3/5 + 1/3
= 9/15 + 5/15
= 14/15
Answer:
9/15 + 5/15 = 14/15
Step-by-step explanation:
The common denominator of 5 and 3 is 15
5 x 3 = 15, so multiply the numerator by 3 too
you get 9/15
3 x 5 = 15, multiply numerator by 5 too
you get 5/15
Please help with this
On what interval is the function h(x) = -2|x + 2| + 2 increasing?
(2, ∞)
(-2, ∞)
(-∞, -2)
(-∞, 2)
Answer:
Step-by-step explanation:
what grade is this ...
this look hard
Are the following functions analytic? Use (1) or (7). 2. f(z)=iz
z
ˉ
3. f(z)=e
−2x
(cos2y−isin2y) 4. f(z)=e
x
(cosy−isiny) 5. f(z)=Re(z
2
)−iIm(z
2
) 6. f(z)=1/(z−z
5
) 7. f(z)=i/z
8
8. f(z)=Arg2πz 9. f(z)=3π
2
/(z
3
+4π
2
z) 10. f(z)=ln∣z∣+iArgz 11. f(z)=cosxcoshy−isinxsinhy
The following functions are analytic:
1. f(z) = iz
2. f(z) = \(e^(^-^2^x^)(cos^2^y - isin^2^y^)\)
4. f(z) = \(e^x(cosy - isiny)\)
5. f(z) = \(Re(z^2) - iIm(z^2)\)
8. f(z) = \(i/z^8\)
11. f(z) = cos(x)cos(hy) - isin(x)sin(hy)
Analytic functions are those that can be expressed as power series expansions, meaning they have derivatives of all orders in their domain. In the given list of functions, we need to determine if each function satisfies this criterion.
f(z) = iz: This function is linear and can be expressed as a power series, therefore it is analytic.f(z) = \(e^(^-^2^x^)(cos^2^y - isin^2^y)\): This function can also be expressed as a power series expansion and has derivatives of all orders, making it an analytic function. f(z) = \(e^x(cosy - isiny)\): Similarly, this function can be written as a power series expansion and has derivatives of all orders, making it analytic. f(z) = \(Re(z^2) - iIm(z^2)\): Although this function involves the real and imaginary parts of \(z^2\), both of these components can be expressed as power series expansions, implying that f(z) itself can be written as a power series and is thus analytic.f(z) = \(i/z^8\): This function can be rewritten as i*\((1/z^8)\) , where \(1/z^8\) can be expressed as a power series expansion. Since the multiplication of a constant (i) and an analytic function (\(1/z^8\)) results in an analytic function, f(z) is analytic. f(z) = cos(x)cos(hy) - isin(x)sin(hy): This function consists of the multiplication and addition of trigonometric functions, which are themselves analytic. Therefore, f(z) is an analytic function.Learn more about Analytic functions
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In a certain country, The true probability of a baby being a boy is 0.529.Among the next six randomly selected births in the country, what is the probability that at least one of them is a girl?
The probability that at least one of them is a girl is 0.9781
What is the probability that at least one of them is a girl?From the question, we have the following parameters that can be used in our computation:
P(Boy) = 0.529
Number of selection, n = 6
Using the above as a guide, we have the following:
P(At least 1 girl) = 1 - P(No girl)
Substitute the known values in the above equation, so, we have the following representation
P(At least 1 girl) = 1 - (0.529)^6
Evaluate
P(At least 1 girl) = 0.9781
Hence, the probability is 0.9781
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Given x=-3, y=6, and z=-4 xz/-2y
Answer:
-1
Step-by-step explanation:
sub in the values of x, y and z into the equation
you get:
(-3)(-4)/(-2)(6)
= 12/-12
= -1
Answer: -1
Step-by-step explanation:
xz/-2y, given x=-3, y=6, and z=-4
------------
xz/-2y
=(-3)(-4)/-2(6) ⇔ substitute x y and z value
=12/-12 ⇔ calculate it
=-1 ⇔ simplify fraction
Hope this helps!! :)
Please let me know if you have any question
Solve 6 - 5x = 7 + 3x
Answer:
hol up
x=-1/8 negative one over eight
Step-by-step explanation:
what is the distance between the points?! round to the nearest tenth i need to show work
Answer:
8.6
Step-by-step explanation:
To find the distance between two points we use the formula posted below
All we need to do is figure out what the points are on the graph and plug them into the formula... we end up with
the square root of (5-(-2)^2+(2-(-3)^2 and get the answer of 8.602325267
then we round to the nearest tenth and get 8.6
8. Set up the artificial variable LP (Phase I LP) and specify the EBV and the LBV. DO not perform a complete pivot (complete with the exchange of basic variables). ( 16pts ) MaxZ=4x
1
+7x
2
+x
3
s.t.
2x
1
+3x
2
+x
3
=20
3x
1
+4x
2
+x
3
≤40
8x
1
+5x
2
+2x
3
≥70
x
1
,x
2
≥0
To set up the artificial variable LP (Phase I LP) for the given problem, we introduce an artificial variable, LP, to the objective function with a coefficient of 1. The artificial variable is used to identify infeasible solutions.
To set up the artificial variable LP (Phase I LP), we modify the objective function as follows:
Maximize Z = 4x1 + 7x2 + x3 + LP
The artificial variable LP is introduced to the objective function with a coefficient of 1. This allows us to track its value during the iterations.
The initial constraints remain the same:
2x1 + 3x2 + x3 = 20
3x1 + 4x2 + x3 + x4 = 40
8x1 + 5x2 + 2x3 - x5 = 70
The initial basic variables (BV) are the slack variables corresponding to the equality and inequality constraints, namely, x3 and x4. The artificial variable LP is initially a non-basic variable.
The initial artificial variables' basic variable (BVB) values are set to the right-hand side values of the constraints:
x3 = 20
x4 = 40
The initial artificial variable LP's value is set to 0.
Next, the artificial variable LP is selected as the entering variable, as it has a positive coefficient in the objective function. To determine the leaving variable, we perform the ratio test using the ratios of the right-hand side values and the entering column values (coefficients of LP) for the respective constraints.
The leaving variable is determined based on the minimum ratio, ensuring that the corresponding row represents a valid pivot element. If no valid pivot element is found, the problem is infeasible.
This completes the setup of the artificial variable LP (Phase I LP) without performing a complete pivot. Further steps would involve applying the simplex method and iteratively pivoting to find the optimal solution or identify infeasibility.
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Find the product of (4 x 106) and (2 x 106). write the final answer in scientific notation. 8 x 106 8 x 1012 8 x 10012 8 x 1036
The product of (4 x 10⁶) × (2 x 10⁶) is 8 × 10⁶.
What is scientific notation?Scientific notation is similar to shorthand for writing extremely large or extremely small numbers. Rather than writing a number in decimal form, it is reduced to a number multiplied by ten.
The "coefficient" is the first number with in mathematical equation. The coefficient has to be greater than one and less than ten. The coefficient for creating scientific notation for number 256, for example, is 2.56.The second number as in equation is a power of ten, written as a power of ten with an exponent, such as 10², which stands for 10 x 10.Now, as per the given question;
The product of the given two number are-
= (4 x 10⁶) × (2 x 10⁶)
= 8 × 10⁶
Therefore, the scientific notation of the product of the give two numbers is 8 × 10⁶.
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The correct question is-
Find the product of (4 x 10⁶) and (2 x 10⁶). write the final answer in scientific notation. write the final answer in scientific notation.
let be a -digit number, and let and be the quotient and the remainder, respectively, when is divided by . for how many values of is divisible by ?
There are a total of possible values of for which is divisible by .
We want to find the number of values of for which is divisible by . Let's consider the possible remainders when is divided by .
If , then is divisible by , since the last digit of any even number is 0, 2, 4, 6, or 8, all of which are divisible by .
If , then is not divisible by , since the last digit of any odd number is 1, 3, 5, 7, or 9, none of which are divisible by .
Therefore, we can assume that is even, and write as , where is an -digit number and is a digit from 0 to 9. We can then write:
We know that is divisible by , so we need to find the values of for which is divisible by . This is equivalent to finding the values of for which is divisible by , since is relatively prime to .
We can rewrite the equation above as:
This shows that is divisible by if and only if is divisible by . Since and are relatively prime, this occurs if and only if both and are divisible by . In other words, we need to find the values of such that both and are divisible by .
There are 5 even digits (0, 2, 4, 6, and 8) that can be chosen for , and 10 digits (0 to 9) that can be chosen for . Thus, there are a total of possible choices for the pair (). We need to determine how many of these pairs result in both and being divisible by .
