The dimensions of a rectangle with an area of 221 cm² and a perimeter of 60 cm are found by solving a system of equations derived from the definitions of area and perimeter. The dimensions are 13 cm by 17 cm, or equivalently, 17 cm by 13 cm.
Explanation:To find the dimensions of a rectangle with an area of 221 cm2 and a perimeter of 60 cm, we will let the length be x and the width be y. The area of a rectangle is found by multiplying the length and width, so we have the equation x * y = 221. The perimeter is twice the sum of the length and width, so we have 2x + 2y = 60, which simplifies to x + y = 30.
To solve these equations, divide the perimeter equation by 2 to find y = 30 - x. Substituting this into the area equation gives x(30 - x) = 221. Expanding this and bringing all terms to one side provides a quadratic equation: x2 - 30x + 221 = 0. Solving this quadratic equation by factoring or using the quadratic formula gives the dimensions of the rectangle.
The solutions to the quadratic equation are x = 13 and x = 17. Since x and y are interchangeable as length and width, the two sets of possible dimensions for the rectangle are 13 cm by 17 cm and 17 cm by 13 cm.
The dimensions of the rectangle are [tex]17\ cm , 13\ cm[/tex]
To find the dimensions [tex]\( l \)[/tex] (length) and [tex]\( w \)[/tex] (width) of the rectangle given its area and perimeter, we start with the following equations:
1. Area equation:
[tex]\[l \times w = 221\][/tex]
2. Perimeter equation:
[tex]\[ 2l + 2w = 60 \][/tex]
Step-by-Step Solution:
The dimensions of the rectangle are [tex]{{17, 13} \) cm.[/tex]
From the perimeter equation, divide everything by [tex]2[/tex] to simplify:
[tex]\[l + w = 30\][/tex]
Now we have a system of equations:
[tex]\[\begincases}l \times w = 221 \\l + w = 30\end{cases}\][/tex]
Let's solve this system using substitution or elimination:
From [tex]\( l + w = 30 \)[/tex], we can express [tex]\( w \)[/tex] in terms of [tex]\( l \)[/tex]
[tex]\[w = 30 - l\][/tex]
Substitute [tex]\( w = 30 - l \)[/tex] into the area equation:
[tex]\[l \times (30 - l) = 221\][/tex]
[tex]\[30l - l^2 = 221\][/tex]
Rearrange this equation to form a quadratic equation:
[tex]\[l^2 - 30l + 221 = 0\][/tex]
Now, solve this quadratic equation using the quadratic formula [tex]\( l = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), where \( a = 1 \), \( b = -30 \), and \( c = 221 \)[/tex]
[tex]\[l = \frac{-(-30) \pm \sqrt{(-30)^2 - 4 \times 1 \times 221}}{2 \times 1}\][/tex]
[tex]\[l = \frac{30 \pm \sqrt{900 - 884}}{2}\][/tex]
[tex]\[l = \frac{30 \pm \sqrt{16}}{2}\][/tex]
[tex]\[l = \frac{30 \pm 4}{2}\][/tex]
Calculate both possible values of [tex]\( l \)[/tex]
[tex]\[l = \frac{30 + 4}{2} = 17 \quad \text{or} \quad l = \frac{30 - 4}{2} = 13\][/tex]
Corresponding values of \( w \)
[tex]If\ \( l = 17 \), then \( w = 30 - 17 = 13 \)[/tex]
[tex]If\ \( l = 13 \), then \( w = 30 - 13 = 17 \)[/tex]
Therefore, the dimensions of the rectangle are [tex]\( 17 \) cm[/tex] by [tex]\( 13 \) cm.[/tex]
Verification:
[tex]Area: \( 17 \times 13 = 221 \) cm\(^2\)[/tex]
[tex]Perimeter: \( 2 \times (17 + 13) = 2 \times 30 = 60 \) cm[/tex]
Both conditions match the given area and perimeter, confirming that the dimensions are correct.
Answers from anybody please??
I need help ASAP I will give brainliest if correct
Math question help :)
Answer:
Step-by-step explanation:
I think its D.
A thief steals an ATM card and must randomly guess the correct three-digit pin code from a 10-key keypad. Repetition of digits is allowed. What is the probability of a correct guess on the first try?
The probability of a correct guess on the first try will be [tex]0.001[/tex] .
What is Probability ?Probability is the ratio of number of favorable outcome to the
i.e. Probability [tex]P(E)=\frac{number\ of\ favorable\ outcome}{Total\ number\ of\ outcomes.}[/tex]
We have,
An ATM Card having three-digit code.
Repetition of digits is allowed.
So,
As Repetition is allowed, and we have [tex]10-[/tex]key keypad, and have to guess [tex]3[/tex] digit code,
Then
Total number of outcomes [tex]=10*10*10=1000[/tex]
And
Number of favorable outcome [tex]=1[/tex]
So,
Probability [tex]P(E)=\frac{number\ of\ favorable\ outcome}{Total\ number\ of\ outcomes.}[/tex]
[tex]P(E)=\frac{1}{1000}[/tex]
[tex]P(E)=0.001[/tex]
So, the Probability of correct guess is [tex]0.001[/tex] .
