The possible lengths of sides of the rectangle will be [tex](6,22)[/tex] or [tex](22,6)[/tex] .
What is area ?Area is the space which is occupied by any [tex]2D[/tex] surface.
Area of rectangle [tex]=Length\ *\ Breadth[/tex]
Perimeter of rectangle [tex]=2(Length\ +\ Breadth)[/tex]
We have,
Perimeter of rectangle [tex]=56[/tex] feet
Area of rectangle [tex]=132[/tex] squared feet
Let,
Length of rectangle [tex]=x[/tex]
Breadth of rectangle [tex]=y[/tex]
So,
Perimeter of rectangle [tex]=2(Length\ +\ Breadth)[/tex]
[tex]56=2(x+y)[/tex]
[tex]28=(x+y)[/tex]
⇒ [tex]x=28-y[/tex] [tex]........(i)[/tex]
Now,
Area of rectangle [tex]=Length\ *\ Breadth[/tex]
[tex]132=x\ *\ y[/tex] [tex]........(ii)[/tex]
Now substitute value of [tex]x[/tex] in [tex](ii)[/tex],
[tex]132=(28-y)y[/tex]
[tex]132=28y-y^2[/tex]
⇒[tex]y^2-28y+132=0[/tex]
Now using Middle term split method;
[tex]y^2-28y+132=0[/tex]
[tex]y^2-22y-6y+132=0[/tex]
[tex]y(y-22)-6(y-22)=0[/tex]
[tex](y-6)(y-22)=0[/tex]
⇒
[tex](y-6)=0[/tex]
⇒ [tex]y=6[/tex]
[tex](y-22)=0[/tex]
⇒ [tex]y=22[/tex]
So,
Now if we take [tex]y=6[/tex], then
[tex]x=28-6[/tex]
[tex]x=22[/tex]
And,
if we take [tex]y=22[/tex], then
[tex]x=28-22[/tex]
[tex]x=6[/tex]
So, the possible lengths of sides of the rectangle are [tex](6,22)[/tex] or [tex](22,6)[/tex] .
Hence, we can say that he possible lengths of sides of the rectangle are [tex](6,22)[/tex] or [tex](22,6)[/tex] .
To know more about rectangle click here
https://brainly.com/question/20693059
#SPJ3
If you know out of 140 pounds, 60 pounds is muscle weight, what is the muscle weight of a 200 pound male?
Mark deposited $9,000 into two saving accounts bearing simple interest. One of the accounts has an interest rate of 8% while the other rate is 7%. If the total interest earned after one year is $700, find the amount deposited into each of the accounts
In an inductive generalization, in order to achieve an error margin of plus or minus 3 percentage points at a confidence level of about 95 percent, whats the smallest random sample we can get away with, regardless of the size of the target population
Two perpendicular lines intersect at the origin. If the slope of the first line is .5, what is the equation of the second line?. .
How do you write 314,207 in word form
After 5 years of earning interest at an annual rate of 3% an investment has earned $950 in interest. To the nearest whole dollar, determine the amount of the initial investment
Round 241,639 to the nearest thousand
Solve 2x2 + 26 = 0 to identify the roots.
Answer:
[tex]x=+/-i\sqrt{13}[/tex]
Step-by-step explanation:
To find the roots, factor and set equal to 0 or use the quadratic formula. This quadratic equation does not factor and must be solved using the quadratic formula.
[tex]x=\frac{-b+/-\sqrt{b^2-4ac} }{2a}[/tex]
where a = 2, b=0, and c=26
[tex]x=\frac{0+/-\sqrt{0^2-4(2)(26)} }{2(2)} \\x=\frac{+/-\sqrt{-208)} }{4} \\x=\frac{+/-i\sqrt{16*13)} }{4}\\x=\frac{+/4i\sqrt{13} }{4}\\x=+/-i\sqrt{13}[/tex]
Answer:
Step-by-step explanation:
X=-i√13,x=i√13
91284 the nearest ten thousand
The average national basketball association player is over 6 feet tall. the average horse jockey is shorter than 5 1/2 feet tall. this is because height provides nba players with:
Final answer:
Height is crucial for NBA players due to its impact on their performance. Z-scores help compare player heights to the average. Taller stature offers basketball players notable advantages.
Explanation:
Height is a critical factor for NBA players as it can significantly impact their performance, especially in areas like rebounding, shot-blocking, and scoring.
Z-score calculations help determine how a player's height compares to the average, with values above the mean indicating taller heights, which are advantageous in basketball.
Being taller provides NBA players with advantages in terms of reaching high for shots, blocking opponents, and having a better field of vision on the court.
The spending limit on John’s credit card is given by the function f(x)=15,000+1.5x , where x is his monthly income. f^-1x . The variable x represents in the inverse function. If John's spending limit is $60,000, his monthly income is .
how much larger is 1 ft in one cubic inch
Tony plans to deposit $1,000 at the end of each of the next three years. if his funds earn 5% compounded annually, how much will he have at the end of three years?
Final answer:
Tony will have a total of $3,152.50 after depositing $1,000 annually for three years in an account with 5% interest compounded annually, by calculating the future value of each deposit and summing them up.
Explanation:
When Tony deposits $1,000 at the end of each year into an account that earns 5% interest compounded annually for three years, we need to calculate the future value of an annuity. Each deposit will earn interest for a different amount of time based on when it was deposited.
The first $1,000 will earn interest for two years.
The second $1,000 will earn interest for one year.
The third $1,000 will not earn interest, as it is deposited at the end of the third year.
The formula to calculate the future value of each deposit is:
Future Value = Principal × [tex](1 + Interest rate)^{number of years}[/tex]
Calculating each separately:
First deposit: $1,000 × [tex](1 + 0.05)^2[/tex] = $1,102.50
Second deposit: $1,000 × [tex](1 + 0.05)^1[/tex] = $1,050.00
Third deposit: $1,000 × [tex](1 + 0.05)^0[/tex] = $1,000 (as it earns no interest)
Adding them together gives us the total amount Tony will have at the end of three years:
Total amount = $1,102.50 + $1,050.00 + $1,000 = $3,152.50.
Therefore, at the end of three years, Tony will have $3,152.50 in his account.
Use the half-angle identities to find the exact value of cos 15 degrees.
This is what I have so far:
cos15 degrees = cos1/2(30 degree) = sqrt (1+cos30)/2 = sqrt (1+ sqrt3/2)/ 2
But.. I don't understand how the cos30 turns into sqrt 3/2??
The cosine value of cos(15) is [tex]\sqrt[/tex](1 + [tex]\sqrt[/tex]3/2)/2
The trigonometry identity of half angles is given as:
cos([tex]\theta[/tex]/2) = [tex]\sqrt{[/tex](1 + cos([tex]\theta[/tex]))/2
Substitute 30 for [tex]\theta[/tex]
So, the equation becomes
cos(30/2) = [tex]\sqrt[/tex](1 + cos(30))/2
In trigonometry, we have:
cos(30) = [tex]\sqrt[/tex]3/2
So, we have:
cos(30/2) = [tex]\sqrt[/tex](1 + [tex]\sqrt[/tex]3/2)/2
Divide 30 by 2
cos(15) = [tex]\sqrt[/tex](1 + [tex]\sqrt[/tex]3/2)/2
Hence, the cosine value of cos(15) is [tex]\sqrt[/tex](1 + [tex]\sqrt[/tex]3/2)/2
Read more about trigonometry identities at:
https://brainly.com/question/7331447
The price of 1 lb of potatoes is $ 1.65. if all the potatoes sold today at the store bring in $ 1220, how many kilograms of potatoes did grocery shoppers buy?
1220/1.65 = 739.39 pounds of potatoes were sold
1 pound = 0.453592 kilograms
739.39 x 0.453592 = 335.38 kilograms
Final answer:
By dividing the total sales of $1220 by the price per pound ($1.65), we find that approximately 739.39 pounds were sold, which converts to roughly 335.38 kilograms of potatoes purchased by grocery shoppers.
Explanation:
To calculate the number of kilograms of potatoes grocery shoppers bought, we need to use the given prices and total sales. Since the price of 1 lb of potatoes is $1.65, we can find the total weight of the potatoes sold by dividing the total sales amount by the price per pound:
Total weight in pounds = Total sales
= $1220
= $1220 / $1.65
= 739.39 pounds approximately
Next, we need to convert pounds to kilograms. There are approximately 2.20462 pounds in 1 kilogram. The conversion is:
Total weight in kilograms = Total weight in pounds / 2.20462
= 739.39 / 2.20462
= 335.38 kilograms approximately
Therefore, grocery shoppers bought approximately 335.38 kilograms of potatoes.
A single batch of cookies requires two cups of sugar and three cups of flour. if more than one batch or a partial batch was made, the unit rate of sugar to flour would remain the same. match the correct amount of sugar to the correct amount of flour to keep the same unit rate of sugar and flour in a single batch. 11.5 cups of flour 4.5 cups of sugar 6.75 cups of flour 12 cups of flour 5 cups of sugar 11.25 cups of flour 7.5 cups of sugar 7.5 cups of flour 8 cups of sugar 4 cups of sugar
Answer:11.5
Step-by-step explanation: 11.5
Hiroto’s texting plan costs $20 per month, plus $0.05 per text message that is sent or received. Emilia’s plan costs $10 per month and $0.25 per text. Using the graph below, which statement is true? Hiroto’s plan costs more than Emilia’s plan when more than 50 texts are sent. Both plans cost the same when 22 texts are sent. Emilia’s plan costs more than Hiroto’s plan when more than 22 texts are sent. Both plans cost the same when 50 texts are sent
Answer:
d
Step-by-step explanation:
took the test yahoot
Round 65.85 to the nearest whole number
What is the value of b2 - 4ac for the following equation? x(x + 8) = 9 28 64 100
Answer:
C) 100
Step-by-step explanation:
The given equation is x(x + 8) = 9
Distributing x insides, we get
x^2 + 8x = 9
Now set the equation equal to zero.
x^2 + 8x - 9 =0
Here a = 1, b = 8, and c = -9
b^2 - 4ac = (8)^2 - 4*1*-9
= 64 + 36
= 100
Therefore, b^2 - 4ac = 100.
Answer: C) 100
Hope this will helpful.
Thank you.
Answer:
C. 100
Step-by-step explanation:
Erika worked 14 hours last week and 20 hours this week. If she earns $9 per hour, how much did she earn during these two weeks? 4 of 60
we know that
Erika earns [tex]\$9[/tex] per hour
so
By proportion
Find how much she earn during the total hours of two weeks
The total hours of two weeks is equal to
[tex]14+20=34\ hours[/tex]
[tex]\frac{9}{1} \frac{\$}{hour} =\frac{x}{34} \frac{\$}{hours} \\ \\x=34*9 \\ \\x=\$306[/tex]
therefore
the answer is
[tex]\$306[/tex]
7^-2 without exponent
If you earn $3500 per month and you expect your earnings to increase by 2.3% per year, how much do you think you will be making in 10 years? (Express your answer rounded correctly to the nearest cent!)
Final answer:
Your expected monthly earnings in 10 years, with a 2.3% annual increase, would be $4424.10, rounded to the nearest cent.
Explanation:
To calculate your expected monthly earnings in 10 years, taking into account a 2.3% annual increase, we will use the formula for compound interest: P(1 + r)^n, where:
P is the principal amount (your current earnings)
r is the annual raise rate
n is the number of years
Your current monthly earnings are $3500. The annual raise rate is 2.3%, so r is 0.023 when expressed as a decimal. The number of years, n, is 10.
Plugging the values into the formula, we get:
Earnings in 10 years = $3500 * (1 + 0.023)^10
Calculating the result, we find that your expected monthly earnings in 10 years are:
$4424.10
A dozen eggs cost $1.10 in Dover. In Ensley, the eggs cost 10% more than in Dover. Find the price of a dozen eggs in Ensley.
Final answer:
The price of a dozen eggs in Ensley is $1.21.
Explanation:
To find the price of a dozen eggs in Ensley, we need to consider that the eggs in Ensley cost 10% more than in Dover. If a dozen eggs in Dover cost $1.10, we can calculate the 10% increase by multiplying $1.10 by 1.10:
$1.10 x 1.10 = $1.21
Therefore, a dozen eggs in Ensley cost $1.21.
The vertex angle of an isosceles triangle measures 40°. What is the measure of a base angle?
Find the value of each determinant
The question is about finding the value of a determinant for matrices, a fundamental concept in Mathematics, especially linear algebra. For 2 × 2 matrices, the determinant calculation is straightforward and essential for various applications.
Explanation:The subject of this question is clearly Mathematics, specifically it pertains to linear algebra and the concept of determinants. The task involves finding the value of a determinant for a given matrix. For a 2 × 2 matrix, the determinant is found using a simple formula: if the matrix is given by
\[\begin{pmatrix} a & b \\ c & d \end{pmatrix}\]
then the determinant is calculated as \(ad - bc\). Additionally, the determinant provides important information about the matrix, such as whether the matrix is invertible and the product of its eigenvalues.
To understand determinants for larger matrices, a recursive approach is often used, breaking down the determinant into smaller matrices until 2 × 2 matrices are reached, where the simple formula can be applied. Also of note is that the determinant of the product of two matrices is equal to the product of their determinants (det(AB) = det(A)det(B)).
This fundamental concept is crucial for many applications in mathematics, including solving systems of linear equations, finding eigenvalues, and understanding linear transformations.
Consider the equation ay'' + by' + cy = d, where a, b, c, and d are constants. (a) find all equilibrium, or constant, solutions of this differential equation. (enter your answers as a comma-separated list of equations.)
The constant solutions are given by [tex]\(y'' = 0\) and \(y' = 0\)[/tex].
The equilibrium solutions of the given differential equation [tex]\(ay'' + by' + cy = d\)[/tex] are found by setting the derivatives equal to zero.
1. Setting [tex]\(y'' = 0\)[/tex]: When [tex]\(y'' = 0\)[/tex], the equation becomes [tex]\(a \cdot 0 + b \cdot 0 + c \cdot y = d\)[/tex]. Solving for y, we get [tex]\(cy = d\)[/tex], and therefore, [tex]\(y = \frac{d}{c}\)[/tex].
2. Setting [tex]\(y' = 0\)[/tex]: When [tex]\(y' = 0\)[/tex], the equation becomes [tex]\(a \cdot 0 + b \cdot 0 + c \cdot y = d\)[/tex]. Again, solving for y, we obtain [tex]\(cy = d\)[/tex], and hence, [tex]\(y = \frac{d}{c}\)[/tex].
So, the constant solutions are [tex]\(y = \frac{d}{c}\)[/tex], and this is the equilibrium solution for the given differential equation.
Therefore, the constant solutions are given by [tex]\(y'' = 0\) and \(y' = 0\)[/tex].
What is the slope intercept equation of the line below
If the rate of inflation is 3.7% per year, the future price pt (in dollars) of a certain item can be modeled by the following exponential function, where t is the number of years from today. =pt400( 1.037)t Find the current price of the item and the price 8 years from today. Round your answers to the nearest dollar as necessary.
Determine whether each of the functions log(n + 1) and log(n2 + 1) is o(log n)
Both functions log(n + 1) and log(n^2 + 1) are not o(log n). For large values of n, log(n + 1) is approximately equal to log n, and log(n^2 + 1) behaves like 2*log n, none of which grows strictly slower than log n.
To determine whether the functions log(n + 1) and log(n2 + 1) are o(log n), we'll use the definition of little-o notation. A function f(n) is said to be o(g(n)) if for any positive constant c > 0, there exists a threshold n0 such that for all n > n0, f(n) < c * g(n). In other words, f(n) grows slower than any constant multiple of g(n) as n approaches infinity.
Analysis for log(n + 1)
When n is very large, the +1 becomes negligible, and log(n + 1) behaves similarly to log n. Therefore,
log(n + 1) ≈ log n when n is large.
This implies that log(n + 1) is not o(log n) because it does not grow strictly slower than any multiple of log n.
Analysis for log(n2 + 1)
Using logarithm properties:
log(n2 + 1) < log(n2 + n2) = log(2n2) = log 2 + 2*log n.
As n grows, the constant term (log 2) becomes insignificant, and the function approaches the behavior of 2*log n. However, since there is a multiple of log n (which is 2*log n), this still means that log(n2 + 1) is not o(log n) because it grows faster, not slower, than log n.
HELP? The two models shown have the same volume. Complete the equation and expression below about the volume of each figure.
Answer : The volume blue prism in Model 1 is, [tex]32in^3[/tex]
Step-by-step explanation :
As we are given that:
Volume of Model 1 = Volume of Model 2
Given:
Volume of blue prism in Model 2 = [tex]36in^3[/tex]
Volume of orange prism in Model 2 = [tex]12in^3[/tex]
Volume of orange prism in Model 1 = [tex]16in^3[/tex]
Now we have to calculate the total volume of Model 2.
Total volume of Model 2 = [tex]36in^3+12in^3[/tex] = [tex]48in^3[/tex]
Now we have to calculate the volume blue prism in Model 1.
Volume of Model 1 = Volume of Model 2
Volume of orange prism in Model 1 + Volume blue prism in Model 1 = Total volume of Model 2
[tex]16in^3[/tex] + Volume blue prism in Model 1 = [tex]48in^3[/tex]
Volume blue prism in Model 1 = [tex]48in^3-16in^3[/tex]
Volume blue prism in Model 1 = [tex]32in^3[/tex]
Thus, the volume blue prism in Model 1 is, [tex]32in^3[/tex]