For to be divisible by , we need the sum of its digits to be divisible by . Since is even, this is equivalent to requiring the sum of the digits of to be divisible by . This means that we can choose any combination of the even digits (0, 2, 4, 6, and 8) to fill the digits of , with no restrictions. There are 5 choices for each digit of , for a total of possible -digit numbers that are divisible by .
For to be divisible by , we need to be divisible by . Since is relatively prime to , this is equivalent to requiring to be divisible by . Since is an -digit number, it follows that is an -digit number. Thus, we need to choose the first digits of to be divisible by .
There are 10 choices for each of the first digits of , and 5 choices for the last digit (since it must be even). Thus, there are a total of possible -digit numbers that have the first digits divisible by .
To count the number of pairs () that result in both and being divisible by , we can use the multiplication principle: we multiply the number of choices for by the number of choices for , since these choices are independent of each other. Thus, the total number of pairs () is:
Therefore, there are a total of possible values of for which is divisible by .
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Find the angle?
Need help please
Answer:
ans - 25.77°
Step-by-step explanation:
tan a = 14/29
a = tan ^ -1 14/29
a = 25.77°
Answer:
25.77
Step-by-step explanation:
It's logically impossible for this angle to be .008.
Alternatively (the harder way), use trigonometric ratios to solve this problem.
Since you know the adjacent and opposite angle, you need to use tangent ratio.
tan = a/o
Use \(tan^-1\)
\(tan^-1(14/29)\)
a = 25.76932762, ~25.77
Write an equation for this graph.
Answer:
y=-5/2x +5
Step-by-step explanation:
The slope is -5/2, because y2-y1 over x2-x1 can be plugged into 0-5 over 2-0 which is -5/2
The y-intercept is 5, because the y-axis when x is 0 is 5.
Hope this helps
complete the steps to evaluate the following expression, given log3a = −0.631. log3 a 3 log3 3
The value of the given logarithm function is found to be log3 a3log3 3 = 3.
The logarithm of a number in a given base is the power to which the base must be raised to obtain that number. The logarithm of x is written as logb(x) (read "log base b of x") and is defined as the power to which the base, b, must be raised to give the value x.
Mathematically, it can be written as:logb(x) = y if by = x where b is the base of the logarithm, x is the number whose logarithm is to be found, and y is the logarithm of x in base b.
We are given log3a = −0.631 and we are to find the value of the expression log3 a3log3 3.
Step 1: Let's recall some properties of logarithm:
logb(b) = 1
logb(1) = 0
logb(xy) = logb(x) + logb(y)
logb(x/y) = logb(x) - logb(y)
We can simplify the given expression using these properties of logarithm:
log3 a3
log3 3= log3 (a3) + log3 3
Now we can simplify a³. We have a = 3log3a, therefore
a³ = (3log3a)³ = 33
log3a = 27log33
= 27
Therefore, a³ = 2
7Now, we can replace a³ with 27 in the expression log3 a³, and we have:
log3 27 = log3 (3³) = 3(log3 3)
We can substitute log3 3 with its value 1 and we have:
3(log3 3) = 3(1) = 3
Therefore, log3 a3log3 3 = 3.
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Answer:
1.631 on edge 2023 :}
Step-by-step explanation:
Solve the system below for x and y in terms of a and b.
\(ax+y=7\\3x-y=b\)
What is equidistant from the three sides of the triangle?
(a) Circumcenter.
(b) Incenter.
c) Centroid.
d) Orthocenter.
Option (a) Circumcenter is equidistant from the three sides of a triangle. The circumcenter of a triangle is the point where the perpendicular bisectors of the three sides of the triangle intersect.
It is the center of the circumcircle, which is the circle passing through all three vertices of the triangle. The circumcenter is equidistant from the three sides of the triangle, and this distance is equal to the radius of the circumcircle. The circumcenter has many geometric properties and is an important point in triangle geometry.
(b) The incenter is equidistant from the three sides of a triangle, but in a different way. The incenter is the point where the angle bisectors of the three interior angles of the triangle intersect. The incenter is equidistant from the three sides of the triangle along the lines that are perpendicular to the sides and intersect them at their midpoint. The incenter is the center of the incircle, which is the largest circle that can be inscribed inside the triangle.
(c) The centroid is not equidistant from the three sides of a triangle. The centroid is the point where the medians of the triangle intersect. The medians are the line segments that connect each vertex of the triangle to the midpoint of the opposite side. The centroid divides each median into two segments, with the segment connecting the centroid to the vertex being twice as long as the segment connecting the centroid to the midpoint of the opposite side.
(d) The orthocenter is also not equidistant from the three sides of a triangle. The orthocenter is the point where the altitudes of the triangle intersect. The altitude is the line segment that is perpendicular to a side of the triangle and passes through the opposite vertex. The orthocenter has many interesting properties and is an important point in triangle geometry.
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4. during an asb fundraiser, twenty-two hundred raffle tickets are sold at $5.00 each. find the expected value, if the grand prize is $2500, the second prize is $500, and the remaining 5 prizes are $100 amazon cards. the solution should be written in a sentence.
Each person who buys a ticket can expect to lose 45 cents. This can be answered by the concept of Average.
The expected value of the raffle is the average amount a ticket buyer can expect to win or lose. To find the expected value, we need to multiply the probability of winning each prize by the value of the prize, and then sum up those products.
Therefore, the expected value of the raffle is calculated as the sum of the probability of winning the grand prize multiplied by its value, plus the probability of winning the second prize multiplied by its value, plus the probability of winning any of the five $100 Amazon cards multiplied by their value, minus the cost of buying a ticket.
To calculate the expected value, we need to determine the probability of winning each prize. Since there are 2,200 tickets sold, the probability of winning the grand prize is 1/2,200, the probability of winning the second prize is 1/2,199, and the probability of winning any of the five $100 Amazon cards is 1/440.
Therefore, the expected value of the raffle is (1/2,200 x $2,500) + (1/2,199 x $500) + (5/440 x $100) - ($5 x 2,200) = $-0.45. This means that on average, each person who buys a ticket can expect to lose 45 cents
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Which of the following terms describe the relationship between the number of notes and each syllable of a text and which do not?
-syllabic
-melismatic
-neumatic
The terms syllabic, melismatic, and neumatic are all related to the number of notes in relation to each syllable of a text. Syllabic means that each syllable of the text is sung to one note.
This is the simplest type of setting for text to music. In contrast, melismatic means that each syllable of the text is sung to many notes, creating a more intricate and ornamental melody. Neumatic is somewhere in between syllabic and melismatic, where each syllable is sung to a few notes, but not as many as in a melismatic setting.
Syllabic, melismatic, and neumatic all describe the relationship between the number of notes and each syllable of a text.
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PLEASE HELP I HAVE A TEST!!A function predicts the number of household online-
devices in the average United States household. Which
domain would be the most appropriate set to use for
this function
Integers
Whole numbers
Rational Numbers
Irrational Number
Answer:
whole numbers probably
Solve this equation with a variable term on both sides:
5.1y + 21.3 = -0.3y - 24.6
What is the solution?
y=
What is the value of x for this triangle.
Answer:
13
Step-by-step explanation:
you have to use Pythagorean Theorem which is
(a^2) + (b^2) = (c^2)
where a and be are the legs 45° from each other and c is the hypotenuse.
so just plug in the numbers
5^2 + 12^2 = c^2
25 + 144 = c^2
169 = c^2
now square root both sides to get rid of the square on c
root(169) = root(c^2)
13 = c
PLEASE HELP !! I NEED HELP GUYS.
3. The function h(x) is a transformed function of f(x) = |x|. The transformation is as follows: 3 units vertical shift down, 2 units horizontal shift right.
a. Write the transformed equation, h(x).
b. Graph f(x) and h(x) on the same coordinate plane. Be sure to label the functions f(x) and h(x). This must be graphed by hand or by using the tools in Word. You may not use a web-based graphing program.
a. The transformed equation is given as follows: h(x) = |x - 2| - 3.
b. The graph of the two functions is shown by the image presented at the end of the answer.
What are translations?The translations are movements to the triangle in each of these directions:
Up.Down.Left.Right.The parent function in this problem is given as follows:
f(x) = |x|.
The first translation was a vertical translation three units down, hence we have that:
g(x) = f(x) - 3 = |x| - 3.
The second translation was a horizontal translation two units right, hence the have that the definition of the transformed equation h(x) is given as follows:
h(x) = g(x - 2) = |x - 2| - 3.
