Which is better? A length of 9 and a perimeter of 22 or A length of 5 and a perimeter of 20?
Answers
SOLUTION:
We are to choose between a Cheez-it's that cover a rectangle with;
(i) A length of 9 and a perimeter of 22,
(ii) A length of 5 and a perimeter of 20.
The prefer one would be the one with a greater area.
\(\begin{gathered} \text{Length = 9 units} \\ \text{Perimeter = 22 units} \\ P\text{ = 2(L + W)}=22\text{ } \\ 2(9\text{ + w) = 22} \\ \frac{2(9+w)}{2}=\text{ }\frac{22}{2} \\ 9+w\text{ = 11} \\ w\text{ = 11-9} \\ w\text{ = 2 units} \end{gathered}\)The area of this rectangle is;
\(\begin{gathered} A=LXW\text{ } \\ A\text{ =9X2} \\ A=18unit^2 \end{gathered}\)\(\begin{gathered} \text{Length }=\text{ 5 units} \\ \text{Perimeter = 20 units} \\ P\text{ = 2(L + W) = 20} \\ 2(5\text{ + w) = 20} \\ \frac{2(5+w)}{2}=\text{ }\frac{20}{2} \\ 5\text{ + w = }10 \\ w=10-5 \\ w\text{ = 5 units} \end{gathered}\)The area of this rectangle is;
\(\begin{gathered} A\text{ = L x W} \\ A\text{ = 5 x 5} \\ A=25units^2 \end{gathered}\)CONCLUSION:
Since the area of a rectangle of length of 5 and a perimeter of 20 is greater than that of a length of 9 and a perimeter of 22.
The preferred is the Cheez-it's that covers a rectangle of a length of 5 and a perimeter of 22.
Related Questions
Given the coordinate matrix of x relative to a (nonstandard) basis B for Rn, find the coordinate matrix of x relative to the standard basis. B = {(1, 0, 1), (1, 1, 0), (0, 1, 1)},
[x]B=
2
1
3
[x]s=?
Answers
The coordinate matrix of x relative to the standard basis is [1, -2, -1]. Formula connecting coordinate matrix of vector x relative to the standard basis is: [x]s = P * [x]B
Where [x]s is the coordinate matrix of x relative to the standard basis, [x]B is the coordinate matrix of x relative to the basis B, and P is the change-of-basis matrix from B to the standard basis.
To find P, we need to express the standard basis vectors in terms of the basis B. Let's denote the standard basis vectors as e1, e2, and e3:
e1 = (1, 0, 0)
e2 = (0, 1, 0)
e3 = (0, 0, 1)
To express e1 in terms of the basis B, we solve the equation:
e1 = a * (1, 0, 1) + b * (1, 1, 0) + c * (0, 1, 1)
Expanding the equation, we get:
(1, 0, 0) = (a + b, b, a + c)
This gives us the system of equations:
a + b = 1
b = 0
a + c = 0
Solving the system, we find a = -1, b = 0, and c = 1. Therefore, e1 in terms of the basis B is (-1, 0, 1).
Similarly, we can find e2 and e3 in terms of the basis B:
e2 = (-1, 1, 1)
e3 = (2, -1, -1)
Now we can form the change-of-basis matrix P by arranging the basis vectors e1, e2, and e3 as columns:
P = [(-1, -1, 2), (0, 1, -1), (1, 0, -1)]
Given [x]B = [2, 1, 3], we can compute [x]s:
[x]s = P * [x]B
= [(-1, -1, 2), (0, 1, -1), (1, 0, -1)] * [2, 1, 3]
Performing the matrix multiplication, we get:
[x]s = [(-1 * 2 + -1 * 1 + 2 * 3), (0 * 2 + 1 * 1 + -1 * 3), (1 * 2 + 0 * 1 + -1 * 3)]
= [1, -2, -1]
Therefore, the coordinate matrix of x relative to the standard basis is [1, -2, -1].
