dental care bags for patients using 56 tubes of toothpaste, 112 packets of floss, and 85 toothbrushes. What is the greatest number of identical dental care bags the dentist can make with the least amount of items leftover. Describe the contents of each bag.
Twelve less than negative nine times a number is equal to 8 minus 4 times the number find the number
Final answer:
The number that satisfies the original equation is -4.
Explanation:
A student's question involves finding a number that satisfies the equation: 'Twelve less than negative nine times a number is equal to 8 minus 4 times the number'.
To solve this, we set up the equation -9x - 12 = 8 - 4x.
Solving for 'x' involves simple algebraic steps.
First, add 9x to both sides to get the variable terms on one side:
-9x - 12 + 9x = 8 - 4x + 9x-12 = 8 + 5xNext, subtract 8 from both sides to isolate the variable term:
-12 - 8 = 5x-20 = 5xFinally, divide both sides by 5 to find 'x':
-20 / 5 = 5x / 5-4 = xThe number that satisfies the original equation is -4.
Tyson and his friends go ice skating. Tyson must pay an initial fee of $18.30 plus $4.80 per hour. Write an equation for the cost c Tyson must pay after skating h hours. Solve the equation to find the cost to go ice skating for four hours. Write your answer as an ordered pair.
A, c = 4.80h – 18.30 (4, 0.9)
B. c = 4.80 + 18.30h (4, 78.00)
C. c = 18.30 + 4.80h (4, 37.50)
D. c = 18.30 + 4.80 + h (4, 27.10)
Louise used this figure to model the expression 20/4
What error did Louise make in her model?
The small arrows are pointed in the wrong direction.
The small arrows should all end in the same place as the large one.
The arrows should start at zero.
There should be one large arrow and 20 small arrows.
Answer:
The arrow should start at zero
Step-by-step explanation:
Because if it star any where else it would be incomplete
7n2 + 8n − 12
A) (7n + 6)(n − 2)
B) (5n − 8)(n + 10)
C) Not factorable
D) (7n − 6)(n + 2)
to dilute a concentrated liquid fabric softener, the directions state to mix 3 cups of water with 1 cup of concentrated liquid. how many gallons of water will you need to make 6 gallons of diluted fabric softener?
if the inequality has the same number on both sides for the answer is that ok?
When is a protractor preferred to a ruler when finding a measurement
A protractor is preferred over a ruler when measuring angles, especially in geometric shapes or when dealing with rotational aspects. While a ruler is great for measuring lengths and distances, it can't accurately measure angles.
For example, let's say you want to measure the angle between two lines on a piece of paper. A ruler can only give you an approximation by comparing lengths, but a protractor will give you an exact measurement of the angle in degrees.
To use a protractor, align the center hole of the protractor with the vertex of the angle. Then, align one side of the angle with the zero-degree mark on the protractor. Finally, read the number where the second side of the angle intersects the protractor scale. This gives you the precise measurement of the angle.
In conclusion, when dealing with angles, a protractor is the preferred tool for accurate measurements, providing exact angles in degrees.