The graph of the functions is given by the image shown at the end of the answer, and the translations are verified on every point of the function, but especially the vertices.
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then, he wants to fill the tank with water until it's completely full. if he uses 85 8585 marbles, he will have to add 20.9 20.920, point, 9 liters of water. what is the volume of each marble?
a. Each marble has a volume of 0.013 liters.
b. 23.4 liters of water would be necessary if William uses 200 marbles.
a. To determine the volume of each marble, we can use the information that 85 marbles fill a tank with a volume of 20.9 liters of water:
Volume of each marble = (26 liters - 20.9 liters) / 85 marbles = 0.26 liters - 0.247 liters/marble = 0.013 liters/marble
So, each marble has a volume of 0.013 liters.
b. To determine the amount of water necessary if William uses 200 marbles, we can use the formula:
Volume of water = Total volume of tank - Volume of marbles
Volume of water = 26 liters - (200 marbles * 0.013 liters/marble) = 26 liters - 2.6 liters = 23.4 liters
So, 23.4 liters of water would be necessary if William uses 200 marbles.
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Complete question:
William has a 26-liter glass tank. First, he wants to put some marbles in it, all of the same volume. Then, he wants to fill the tank with water until it is completely full. If he uses 85 marbles, he will have to add 20.9 liters of water.
a. What is the volume of each marble?
b. How much water is necessary if William uses 200 marbles?
A truck holds 48,000 pounds of sand.
How many tons are in 48,000 pounds?
Answer:
24
Step-by-step explanation:
dont exaclty have an explanations - its just the calculations
Plz help fast!!!!!!!
Answer:
90=square
72=nonagon
60=hexagon
45=pentagon
40=octagon
I am not entirely sure tho
jane is 2 mi offshore in a boat and wishes to reach a coastal village 6 mi down a straight shoreline from the point nearest the boat. she can row 2 mph and can walk 5 mph. where should she land her boat to reach the village in the least amount of time?
She needs to dock her yacht 5.13 miles from the settlement.
As per the details given in the above question is as follow,
Where r is the distance she rowed
w is the distance she walked
t is the total time taken to reach village
Consider the time,
\(t = \frac{r}{2} + \frac{w}{5}\)
Further,
\(r^2 = 2^2 + (6 - w)^2\\r = (4 + 36 - 12w + w^2)^{\frac{1}{2}}\\r = (w^2 - 12w + 40)^{\frac{1}{2}}\)
Thus substitute the value of r in above t equation we get,
\(t = (w^2 - 12w + 40)^(1/2)/2 + w/5t' \\= (\frac{1}{2})(\frac{1}{2})(w^2 - 12w + 40)^(-\frac{1}{2})(2w - 12) + \frac{1}{5} = 0\)
Shift \(\frac{1}{5}\) on right side of the equation,
\((\frac{1}{2})(\frac{1}{2})(w^2 - 12w + 40)^(-\frac{1}{2})(2w - 12) = -\frac{1}{5}\\(\frac{1}{2})(w - 6) = -\frac{1}{5}(w^2 - 12w + 40)^(\frac{1}{2})\\5(w - 6) = -2(w^2 - 12w + 40)^(\frac{1}{2})\\25(w^2 - 12w + 36) = 4(w^2 - 12w + 40)\\(25 - 4)w^2 + (-25\times 12 + 4 \times 12)w + 25 \times 36 - 4 \times 40 = 0\\21w^2 - 252w + 740 = 0\)
w = 6.87, 5.13 mi
discard 6.87 ( > 6)
\(r = (w^2 - 12w + 40)^(\frac{1}{2})\)
r = 2.18 mi
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Help 4,5 and ,6 please
Answer:
i only know 4 number only
a group of employees of unique services will be surveyed about a new pension plan. in-depth interviews with each employee selected in the sample will be conducted. the employees are classified as follows. classification event number of employees supervisors a 390 maintenance b 185 production c 670 management d 824 secretarial e 141 what is the probability that the first person selected is either in management or in supervision?
The probability that the first person selected is either in management or Supervision is 0.55.
What is probability?
Mathematical explanations of the likelihood that an event will occur or that a statement is true are referred to as probabilities. A number between 0 and 1 represents the likelihood of an event, with 0 generally denoting impossibility and 1 denoting certainty.
In the given question :
No. of Supervisors ( Event A)= 390
No. of employees in management ( Event D)= 824
Total number of employers = 390 + 185 + 670 + 824 + 141 = 2210
The likelihood that two events (let's say W and S) will not occur is provided by the sum of the probabilities of the two events, i.e.
P (W or S) = P (W) + P (S)
In order to determine the likelihood that the first person chosen is in management or supervision, use the following formula:
P(A or D) = P(A) + P(D)
P(A) = Event A/ total employees = 390 / 2210 = 0.18
P(D) = Event D/total employees = 824 / 2210 = 0.37
Therefore,
P(A or D) = P(A) + P(D) = 0.18 + 0.37 = 0.55
Hence, the probability that the first person selected is either in management or Supervision is 0.55.
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Lame Example Furniture Company makes two products for its adoring public: chairs (C)and tables (T). Each chair requires 5 hours of labor (L) and 4 linear feet of rich mahogany (M), and each table requires 3 hours of labor and 20 linear feet of rich mahogany. The company has 240 labor hours available this week, and the warehouse has 700 linear feet of rich mahogany available. Profit for each chair is $150 and for each table is $750. At the optimal solution, how many tables should be produced? What is the maximum profit?
Maximize: Profit = 150C + 750T
Subject to:
5C + 3T ≤ 240 (Labor constraint)
4C + 20T ≤ 700 (Material constraint)
C ≥ 0
T ≥ 0
To determine the optimal production quantity of tables and the maximum profit, we can set up a linear programming problem based on the given information.
Let's define the decision variables:
Let C represent the number of chairs produced.
Let T represent the number of tables produced.
Objective function:
The objective is to maximize profit. The profit for each chair is $150, and the profit for each table is $750. Therefore, the objective function can be expressed as:
Profit = 150C + 750T
Constraints:
Labor constraint: The total labor hours available is 240, and each chair requires 5 hours, while each table requires 3 hours. So the labor constraint can be represented as:
5C + 3T ≤ 240
Material constraint: The warehouse has 700 linear feet of rich mahogany available, and each chair requires 4 linear feet, while each table requires 20 linear feet. Therefore, the material constraint can be expressed as:
4C + 20T ≤ 700
Non-negativity constraint: Since we cannot produce a negative quantity of chairs or tables, both C and T should be greater than or equal to zero:
C ≥ 0
T ≥ 0
Now, we can solve the linear programming problem to find the optimal solution:
Maximize: Profit = 150C + 750T
Subject to:
5C + 3T ≤ 240 (Labor constraint)
4C + 20T ≤ 700 (Material constraint)
C ≥ 0
T ≥ 0
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What are the 4 identities of algebraic expressions Class 8?.
The four basic algebra identities are as follows.
(a + b)² = a² + 2ab + b²(a - b)²= a²- 2ab + b²(a + b)(a - b) = a² - b²(x + a)(x + b) = x² + x(a + b) + abAlgebraic expression:Algebraic expressions are mathematical expressions that result when we perform operations such as addition, subtraction, multiplication, and division on variables and constants. For example, let's say James and Natalie were playing with matches and wanted to create a pattern of numbers in matches. James played four games and formed No. 4. Natalie added three more games and two he formed a pattern of four. They realized they could add 3 matches to each round to get an extra '4'. From this, they concluded that, in general, 4 + 3 (n-1) double crochet stitches are required to create n 4 patterns. Here 4+ 3(n-1) is called an algebraic expression.
Algebraic Identities:Algebraic identities are an important set of formulas in mathematics. They form the basis of algebra and help us perform calculations in simple and easy steps. Certain algebraic problems require a number of mathematical steps to be performed in order to arrive at an answer. Here, algebraic identities can be used to perform calculations without additional steps.
An algebraic identity is an algebraic equation in which the value of the left side of the equation is exactly equal to the value of the right side of the equation. The four basic algebra identities are as follows.
(a + b)² = a² + 2ab + b²(a - b)² = a² - 2ab + b²(a + b)(a - b) = a² - b²(x + a)(x + b) = x² + x(a + b) + abLearn more about algebraic Identities:
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what is (5x^4 +3x^2 -x)-(-5x^4-2x^2 +45) in FOIL Method?
can't be solve sa foil method Yung ganyan equation