Four identical trapeziums are placed on a coordinate grid as shown.
a) Write down algebraic expressions for the coordinates of point L.
b) M has coordinates (9,9).
N has coordinates (15,15).
Work out the value of a and the value of b
Answers
a) The algebraic expression for the coordinates of point L is (a-b,b).
b)The value of a is 9, and the value of b is 3
What are coordinate points?
A specific point on a grid referred to as a coordinate plane can be located using coordinates, which are two numbers. In a plane, a point is known to have specific coordinates. The coordinates are the ordered pairs of numbers (x, y) that describe the location of any point on a plane. In our everyday lives, we use coordinates for things like map location, classroom seating, and more.
a) Extending point L towards the y-axis, we see that it corresponds to the given coordinate, i.e., (0,b). Therefore the y coordinate is b.
Next, extending the point L towards the x-axis, we see that the point lands somewhere between the distance 'a' from the origin. As the height is 'b', and as the trapeziums are identical, we can say that the extended point of L lands at a point that is 'b' distance from 'a'. Hence the x coordinate is a-b.
Hence, the coordinates of point L are (a-b,b).
b) Given M(9,9) and N(15,15).
Extending the point M towards the x-axis, we get that it coincides with the point 'a', therefore we get the value of a=9.
Now extending point N towards the x-axis, we get that it lands at a distance of 15 from the origin. We got the value of a=9, so the remaining distance between the point (9,0) and (15,0) is 6 units.
Extending the point (9,0) upwards, we see that it cuts the uppermost trapezium giving us the distance of the trapezium excluding the small triangle formed. Now taking the same information, if we cut the bottom-most trapezium, we see that it cuts at point (6,0).
Now we know the height of the trapezium is 'b'. So, we get b=9-6 (as 9 is the distance of the entire trapezium, and 6 is from the above calculations).
We get b=3.
Hence we got the value of 'a'=9 and 'b'=3.
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Related Questions
cassie prepaid a 6-month membership to the summer lotus yoga studio. she received a one-time discount of $40 for prepaying. cassie paid a total of $650.
Answers
The amount which Cassie will pay the studio per month will be $115.
The equation by taking data from the question will be
6m - 40 = 650
6m−40=650
On solving this we get ,
6m = 610
m = 115
The regular cost per month is $115.
The above question is an example of multi-step equation.
Multi-step equations are algebraic expressions that must be solved using more than one operation, such as subtraction, addition, multiplication, division, or exponentiation. When solving multi-step equations, it is critical to understand the order of operations.
Solve an equation with a single unknown variable, x, by using algebraic operations on both sides of the equation to isolate x. The goal is to select an algebraic operation sequence that will leave x on one side of the equal sign and put everything else on the other side.
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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
Answers
Who the check is being written to is 1
Amount of check, written in numeric format is 3
Amount of check, written in word format is 4
A description of what the check is for is 5
And the checking account owners signature is 6.
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
Help solve systems of equations
Answers
Answer:
b!vch I am up b!vch I am up b!vch I am up
HELP THANK YOU SO MUCH
Kyle works at a local music store. The store receives a shipment of new CDs in a box. In the shipment, there are 10 country CDs5 rock CDs12 hip hop CDs, and 3 jazz CDs. What is the probability that the first CD that Kyle pulls from the box will NOT be hip hop?
A. 3/5
B. 2/5
C. 12/30
D. 17/30
Answers
The probability of not pulling hip hop CDs is equal to 3/5. The correct option is (A).
What is probability?Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.
The probability of any event always lies in the close interval of 0 and 1 [0,1].
The zero value of probability indicates that the event will not happen while its value equal to one indicate that it will happen.
Given that,
The number of country, rock, hip hop, and jazz CDs are 10, 5, 12 and 3 respectively.
Then, the total number of CDs are 10 + 5 + 12 + 3 = 30
Now, the probability of not selecting hip hop is equal to the probability of selecting the remaining types of CDs which is given as,
P(Not hip hop CDs) = (10 + 5 + 3)/30
= 18/30
= 3/5
Hence, the probability that the first CD that Kyle pulls from the box will not be hip hop is 3/5.
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In how many ways can the digit in the number 7,600,000 be arranged
Answers
Answer:Answer to Solved In how many ways can the digits in the number 7, ... Question: In how many ways can the digits in the number 7, 600,000 be arranged?
1 answer
·
Top answer:
Concept used : The number of permutations (arrang...
Step-by-step explanation:
Carrie is creating a painting for art class. The width of the canvas is 5 inches greater than the height of the canvas. Write a simplified equation in terms of h (the height) for the perimeter, p, of the canvas. (Please show work!)50 points!!!!!!
Answers
Length is 4 ft and width is is 3ft.
What is width ?
The "size" of a body is measured in geometry by its mean width; for more information on the various body measures, see Hadwiger's theorem. One must take into account -dimensional hyperplanes parallel to a specific direction in where is the n-sphere.
