The rectangle has the consecutive integers of 21 inches and 22 inches for its width and length respectively.
What are consecutive integersConsecutive integers are numbers that follow in a particular order, usually just one after the for example, 1, 2, 3,... and so on.
Let the width of the rectangle be represented by x so that the length will be x + 1 as they consecutive integers
The perimeter of the rectangle will have the equation;
x + x + x + 1 + x + 1 = 86 inches
4x + 2 = 86 inches {collect like terms}
4x = (86 - 2) inches {subtract 2 from both sides of the equation}
4x = 84 inches
x = (84/4) inches {divide through by the coefficient of x}
x = 21 inches
Therefore, the rectangle has width of 21 inches and length of 21 + 1 = 22inches.
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I need help with the last part. I don’t know what to do with the pi part. If someone can help, that would be great!!
Answer:
Error: 131π
Surface Area = 131π=411.5 yd^2
Step-by-step explanation:
All the other steps were correct but 131π = 411.5486376, so there's no way the person should have gotten 411.3 yd^3.
Finally, if we round 411.5486376 to the nearest tenth, we get 411.5 yd^2.
What is the relationship between multiplying polynomials and factoring? How are these two concepts related? How can they be used to check your work? Give an example and work it out to explain your reasoning. Be sure to explain how your example shows the relationship you describe.
Things you MUST include:
- A verbal/written explanation that describes the relationship between the two concepts. (3 points)
- An example that shows how multiplying polynomials
Explain how your example shows the relationship. (2 points)
By spreading (by multiplying) that 3 back in, we may obtain our original expression 12.
What do you mean by Factoring of polynomial?
The process of multiplying polynomial factors is known as factoring polynomials. A polynomial of degree "n" in variable x is an equation of the form axn + bxn-1 + kcxn-2 +....+kx+ l, where each variable has a constant acting as its coefficient. A polynomial is an expression that has a constant and a variable together with an addition or a subtraction sign between them.
Factors of polynomials are zeros of polynomials that may be expressed as another linear polynomial. If we divide a given polynomial by any of its components after factorization, the residual will be zero.
Contingents: 1, 2, 5, and 7.variables: x, y, and hTerms: 3x, 8y, and 2h (terms are often separated by a + or a -).(Note that words can also include variables and constants)
Formulas: 3x+1, 4x +5, 2h + 2wEquations: P = 2h + 2w, x = 4, y = x + 2One of the variables or constants that is multiplied by another factor to create a phrase is called a factor. Factors 4 and x make up the phrase 4x. To factor is to divide the object of the multiplication. Therefore, factoring "disassembles" the result of multiplication.
We frequently need to factor a term in order to "solve" (that is, get the value of, say, x) an equation
For Example:
The operation of factoring falls in between multiplication and dividing. Let's examine the following statement:
3x + 12
We can factor out the third because 3x and 9 both share the number three:
3x ÷ 3 = x 12 ÷ 3 = 4
We set it aside what's left after factoring out 3:
3(x + 4)
By spreading (by multiplying) that 3 back in, we may obtain our original expression: x * 3 = 3x 4 * 3 = 12.
We now have: 3x + 12
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-5y^2+17y-84 / y^3+12y^2+36y partial fraction decompostion
[tex]5y^2+17y-84 / y^3+12y^2+36y[/tex] partial fraction decomposition is [tex]= -5y/(y² + 12y + 36) + 17/(y² + 12y + 36) - 84 (y³+12y²+36y)[/tex]
What is partial fraction decomposition?Partially decomposing a rational fraction, also known as partially expanding it, in algebra includes expressing the fraction as the sum of a polynomial and one or more fractions with a lower common denominator.
One technique for breaking down rational expressions into smaller partial fractions is partial fraction decomposition. This method serves the integration process better.
In order to integrate a rational function, it is condensed to a valid rational function. The integrand can be expressed as the sum of more elementary rational functions through the use of partial fraction decomposition.
Therefore, starting with the simplified solution and proceeding backwards, the final expression is “decomposed” into the original polynomial fractions.
[tex]= -5y²+ 17y-84 / y³+12y²+36y[/tex]
[tex]= -5y/(y² + 12y + 36) + 17/(y² + 12y + 36) - 84 (y³+12y²+36y)[/tex]
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given an integer x and an array of numbers, find if two numbers in the array sum up to x. (or, find the pair of numbers whose sum is closest to x.)
The program for finding the two numbers in the array sum up to x is made.
Explain the term sorting?Sorting involves putting data into a meaningful order so how you can more efficiently evaluate it. For instance, if you want to plot a graph of sales performance, you could wish to sort the sales data per calendar month.Array A[n], x
Sort by the use of Mergesort ------- O(nlogn)Initialize 2 index variables to estimate candidit.Initialize 1st to that leftmost index: l = 0Initializ 2nd to that rightmost index: r = n - 1While l < r -----------O(n)if A[l] + A[r] == x; return trueelse if A[l] + A[r] < sum; increment lelse decrement rreturn falseTime Complexity:
As was covered in class, step one employs mergesort, which has an O(nlogn) complexity.
Since the worst-case scenario involves traversing through the full array, step three consumes O(n) time.
Total Running Time = O(nlogn + n) = O(nlogn)
Thus, the program for finding the two intergers in the array sum up to x is made.
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Write the expression as a number in scientific notation.
quantity 8 times 10 squared end quantity times quantity 3.2 times 10 to the fifth power end quantity all divided by the quantity 4 times 10 cubed
7.2 x 107
7.2 x 104
6.4 x 107
6.4 x 104
The value of the expression in the scientific notation will be 6.4 × 10⁴. Then the correct option is D.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The expression is given below.
⇒ [(8 × 10²) × (3.2 × 10⁵)] / (4 × 10³)
Simplify the expression, then we have
⇒ [(8 × 10²) × (3.2 × 10⁵)] / (4 × 10³)
⇒ [(25.6 × 10⁷)] / (4 × 10³)
⇒ 6.4 × 10⁷⁻³
⇒ 6.4 × 10⁴
The value of the expression in the scientific notation will be 6.4 × 10⁴. Then the correct option is D.
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Solve the triangle, if possible.
C=61° 50, c=31.2, b=23.6
a=34.697, only one triangle is formed.
And B=40°.7'
A≈77°.79'.So, option A is correct.
What is meant by triangle?Three edges and three vertices define a triangle as a polygon. One of geometry's fundamental shapes is this one.
Any three points determine a distinct triangle and a distinct plane in Euclidean geometry when they are non-collinear (i.e. a two-dimensional Euclidean space). To put it another way, each triangle is contained in a plane, and there is only one plane that includes that particular triangle. All triangles are contained in one plane if and only if all geometry is the Euclidean plane, however this is no longer true in higher-dimensional Euclidean spaces. Except as otherwise specified, the subject of this article is triangles in Euclidean geometry, more specifically, the Euclidean plane.
Given,
C=61° 50, c=31.2, b=23.6
Sine rule:
sin B/b=Sin C/c
sin B=b sin C/c
=(23.6 sin 61° 50)/31.2
sin B=0.65219
sin B=139.3
A+B+C=180
A=180-B-C
A=180-139.3-61.50
A= -20.8 which is not possible.
Because the angle must be positive.
sin B=sin 40.70
A+B+C=180
A=180-40.70-61.50
A=77.79'
sin A/a=sin C/c
a=c sin A/sin C
So, a=34.697
Only one triangle is formed
And B=40°.7'
A≈77°.79'
Hence, option A is correct.
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3- =11 pls im scared to put 14 i over think
Answer: i believe it is 14 too
Step-by-step explanation:
The teacher is planning a party for the students. She needs to pick 2 of 6 dinners to offer and 3 to 5 desserts. How many different combinations can she pick?
She can choose from the various combinations of 6 of 2, 5 to 3.Permutation is the name given to the various techniques of putting a group of objects in a sequential sequence.
A permutation and a combination can be distinguished by how they are ordered.Permutation is the name given to the various techniques of putting a group of objects in a sequential sequence. Combination is one of the various methods for selecting elements from a huge collection of objects without taking the order into account.Permutations and combinations are the several ways that items from a set can be chosen, usually without replacement, to generate subsets.The order matters, for instance, if you have a lock that requires four digits to unlock. You cannot type the same numbers in any other order (for example, 6 8 2 3) and expect the lock to open if the right values are 8 3 6 2! That's a permutation, so.Explanation:
2 of 6 = 6 of 2
3 to 5 = 5 to 3.
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How much money does Dana Jones have after 7 years if she invests $ 1100 at 5% interest compounded continuously?
Dana Jones has $__-after 7 years.
(Simplify your answer. Type an integer or a decimal. Round to the nearest cent as needed.)
Dana Jones has amount after 7 years is $1560.97.
What is compounded continuously?
Theoretically, continuously compounded interest means that an account balance continuously earns interest as well as reinvesting that interest into the balance so that it too earns interest.
Given: Dana Jones invests $ 1100 at 5% interest compounded continuously for 7 years.
We have to find the amount after 7 years.
Consider, the formula
A = Pe^rt
where,
A is the amount after t years
P is the invested amount
r is the interest rate
t is the number of years
Plug P = 1100, r = 5% = 0.05, and t = 7 in the above equation.
[tex]A = 1100e^0^.^0^5^(^7^)\\A = 1560.9743\\A = 1560.97[/tex]
Hence, Dana Jones has amount after 7 years is $1560.97.
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Given: Line m is parallel to line n
prove : <1 is supplementary to < 3 HELP PLEASE
Supplementary angles are two angles whose combined angle is 180 degrees. As shown below, the table of the proof that (1) is an addition to (3) can be completed.
What are Supplementary angles?Supplementary angles are two angles whose combined angle is 180 degrees. When a straight line crosses another line, two angles are created on either side of the initially imagined straight line. Two sets of additional angles make up those two-two angles. This implies that a straight line will be formed by the outside sides of any extra angles that are positioned next to one another.
For the demonstration that 1 is an addition to 3, the preceding table can be completed as shown below.
1) Line m in is parallel to line n;
2) ∠1 = ∠2 → Corresponding angles
3) m∠1 = m∠2 → Definition of Congruent angles
4) ∠2 and ∠3 for a linear pair → Adjacent angles on a straight line
5) ∠2 is supplementary to ∠3 → Definition of linear pair
6) m∠2 + m∠3 = 180° → Definition of supplementary angles
7) m∠1 + m∠3 = 180° → Substitution Property
8) ∠1 is supplementary to ∠3
As a result, the table containing the proof that item 1 is an addition to item 3 can be completed as displayed above.
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If the hours of daylight in Miami can be
approximated using a sinusoidal wave, what is the
amplitude of the function if the shortest day in
Miami is 10 hours and 52 minutes long and the
longest day in Miami is 13 hours and 45 minutes
long?
Answer:
the sinusoidal function that approximates the hours of daylight in Miami has an amplitude of approximately 1.44 hours.
Step-by-step explanation:
The amplitude of a sinusoidal function is half the difference between the maximum and minimum values of the function. In this case, the shortest day in Miami is 10 hours and 52 minutes long, and the longest day is 13 hours and 45 minutes long, so the difference between the maximum and minimum values is 2 hours and 53 minutes, which is equal to 173 minutes. Half of this is 86.5 minutes, which is the amplitude of the function.
To express this in hours, divide the amplitude in minutes by 60. This gives an amplitude of 86.5 / 60 = 1.44 hours.
So, the sinusoidal function that approximates the hours of daylight in Miami has an amplitude of approximately 1.44 hours.
What is the value of y in the solution to the system of equations?
1/3*+1/4y=1
2x - 3y = -30
-8
-3
8
Answer:
(-3,6)
Step-by-step explanation:
[tex]\frac{1}{3}[/tex] x + [tex]\frac{1}{4}[/tex] y = 1 Divide all the way through by 12 to clear the fraction
4x + 3y = 12 Add this to the second equation
2x -3y = -30
6x = -18 Divide both sides by 6
x = -3
Substitute -3 into either of the original equations to solve for y
4x + 3y = 12
4(-3) + 4y = 12
-12 + 4y = 12 Add 12 to both sides
4y = 24 Divide both sides by 4
y = 6
In a popular online role playing game, players can create detailed designs for their character's "costumes," or appearance. Moussa sets up a website where players can buy and sell these costumes online. Information about the number of people who visited the website and the number of costumes purchased in a single day is listed below.
81 visitors purchased no costume.
6 visitors purchased exactly one costume.
3 visitors purchased more than one costume.
Based on these results, express the probability that the next person will purchase more than one costume as a decimal to the nearest hundredth.
The probability that the next person will purchase more than one costume will be 1/30.
What is probability?The probability of an event occurring is defined by probability.
Probability is also called chance because if you flip a coin then the probability of coming head and tail is nothing but chances that either head will appear or not.
As per the given,
Total visitors of a day = 81 + 6 + 3 = 90
The number of purchasing more than one costume = 3
Probability of purchasing more than one costume = 3/90 = 1/30
Hence"The probability that the next person will purchase more than one costume will be 1/30".
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Find the area of the shaded region, the graph to the right, depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15.
The area of the shaded region is ——?
Round to four decimal places as needed
Answer:
68%
Step-by-step explanation:
93 is 7 pts BELOW 100 this represents -7 /15 = -.4666 Z-score
From Z-score table this represents .3192 ..or 31.92 % to the LEFT of the 93 ...... to the RIGHT is 100% - 31.92 % = ~ 68%
HELP NOW 50 POINTS IMPORTANT!
Using the image of the blank check below, match each item with what would go in that space.
Column A
1.
Date:
Date
2.
Who the check is being written to:
Who the check is being written to
3.
Amount of check, written in numeric format:
Amount of check, written in numeric format
4.
Amount of check, written in word format:
Amount of check, written in word format
5.
A description of what the check is for:
A description of what the check is for
6.
The checking account owner's signature:
The checking account owner's signature
Column B
a.Item 1
b.Item 4
c.Item 3
d.Item 5
e.Item 6
f.Item 2
Answer:
HOPE IT HELPED
Step-by-step explanation:
Date is item 2
Who the check is being written to is item 1
Amount of check, written in numeric format is item 3
Amount of check written in word format is item 4
A description of what the check is for is item 5
The checking account owner's signature is item 6
A hose fills a hot tub at a rate of 3.49 gallons per minute. How many hours will it take to fill a 343-gallon hot tub? Question content area bottom Part 1 It will take enter your response here hours to fill the hot tub.
Answer:
answer = 98.2808022923 i think
Use point-slope form to write the equation of a line that passes through the point
(-11, -8) with slope -2/-3
can someone help me with this thank you
Answer:
a, b, d: No
c: Yes
Step-by-step explanation:
You want to identify statements that are and are not the negation of "I am not drawing a rectangle."
NegationThe negation of a statement is a statement using the same subject and predicate, but with the opposite truth value.
The negation of ...
I am not drawing a rectangleis the statement ...
I am drawing a rectangleStatements about circles are irrelevant, as are statements about any action other than drawing (or not drawing).
In a survey of 2926 adults, 1476 say they have started paying bills online in the last year.
Construct a 99% confidence interval for the population proportion. Interpret the results.
The confidence interval for the given equation will be: 0.504.
What is confidence interval?
In frequency statistics, the confidence interval (CI) is the range of estimated values for an unknown parameter. Confidence intervals are computed at the specified confidence level. A 95% confidence level is the most common, but other levels such as 90% and 99% are sometimes used. The confidence level represents the proportion of corresponding CIs over time that contain the true value of the parameter. For example, 95% of all intervals computed at the 95% level must contain the true value of the parameter.
Factors that affect the width of the CI include sample size, sample variability, and confidence level. All else being equal, a larger sample results in a narrower confidence interval, a more varied sample results in a wider confidence interval, and a higher confidence level results in a wider confidence interval.
Therefore, The confidence interval for the given equation will be: 0.504.
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The two red trapezoids have the same area.
Can you find the area of one of the blue triangles?
Triangle ABC and DEF are similar what is the measure of side DF?
Answer:
15
Step-by-step explanation:
25 / 15 = 1.666...
9 x 1.666.... = 15
Answer:
Step-by-step explanation:
375
if they are simiar than 15 from abc would have been the same length
A sweater is priced at $60 normally. It is on sale for $45. By what percentage was the
sweater's price decreased?
In each blank below a single digit is inserted such that the following six three-digit numbers, in this order, form an arithmetic sequence: 1_ _, _ _ 9, 2 _ 2, _ 6 _, 2 _ _, _ 3 _What is the value of the next number in the sequence?
The series appears to be 166, 199, 232, 265, 298, 331
With examples, define sequence?
A list of numbers in a certain order is known as a sequence. A term is the name given to each number in a sequence.
In a series, each term has a place (first, second, third and so on). Take the sequence 5, 15, 25, 35, as an example. Each number is referred to as a word in the sequence.
The last number of the common difference must end in 3
And this must be a 2 digit number
So....the first number must end in 6
The the 4th number must be 265
So..... the 5th number must end in 8
And the last digit of the last term must end in 1 [ and begin with 3 ]
Putting all this together we have that
265 + 2d = 331
2d = 66 ⇒ d = 33
So the first term must be 265 - 3 (66) = 166
the series appears to be 166, 199, 232, 265, 298, 331
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Find the absolute maximum and absolute minimum values of f on the given interval. (Round all answers to two decimal places.)f(t) = 2 cos t + sin 2t[0,pi/2]____min____max
The absolute minima of the function is at 12.85 and the absolute maxima is at 15.42.
Let the function be ,
f(t) = 5t + 5 cot( t/2 ).
first derivative of the function,
f'(t)
= d/dt ( 5t + 5 cot(t/2))
= d/dt(5t) + d/dt ( 5 cot (t/2))
= 5 - 5/2cos^2(t/2)
Taking the derivative equal to 0,
f'(t) = 0
t = pi/2 , 3pi/2 f
On evaluating the equation wrt to obtained critical value,
we will get ,
absolute minimum value 12.85
absolute maximum value 18.56.
The extrema of a function are the maxima and minima. The maximum and minimum values of a function inside the specified ranges are known as maxima and minima, respectively. Absolute maxima and absolute minima are terms used to describe the function's maximum and minimum values, respectively, over its full range.
The terms "local maxima" and "local minima" refer to additional maxima and minima of a function that are not its absolute maxima and minima.
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A 0.60-kg basketball is dropped out of a window that is 6.1mabove the ground. The ball is caught by a person whose handsare 1.5m above the gound.1. How much work is done on e the ball by its weight?What is the gravitational potential energy of the basketball,relative to the ground, when it is ... 2. released and 3. caught?4. How is the change (PEf- PE0) in the ball'sgravitational potential energy related to the workdone by its weight?
The work that gravity does;
W = F.S = mgΔh
In light of the fact that gravity points downward and that displacement is also downward, their angle is 0 and their cosine 1, respectively.
W = mgΔh
g = 9.8 m/s²
Δh = 4.6 m
m = 0.60 kg
W = 0.60 x 9.80 x 4.6
W = 2.7 J
The source of gravitational potential energy in relation to the ground is;
U = mgh
The release point therefore
Ug = mgh(0)
U0 = 0.60 x 9.8 x 6.1
U0 = 35.87 J
At the point of release
U(gf) = mgh(f)
U(gf) = 0.60 x 9.80 x 1.5
U(gf) = 8.820 J
Gravitational potential energy changes are;
ΔU(g) = U(gf) - U0
ΔU(g) = 8.820 J - 35.87 J
ΔU(g) = -27.05 J
Result, we can see that the work done through gravity is the opposite of how the gravitational potential energy has changed.
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A family rents a truck to move from Buffalo to Chicago. The rental has a base cost of $49.95, plus, an additional cost of $1.19 per mile driven. The family also pays for gas, which costs $3.89 per gallon. The truck’s average gas mileage is 18 miles per gallon. The family decided to take a rest in Cleveland, what would be the distance travelled from Buffalo to Cleveland if the total cost of the move is $724.85?
By solving a linear equation, we will see that the distance is 479.98 miles.
How to find the distance?We know:
The rental has a base cost of $49.95 plus $1.19 per mile.
There is also an extra cost of $3.89 per gallon of gas, and with one gallon they can travel 18 miles, then there is another extra cost of:
$3.89/18 per mile.
Then, if you travel x miles, the total cost is given by the linear equation:
C(x) = $49.95 + ($1.19 + $3.89/18)*x
We want to find the value of x, number of miles, such that the total cost is $724.85, then we need to solve:
$724.85 = $49.95 + ($1.19 + $3.89/18)*x
Let's solve that for x:
$724.85 - $49.95 = ($1.19 + $3.89/18)*x
$674.90 = ($1.19 + $3.89/18)*x
$674.90/($1.19 + $3.89/18) = x
479.98 = x
So the distance is 479.98 miles.
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Find the 11th term in the following
arithmetic sequence :
20, 18, 16, 14, . . .
Hint: Write a formula to help you.
Answer is 0
Given:- arithmetic sequence 20,18,16,14,....
To find:- 11th term of given arithmetic sequence
Arithmetic Progression (AP) is sequence of numbers in order, in which the difference between any two consecutive numbers is constant value. It is also known as Arithmetic Sequence.
The 11th term of the A.P. can be found by a formula, a(n)=a(1)+(n-1)d , where n is the number of terms, a(1) is teh first term of A.P and d is difference between any two continuously terms.
Number of terms to be found = 11
therefore, a(11) = a(1)+(n-1)d
d=a(2)-a(1)
d=18-20
d=-2
putting value of d in above equation,
a(11) = 20 + (11-1)(-2)
a(11) = 20 - 20
a(11) = 0
hence the 11th term of arithmetic sequence 20,18,16,14,.... is 0.
Inga is solving 2x2 + 12x – 3 = 0. Which steps could she use to solve the quadratic equation? Select three options.
Answer:
Step-by-step explanation:
1) She can use the CUADRATIC FUNCTION for to solve
2) She can use factorization for to solve
3) She can use the ZERO method for to solve
Answer for free9+10 =
Answer: 19
Step-by-step explanation:
Answer:19
Step-by-step explanation: 10 add the 9
solve the equation
-(1+7x)-6(-7-x)=36
The solution to the equation is x = -1.
What are arithmetic operations?
Arithmetic operations is a branch of mathematics that studies numbers and the operations on numbers that are useful in all other branches of mathematics. It consists primarily of operations like addition, subtraction, multiplication, and division.
To solve this equation, we need to use the order of operations to simplify the expression on the left side of the equal sign.
The order of operations tells us that we should perform operations within parentheses first, then perform any exponents or radicals, then perform any multiplications or divisions (working from left to right), and finally perform any additions or subtractions (also working from left to right).
Using the order of operations, we can simplify the left side of the equation as follows:
-1 - 7x - 6(-7 - x) = 36
(-1 - 7x) - 6(-7 - x) = 36
-1 - 7x - (-42 - 6x) = 36
-1 - 7x + 42 + 6x = 36
5x + 41 = 36
5x = -5
x = -1
Therefore, the solution to the equation is x = -1.
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