Hence, we can say that the probability of a correct guess on the first try is [tex]0.001[/tex] .
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I need help with this
how many fluorine atoms are found in 1.92 grams of AsF3?
*Please answer*
Don't understand. Please help.
Write an expression for the following situation and solve. Mr. Simms bought 20 pencils. He used 1/4 of the pencils and then gave 4 to his students. How many total pencils does Mr.Simms use and give away? Show your work.
Mr. Simms used 1/4 of the 20 pencils he bought, which equals 5 pencils, and gave away an additional 4 pencils, totaling to 9 pencils used and given away.
To solve how many total pencils Mr. Simms uses and gives away, we first find out how many pencils he used by taking 1/4 of the 20 pencils he bought. To do this, we multiply 20 by 1/4:
20 times 1/4 = 5
Mr. Simms used 5 pencils. He also gave away 4 pencils to his students. To find the total number of pencils used and given away, we add the pencils used to the pencils given away:
5 (used) + 4 (given away) = 9
Therefore, Mr. Simms used and gave away a total of 9 pencils.
Which graph represents a phase shift of pi/2 units right for the graph of y=cos x
Solution:
we are given that [tex]y=cos x[/tex]
Here we are going to plot two curves one for cosx and the othere also of cosx but after making a phase shift of [tex]\pi/2[/tex]
When we do a phase shift by an angle of theta , in that case actaully we add angle negative theta .
For example when we shift the phase of sinx by [tex]\pi/2[/tex] we get [tex]sin(x-\pi/2).[/tex]
Hence we are going to plot the curve of
[tex]y=cosx\\ \\ y=cos(x-\pi/2)=sinx\\[/tex]
Hence the correct option is B.
I need to spend exactly £200, how?
Select the correct product.
(2x + 9)(x + 1)
2x2 + 11x + 9
3x2 + 11x + 9
2x2 - 7x + 9
2x2 + 11x + 10
Final answer:
To find the product of (2x + 9) and (x + 1), we use the distributive property and combine like terms, resulting in 2x² + 11x + 9.
Explanation:
The student is asking for the correct product when multiplying the binomials (2x + 9) and (x + 1). This is a math problem involving algebraic multiplication.
To find the product, we apply the distributive property (also known as FOIL method in binomials):
Multiply 2x by x to get 2x².Multiply 2x by 1 to get 2x.Multiply 9 by x to get 9x.Multiply 9 by 1 to get 9.Combine the terms to get the final product: 2x² + 2x + 9x + 9, which simplifies to 2x² + 11x + 9.
The correct product of (2x + 9)(x + 1) is 2x² + 11x + 9.
You have a cd-rw drive that advertises speeds of 32x/12x/48x. what is the read speed of the drive?
a basketball player made 27 free throws in her last 45 tries. what is the experimental probability that she will make her next free throw?
Analyze the key features of the graph of the quadratic function f(x) = -x2 + 2x + 10. A. Does the parabola open up or down?
B. Is the vertex a minimum or a maximum?
C. Identify the axis of symmetry, vertex and the y-intercept of the parabola.
SOS
Answer
A: Down
B: Max
C:
AOS: x = 1Vertex: (1, 11)Y-Int: (0, 10)Step-by-step explanation:
A: If the leading coefficient (a) is positive, the graph opens UP. If it is negative, the graph opens DOWN.
B: Anytime the graph goes UP, there's a minimum. Anytime the graph goes DOWN, there's a maximum
C:
AOS: [tex]x = \frac{-b}{2a}, a=-1, b=2, c=10[/tex]
Vertex: [tex](\frac{-b}{2a}, y)[/tex]
Y-INT: let x=0 and solve for y. The coordinate of the y-intercept is (0, y).
Hope this helps!!
Suppose that an individual has a body fat percentage of 16.4% and weighs 153 pounds. how many pounds of her weight is made up of fat? round your answer to the nearest tenth.
Four consecutive integers sum to 70. What is the least of the 4 integers?
△JKL∼△QRS , JK is 8 centimeters, QR is 12 centimeters, and RS is 9 centimeters.
What is KL ?
Enter your answer in the box.
Answer:
The measure of KL is 6 centimeters.
Step-by-step explanation:
It is given that △JKL∼△QRS.
The corresponding sides of two similar triangles are proportional.
[tex]\frac{JK}{QR}=\frac{KL}{RS}[/tex]
[tex]\frac{8}{12}=\frac{KL}{9}[/tex]
[tex]8\times 9=KL\times 12[/tex]
Divide both sides by 12.
[tex]KL=\frac{72}{12}[/tex]
[tex]KL=6[/tex]
Therefore we can say that if △JKL∼△QRS, then the measure of KL is 6 centimeters.
Answer:
6
Step-by-step explanation:
He did too much math lol, a simple way of this is by dividing both sides initially.
12/9 = 1.5
9/1.5 = 6
If cos B = 7 over 22, then which of the following is correct?
a. csc B = 7 over 22
b. csc B = 22 over 7
c.sec B = 7 over 22
d.sec B = 22 over 7
Today a car is valued at $42000. The value is expected to decrease at a rate of 8% each year. Choose the equation that can be used to solve the problem.
A.) y=42000(1+.08)^6
B.) y=42000(1+6)^8
C.) y=42000(1−.08)^6
D.) y=42000(1−.8)^6
And then: What is the value of the car expected to be 6 years from now?
This is the only question I don't understand, someone help please!
Answer:
Option (c) is correct.
[tex]y=42000(1-0.08)^6[/tex] equation that can be used to solve the given problem and the value of the car expected to be 6 years from now is $25466.91
Step-by-step explanation:
Given : Today a car is valued at $42000. The value is expected to decrease at a rate of 8% each year.
We have to choose the equation that can be used to solve the given problem.
We know
Depreciation formula given as,
[tex]A=P(1-\frac{r}{100} )^n[/tex]
Where A is the amount value after depreciation.
P is present value
r is depreciate rate.
n is time period.
Given : P = 42000 and r= 8% also given time period is 6.
Substitute , we have,
[tex]y=42000(1-\frac{8}{100} )^6[/tex]
Simplify , we have,
[tex]y=42000(1-0.08)^6[/tex]
Simplify we get,
[tex]y=25466.91[/tex]
Thus, [tex]y=42000(1-0.08)^6[/tex] equation that can be used to solve the given problem and the value of the car expected to be 6 years from now is $25466.91
Tiny's Tattoo Parlor sold 389 tattoos this month. 43 of those tattoos were arm tattoos. Based on this data, what is a reasonable estimate of the probability that the next customer does not get an arm tattoo?
Answer:
346/389
Step-by-step explanation:
correct on khan academy!
The reasonable estimate of the probability that the next customer does not get an arm tattoo is 346/389.
What is Probability?
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1.
Here, Based on the given conditions, formulate
Probability = Favorable outcome / Total outcome
Calculate the sum or difference: (389-43)/389
get the result: 346/389
Thus.the reasonable estimate of the probability that the next customer does not get an arm tattoo is 346/389.
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The domain of f(x) is the set of all real values except 7, and the domain of g(x) is the set of all real values except –3. What describes the domain of (gºf)(x)?
How long is the base of a parallelogram if it has an area of 100 m2 and a height of 5 m? Enter your answer in the box.
What are the solutions to the equation?
n^2−8n+16=25
Enter your answers in the boxes.
n1=
n2=
Answer:
help
Step-by-step explanation:
The staff at Larry's Lawns spends their workday mowing lawns, raking, and bagging leaves. They work an average of nine hours per day. The mowing and raking typically takes six hours and an average of thirty-six bags of leaves are filled. Assuming the bags are filled at a constant rate, what is the average time it takes to fill one bag of leaves?
The average time it takes to fill one bag of leaves is approximately 0.17 hours.
Explanation:To find the average time to fill one bag of leaves, we use the formula
Average Time=Total Time÷Total Bags. In this scenario, the total time spent is the average workday hours, which is 9 hours, and the total number of bags filled is 36.
So,
Average Time=9hours÷36bags=0.25 hours/bag.
Therefore, the average time it takes to fill one bag of leaves is 0.25 hours or 15 minutes. This means, on average, it takes 15 minutes to fill each bag of leaves.
In summary, the staff at Larry's Lawns spends 9 hours a day on lawn-related tasks, with mowing and raking taking 6 hours. Since they fill an average of 36 bags of leaves in that time, each bag takes approximately 0.25 hours or 15 minutes to fill, assuming a constant rate of filling.
To find the average time it takes to fill one bag of leaves at Larry's Lawns, divide the total time spent filling bags by the number of bags filled. Time per bag = 1/6 hours per bag.
Explanation:To find the average time it takes to fill one bag of leaves, we need to divide the total amount of time spent filling bags by the number of bags filled. In this case, the staff at Larry's Lawns spend 6 hours mowing and raking and fill 36 bags of leaves. So to find the average time per bag, we divide 6 hours by 36 bags:
Time per bag = Total time / Number of bags = 6 hours / 36 bags
Since we want the average time per bag, we can simplify the fraction:
Time per bag = 1/6 hours per bag.
What is the name of a ray that divides an angle into two equal angles?
help me please asap and plz be correct :)
BRAINLIESTTT ASAP!!!!!!!!!
How could you find an equation of a quadratic function with the zeroes of -3 and 1?
Goran runs 6 miles in 57 minutes how many miles does he run per minute?