Answer: It is not always true, so it's not an identity
========================================================
Explanation:
Let's try replacing each 'a' with 1, and each b with 2. Feel free to pick two of your favorite nonzero numbers.
So we'll plug in a = 1 and b = 2
[tex](a+b)^2 = a^2+b^2\\\\(1+2)^2 = 1^2+2^2\\\\(3)^2 = 1^2+2^2\\\\9 = 1+4\\\\9 = 5\\\\[/tex]
The last equation is a false statement. This means the first equation is also false for a = 1 and b = 2.
This is one counter-example to disprove that (a+b)² = a² + b² is true in general.
Therefore, the equation is not an identity.
--------------
What is an identity however is this
(a+b)² = a² + 2ab + b²
If you were to plug in a = 1 and b = 2, then you'd get 9 on each side. This is one example to help partially confirm it's an identity.
More rigorous proof is in the form of using the FOIL method, the distributive property, or the box method.
Find the tenth term of each arithmetic sequence. 2,8,14,20, ...........
The 10th term of the given arithmetic sequence 2,8,14,20, ........... is ( a₁₀ = 56.)
Describe the AP arithmetic progression series?The difference between two mathematical orders is a fixed value in Arithmetic Progression (AP). Arithmetic Sequence is another term for it.
We'd come across a few key words in AP which have been classified as:
The first term (a)Common difference (d)Term nth (an)The total of first n terms (Sn)The AP can also be viewed in terms of common differences, as illustrated below.
The following is the process for evaluating an AP's n-th term: an = a + (n − 1) × dThe so these is the arithmetic progression sum: Sn = n/2[2a + (n − 1) × d].Common difference 'd' of an AP: d = a2 - a1 = a3 - a2 = a4 - a3 = ...... = an - an-1.Now, the sequence given in the question is; 2,8,14,20, ...........
Define the first term as 'a₁' = 2.
Define 'a₂' = 8 is the second term.
Define the third term as 'a₃' = 14.
Evaluate the common difference;
d = a₂ - a₁
Put the values in the obtained equation;
d = 8 - 2 = 6
Now, to evaluate the value of the 10th term imply the formula of nth term.
an = a + (n − 1) × d , n = total number of terms = 10.
Substitute all the values;
a₁₀ = 2 + (10 - 1) × 6
a₁₀ = 2 + 9 × 6
a₁₀ = 2 + 54
a₁₀ = 56.
Therefore, the value of the 10th term is found as a₁₀ = 56.
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If P(-3, 6) is tranlated 4 units up and 8 units down what are the coordinates of P?????
The coordinates of P' is (-3,2).
Given that P(-3, 6) is translated 4 units up and 8 units down.
The translation of a point involves moving it a certain distance horizontally and/or vertically. You can find the address of a translated point like this:
To translate a point to the right, add the translation to the x-value.To translate a point to the left, subtract the translation from the x value.To translate a point up, add the translation to the y-value.To translate a point down, subtract the translation from the y-value.The point P(-3,6) is shown in blue above.
Travel 4 unit to the up and 8 units down from point P, and you arrive at point P'(-3,2), shown in red.
Hence, the coordinates of P' when P(-3, 6) is translated 4 units up and 8 units down is P'(-3,2).
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Rewrite x4y2-6x3y3 using a common factor
Answer:
[tex]x^4y^2-6x^3y^3 = x^3y^2(x - 6y)[/tex]
Step-by-step explanation:
to pick out common factors, you have to find the highest common denominator. We start by listing units and variables:
we can divide the x^4y^2 by up to x^4 and up to y^2, cannot divide by non-variable numbers
we can divide 6x^3y^3 by up to x^3 and up to y^3, and by 6 if we needed to.
This means that for units, we're not dividing (because we can't simplify x^4y^2 dividing by a bare number.
For x, we can divide both by x^3, because we can divide both by x^3, but cannot divide 6x^3y^3 by x^4 or more.
For y, we can divide both by y^2, because we can divide both by y^2, but cannot divide x^4y^2 by x^3 or more.
We take the x^3y^2 and bring it in front of the brackets.
Disclaimer: when I say "cannot divide" I mean "cannot divide without introducing fractions or negative exponents".
t is a positive whole number.
The expression 2f² + 5t + 2 can never have a value that is a prime number.
Can someone PLEASE explain why.
Since the given expression can be factored in the form (2t+1) and (t+2) so 2t² + 5t + 2 cannot be a prime number.
A whole number greater than 1 that has no factor other than 1 and the number itself is called a prime number.
Some examples of prime numbers are 3,11,19 ... all these numbers can only be divided by 1 or the number itself so they are called prime.
In the given expression 2t² + 5t + 2 , it is said that t is positive whole number. So if t is a positive whole number then the expression can be written as another positive whole number.
Now the expression 2t² + 5t + 2 can be factored into two smaller factors.
2t² + 5t + 2
= 2t² + 4t + t + 2
= 2t (t + 2 )+1 (t+2)
= (t+2) (2t+1)
If t is a positive whole number then t+2 is a whole number and 2t+1 is another positive whole number.
Hence these two numbers are factors of 2t² + 5t + 2 . But a prime number does not have any factors.
So 2t² + 5t + 2 is not a prime number.
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If x is 6, then 7x =
Answer:
42
Hope this helps :)
Step-by-step explanation:
1. Substitute x with 6 since x is 6. When a variable is next to a number multiply them. Also, multiply when number is next to parenthesis.
7(6)
2. Solve by multiplying.
7(6) = 42
Check:
42 ÷ 7 = 6 ✓
Find the solution for 4a+3=7-(5-8a)
Answer:
[tex]4a+3=7-5+8a\\4a-8a=7-5-3\\-4a=-1\\\frac{-4a}{-4} =\frac{-1}{-4} \\a=\frac{1}{4}[/tex]
Name two angles that form a linear pair
Answer: [tex]\angle APC[/tex] and [tex]\angle CPB[/tex]
Step-by-step explanation:
See attached image.
LA and ZB are vertical angles. If mA = (6x - 26)° and m/B = (5x + 6)°,
then find the measure of ZB.
Answer:
∠ B = 166°
Step-by-step explanation:
since ∠ A and ∠ B are vertical angles then they are congruent, that is
∠ A = ∠ B
6x - 26 = 5x + 6 ( subtract 5x from both sides )
x - 26 = 6 ( add 26 to both sides )
x = 32
Then
∠ B = 5x + 6 = 5(32) + 6 = 160 + 6 = 166°
Beth ann wants to make brownies for 5 third grade teachers 6 brownies for each teacher if one box makes 7 brownies how many boxes should she buy to have enough
can 4 x 2/3 be 2/1 ?
Answer:
noStep-by-step explanation:
can 4 x 2/3 be 2/1 ?
2/1 = 2
solve with an equation
4 * 2/3 = 2
8/3 = 2
or
2.66666666667 = 2
the equation is false, so your answer is no
Which of the following best describes the ordered pairs listed below? (-3, 2), (3, -10), (5, -14), (10, -24) A. both a relation and a function B. relation only C. function only D. neither a relation nor a function
Since each input is mapped to only one output, the best description of the ordered pairs is given by:
A. both a relation and a function.
When does a relation represents a function?A relation represents a function if each value of the input is mapped to only one value of the output.
For a point in the format (x,y), we have that:
x is the input.y is the output.The meaning is that the input x is mapped to the output y.For this problem, the points are given as follows:
(-3, 2), (3, -10), (5, -14), (10, -24)
Each input is mapped to only one input, that is, there are no repeated values of x, hence the best description of the ordered pairs is given by:
A. both a relation and a function.
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Giving brainlyist HELPP Use the equation one fourth plus s equals 18 over 20 to answer the questions.
Part A: Determine two numbers that the solution to the equation is between. Support your answer using the correct vocabulary. (2 points)
Part B: Solve for the variable. Show your work. (2 points)
Answer:
1/4+s=18/20
Step-by-step explanation:
The answer is between 0 and 1
18/20 = 0.9
1/4+s=0.9
0.9-0.25=0.65
s=0.65
Convert 459 L to mL
O 0.459 mL
O 459, 100 mL
O 4.59 x 105 mL
O 0.000439 mL
Answer:
0.456
Step-by-step explanation:
456÷1000
=0.456ml
What is the common ratio in the geometric sequence 9/2, 3,2, 4/3, . . . . . ?
(F) 3/2 (G) 9/2 (H) 2/3 (I) 27/2
The correct answer to this problem is an option (H) 2/3.
A sequence is a sequence of things (usually numbers) in order 3, 5, 6, 7, 8, and so on. A geometric sequence is known as a particular type of sequence ]. A sequence multiplies each term (except the first) by a constant to get the next term in the sequence. So, from the information, we can conclude that to get the next term in the geometric sequence, we need to multiply that with a specific term (known as the common ratio), and to find the last term in the sequence, we multiply that term by the same standard ratio. Just split it.
Given GP is 9/2,3,2,4/3
Common ratio = Second number / first number
= 3/ (9/2) =2/3
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I need help asap!!!!
For given polynomial 1/2a^4 + 3a³ + a
1) There is no coefficient for the third term.
2) The constant term is 0.
In this question, we have been given a polynomial 1/2a^4 + 3a³ + a
We need to determine the coefficient of the third term and the constant term.
we can rewrite given polynomial as 1/2a^4 + 3a³ + 0a² + a + 0
The general form of the fourth degree polynomial is:
a_0 + a_1x + a_2x^2 + a_3x^3 + a_4x^4
where a_0 is the constant term
Comparing given polynomial with above general form.
a_0 = 0
a_1 = 1
a_2 = 0
a_3 = 3
a_4 = 1/2
So, the constant term is a_ 0 = 0
And there is no coefficient for the third term.
Therefore, for given polynomial 1/2a^4 + 3a³ + a
1) There is no coefficient for the third term.
2) The constant term is 0.
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solve
6(x+4)=30 ………………
Answer:
Step-by-step explanation:
6(x+4)=30
So wee need to find out what multiplied by 6 =30
30/6=5
Now wee need to figure out what plus 4 equals 5
5-4=1
1+4=5
6(1+4)=30
So x=1
Hope this helps!^^
Solve each system by elimination.
3a+4b = 9 , -3a - 2b = -3
Answer: 1. D.0.5, 2.5
2. B 10,-1
3. B.-6,-6
4. C 7,5
5. D. Infinite number of solutions
6. A. -1,3
7. C. -1,-0.5
8. B. Seven $1....eight $5...
9. D. 200 muffins
10. A. 2y=1.5x-2 D.-4y+3x=-2
Step-by-step explanation:
i did the quiz, Gl, and thx!
what is the equation for the standard form of the line that has an x-intercept of 3 and a y-intercept of 5
5x+3y=15 is the equation for the standard form of the line .
What is in slope-intercept form?
Given the slope of the line and the intercept it forms with the y-axis, one of the mathematical forms used to derive the equation of a straight line is called the slope intercept form. Y = mx + b, where m is the slope of the straight line and b is the y-intercept, is the slope intercept form.We are given two coordinates (3,0) (0,5)
Start by finding slope
y2-y1/x2-x1= 5-0/0-3= -5/3 this is your slope m.
y=mx+c
y= -5/3x+c (but remember standard line is ax+by=c) so we have to switch sides
5/3x + y=5 (remember standard form has no fraction so multiply by 3 on all sides)
5x+3y=15
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Calculate the value of x.
Give your answer as an integer or as a fraction in its simplest form.
What is the sum? Enter your answer as a mixed number in the simplest form.
HELLPPPPPPPPPPP
1/3+ 5 3/4
Quadrilateral A B C D is circumscribed about \odot H . Find m .
The value of m is 9 .
What is a Quadrilateral:
A quadrilateral is a closed shape and a type of polygon that has four sides, four vertices and four angles. It is formed by joining four non-collinear points. The sum of interior angles of quadrilaterals is always equal to 360 degrees.
What is Circumscribed:
Circumscribed meaning is, a shape is restricted within any other shape. There is no circumvent for the inside figure to pass the outer figure. When we draw a figure around another figure, in such a way, that the outer figure which is surrounding the inside figure touches all its vertices, but doesn’t cross it. The outer figure touches the maximum points of the inside figure without crossing it. These geometrical shapes could be a circle, a square, a triangle, a rectangle or a quadrilateral.
Now,
we know length of tangent from a point to a circle are equal
therefore,
AS=AP,,BP=BQ,CQ=CR,DR=DS
x=BC=BQ+QC=BP+RC=BP+CD−DR=BP+CD−DS
⇒x=5+7−3=9
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43.95 divided by 16.2
Answer:
2.712
Step-by-step explanation:
2.712
if rectangle a is a 2 by 4 would a 4 by 8 be a scale factor
The required scale factor for the small rectangle is 8.
Given that,
Rectangle a is a 2 by 4 would a be 4 by 8,
To determine the scale factor,
The scale factor is defined as the ratio of modified change in dimensions to original dimensions
Area of the rectangle = product of dimensions = length * width
Area of the former rectangle = 2 * 4
= 8
Area of the later rectangle = 4 * 8 = 32
Scale factor = area of the later rectangle/area of the former rectangle
= 32 / 8
= 8
Thus, the required scale factor for the small rectangle is 8.
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The domain is 0, 1, 2, 3, 4, and 5. What is the range? Select all that apply.
Considering the numeric values and the range concept, we have that:
The range of the function is given by: {f(0), f(1), f(2), f(3), f(4), f(5)}.
How to find the numeric value of a function/expression?To find the numeric value of a function, we replace each instance of the variable by the desired value.
The range of a function is the set that contains all possible output values for the function. These outputs are the numeric values for the domain of the function, which compose the input values.
For this problem, we have that:
The domain is composed by: 0, 1, 2, 3, 4 and 5.The outputs for the function will be given by: f(0), f(1), f(2), f(3), f(4), f(5).Hence:
The range of the function is given by: {f(0), f(1), f(2), f(3), f(4), f(5)}.
The function is not given, hence this problem was solved speaking in general terms. In your problem, you will mark the numeric values of the function given.
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Find the distance AB between the points A(8,2) and B(3,9) round the answer to nearest tenth
The distance between the points is 8.6 units
How to determine the distance between the points?The points are given as:
(8, 2) and (3,9).
The distance is calculated using
d = √(x2 - x1)^2 + (y2 - y1)^2
This gives
d = √(8 -3)^2 + (2 - 9)^2
Evaluate
d = 8.6
Hence, the distance between the points is 8.6 units
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Fill in the blank question.
Find the values of x and y.
(2x+25)+(3x-10)=180
Answer:
x=33
Step-by-step explanation:
Simplifying 2x + 25 + 3x + -10 = 180 Reorder the terms: 25 + -10 + 2x + 3x = 180 Combine like terms: 25 + -10 = 15 15 + 2x + 3x = 180 Combine like terms: 2x + 3x = 5x 15 + 5x = 180 Solving 15 + 5x = 180 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + 5x = 180 + -15 Combine like terms: 15 + -15 = 0 0 + 5x = 180 + -15 5x = 180 + -15 Combine like terms: 180 + -15 = 165 5x = 165 Divide each side by '5'. x = 33 Simplifying x = 33
Answer:
x=33
Step-by-step explanation:
(2x+25)+(3x-10)=180
2x+25+3x-10=180
2x+3x+25-10=180
5x+15=180
5x=180-15
5x=165
5x/5=165/5
therefore x=33
Hey i am a student of Grade 10 . due to online classes i havent studied for 2 years and i have no idea about maths. what order do i got to recap everything . some one please help! (CBSE)
Answer:
Khan academy could really help it has videos and lessons so start there.
Step-by-step explanation:
The height in inches, h, of s sheets of paper can be described by the equation h=0.004s. What does the 0.004 mean in this situation?
The "0.004" is the constant of proportionality, in this particular case, that value represents the height if a single sheet of paper.
What does the 0.004 mean in this situation?We know that the height, in inches, of s sheets of paper can be described by the equation:
h = 0.004*s
So, if we have a single sheet, the height is:
h = 0.004*1 = 0.004
The height of a single sheet if 0.004 inches.
If instead we have two, then s = 2, we will have:
h = 0.004*2 = 0.008
The height is 0.008 inches.
So, the given equation:
h = 0.004*s
Is a proportional relation.
The "0.004" is the constant of proportionality, in this particular case, that value represents the height if a single sheet of paper.
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who needs special prayer
Answer: me man
Step-by-step explanation:
holy god
Y=44 when x=a^3
Y is inversely proportional to the cube of x
Show us that y=5.5 when x=2a
Answer:
0.283258167471352[tex]\sqrt[3]{k}[/tex]
Step-by-step explanation:
Based on the given conditions, formulate:
Write the equation of the function:
Substitute and calculate:
