It is linear if and only if the coefficients of y (the dependent variable) and all order derivatives of y are functions of t or constant terms.
What is equation?An equation is a formula in mathematics that expresses the equality of two expressions by connecting them with the equals sign =. In its most basic form, an equation is a mathematical statement that shows that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical equation that depicts the relationship between two expressions on opposite sides of the sign. It mostly consists of one variable and one equal to symbol. 2x - 4 = 2 is an example.
Here,
It is linear if and only if all order derivatives of y (the dependent variable) are functions of t or constant terms.
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1. You have always wanted to learn how to juggle, so you decide to buy a brand new chainsaw that retails for $153. If sales tax is 6%, what is the total price you pay?
2. You are a real estate agent, and you sell your client's house for $350,000, earning a 5% commission. How much did you earn?
3. You fail out of school and are forced to become a traveling hamster salesperson. You earn 4% commission on all sales, and after two grueling weeks you manage to sell $710 worth of product. How much do you make?
Answer:
1. The total price you pay is $162.18
2. You earn $17,500
3. You earn $28.40
Step-by-step explanation:
1. 153 times 6% or 153 times 0.06 = 9.18
153 + 9.18 = 162.18
2. 350,000 times 5% or 350,000 times 0.05 = 17500
3. 710 times 4% or 710 times 0.04 = 28.4
What’s 900+900
Just doing this cause it’s fun
What are the 4 properties of multiplication examples?.
The 4 properties of multiplication are Associative Property, Commutative Property, Distributive Property, and Identity Property.
The properties of multiplication are particular rules that are used while multiplying numbers. These properties help simplify expressions easily and, hence, have a significant role in solving all kinds of mathematical expressions, whether algebraic expressions, fractions, or integers.
Associative Property: (P × Q) × R = P × (Q × R)
For example, (4 × 5) × 3 = 4 × (5 × 3) = 60.
Commutative Property: P × Q = Q × P
For example, 3 × 4 × 2 = 2 × 3 × 4 = 24.
Distributive Property: P(Q + R) = PQ + PR; P(Q - R) = PQ - PR
For example, 3(2 + 4) = (3 × 2) + (3 × 4) = 6 + 12 = 18.
Identity Property: P × 1 = P
For example, 4 × 1 = 4, or 1 × 27 = 27.
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There are 16 ounces in one pound.
A box of nails weighs 4 pounds. Using
the variable w. Write and solve a
division equation to find how many
ounces the box weighs.
According to the equation, the weight of box in ounces is 64.
Firstly let us represent the weight of box with w. Now, the formula to be used for calculation of the weight of box is -
The weight of box in ounces = weight of box in pounds × number of ounces in one pound/one
Keeping the values in formula to find the value of weight of box in ounces.
The weight of box in ounces = 4 × 16/1
Performing multiplication and division on Right Hand Side of the equation to find the weight of box in ounces
The weight of box in ounces = 64 ounces
Thus, the weight of box in ounces is 64.
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Which data set could be represented by the boxplot shown?
A. {6, 6, 8, 8, 9, 12, 13, 13, 14}
B. {6, 6, 7, 9, 9, 12, 13, 14, 16}
C. {6, 7, 8, 9, 10, 11, 12, 13, 14}
D. {6, 7, 9, 9, 9, 12, 13, 14, 14}
A data set which could be represented by the boxplot shown include the following: A. {6, 6, 8, 8, 9, 12, 13, 13, 14}.
What is a box-and-whisker plot?In Mathematics, a box plot is sometimes referred to as box-and-whisker plot and it can be defined as a type of chart that can be used to graphically or visually represent the five-number summary of a data set with respect to locality, skewness, and spread.
Based on the information provided above, the five-number summary for the given data set include the following:
Minimum = 6First quartile = 7.Median = 9.Third quartile = 13.Maximum = 14.For the median, we have:
Median = 6, 6, 8, 8, 9, 12, 13, 13, 14
Median = 9.
In conclusion, we can logically deduce that the median of the given data set is equal to 9 while the first quartile is 7 and the third quartile is 13.
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What is the value of ƒ(g(3)) when ƒ(x) = x³ + 5x² − 2x − 1 and g(x) = x² –
- -
- 4?
The value of the function ƒ(g(3)) is 239, when ƒ(x) = x³ + 5x² − 2x − 1 and g(x) = x² – 4.
What is function?A function is an equation with just one solution for every value of y in the equation. A function pairs each input of a particular type with exactly one output.
Instead of y, it is typical to name functions f(x) or g(x). f(2) instructs us to calculate the value of our function when x is equal to 2.
We have given to find ƒ(g(3))
when ƒ(x) = x³ + 5x² − 2x − 1
and g(x) = x² – 4
When g(3) = (3)² – 4
= 9 - 4
= 5
For
ƒ(g(3)) = (5)³ + 5(5)² − 2(5) − 1
= 125 + 125 - 10 - 1
= 239
Thus, the value of the function ƒ(g(3)) is 239, when ƒ(x) = x³ + 5x² − 2x − 1 and g(x) = x² – 4.
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For what values of k is the quadratic equation 9x2?.
The possible values of k for the quadratic equation 9x² - 5kx + 1 = 0 has equal roots are 6/5 and -6/5.
The standard form of an quadratic equation is, ax² + bx + c = 0, a ≠ 0 and a,b,c --> constants. The quadratic formula for solution of above equation is, x = ( - b ±√b² - 4ac)/2a , where Discriminate, D is equals to b² - 4ac . We have an quadratic equation, 9x² - 5kx + 1 = 0 --(*)
Step 1 : Determining the discriminant of the quadratic equation : After comparing the equation (*) with standard one , a = 9 , b = - 5k and c = k . So, discriminate formula , D = b² - 4ac
=> D = (- 5k)² - 4×9×1
=> D = 25 k² - 36
Step 2: Determining the values of k : We have equation (*) has equal roots then according to the nature of the roots of an quadratic equation When the value of discriminant, D = 0, then the quadratic equation has real and equal roots.
So, 25 k²- 36 = 0
=> 25 k² = 36
=> k² = 36/25
=> k = ±√36/25
=> k = ± 6/5
Hence, the values of k are ± 6/5.
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Complete question:
For what values of k is the quadratic equation 9x² - 5kx + k = 0, has equal roots?
find (gof)(x) f={(1,2)(3,3)(2,4)(41} g={(1,3)(3,4)(2,2)(4,3)
Answer: g o f = {(2,2), (3,4), (4,3), (1,3)}
Step-by-step explanation: First we'll find f(x):-
f(1) = 2
f(3) =3
f(2) =4
f(4) =1
Now we'll find g(x):-
g(2) = 2
g(3) = 4
g(4) = 3
g(1) = 3
Therefore, gof(x) = {(2,2),(3,4),(4,3),(1,3)}
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(gof)(x) is a function that takes the input x and returns 3 if x = 1, 2, or 4, and 4 if x = 3.
To find the composite function (gof)(x), we first apply the function g to the input x, then apply the function f to the result.
For example, if we want to find (gof)(2), we first find g(2) = 2, then find f(2) = 4, so (gof)(2) = f(g(2)) = f(2) = 4.
So to find (gof)(x) we have to substitute the value of x in function g, then the output of function g in function f.
For the given set of functions f and g, the composite function (gof)(x) is:
(gof)(1) = f(g(1)) = f(3) = 3
(gof)(2) = f(g(2)) = f(2) = 4
(gof)(3) = f(g(3)) = f(4) = 3
(gof)(4) = f(g(4)) = f(3) = 3
So (gof)(x) is a function that takes the input x and returns 3 if x = 1, 2, or 4, and 4 if x = 3.
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a+b=b-a
what are some numbers to make this equation true?
Answer:
b =0nand a =0 simple beacaes3 0-0=0and 0+0=0
Carly tried to solve an equation step by step.
−
4
(
7
j
+
2
)
=
10
7
j
+
2
=
−
40
Step
1
7
j
=
−
42
Step
2
j
=
−
6
Step
3
−4(7j+2)
7j+2
7j
j
=10
=−40
=−42
=−6
Step 1
Step 2
Step 3
Subtract 33 1/3% of 36 from 50% of 88.
Add explanation.
The value of the expression is 32.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
50% of 88 - 33(1/3)% of 36
This can be written as,
= 50/100 x 88 - (100/3)/100 x 36
= 44 - 12
= 32
Thus,
The value is 32.
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What is range and X range?.
The range of a set of numbers is the difference between the maximum and minimum values in the set. X range is a type of range chart used to identify patterns in data points over a period of time.
The Range of a dataset is determined by subtracting the smallest value from the largest value in that dataset, providing an indication of the total spread of the data points. Range is a useful metric for understanding the variability of data points and for comparing different datasets.
X Range is a type of range chart used to identify patterns in data points over a period of time. It is a graphical representation of the range of data points and can help to identify trends and seasonal patterns. X Range charts are particularly useful for understanding how data points fluctuate over time, and can be used to identify any outliers in the data that may require further investigation.
X Range charts can be used to identify any clusters of data points, and to compare different data sets. X Range charts are also useful for understanding the overall volatility of a dataset and for making predictions about future data points.
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For a project in his Geometry class, Jevonte uses a mirror on the ground to measure
the height of his school's flagpole. He walks a distance of 10.85 meters from the
flagpole, then places a mirror on flat on the ground, marked with an X at the center.
He then steps 1.15 meters to the other side of the mirror, until he can see the top of
the flagpole clearly marked in the X. His partner measures the distance from his
to the ground to be 1.65 meters. How tall is the flagpole? Round your answer to the
eyes
nearest hundredth of a meter.
1.65 m
1.15 m
(Diagram is not to scale.)
10.85 m-
Using the formula for angle of depression if the mirror is at a distance of 10.85 meters from the flagpole, then the height of the flagpole is 15.56 meters.
What is angle of depression?
An angle formed between a horizontal line and the line connecting an object and the observer's eye is referred to as the angle of depression. Two variables, namely height and distance, affect this angle.
The height of the school's flagpole = h
The distance from flagpole to mirror = 10.85 m
The distance from mirror to other side = 1.15 m
The height of Jevonte eyes' to the ground = 1.65 m
Let the angle of depression from Jevonte's point of view be represented by θ. Then apply the required trigonometric function -
tan θ = opposite / adjacent
tan θ = 1.65/1.15
tan θ = 1.4347
θ = tan^-1 (1.4347)
θ = 55.12°
For the given mirror, the angle of incidence is equal to that of reflection. Then apply the required trigonometric function -
tan θ = opposite / adjacent
tan 55.12° = h/10.85
1.4347 = h/10.85
h = 1.4347 × 10.85
h = 15.56
Therefore, the height value is obtained as 15.56 m.
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A bracelet has two colors of beads. The ratio of green beads to blue beads is 2:7. There are 18 green beads. How many beads are there in total?
Answer:
81 Bead in total
Ratio: 18:63
Step-by-step explanation:
2*9 = 18
7*9 = 63
Is the inverse of a function always a function example?.
Every function has an inverse, but not every inverse will be a function.
A function takes a starting value, performs some operation on this value, and creates an output answer.
The inverse function takes the output answer, performs some operation on it, and arrives back at the original function's starting value.
An inverse relation is the set of ordered pairs obtained by interchanging the first and second elements of each pair in the original function.
A function is a one-to-one function if and only if each second element corresponds to one and only one first element.
Example:
consider the inverse of the function an f(x)=2x-4.
y=2x-4
x=y-4
x+4=y
f⁻¹(y)=x+4
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What is the nature of roots of quadratic equation x² 5x 14 0?.
The nature of roots of the equation x² + 5x + 14 = 0 are of the form x = (-5 ± √(-31))/2, which are complex numbers and not real.
A quadratic equation is an equation of the form ax² + bx + c = 0, where a, b, and c are constants, and x is the variable. The nature of the roots of a quadratic equation can be determined by the discriminant, which is the value of b² - 4ac.
In this case, the quadratic equation is x² + 5x + 14 = 0. To find the nature of the roots, we need to find the discriminant, which is b² - 4ac:
Discriminant = 5² - 4 * 1 * 14 = 25 - 56 = -31
The discriminant can be used to determine the nature of the roots:
If the discriminant is greater than 0, the roots are real and distinct.
If the discriminant is equal to 0, the roots are real and identical (i.e., the equation has only one root).
If the discriminant is less than 0, the roots are complex and not real numbers.
In this case, the discriminant is negative, so the roots of the equation x² + 5x + 14 = 0 are complex. The roots can be found by factoring the equation into (x + a + bi)(x + a - bi), where a and b are real numbers, and i is the imaginary unit (i² = -1).
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What is cos concept?.
For Trigonometric ratios, the values of sin, cos, and tan are defined by the ratio of sides of a right-angled triangle. The cosine of an acute angle in a right triangle is calculated using trigonometry.
By dividing the measurements of the side that it is adjacent to by the hypotenuse of the triangle.
The neighboring base-to-hypotenuse ratio is known as the cos function. It aids in determining the triangle's side lengths regardless of the provided angle.
If the angle between the neighboring side and the hypotenuse of a right triangle is, we can write this using the cos function.
In a right-angled triangle, We calculate their values by the ratio
Cos = Base of the right-angled triangle/ Hypotenuse of the right-angled triangle.
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What is the length of the side opposite the angle θ?.
A right triangle's hypotenuse is its longest side, its "opposite" side is the one that faces a certain angle, and its "adjacent" side is the one that faces the angle in question.