Learn more about matrix here: https://brainly.com/question/28180105
#SPJ11
The lengths of two pieces of fabric are in the ratio 7:5. If the first length is 210 meters, what is the second length? *
Answers
Answer:
150 meters
Step-by-step explanation:
\(\frac{7}{5} =\frac{210}{x\\}\)
cross multiply:
7x = 1050
solve for x by dividing both sides by 7:
x = 150
the second length is 150 meters
Answer:
150 meters
Step-by-step explanation:
To get from 7 to 210 it was multiplied by 30 (we know this because 210 divided by 7 is 30) so that means to get from 5 to the missing length of the second rope, you multiply by 30. 5 times 30 is 150, so the second rope is 150 meters long.
:) ur welcome
It is known that 2x-3/x = x + 1 What is the value of x^2 -x + 3
Answers
The value of the equation x² - x + 3 is 37/9.
We have,
We can start by multiplying both sides of the equation by x:
2x - 3/x = x + 1
2x - 3 = x^2 + x
Rearranging and simplifying, we get:
x^2 - x + 3 = (2x - 3) + x^2
x^2 - x + 3 = x^2 + 2x - 3
-x + 3 = 2x - 3
5 = 3x
x = 5/3
Now we can substitute x into the equation x^2 - x + 3:
x^2 - x + 3 = (5/3)^2 - 5/3 + 3
x^2 - x + 3 = 25/9 - 15/9 + 27/9
x^2 - x + 3 = 37/9
Therefore,
The value of x² - x + 3 is 37/9.
Learn more about equations here:
https://brainly.com/question/17194269
#SPJ1
Find the value of c that satisfy the equation f(b)-f(a)/b-a = f'(c) :
5. f(x) = x^3 - x^2 , [-1,2]
Answers
The value of c that satisfies the given function is 1 or -1/3.
We have to find the value of c that satisfy the equation f(b)-f(a)/b-a = f'(c) in the given function.
The function is f(x) = x³ - x² over [-1, 2].
Given function is:f(x) = x³ - x² over [-1, 2].
The value of a and b are given as follows:a = -1, b = 2
The first step is to calculate f(b) - f(a) as well as f′(c) and afterward equate them using the given formula which is shown below:
f(b) - f(a) / b - a = f′(c)
We need to calculate the value of c.
We begin by calculating f(b) - f(a):f(2) - f(-1) = (2)³ - (2)² - (-1)³ - (-1)²= 8 - 4 + 1 - 1= 4
Now we need to calculate the value of f′(c).f′(x) = 3x² - 2xf′(c) = 3c² - 2c
Now substitute the values of f(b) - f(a) and f′(c) in the given formula:
f(b) - f(a) / b - a = f′(c)4/3 = 3c² - 2c4 = 9c² - 6c2 = 3c² - 2c + 1
⇒ 3c² - 2c - 1 = 0
By solving this quadratic equation, we get:c = 1 or c = -1/3
Hence, the value of c that satisfies the given equation is 1 or -1/3.
Know more about the function
https://brainly.com/question/11624077
#SPJ11
−8tan 1+tan2x Use appropriate identities to rewrite the following expression in terms containing only first powers of sine
Answers
By using Pythagorean identities the expression can be written as
-8 (sin ( x ) + 1 -sin 2x)
The Pythagorean identity is an important identity in trigonometry derived from the Pythagorean theorem. These identities are used to solve many trigonometric problems where, given a trigonometric ratio, other ratios can be found. The basic Pythagorean identity, which gives the relationship between sin and cos, is the most commonly used Pythagorean identity:
sin2θ + cos2θ = 1 (gives the relationship between sin and cos)
There are two other Pythagorean identities as follows :
sec2θ - tan2θ = 1 (gives the relationship between sec and tan)
csc2θ - cot2θ = 1 (gives the relationship between csc and cot)
Given expression is:
-8tanx/ 1 +tan2x
we know that:
By the Pythagorean Theorem:
1 + tan²x = sec²x
and tan x = sin x/cos x
and, sec x = 1/cos x
Now, we can write as:
-8tanx / 1 +tan²x
= -8 tan x / sec²x
= -8 sin x /cos x ÷ 1/cos²x
= -8 sin x/cos x × cos²x/1
= -8 (sin ( x ) + 1 -sin 2x)
Complete Question:
Use appropriate identities to rewrite the following expression in terms containing only first powers of sine:
−8tan 1 + tan2x.
Learn more about Pythagorean identities
https://brainly.com/question/10285501
#SPJ4
When Ram was 16 years old, he deposited a certain sum of money in a bank at the rate of 10% p. a. Compounded annually. After his balance became 121 /700 times of the initial principal, he deposited 1/70 of the existing balance in the same account. After 1 year to this deposition, the bank changed it's policy to give interest at 20%p.a. simple interest. At the age of 24 years, Ram planned to start a business so, he withdrew all the money from his account. He found that the withdrawn amount was Rs. 359 less than thrice of the initial principal. Then,
1) Find the sum deposited by Ram at the age of 16 years.
2)The amount withdrawn from the bank was not enough so, he borrowed a loan of Rs. 1,10,000 from the bank and agreed to pay within 4 years, at a rate of 15% pa. compounded annually. He paid the interest of the first year at the end of the 1st year. He cleared his debt by paying equal installments in next year 2 years and 1 year. Find the total interest paid by him to the bank.
3) For how many years, he should have waited -to start the business so that he need not borrow an entra loan?
Answers
Step-by-step explanation:
Let the principal deposited by Ram at the age of 16 be P.
After the balance became 121/700 times of the initial principal, we have:
(121/700)P = P(1 + 10/100)^n
where n is the number of years for which the amount is compounded annually.
Simplifying the above equation, we get:
n = log(121/700)/log(1.1)
After Ram deposited 1/70 of the existing balance, his new balance became:
(121/700)P + (1/70)[(121/700)P] = (121/700)P(1 + 1/10)
After 1 year of this deposit, the new balance became:
(121/700)P*(1 + 1/10)(1 + 20/100) = (121/700)P(11/10)*(6/5) = (363/350)P
Given that this amount is Rs. 359 less than thrice of the initial principal, we get:
(363/350)P = 3P - 359
=> P = Rs. 2450
Therefore, the sum deposited by Ram at the age of 16 years was Rs. 2450.
The loan amount borrowed by Ram from the bank is Rs. 1,10,000 at a rate of 15% p.a. compounded annually for 4 years. Let the interest paid by Ram at the end of the 1st year be I1.
The amount to be paid by Ram at the end of the 1st year = 1,10,000*(1 + 15/100) = Rs. 1,26,500
Out of this, Ram pays only the interest amount, i.e., I1.
The remaining amount to be paid by Ram after the 1st year = 1,26,500 - I1
This amount is to be paid in 3 years, at a rate of 15% p.a. compounded annually.
Let the equal installments to be paid by Ram for the next 3 years be X.
Therefore, we have:
X*(1 + 15/100)^3 + X*(1 + 15/100)^2 + X*(1 + 15/100) = 1,26,500 - I1
Solving the above equation, we get:
X = Rs. 36,285.47
Therefore, the total interest paid by Ram to the bank is:
I1 + 3X - 1,10,000 = I1 + 336,285.47 - 1,10,000 = Rs. 59,856.41
To avoid borrowing an extra loan, the withdrawn amount should be equal to or greater than the amount required to start the business.
The withdrawn amount is given by:
3P - 359 = 3*2450 - 359 = Rs. 6891
Therefore, Ram should have waited for the amount in his bank account to become Rs. 6891 or more, which would take n years, where:
(121/700)2450(1 + 10/100)^n >= 6891
Solving the above equation, we get:
n >= 4.52
Therefore, Ram should have waited for at least 5 years to start the business, to avoid borrowing an extra loan.
elijah has some dimes and some quarters. he has a minimum of 18 coins worth at most $3.60 combined if Elijah has 12 dimes determune the maximum number of quarters that he could have
Answers
We have the following:
let x number of dimes
let y number of quarters
\(\begin{gathered} 0.10x+0.25y\ge3.6 \\ x+y\ge18 \end{gathered}\)Therefore,
\(\begin{gathered} x=12 \\ 12+y\ge18 \\ y\ge18-12 \\ y\ge6 \\ 0.10\cdot12+0.25y\ge3.6 \\ 1.2+0.25y\ge3.6 \\ y\ge\frac{3.6-0.12}{0.25} \\ y\ge9.6 \end{gathered}\)Therefore, The quarters can range from 6 coins to 9.6 coins, that is, the maximum can be 10 coins.
