By decreasing each dimension by 1 unit, the area of a rectangle decreased from 40 square feet (on the left) to 28 square feet (on the right). Find the percent decrease in area.
Answers
The percent decrease in the area of a rectangle from 40 square feet to 28 square feet is calculated by dividing the difference in areas (12 sq ft) by the original area (40 sq ft) and multiplying by 100%. The result is a 30% decrease in area.
Explanation:The percent decrease in the area of a rectangle can be found by first calculating the difference in the areas and then dividing that difference by the original area. In this case, the original area of the rectangle was 40 square feet and it decreased to 28 square feet, a difference of 12 square feet.
We use the formula for percentage change which is:
(change in value) / (original value) × 100%
Here, the change in value is the difference in areas (12 square feet) and the original value is the original area of the rectangle (40 square feet). Thus we calculate:
(12 sq ft/ 40 sq ft) * 100% = 30%
So, the percent decrease in the area of the rectangle is 30%.
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Related Questions
Connect in Justin's school, 0.825 of the students participate in a school sport. If there are thousand students in Justin school, how many participate in a school sport?
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Please vote my answer brainliest . thanks!
Answer: 825.
Step-by-step explanation:
the distance between the points 5,1 and 5,-6 is the square root of length?
Answers
please help ASAP!!!
Fill in the truth table below for the disjunction p ∨ q. Type T for true or F for false.
p q p ∨ q
T T a0
T F a1
F T a2
F F a3
Answers
T T = T
T F = T
F T = T
F F = F
Answer: The filled truth table for p ∨ q is shown below.
Step-by-step explanation: We are given to fill the truth table for the p ∨ q.
We know that
If any one of p or q is true, then p ∨ q is also true. And it is false, only when both p and q are false.
The filled truth table is as follows :
p q p ∨ q
T T T
T F T
F T T
F F F
Thus, a0 = T, a1 = T, a2 = T and a3 = F.
Find a power series solution to the differential equation at the point x0. (2+x2)y′′-xy′+4y=0
Answers
I'll assume you are looking for a series centered at [tex]x=0[/tex], which is an ordinary point for the ODE. Substituting
[tex]y=\displaystyle\sum_{n\ge0}a_nx^n[/tex]
into the ODE, we can rewrite it as
[tex]\displaystyle\sum_{n\ge2}n(n-1)a_nx^n+2\sum_{n\ge2}n(n-1)a_nx^{n-2}[/tex]
[tex]\,\,\,\,\,\,\,\,-\displaystyle\sum_{n\ge1}na_nx^n+4\sum_{n\ge0}a_nx^n=0[/tex]
[tex]\displaystyle\sum_{n\ge2}n(n-1)a_nx^n+2\sum_{n\ge0}(n+2)(n+1)a_{n+2}x^n[/tex]
[tex]\displaystyle\,\,\,\,\,\,\,\,-\sum_{n\ge1}na_nx^n+4\sum_{n\ge0}a_nx^n=0[/tex]
[tex]\displaystyle4(a_0+a_2)+3(a_1+4a_3)x+\sum_{n\ge2}\bigg[2(n+2)(n+1)a_{n+2}+(n^2-2n+4)a_n\bigg]x^n=0[/tex]
so the coefficients of the power series are defined by the recurrence
[tex]\begin{cases}a_0=a_0\\\\a_1=a_1\\\\a_n=-\dfrac{(n-3)^2+3}{2n(n-1)}a_{n-2}&\text{for }n\ge2\end{cases}[/tex]
For even [tex]n[/tex], i.e. [tex]n=2k[/tex] [tex](k\ge0)[/tex], we have
[tex]a_0=a_0[/tex]
[tex]a_2=-a_0[/tex]
[tex]a_4=-\dfrac4{4\times3\times2}a_0=\dfrac4{4!}a_0[/tex]
[tex]a_6=-\dfrac{12}{2\times6\times5}a_4=-\dfrac{12\times4}{2\times6!}a_0[/tex]
[tex]a_8=-\dfrac{28}{2\times8\times7}a_6=\dfrac{28\times12\times4}{2^2\times8!}a_0[/tex]
and so on. The pattern in the denominator is pretty clear, but we can also find a compact form for the numerator. When [tex]k=5[/tex], we can write it as
[tex]4\times12\times28\times52=4^4(1\times3\times7\times13)[/tex]
[tex]=4^4\bigg(1\times(1+2)\times(1+2+4)\times(1+2+4+6)\bigg)[/tex]
[tex]=4^4\bigg(1\times(1+2(1))\times(1+2(1+2))\times(1+2(1+2+3)\bigg)[/tex]
[tex]=4^4\displaystyle\prod_{i=1}^3\left(1+2\sum_{j=1}^{i-1}j\right)[/tex]
[tex]=4^4\displaystyle\prod_{i=1}^3(i^2-i+1)[/tex]
So in general we have
[tex]a_{2k}=\dfrac{(-1)^k2^k\displaystyle\prod_{i=1}^{k-1}(i^2-i+1)}{(2k)!}[/tex]
We can treat the odd-indexed terms similarly. For [tex]n=2k-1[/tex] [tex](k\ge1)[/tex] we have
[tex]a_1=a_1[/tex]
[tex]a_3=-\dfrac14a_1=-\dfrac3{2\times3\times2}a_1=-\dfrac3{2\times3!}a_1[/tex]
[tex]a_5=-\dfrac7{2\times5\times4}a_3=\dfrac{7\times3}{2^2\times5!}a_1[/tex]
[tex]a_7=-\dfrac{19}{2\times7\times6}a_5=-\dfrac{19\times7\times3}{2^3\times7!}a_1[/tex]
and so on. Again, the pattern in the denominator is simple. For [tex]k=5[/tex], we would get a numerator of
[tex]3\times7\times19\times39=3\times(3+4)\times(3+4+12)\times(3+4+12+20)[/tex]
[tex]=3\times(3+4(1))\times(3+4(1+3))\times(3+4(1+3+5))[/tex]
[tex]=\displaystyle\prod_{i=1}^4\left(3+4\sum_{j=1}^{i-1}(2j-1)\right)[/tex]
[tex]=\displaystyle\prod_{i=1}^4(4i^2-8i+7)[/tex]
and in general we'd have
[tex]a_{2k-1}=\dfrac{(-1)^{k+1}\displaystyle\prod_{i=1}^{k-1}(4i^2-8i+7)}{2^{k-1}(2k-1)!}[/tex]
Thus the power series solution to this ODE is
[tex]y(x)=\displaystyle\sum_{k\ge0}a_{2k}x^{2k}+\sum_{k\ge1}a_{2k-1}x^{2k-1}[/tex]
Attached below is a plot of a numerical solution (blue) compared to the first 9 terms [tex](0\le n\le8)[/tex] and first 21 terms [tex](0\le n\le21)[/tex] of the series solution over the interval [tex]|x|\le3[/tex], assuming initial values of [tex]y(0)=y'(0)=1[/tex] [tex](a_0=a_1=1)[/tex].
In the general linear equation, y = bx + a, what is the value of b called?
Answers
What is 45 1/2% as a fraction in the simplest form?
Answers
[tex] \frac{45 \frac{1}{2} }{100} [/tex]
Converting the mixed number 45 1/2 to the improper fraction 91/2, we now have:
[tex] \frac{ \frac{91}{2} }{100} [/tex]
Dividing a number by 100 is the same thing as multiplying it by 1/100, so we can rewrite this complex fraction as the product
[tex] \frac{91}{2}\times \frac{1}{100} = \frac{91}{200} [/tex]
91/200 is irreducible, so we have our answer.
Three-fourths of the sixth grade students at Ashlee’s school are twelve years old. One-half of the twelve year old students are boys. What fraction of the sixth grade students are twelve year old boys? Use numbers to explain your answer.
Answers
I'm not sure if that's correct or not though.
During study hall, 58% of the students are studying for tests, 29% of the students are doing homework, and the remaining students are writing papers. What percentage of the students are writing papers?
Answers
The percentage of the students writing papers will be 13%.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
The quantity of anything is stated as though it were a fraction of a hundred. A quarter of 100 can be used to express the ratio.
During study hall, 58% of the students are studying for tests, 29% of the students are doing homework, and the remaining students are writing papers.
The percentage of the students writing papers will be given by the difference of the 100% and the sum of 58% and 29%. Then we have
⇒ 100% - 58% - 29%
⇒ 100% - 87%
⇒ 13%
The percentage of the students writing papers will be 13%.
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Final answer:
The percentage of students writing papers during study hall is 13%.
Explanation:
To find out what percentage of students are writing papers during study hall, we need to find the remaining percentage after accounting for the students studying for tests and doing homework.
Since 58% of the students are studying for tests and 29% of the students are doing homework, the percentage of students writing papers can be found by subtracting the sum of these two percentages from 100%:
Percentage of students writing papers = 100% - (58% + 29%) = 13%
Therefore, 13% of the students are writing papers during study hall.
Given two parallel lines and a transversal, at what angle do the angle bisectors of two same side interior angles intersect?
Answers
The angle bisectors of the same side interior angles, formed by two parallel lines and a transversal, intersect at a 90-degree angle.
Explanation:In geometry, when you have two parallel lines intersected by a transversal, the same side interior angles are those which are in the same position on the two lines. If we bisect these angles (i.e., divide them in two equal parts), the angle bisectors will intersect forming an angle that is 90 degrees.
To understand why, note that the same-side interior angles are supplementary (i.e., they sum up to 180 degrees) because they are on the same side of the transversal. So, if we bisect these angles, each pair of congruent angles will add up to 90 degrees. When these bisectors intersect, they form four right angles. Therefore, the angle at the intersection of the bisectors is 90 degrees.
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the length of a rectangle is 3 ft longer than its width if the perimeter of the rectangle is 26 feet find its area
Answers
length=3+x
perimeter=26
2(l+b)=26
2(3+x+x)=26
2(3+2x)=26
6+4x=26
4x=26-6
x=20/4=5. l=3+5=8. width=5
area of =l*b
=8*5=40
The problem primarily involves the calculation and understanding of the concepts of perimeter and area in Mathematics. Given the length is 3 ft longer than the width, and the perimeter of the rectangle is 26 feet, first, we find that the width is 5 feet and the length is 8 feet. The area is thus, 40 square feet.
Explanation:To solve this problem, we need to understand the formula for the perimeter of a rectangle, which is 2l + 2w, where 'l' stands for length and 'w' for width. Also, the area of a rectangle is calculated by l*w. The problem states that the length is 3 ft longer than the width and that the perimeter is 26 feet. Firstly, we can express the length as 'w + 3' and substitute into the perimeter formula:
2(w + 3) + 2w = 26
After simplifying, we get the width equals to 5 feet. Substituting 5 for width, we get the length as 8 feet, because length is 3 feet longer than the width. Then, the area of the rectangle can be calculated by multiplying the width by the length:
Area = l * w = 8 ft * 5 ft = 40 square feet
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Over the last three evenings, Raina received a total of 83 phone calls at the call center. The first evening, she received 7 more calls than the third evening. The second evening, she received 2 times as many as the third evening. How many phone calls did she receive each evening?
Answers
Raina received a total of 83 calls
First evening she received 7 more than the third so let x = third and since we know she received 7 more we know to add 7 to the third so (x + 7)
Second evening she received 2 times as many as the third so 2 time third, which x is the third so (2 times x) or we could say 2x
Third evening = x
So now lets solve for x and then we can find how many she received each evening.
Our Model: (x + 7) + 2x + x = 83
(x + 7) + 2x + x = 83
x + 7 + 2x + x = 83
x + 2x + x + 7 = 83
4x + 7 = 83
4x + 7 - 7 = 83 -7
4x = 76
4x / 4 = 76 / 4
x = 19
First evening:
19 + 7 = 26 calls
Second evening
2 times 19 = 38
Third evening
19
Check our answer:
26 + 38 + 19 = 83
Raina received 19 phone calls on the third evening, 26 phone calls on the first evening, and 38 phone calls on the second evening.
Explanation:Let's consider the number of phone calls Raina received each evening.
Let x represent the number of phone calls on the third evening.
The first evening, Raina received 7 more calls than the third evening, so the number of phone calls on the first evening is x + 7.
The second evening, Raina received 2 times as many calls as the third evening, so the number of phone calls on the second evening is 2x.
Given that Raina received a total of 83 phone calls over the three evenings, we can set up the equation:
x + (x + 7) + 2x = 83
Combining like terms, we have:
4x + 7 = 83
Subtracting 7 from both sides, we get:
4x = 76
Dividing both sides by 4, we find that x = 19.
Therefore, Raina received 19 phone calls on the third evening, 26 phone calls on the first evening, and 38 phone calls on the second evening.
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Which expressions are equivalent to the one below? Check all that apply.
log 2 - log 6
Answers
Expressions equivalent to 'log 2 - log 6' are based on the property of logarithms that states 'log a - log b' is equivalent to 'log (a/b)'. Thus, the equivalent expression is 'log (1/3)'.
The expressions equivalent to log 2 - log 6 can be found using the property of logarithms that deals with the difference of logarithms. According to this property, log a - log b is equivalent to log (a/b). Therefore, one equivalent expression for log 2 - log 6 would be log (2/6), which can be simplified to log (1/3).
the average rate of elevation change in feet per second if a submarine dives 440 feet in 20 seconds?
Answers
The average rate of elevation change is 22 feet per second
hope this helps
The marginal-revenue equation is
Answers
[tex]\bf R(x)=0.0683x^2+1.25235x+2.1653\\\\\\ \cfrac{dR}{dx}=0.1366x+1.25235[/tex]
what is the correct way to read this number 6.3078
Answers
A bucket holds c liters of water, but a jar holds 8 liters less. How many times as much water can the bucket hold as the jar?
Answers
Answer:
The bucket hold 3x the capacity of the jar
Step-by-step explanation:
First we have to write down the amount of both, the jar and the bucket, to make a small equation to see the problem mathematically.
Bucket = c liters of water
Jar = c - 8
so we can say that:
c = c - 8
Now that we have the equation, we can determine that the variable 'c' on the right is substracting to the number 8. So we can pass the 'c' to the left of the equation by adding it to the elements on the left, like this:
c + c = 8
Now, two 'c' are the same, we can add them:
2c = 8
This two on the equation of the left is multiplying the variable 'c', so we can move it to the right by dividing the number 8 with this number:
c = 8/2
If we solve this operation, we'll get:
c = 4
That means that the amount of liters of water a jar can hold is 4 liters
Jar = 4 liters
Now that we have this value, we can solve the problen. If the jar holds 8 liters of water les than a bucket, we can now represent it like this:
Bucket = Jar capacity + 8 liters
Wich can be represented like this as well:
Bucket = 4 + 8
And the result is:
Bucket = 12 liters
If we try to fit the jar's capacity on the bucket, we find that the bucket hold 3x the capacity of the jar
Let me know if you have any doubts :D
You are giving the following amounts: $190,258.50; $152,698.00; $122,753.00; $220,523.00; $231,951.00. What is the average of these five amounts?
Answers
lily swims a 100-meter race. she swims the first half in 27.8 seconds. she swims the second half in 30.12 seconds. how long does it take lily to swim the whole race?
Answers
we know that
1) Lily swims a [tex]100[/tex]-meter race
2) She swims the first half in [tex]27.8[/tex] seconds
3) She swims the second half in [tex]30.12[/tex] seconds
so
To find the total time to swim the whole race sum the time in the first half plus the time in second half
[tex](27.8+30.12)=57.92\ seconds[/tex]
therefore
the answer is
[tex]57.92\ seconds[/tex]
By adding the two given times, we will see that she completes the race in 57.92 seconds.
How to find the time in which she finishes the race?
We know that:
She swims the first half on 27.8 seconds.She swims the second half on 30.12 seconds.Then the time that it took to complete the whole race is just the sum of these two times, we will get:
Total time = 27.8 seconds + 30.12 seconds = 57.92 seconds.
We can conclude that Lily swims the whole race in 57.92 seconds.
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The graph shows the distance, in feet, required for a car to come to a full stop if the brake is fully applied and the car was initially traveling x miles per hour. Which equation can be used to determine the stopping distance in feet, y, for a car that is traveling x miles per hour?
Answers
Answer:
y=[tex]\frac{x^{2} }{18}[/tex]
Side "a" of a triangle is twice side "b." Side "c" is 2 meters shorter than side "a." The perimeter is 98 meters. Find the lengthy of each side. (show work)
Answers
Final answer:
By setting up a system of equations based on the given information and solving for b, we find that side a is 40 meters, b is 20 meters, and c is 38 meters.
Explanation:
To solve for the lengths of the sides of the triangle, we can set up a system of equations based on the information given:
Let b be the length of one side.Side a is twice the length of side b, so a = 2b.Side c is 2 meters shorter than side a, so c = a - 2 = 2b - 2.The perimeter of the triangle is the sum of its sides, which equals 98 meters: a + b + c = 98.Substituting the expressions for a and c into the perimeter equation gives:
2b + b + (2b - 2) = 985b - 2 = 985b = 100b = 20With the value for b, we can now find a and c:
a = 2b = 2(20) = 40 metersc = 2b - 2 = 40 - 2 = 38 metersThe lengths of the sides of the triangle are 20 meters (b), 40 meters (a), and 38 meters (c).
Final answer:
To solve for the lengths of the triangle's sides, we formulate equations based on the given relationships and perimeter. We find that side b is 20 meters, side a is twice b (40 meters), and side c is 2 meters shorter than a (38 meters).
Explanation:
The student's question involves finding the length of each side of a triangle given specific relationships between the sides and the overall perimeter. The problem can be formulated using algebra. Let's denote side b as the baseline. From the question, we know that side a is twice side b (a = 2b), and side c is 2 meters shorter than side a (c = a - 2 = 2b - 2). The perimeter (P) is given as 98 meters, so we have P = a + b + c = 98 meters.
Substituting for a and c in terms of b we have P = 2b + b + (2b - 2) = 98, simplifying to 5b - 2 = 98. Solving for b we add 2 to both sides, 5b = 100, and then divide by 5 to get b = 20 meters. Now we easily find that a = 2(20) = 40 meters, and c = 40 - 2 = 38 meters. Therefore, the lengths of the sides of the triangle are 40 meters for side a, 20 meters for side b, and 38 meters for side c.
Find the interval of convergence of the series (5x-1)^n
Answers
As a geometric series, this will converge for
[tex]|5x-1|<1\implies -1<5x-1<1\implies 0<5x<2\implies 0<x<\dfrac25[/tex]
There are currently 3 students signed up for a trip. The van can transport only 7 students.
Which graph shows all the possible values for the extra number of students that need to sign up so that more than one van is needed to transport them?
Answers
Solution:
Call x the number of students that need to sign up so that more than one van is neeed to transport them, then:
x + 3 > 7
=> x > 7 - 3
=> x > 4
That is the numbers greater than 4, without including the number 4.
That, in the number line, is the set of numbers to the right of 4, and the open circle is used to indicate that the number 4 is not included (a closed circle would indicate that the number 4 is included, which is not the case).
Which translation maps the vertex of the graph of the function f(x) = x2 onto the vertex of the function g(x) = x2 + 2x +1?
right 1 unit
left 1 unit
right 2 units
left 2 units
Answers
Answer:
Option B is correct
Left 1 unit.
Explanation:
According to the graph theory of transformation:
y = f(x+k)=[tex]\left \{ {{k>0 shift graph of y= f(x) left k unit} \atop {k<0} shift graph of y= f(x) right |k| unit} \right.[/tex]
Given the parent function: [tex]f(x)=x^2[/tex]
and the function [tex]g(x)=x^2+2x+1[/tex]
we can write it as:
g(x)= [tex](x+1)^2[/tex] [ ∴[tex](a+b)^2 = a^2+2ab+b^2[/tex] ]
Therefore, vertex of the graph of the function [tex]g(x)=(x+1)^2[/tex] is 1 units to the left of the vertex of the graph of the function [tex]f(x)=x^2[/tex] .
Answer:
Shift 1 unit left
B is correct
Step-by-step explanation:
Given: The vertex of f(x) shift to g(x)
[tex]f(x)=x^2[/tex]
Vertex of f(x): (0,0)
[tex]g(x)=x^2+2x+1[/tex]
Vertex form: [tex]y=a(x-h)^2+k[/tex]
[tex]g(x)=(x+1)^2[/tex]
Vertex of g(x): (-1,0)
[tex](0,0)\rightarrow (-1,0)[/tex]
Only x-coordinate change and y-coordinate remain same.
[tex]0\rightarrow -1[/tex]
Hence, The vertex of f(x) shift 1 unit left to get vertex of g(x)
a rectangular garden has an area of 9 5/24 square yards. The garden is 2 1/6 yards wide. how long is it?
Answers
Area = L x W
L = 9 5/24 / 2 1/6
= 4 1/4
Hope this helps :))
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Find the derivative of the function using the definition of derivative. f(x) = 1 5 x − 1 6
Answers
To find the derivative of the given function using the definition of derivative, we can start by taking the limit of the expression. By simplifying the expression and canceling out terms, we can find the derivative as -10/(20x√x-√x)(10x-1/2).
The function f(x) = 1/(10x-1/2)
To find the derivative of the function using the definition of derivative, we can start by writing the expression of the derivative:
f'(x) = lim(h->0) [f(x+h) - f(x)] / h
Substituting the function f(x) into the expression, we have:
f'(x) = lim(h->0) [1/(10(x+h)-1/2) - 1/(10x-1/2)] / h
To simplify the expression, we can find a common denominator and combine the fractions:
f'(x) = lim(h->0) [(10x-1/2) - (10(x+h)-1/2)] / h[(10(x+h)-1/2)(10x-1/2)]
Expanding and simplifying the expression, we get:
f'(x) = lim(h->0) -10/(2√x-√(x+h)) / h(10x-1/2)(10(x+h)-1/2)
Now, we can cancel out the h in the denominator:
f'(x) = lim(h->0) -10/(2√x-√(x+h))(10x-1/2)(10(x+h)-1/2)
Taking the limit as h approaches 0, we get:
f'(x) = -10/(2√x-√x)(10x-1/2)(10x-1/2)
Now, we can simplify further:
f'(x) = -10/(20x√x-√x)(10x-1/2)
So, the derivative of the function is f'(x) = -10/(20x√x-√x)(10x-1/2)
complete question given below:
Find the derivative of the function using the definition of derivative.
1 f(x) = 1/10x-1/2
f'(x) =
State the domain of the function, f(x). (Enter your answer in interval notation.)
State the domain of its derivative, f'(x). (Enter your answer in interval notation.)
Find the percent of change from $240 to $320
Answers
1.33 = 133% (move the decimal point over two places to the right)
133% is your answer
hope this helps
Then the percentage change was
$80
-------- * 100% = +33.33%
$240
5% of the soccer team is on the honor roll. Rewrite this percent as a fraction in simplest form
Answers
An American green tree frog tadpole is about 0.00001 kilometer in length when it hatches. Write this decimal as a power of 10
Answers
you multiply .00001 by itself 10 times
The decimal number 0.00001 can be written as a power of 10 as 1 x 10^-5. This is because the decimal is shifted five places to the right.
Explanation:The student is asked to express the number 0.00001 as a power of 10. This can be achieved by understanding that the power (exponent) of 10 is equal to how many places the decimal is shifted. Here, the decimal is shifted five places to the right so we use the negative exponent -5 to denote this shift. Therefore, 0.00001 written as a power of 10 is 1 x 10^-5.
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An employee's annual salary was increased from $22,464.00 to$24,710.40 last year. If it is increased by the same percent this year, what will the employee's salary?
Answers
Simplify by combining like terms.
12−a+a+12
Thanks!