[tex]\begin{aligned}& w^2+(w+1)^2=5^2 \\& \frac{w^2+w^2+2 w+1}{}=25 \\& 2 w^2+2 w-21\end{aligned}[/tex]
[tex]\begin{aligned}& 2 w^2+2 w-24=0 \\& w^2+w-12=0\end{aligned}[/tex]
[tex]\begin{gathered}(w-3)(w+4)=0 \\w=3,-4\end{gathered}[/tex]
The width must be three because we can't have negative widths. Since the length is four feet, we have the dimensions of our poster.
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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.)
Answers
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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Factor 2x^4-5x^3+6x^2-15x completely over the set of integers
Answers
[tex]2x^4 - 5x^3 + 6x^2 - 15x \\ \\ =x(2x^3 - 5x^2 + 6x-15) \\ \\ =x(x^2(2x-5)+3(2x-5)) \\ \\ =\boxed{x(2x-5)(x^2+3)}[/tex]
A sweater is priced at $60 normally. It is on sale for $45. By what percentage was the
sweater's price decreased?
Answers
The size of a wolf population in a national park increases according to the formula y=y₀ e^{0.027 t}, where t is time in years and y₀ is the initial population at time 0 . If the size of the current population is 58 wolves, find how many wolves there will be in 5 years.
In 5 years, there will be ? wolves.
(Round to the nearest whole number as needed.)
Answers
There will be 66 wolves there will be in 5 years according to given exponential function.
What is exponential equation?
The exponential function may be a function denoted by f(x)=\exp or e^. Unless otherwise fixed, the term usually refers to the positive-valued operate of a true variable
Main body:
given = y=y₀ e^{0.027 t}
here , y₀ = 58
t = 5 years
y = 58 e^(0.027 * 5)
y = 58 e^(0.135)
y = 58 * 1.144537
y = 66.383133
y = 66
Hence there will be 66 wolves there will be in 5 years.
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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.)
Answers
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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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?
Answers
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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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.
Answers
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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Evaluate b(-7), when b(c) = 2c³5c² - 6c - 13.
Answers
Answer:
168015
Step-by-step explanation:
b(c) = 2c³5c² - 6c - 13
b(7)=2(7)³5(7)²-6(7)-13
b(7)=2(343)5(7)²-6(7)-13
b(7)=(686) 5(49)-6(7)-13
b(7)=(686) (245)-6(7)-13
b(7)=(686) (245) -42-13
b(7)=168070-42-13
b(7)=168028-13
b(7)=168015
(Usually this is how you would solve it but because there was no sign between the 2c^35c^2 I got sort of confused so I just multiplied, if wrong I'm sorry..)
[tex]b(-7)=-168041[/tex].
Step-by-step explanation:1. Write the function.[tex]b(c)=2c^{3} 5c^{2} -6c-13[/tex]
2. Substitute "c" by "-7" in the function.[tex]b(-7)=2(-7)^{3} 5(-7)^{2} -6(-7)-13[/tex]
3. Calculate.[tex]b(-7)=2(-343) 5(49) -(-42)-13\\ \\b(-7)=-168070 +42-13\\ \\b(-7)=-168041[/tex]
help meeeeeeeeeee pleaseee
Answers
(a) 794g of the initial sample will be left in the sample after 25 years. (b) Time taken to decay to half of its original amount is 3.39 years.
Isotopes(200g) are atoms that have the same number of protons in their nucleus, but a different number of neutrons. This means that they have the same atomic number, but a different atomic mass. Because of this, isotopes have different physical and chemical properties. Isotopes can be stable, meaning that they do not undergo radioactive decay, or they can be unstable, meaning that they will undergo radioactive decay over time.
(a) Substituting 25 for t in the expression, we get:
[tex]A(25) = 200e^{0.0541 \times 25}[/tex]
[tex]= 200e^{1.3525}[/tex]
Thus, after 25 years, there will be
[tex]200e^{1.3525} = 2003.97[/tex]
794 g of the initial sample left in the sample.
(b) We want to find t such that
[tex]A(t) = 200e^{0.0541}[/tex]
= 100.
Solving for t, we get:
[tex]= 200e^{0.0541} \times t=100[/tex]
Dividing both sides by 200 and applying the natural logarithm to both sides, we get:
0.0541 × t = ln(0.5)
Therefore,
[tex]t = \frac{ln(0.5)}{0.0541}[/tex]
= 3.39 years.
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What is greater 7/8 or 5/6?
Answers
Answer:
7/8
Step-by-step explanation:
First, we need to get 7/8 and 5/6 to the same denominator which is 48. 7/8 becomes 42/48 whilst 5/6 becomes 40/48
we can simply put them both with the same denominator and check, the larger numerator will be it.
so hmmm let's multiply one by the denominator of the other
[tex]\cfrac{7}{8}\hspace{5em}\cfrac{5}{6} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{7}{8}\cdot \cfrac{6}{6}\implies \cfrac{42}{48}\hspace{5em}\cfrac{5}{6}\cdot \cfrac{8}{8}\implies \cfrac{40}{48}\hspace{9em}\boxed{\cfrac{42}{48} ~~ {\Large \begin{array}{llll} > \end{array}}~~ \cfrac{40}{48}}[/tex]
solve the equation
-(1+7x)-6(-7-x)=36
Answers
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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The data in the table represent the height of an object over time. Which model best represents the data ? Height of an Object quadratic, because the height of the object increases or decreases with a multiplicative rate of change quadratic, because the height increases and then decreases Time (seconds) 0 1 2 Heiaht(feet) 5 50 70 48 3 exponential, because the height of the object increases or decreases with a multiplicative rate of change exponential , because the height increases and then decreases
Answers
Since the data in the table represent the height of an object over time, a model which best represents the data is: B. quadratic, because the height increases and then decreases.
What is a quadratic equation?In Mathematics, a quadratic equation can be defined as a mathematical expression (equation) that can be used to define and represent the relationship that exists between two or more variable on a graph.
Additionally, the standard form of a quadratic equation in mathematics is given by the following mathematical expression:
ax² + bx + c = 0
In Mathematics, the graph of all quadratic equations (functions) is either an upward or downward parabola, which is typically a u-shaped curve.
In conclusion, we can logically deduce that the graph of a quadratic equation (function) would always form a parabolic curve with the data value increasing on one end and decreasing on the other end as shown in the image attached below.
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Complete Question:
The data in the table represent the height of an object over time.
Which model best represents the data?
quadratic, because the height of the object increases or decreases with a multiplicative rate of change
quadratic, because the height increases and then decreases
exponential, because the height of the object increases or decreases with a multiplicative rate of change
exponential, because the height increases and then decreases
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
Answers
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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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!!
Answers
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.
Help Please!!
Line q has an equation of y+7=9(x+4). Line r is perpendicular to line q and passes through (9,–10). What is the equation of line r?
Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.
Answers
The equation of line r, in slope-intercept form, is: y = -1/9x - 9.
How to Write the Equation of a Line in Slope-intercept Form?The equation that represents a line, in slope-intercept form, is expressed or written as:
y = mx + b, where the slope is m, and the y-intercept is b.
The slope of line q, with the equation y + 7 = 9(x + 4) is 9. The negative reciprocal of 9 is -1/9. This means line r that is perpendicular to line q and passes through (9, -10) has a slope, m = -1/9.
To write the equation of the line in slope-intercept form, first, substitute m = -1/9 and (a, b) = (9, -10) into y - b = m(x - a):
y - (-10) = -1/9(x - 9)
y + 10 = -1/9(x - 9)
Rewrite in slope-intercept form:
y + 10 = -1/9x + 1
y = -1/9x + 1 - 10
y = -1/9x - 9
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What is the area of the triangle?
7 cm
10 cm
Area = [?] cm²
Enter
Answers
Answer:
35 cm²
Step-by-step explanation:
Base of triangle = 10 cm
Height of triangle = 7 cm
Area of triangle = 1/2 x (base x height)
= 1/2 x (10 x 7)
= 1/2 x 70
= 35
So, area is 35 cm²
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?
Answers
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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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.
Answers
Answer:
answer = 98.2808022923 i think
PLEASE HELP ASAP
Choose the expression that is equivalent to the quantity 7 raised to the negative second power times 7 raised to the third power end quantity all raised to the negative third power.
−76
1 divided by 7 raised to the third power
negative 1 divided by 7 raised to the sixth power
718
Answers
The correct answer is therefore negative 1 divided by 7 raised to the sixth power, which is the same as 1/7^2. The other choices do not match this expression.
What is power?
The power (or exponent) of a number says how many times to use the number in multiplication. It is written as a small number to the right and above the base number.
The expression 7 raised to the negative second power times 7 raised to the third power is equivalent to 7 raised to the (negative second + third) power, which is 7 raised to the first power. This is equal to 7.
The quantity 7 raised to the first power all raised to the negative third power is equal to 7 raised to the (first + negative third) power, which is 7 raised to the negative second power.
Therefore, the expression that is equivalent to the quantity 7 raised to the negative second power times 7 raised to the third power all raised to the negative third power is 7 raised to the negative second power, which is 1/7^2 = 1/49.
Hence, The correct answer is therefore negative 1 divided by 7 raised to the sixth power, which is the same as 1/7^2. The other choices do not match this expression.
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can someone help me with this thank you
Answers
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).
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)
Answers
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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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?
Answers
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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-5y^2+17y-84 / y^3+12y^2+36y partial fraction decompostion
Answers
[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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What is the height of the flag pole?
Answers
the height of the flag pole should be 108 inches.