53°
R
A. Write and solve an equation to find mzPQT, where x = mzPQT.
+
112 3
4 5 6
s
= 2 >
ve
7 8 9
# 0° 0 I VO WO IT
0
B. Solve your equation.
I just don’t understand it that’s all and I need help
Answers
Answer:
Step-by-step explanation
Fhfjhrtsjz
A triangle has a height of 6mm and an area of 27mm2. What is the length of the base of the triangle?
Answers
Answer:
9 mmStep-by-step explanation:
A triangle has a height of 6mm and an area of 27mm2. What is the length of the base of the triangle?
----
To calculate the area of a triangle, multiply the height by the width (this is also known as the 'base') then divide by 2.
We use the inverse formula
base = 2A : height
2 * 27 : 6 = 9
------------------------
check
6 * 9 : 2 = 27
the answer is good
Use cylindrical shells to find the volume of the solid that is generated when the region that is enclosed by y=1/x^3, x=1, x=2, y=0 is revolved about the line x=-1
Answers
The volume of the solid that is generated is: \(2\pi\)\([ In|x| - x^-^1]^2_1\)
Now, According to the question:
The formula for the shell method is :
\(=\int\limits^a_b {2\pi rh} \, dx\)
where, a and b are the x - bound, which are x=1 and x=2,
So, a = 1 and b = 2
r is the distance from a certain x-value in the interval [1, 2] and the axis of rotation, which is x = -1 .
r = x - (-1) = x + 1
h is the height of the cylinder at a certain x-value in the interval [1, 2], which is \(\frac{1}{x^{2} } - 0\) = \(\frac{1}{x^{2} }\) (because \(\frac{1}{x^{2} }\) is always greater than 0 and h must be positive).
Plugging it all in volume
\(\int\limits^2_1 {(2\pi (x + 1)(\frac{1}{x^2} ))} \, dx\)
= \(2\pi \int\limits^2_1 { (x + 1)(\frac{1}{x^2} ))} \, dx\)
\(2\pi\)\([ In|x| - x^-^1]^2_1\)
Hence, The volume of the solid that is generated is: \(2\pi\)\([ In|x| - x^-^1]^2_1\)
Learn more about Cylindrical Volume at:
https://brainly.com/question/25562559
#SPJ4
What is the distance from the point (3,8) to the point (7,-6)?
Answers
Answer: Distance is 14.6
Step-by-step explanation:
\(d = √((x2-x1)2 + (y2-y1)2)\)
\((x2-x1) = (7 - 3) = 4\)
\((y2-y1) = (-6 - 8) = -14\)
add it all together
\((4)2 + (-14)2 = 16 + 196 = 212\)
Square 212
\(\sqrt{212} =14.5602\)
round to the nearest tenth
=14.6
PLEASE MARK BRAINLIEST
Answer: d=14.6
Step-by-step explanation:
√212=14.5602
round=14.6
The dollar. to rand exchange is $1=R15,35.How many dollars will you get for R2000
Answers
Answer:
The answer is $130, 29
Step-by-step explanation:
R2000 ÷ R15,35 = $130, 29
Answer:
the answer is 130,29
Step-by-step explanation:
2000 ÷ 15 , 35 = 130,29
What is the value of this expression -4.2(0.35-3.5)
Enter your answer in the box as a decimal
Answers
Answer:
13.23
Step-by-step explanation:
Answer: When we use the order of operations to solve this expression we get the Answer 13.23 Hope this helps
Step-by-step explanation:
Assume X is a continuous random variable and has a pdf f (x) = 3x^2, 0 < x < 1 Let Y = X^3
a. Find the pdf of Y
b. What type of distribution does Y have?
Answers
The distribution of Y is a Beta distribution
Assume X is a continuous random variable and has a pdf f (x) = 3x2, 0 < x < 1. Let Y = X3.
a. The pdf of Y can be found by substituting X3 into f (x) to get:
fY(y) = 3y2/3, 0 < y < 1
b. The distribution of Y is a Beta distribution, since it is a continuous random variable with a pdf f (x) = 3x2, 0 < x < 1.
Learn more about continuous random variable
brainly.com/question/17217746
#SPJ11
Cora has 6.6 feet of silver wire in her craft box. She plans to use the wire to make jewelry for her friends and family. She needs 0.6 feet of wire to make a bracelet and 1.4 feet of wire to make a necklace. If Cora makes 4 bracelets, how many necklaces can she make with the leftover wire?
Answers
Answer:3 necklaces
Step-by-step explanation:
6.6=0.6x+1.4y
6.6=0.6(4)+1.4y
6.6=2.4+1.4y
6.6-2.4=(2.4-2.4)+1.4y
4.2=1.4y
4.2/1.4=1.4/1.4y
y=3
Cora can make total of 3 necklaces with the leftover wire.
What is Multiplication?Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.
a × b means that a is added to itself b times or b is added to itself a times.
Given that,
Total length of wire that Cora has = 6.6 feet
Length of wire needed to make a bracelet = 0.6 feet
Length of wire needed to make a necklace = 1.4 feet
Cora has made 4 bracelets.
Length of wire used for 4 bracelets = 4 × 0.6 = 2.4 feet
Remaining length = 6.6 feet - 2.4 feet = 4.2 feet
Number of necklaces which can be made using the remaining wire is,
= 4.2 / 1.4
= 3
Hence Cora can make 3 necklaces with the remaining wire.
To learn more about Multiplication, click :
https://brainly.com/question/6281194
#SPJ2
Help soon pls!!!!!
A water drilling rig is drilling at a constant rate. At 5:00 the drill is at a depth of 5 feet. Twenty minutes later the drill is at a depth of 9 feet.
How many more minutes will it take for the drill to reach a depth of 15 feet?
Answers
Answer:
30 minutes
Step-by-step explanation:
It took 20 minutes to progress from 5 to 9 feet meaning it goes 1 foot every 5 minutes. 15 - 9 is 6 and 6 * 5 = 30 meaning in 30 minutes it will reach 15 feet.
Find the coordinates of P', the image of point P after a dilation with center (0, 0) and a scale factor of 0.
Answers
A scale factor of 0 won’t change the image at all. All the points would remain where they are now.
P’ would be (3,-4)
Please answer correctly !!!!!!!!!!!!!! Will mark brainliest !!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
x = 45
Step-by-step explanation:
x + 135 = 180 {linear pair}
x = 180 - 135
x = 45
Write a proportion to find how many points a student needs to score on the test to get the given score. Test worth 50 points; test score of 84%
Answers
Answer:
42
Step-by-step explanation:
Test worth = 50
To obtain a grade percent = 84%
Score to obtain = x
Using the expression :
84% of test worth = x
84/100 * 50 = x
0.84 * 50 = x
42 = x
Score to obtain = 42
Explain what is the difference between (-6) to the power of 2 and -6 to the power of 2.
Answers
Answer:
Step-by-step explanation:
(-6)² = -6*-6
(-6)² = 36
-(6)² = -(6*6)
-(6)² = -36
The sign is affected by potency
Line b. 2y - x = 5
Is this parallel. Explain
Answers
Line b. 2y - x = 5 is Not parallel, the given line is not parallel to the x-axis or y-axis. A line is parallel to the x-axis if its slope is equal to 0 and it is parallel to the y-axis if its slope is undefined.
What is Line b?Generally, The slope of the given line can be found by rearranging the equation to the form y = mx + b, where m is the slope.
In this case, the equation is already in that form, so the slope is 2.
Therefore, the given line is not parallel to either the x-axis or the y-axis.
Read more about Line
https://brainly.com/question/30003330
#SPJ1
In one U.S. city, the taxi cost is $5 plus $0.70 per mile. If you are traveling from the airport, there is an additional charge of 6$ for tolls. How far can you travel from the airport by taxi for $39?
Answers
Answer:
47 miles
Step-by-step explanation:
first subtract 6 from 39 and divide the remainder by 0.7. Round to 47 for answer.
simplify -26+7r-15p-7p
Answers
Answer:
-26+7r-22p
Step-by-step explanation:
Answer:
Step-by-step explanation:
subtract 7 p from − 15 p .
26 + 7 r − 22 p
An architect is designing a building. Each floor will be 12 feet tall. Use an expression for the number of floors the building can have for a given building height.
If the architect is designing a building that is 132 feet tall, how many floors can be built?
Answers
Answer:
11 floors
Step-by-step explanation:
132 divided by 12 = 11
Consider a sample with data values of 27, 25, 20, 15, 30, 34, 28, and 25. compute the 20th, 25th, 65th, and 75th percentiles. if needed, round your answers to two decimal digits.
Answers
The 20th percentile is 20,
The 25th percentile is 22.50.
The 65th percentile is 28.
The 75th percentile is 29.
Given values:
27, 25, 20, 15, 30, 34, 28, and 25.
n = 8
sorting the data gives:
15, 20, 25, 25, 27, 28, 30, and 34.
How to solve for 20th percentile= 20/100 * 8
= 1.6 ≈ 2
1.6 is rounded to 2, the second value is in the sorted data set is 20 hence the 20th percentile is 20
How to solve for 25th percentile= 25/100 * 8
= 2
Since 2 is an integer, the mean of the 2nd and the 3rd values in the sorted data set gives the 25th percentile.
( 20 + 25 ) / 2 = 22.5
hence the 25th percentile is 22.50
How to solve for 65th percentile
= 65/100 * 8
= 5.2 ≈ 6
5.6 is rounded to 6, the sixth value is in the sorted data set is 28 hence the 65th percentile is 28
How to solve for 75th percentile
= 75/100 * 8
= 6
Since 6 is an integer, the mean of the 6th and the 7th values in the sorted data set gives the 75th percentile.
( 28 + 30 ) / 2 = 29
hence the 75th percentile is 29
Read more on percentile here; https://brainly.com/question/2263719
#SPJ1
Question 1
Find the area of AJKD (Triangle JKD)
+y
F
4
2
A
0
B
6
с
8
D
10
2
4
12
А
12units2
B
15units
С
bunits2
D
14units
Answers
Answer:
6 units^2
Step-by-step explanation:
To solve this problem i use the net to find the area. Each square is a unit. there was 4 units and 4 halves. 4 halves combined, would be 2.
2 + 4= 6.
Sylvia's family members are choosing numbers to see in what order they will choose gifts. The numbers 1 through 10 are written on pieces of paper. All numbers are equally likely to be chosen. What is the probability that the first person chooses a number greater than 7?
A. 10/7
B. 7/10
C. 10/3
D. 3/10
Answers
Answer:
The answer is D
Step-by-step explanation:
Answer:
D. 3/10
Step-by-step explanation:
Numbers greater than 7: 8,9,10. There are 3 numbers, so the probability is 3/10.
can someone help right away!! please!!
Answers
Answer:
y = - 2x + 1
Step-by-step explanation:
Substitute an x value from the table into the equation
x = 1 : y = - 2(1) = - 2 ← require to add 1 to obtain y = - 1
x = 4 : y = - 2(4) = - 8 ← require to add 1 yo obtain y = - 7
Then equation describing the relationship is
y = - 2x + 1
The radioactive element plutonium 238 (Pu-238) has a half-life of 88 years. This means that the element loses half of its mass every 88 years. A sample of Pu-238 has a mass of N grams today. How do you determine the amount of the sample remaining after 352 years (4 half-lives)?
Answers
Answer:
Uhhhhhh plz someone answer this persons question....cus I need it as well
Step-by-step explanation:
5) There are 23 students in Mr. Lee's class. Each student has a box containing 28 pastel crayons. Use rounding to estimate the total numbe pastel crayons in Mr. Lee's class. * 600 crayons O 400 crayons O 900 crayons 0 644 crayons