A right triangle's hypotenuse is always the side that faces away from the right angle. It is the right triangle's longest side. The adjacent and opposing sides are the other two sides. These sides have labels that relate to angles. From a particular angle, the other side is across.
The non-hypotenuse side next to a specific angle is referred to as the neighboring side. Sine, cosine, and tangent are three trigonometric functions that are defined by the terms hypotenuse, opposite, and adjacent.
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The complete question is:
What is the length of the side opposite the right angle?
Your rectangular claroom rug ha an area of 110. 5 quare feet. What i the perimeter of the rug?
The perimeter of the rug that has 110.5 square feet area is 43 ft
What is the area?Area is the measure of the space occupied by a body bounded by an environment called perimeter, the same is expressed in units of squared side. Example: ft^2, m^2
To solve this geometry exercise the equation and procedure we will use is:
P = (2*L) + (2*W)A = L * WWhere:
P= perimeterL= lengthW= widthA = areaInformation about the problem:
L = ?P = ?W = 13 ft (check the image attached)A = 110.5 ft^2Clearing the width from the rectangle area formula, we get:
A = L * W
W = A / L
W = 110.5 ft^2 / 13 ft
W = 8.5 ft
With the width calculated we get the perimeter of the rectangular classroom:
P = (2*L) + (2*W)
P = (2*13 ft) + (2*8.5 ft)
P = 26 ft + 17 ft
P = 43 ft
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In a certain tate about 3/5 of regitred voter particated in 2016 election what fraction of regitred voter did not
The fraction of registered voter that did not participate was 2/5
What is a fraction?Is a number that expresses the portion of some number over a total. The number that expresses the portion is known as the numerator and the number that expresses the total is known as the denominator.
To solve this exercise we have to perform a mathematical operation with fractions:
Information about the problem:
Total = 1Registered voter participated= 3/5No. did not participate = ?Calculating the fraction of the registered voter that did not vote we get:
No. did not participate = Total - Registered voter participated
No. did not participate = 1 - 3/5
No. did not participate = (5 - 3) /5
No. did not participate = 2/5
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What is 30% of 85  URGENT
Answer: 30 percent of 85 is 25.5
Answer:
the answer is 25.5
Step-by-step explanation:
this is because 85 in our question is equivalent to thus you just need to cross multiply
The lateral height of a cone is 6 inches and the area of the base of the cone is 49π in². It requires 1.5 minutes to paint the cone. The area of the base is doubled. How long will it take to paint this cone if it can be painted at the same rate? Use π≈3.14. Enter your answer, rounded to the nearest tenth, in the box. min
It would take 4.0 minutes to paint the cone.
solving for how long will it take to paint this cone if it can be painted at the same rate:The original radius of the cone is √(49/π) inches
= √(49/3.14)
= √(15.7)
= 3.5 inches.
The new base area is 2 * 49π
= 98π square inches.
The new radius is √(98/π)
= √(98/3.14)
= √(31.4)
= 5.6 inches.
The new lateral surface area is π * 5.6 * 6
= 33.6 * π square inches.
The new total surface area is 33.6π + 98π
= 131.6π square inches.
Since it takes 1.5 minutes to paint the original cone, it would take
1.5 * (131.6/33.6) = 4.0 minutes to paint the new cone.
Hence, it would take 4.0 minutes to paint the cone.
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Need help with this question please
Ps they all yes and no
Yes, the equation 9x^2 = 1 has zeroes at ±1/3. The solution is obtained by solving the algebraic equation.
What is algebraic equation?
The term "algebraic expression" refers to a mathematical expression that contains variables, constants, and algebraic operations (addition, subtraction, etc.). The expression must have an equals to sign in order to satisfy the algebraic equation.
We are given 9x^2 = 1
In order to find its roots, we need to find the value of x which are the zeroes for the equation.
So,
⇒9x^2 = 1
⇒x^2 = 1/9
⇒x = √1/9
⇒x = ±1/3
We are given 3x-1 = 0
So,
⇒ 3x = 1
⇒ x = 1/3
So, the given equation does not have its zeroes at ±1/3.
Hence, the equation 9x^2 = 1 has zeroes at ±1/3.
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The third part of the question is not complete as the complete equation is not visible.
The ratio of markers to crayons in an artist's collection is 4:3. Which of the following ratios is equivalent to 4:3?
Answer:
A
Step-by-step explanation:make brainiest
Jayden invests $2,644.93 in a retirement account with an interest rate of 8% compounded annually. What will the account balance be after 5 years?
The balance in the account of Jayden after 5 years will be $3,886.27.
What is compound interest?A loan or deposit's interest is computed using the starting principle and the interest payments from the ago decade as compound interest.
We know that the compound interest is given as
A = P(1 + r)ⁿ
Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.
Jayden invests $2,644.93 in a retirement account with an interest rate of 8% compounded annually. Then the amount after 5 years is calculated as,
A = $2,644.93 x (1 + 0.08)⁵
A = $2,644.93 x (1.08)⁵
A = $2,644.93 x 1.469
A = $3,886.27
The balance in the account of Jayden after 5 years will be $3,886.27.
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FV of $600 each 6 month for 4 year at a nominal rate of 8%, compounded emiannually. Do not round intermediate calculation. Round your anwer to the nearet cent
The future value of the $600 invested semi-annually at 8% nominal interest rate for 4 years is $1369.44 rounded to the nearest cent.
The formula to use in this case is FV = PV(1 + r/n)^nt, where FV is the future value, PV is the present value, r is the nominal interest rate, n is the number of times the interest is compounded per year, and t is the number of years.
Given the information in the problem, we know that:
PV = $600 (the present value)
r = 0.08 (the nominal interest rate as a decimal)
n = 2 (the interest is compounded semi-annually)
t = 4 (the number of years)
Plugging these values into the formula, we get:
FV = $600(1 + 0.08/2)^(2*4)
To solve for FV, we need to calculate (1 + 0.08/2)^(2*4)
= (1.04)^8
=2.2824
FV = $600*2.2824
FV = $1369.44
Thus, the future value of the $600 invested semi-annually at 8% nominal interest rate for 4 years is $1369.44 rounded to the nearest cent.
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PV = $600 (the present value)
r = 0.08 (the nominal interest rate as a decimal)
n = 2 (the interest is compounded semi-annually)
t = 4 (the number of years)
Plugging these values into the formula, we get:
FV = $600(1 + 0.08/2)^(2*4)
To solve for FV, we need to calculate (1 + 0.08/2)^(2*4)
= (1.04)^8
=2.2824
FV = $600*2.2824
FV = $1369.44
Susan has $60 in a savings account. The interest rate is 10% per year and it's not compounded. How much interest will she earn in 4 years?
Susan will earn $24 of interest in 4 years.
What is the simple interest?Simple interest is the borrowing amount added only to the principal amount.
The formula to calculate the simple interest is;
S.I. = P x T x R / 100,
Where S.I. is simple interest, P is principal amount, T is time period and R is interest rate in a year.
Given:
Susan has $60 in a savings account.
The interest rate is 10% per year, and it's not compounded.
In 4 years,
S.I. = P x T x R / 100
S.I. = 60 x 4 x 10 / 100
S.I. = $24
The earned amount in 4 years is $74.
Therefore, the earned amount in 4 years is $74.
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Brian paid a total of $46.44 for a jacket at a department store. The jacket was on sale for 20% off the regular price, and he used a coupon for an additional $5.00 off of the discounted price. Brian had to pay 8% sales tax on the cost of the jacket after any discounts and coupons.
Select the equation where p represents the original price of the jacket and the solution of that equation.
A.
1.08(0.8p - 5) = 46.44
The original price of the jacket was $60.00.
B.
1.08(0.8(p - 5)) = 46.44
The original price of the jacket was $60.00.
C.
1.08(0.8(p - 5)) = 46.44
The original price of the jacket was $58.75.
D.
1.08(0.8p - 5) = 46.44
The original price of the jacket was $58.75.
The equation, where p represents the jacket's original price, and the equation's solution is A. 1.08(0.8p - 5) = 46.44. The original price of the jacket was $60.00.
What is an equation?An equation is a mathematical statement showing that two mathematical expressions are equivalent or equal.
Equations are depicted using the equation symbol (=).
The total cost paid by Brian = $46.44
The discount on offer = 20%
Amount after the initial discount = 0.8p (1 - 20%)
Additional coupon = $5
Amount after the additional coupon = 0.8p - 5
Total discount = 20% + $5
Sales tax = 8%
Amount paid after the sales tax = (0.8p - 5)(1.08)
Original price = p
p = $60
1.08(0.8p - 5) = 46.44
1.08(0.8 x 60 - 5) = 46.44
1.08(43) = 46.44
46.44 = 46.44
Thus, Option A is correct.
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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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Which equation is true?
A.
3
4
=
9
16
B.
6
8
=
4
3
C.
3
5
=
8
10
D.
12
16
=
36
48
Answer: a and c
Step-by-step explanation:
