Answers
Factor x^8+x^4+1
Rewrite the middle term.
X^8+2x^4.1-x^4+1
Rearrange terms.
x^8+2x^4.1+1 -x^4
Factor first three terms by perfect square rule
(X^4+1)^2-x^4
Rewrite
x^4
as
(X^2)^2
(X^4+1)-(x^2)^2
Since both terms are perfect squares, factor using the difference of squares formula,
a^2-b^2=(a+b)(a-b)
where
a=x^4+1
and
b=x^2
Simplify.
(X^4+1+x^2)(x^4+1-x^2)
Step-by-step explanation:
Have a great day
[tex] {x}^{8} + {x}^{4} + 1[/tex]
to find:factorise
solution:[tex] {x}^{8} + {x}^{4} + 1[/tex]
[tex] = x ^{8} + 2 {x}^{4} + 1 - {x}^{4} [/tex]
[tex] = ( {x}^{4} + 1 {)}^{2} - ( {x}^{2} {)}^{2} [/tex]
[tex] = ({x}^{4 } + 1 + {x}^{2}) ( {x}^{4} + 1 - {x}^{2} )[/tex]
[tex] = ( {x}^{4} + 2 {x}^{2} + 1 - {x}^{2} )( {x}^{4} - {x}^{2} + 1)[/tex]
[tex] = (( {x}^{2} + 1 {)}^{2} - {x}^{2} )( {x}^{4} - {x}^{2} + 1)[/tex]
[tex] = ( {x}^{2} + 1 + x)( {x}^{2} + 1 - x)[/tex]
[tex] = ( {x}^{4} - {x}^{2} + 1)[/tex]
Related Questions
Is the length of the hypotenuse of a right triangle with legs that measure 5 cm and 6 cm a rational number or an irrational number? Justify your answer.
Answers
Answer:
irrational
Step-by-step explanation:
Use the Pythagorean theorem.
5² + 6² = c²
25 + 36 = c²
c² = 61
7² = 49
6² = 64
61 is between 7² and 8², so it is not rational.
Allie identifies the coordinates of point D as (3, 7). Explain her error and explain how to correctly identify the ordered pair. hurry
Answers
Here Allie mistook the x and y axis completely oppositely.
→ First should be the x axis and then the y axis, (x, y)
Answer:
Step-by-step explanation:
Coordinates of a point are usually represented by (x, y) where x describes the horizontal distance from the y-axis and y describes the vertical distance from the x-axis.
Point A
4 units from the y-axis ⇒ x = 4
6 units from the x-axis ⇒ y = 6
A = (4, 6)
Point B
2 units from the y-axis ⇒ x = 2
9 units from the x-axis ⇒ y = 9
B = (2, 9)
Point C
0 units from the y-axis ⇒ x = 0
4 units from the x-axis ⇒ y = 4
C = (0, 4)
Point D
Allie has mixed up the x and y coordinates of D.
7 units from the y-axis ⇒ x = 7
3 units from the x-axis ⇒ y = 3
D = (7, 3)
She can choose from 7 pairs of pants, 6 t-shirts, 7 sweaters or hoodies, and 2 pairs of shoes. How many different outfits does Kaylee have to choose from?
Answers
Answer:
So, there are seven choices, etc, so the equation is
7x6x7x2
because there are multiple ways
so, 588
What are the coordinates of point B on AC such as that ratio of AB to BC is 5:1?
Answers
Answer:
Lines can be divided in smaller segments by using ratios
The coordinates of B are:
The given parameters are:
The coordinate of B is calculated using:
So, we have:
Simplify fraction
Hence, the coordinates of B are:
Step-by-step explanation:
An earned run average (ERA) in baseball is the average number of earned runs a pitcher gives up per 9 innings. One year, a professional baseball pitcher had a 3.91 ERA. His ERA was 0.74 points lower the next year. What is the new ERA?
Answers
Applying a subtraction operation, it is found that his new ERA was of 3.17.
What is the relation between his two ERA's, in last year's and this year?ERA is a baseball concept, but understanding of baseball is not relevant to this question.
One year, a professional baseball pitcher had a 3.91 ERA. The next year, it was 0.74 points lower, hence it was given by the subtraction of 3.91 and 0.74, that is:
ERA = 3.91 - 0.74 = 3.17.
His new ERA was of 3.17.
More can be learned about subtraction operations at https://brainly.com/question/2475734
The graph shown below expresses a radical function that can be written in the form f(x)=a(x+k)^1/n +c.what does the graph tell you about the value of a in this function?
Answers
Answer:
a is less than 0
Step-by-step explanation:
The value of a in this function is a is less than 0 .
What is radical function?A radical function contains a radical expression with the independent variable (usually x) in the radicand. Usually radical equations where the radical is a square root is called square root functions. An example of a radical function would be. y=√x.
According to the question
Radical function that can be written in the form
[tex]f(x)=a(x+k)^{1/n} +c.[/tex] ------------------------(1)
By solving this equation we will get value of a and c
differentiating the equation
[tex]f'(x)=\frac{1}{n}* (a(x+k)^{1/n-1})[/tex]
therefore
[tex]((x+k)^{1/n-1}) > 0[/tex]
As graph is decreasing monotonically
[tex]\frac{a}{n} < 0[/tex]
as n will be always n>0 ,
so a < 0
Now taking value of f(x)= 0 in equation (1)
[tex]f(x)=a(x+k)^{1/n} +c[/tex]
[tex]0 =-a(x_{0} + k)^{1/n} +c[/tex] as (a < 0)
[tex]0=-a(k)^{1/n} +c[/tex]
[tex]-c =-a(k)^{1/n}[/tex] multiplying (-1) both side
[tex]c =a(k)^{1/n}[/tex]
i.e
c > 0
Hence, the value of a in this function is a is less than 0 .
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What is the area of the figure?
Answers
=6*2*1/2
=6cm^2
Area of two triangles=6*2=12cm^2
Area of the rectangle=4*11=44cm^2
Total area=44+12=56cm^2
Therefore answer is B
Triangle Congruence, Flowchart Proof (Level1) _ 10th Grade - Int.1 (almost complete)
Answers
Answer:
Step-by-step explanation:
Solve one fourth ÷ 7 = ___. one eighth alt=one twenty fifth one twenty eighth one thirtieth
Answers
Answer:
[tex]\frac{1}{28}[/tex]
__________________________________________________________
SolveWhen doing problems like this where you have to divide fractions by whole numbers, you can try skip counting or multiplying.
So:
[tex]\frac{1/4}{7} = 28[/tex]because it skip counts 28 times.
28 as a fraction is [tex]\frac{28}{1}[/tex], which we have to flip to make [tex]\frac{1}{28}[/tex] as our answer.
__________________________________________________________
Questions?Ask in the comments box.
The points P (4, 1) and Q (-2, 4) are
reflected in line y = 3. Find the co-ordinates
of P', the image of P and Q', the image of
Q.
Answers
Step-by-step explanation:
hope it will help you
thank you
Answer:
Step-by-step explanation:
The line y = 3 is a horizontal line.
In order for us to reflect these two points, we need to draw our horizontal line and graph those points on the coordinate plane. Then you count the number of points that your original coordinates are away from the horizontal line. Once you have got that down, you count the same number on the other side (over line) and then plot and label your new coordinates.*View the attached graph*
Hope this helps!
simplified form of 2460−78+6884
Answers
Answer:
4502
Step-by-step explanation:
6884+78=6962
6962-2460=4502
4/3 of a number is more than 3/4 of its number by 1 . find the number
Answers
4/3 of a number is more than 3/4 of its number by 1 . find the number .
Given : -4/3 of a no. is more than 3/4 of its no. by 1To Find : -We have to find the number .To Assume : -Let the no. be xSo Solution goes from here :According to question 4/3 of a number is equal to :
[tex] \longmapsto \: \frac{4}{3} \times x[/tex]
Which means ,
[tex]\longmapsto \: \frac{4x}{3} [/tex]
According to question 3/4 of a number is equal to :
[tex]\longmapsto \: \frac{3}{4} \times x[/tex]
Which means ,
[tex]\longmapsto \: \frac{3x}{4} [/tex]
Now , forming equation :
As the question says that 4/3 of a number is more than 3/4 of its number by 1 . So :
[tex]\longmapsto \: \frac{4x}{3} = \frac{3x}{4} + 1[/tex]
Now , transposing 3x/4 to left hand side :
[tex]\longmapsto \frac{4x}{3} - \frac{3x}{4} = 1[/tex]
Now , taking L.C.M :
[tex]\longmapsto \: \frac{4(4x) - 3(3x)}{12} = 1[/tex]
Now by calculating :
[tex]\longmapsto \: \frac{16x - 9x}{12} = 1[/tex]
Now Subtracting 16x with 9x and transposing 12 to right hand side :
[tex]\longmapsto \: 7x = 12[/tex]
So ,
[tex]\longmapsto \: \boxed{ \bold{ x = \frac{12}{7} }}[/tex]
Therefore , the number is 12/7 .#[tex] \sf{Keep \: Learning }[/tex]If the expression √⋅√ is written as , what is the value of ?
Answers
Answer:
rhe base a for u
Step-by-step explanation:
kk
If m∠4 = 90°, find the m∠5 and m∠3.
Answers
Answer:
∠5 = 90°
∠3 =90
Step-by-step explanation:
∠4 + ∠5 = 180 {Linear pair}
90 +∠5 = 180
∠5 = 180 - 90
∠5 = 90°
∠3 = ∠4 {Verically opposite angles}
∠3 = 90°
someone I need help with this thank you !!
Answers
Answer:
Question 4) 90 in^3
Question 5) D
Step-by-step explanation:
For question 4 I divided 270 by 1/3 and I got 90 inches^3
For question 5 I mulitplied 1 times 9 times 10 and got 90 inches ^3
A(n) _____ is a tool used to measure or draw angles.
Answers
Which table represents a relation that is not a funtion?
Answers
Answer:
D
Step-by-step explanation:
because in D one input value (3) has 2 different assigned output values (0 and -4).
that violates the definition of a function, where every input value must have exactly 1 assigned output value (but the output values themselves don't have to be different for different input values, so, e.g. A is still a function).
Please answer this question.
Answers
Answer:
B
Step-by-step explanation:
given that x and y vary inversely then the equation relating them is
y = [tex]\frac{k}{x}[/tex] ← k is the constant of variation
to find k use the condition y is 24 when x is 8 , then
24 = [tex]\frac{k}{8}[/tex] ( multiply both sides by 8 to clear the fraction )
192 = k
y = [tex]\frac{192}{x}[/tex] ← equation of variation
when y = 18 , then
18 = [tex]\frac{192}{x}[/tex] ( multiply both sides by x )
18x = 192 ( divide both sides by 18 )
x = [tex]\frac{192}{18}[/tex] = [tex]\frac{32}{3}[/tex]
Answer:
Step-by-step explanation:
Write the inverse variation
y = k/x
Solve for k
y = 24
x = 8
y = k/x Substitute the givens into this equation
24 = k/8 Multiply both sides by 8
8*24 = k
k = 192
Solve for x when y = 18
y = k/x Multiply both sides by x
xy = k Divide by y
x = k/y
x = 192/18
x = 10 2/3 The answer is given as an improper fraction.
x = (10*3 + 2)/3
Answer: x = 32/3
the quotient of 254 and k is 94
Answers
Answer:
k is 23876
Step-by-step explanation:
you have to multiply 254 and 94 by eachothe then that's your answer!
How many cubes with side lengths of 1/2 cm does it take to fill the prism?
Answers
Check the picture below.
so, let's get the volume of the prism.
then let's get the volume of the smaller cube.
then let's see how many times the volume of the cube goes into the prism's volume, so in short a division.
[tex]\stackrel{\textit{prism's volume}}{\left( \frac{5}{2} \right)(2)(1)\implies 5~cm^3}~\hfill \stackrel{\textit{cube's volume}}{\left( \frac{1}{2} \right)\left( \frac{1}{2} \right)\left( \frac{1}{2} \right)\implies \frac{1}{8}~cm^3} \\\\[-0.35em] ~\dotfill\\\\ 5\div \cfrac{1}{8}\implies \cfrac{5}{1}\div \cfrac{1}{8}\implies \cfrac{5}{1}\cdot \cfrac{8}{1}\implies 40~~cubes[/tex]
Mr. gonzalez earns his living as a salary plus commission employee. his annual salary is $18,000. he makes 4% commission on all of his sales. mr. gonzalez wants to earn $60,000 this year. if his earnings are divided evenly throughout the year, how much in monthly sales would mr. gonzalez need to have? a. $37,500 b. $87,500 c. $100,000 d. $125,000 please select the best answer from the choices provided a b c d
Answers
In monthly sales would mr. gonzalez need to have $100000
Mr. Gonzalez earns his living as a salary plus commission employee, then his annual earnings can be represented by
What is the formula for monthly earning?Monthly earnings=a+bx
Where a =his annual salary (fixed),
b = the percentage of sales commission and
X =represents the volume of sales made each year.
Therefore When Mr. Gonzalez annual salary is $18,000 and makes a commission of 4%, his annual sales that will enable him earn an annual salary of $60,000 will be equal to
$60000 = $18000 + 0.04X
$60000 - $18000 = 0.04X
$48000 = 0.04X
0.04X = $1200000
X = $48000/0.04=12000000
X=$12000000
Therefore, his monthly sales is given by his earnings divided evenly each month is equal to
$1200000/12=$100000
So the option c is correct.
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Answer:c
Step-by-step explanation:
What integer best represents
ascending 800 feet?
Answers
Answer:
positive interger.....
Simplify 4x2−−−√.
the simplified expression is
Answers
Answer:
8
Step-by-step explanation:
The product of two rational numbers is 117/40. If one of them is - 13/5, find the other.
Answers
Answer:
= - 9/8
Step-by-step explanation:
(-13/5) * x = 117/40 multiply both sides by - 5/13
x = 117 / 40 * - 5/13 = - 9/8
help mean is 7.8 and standard deviation is 1 will give brainly
Answers
Answer:
a) Mean shoe size = 7.8
b) 8.8, 9.8 and 10.8
c) see attached
d) Shoe size
Step-by-step explanation:
[tex]\sf Mean \ \mu= 7.8[/tex]
[tex]\sf Standard \ deviation \ \sigma= 1[/tex]
Therefore,
[tex]\sf 1 \sigma=\mu+1 \sigma=7.8+1=8.8\\\sf 2 \sigma=\mu+2 \sigma=7.8+2 \cdot 1=9.8\\\sf 3 \sigma=\mu+3 \sigma=7.8+3 \cdot 1=10.8[/tex]
What is the range of the fallowing numbers 29, 47, 32, 36, 57, 20, 39, 38, 52, 51, 28, 24, 44, 40, 45, 35, 50, 50, 32, 31
Answers
Answer: 37
Step-by-step explanation:
range = max - min
max = maximum value in a data set
min = minimum value in a data set
Maximum value: 57
Minimum value: 20
Range: 37
Answer:
37
Step-by-step explanation:
First of all, let's define what range is. The range is the highest value of a set of numbers minus the lowest value of the same set. In this case, your highest value is 57 and your lowest value is 20. The sum would be 57 - 20 which would equal 37 and that is your answer.
Hope I helped you out :)
Find the surface area of the can of milk at the right. [tex] \bold{Use \: π = 3.14}[/tex][tex] \red{*}[/tex]
Answers
The milk can is in the shape of a cylinder.
The surface area of cylinder is defined as the sum of curved surface and the two circular bases of the cylinder;
ㅤㅤㅤ➙ (curved surface ) + 2(base area )
ㅤㅤㅤ➙ 2πrh + 2πr²
ㅤㅤㅤ➙ 2πr( h + r )
Here, in this question we have;
radius ( r ) = 2/2 = 1 cm height ( h ) = 6 cmTherefore, Surface Area ( S.A ) :
➝ S.A = 2πr( r + h )
➝ S.A = 2 × π × 1 ( 1 + 6 )
➝ S.A = 2π ( 7 )
➝ S.A = 2 × 3.14 × 7
➝ S.A = 14 × 3.14
➝ S.A = 43.96cm²
Answer:
Surface area of cylindrical milk can is 43.96cm²
Step-by-step explanation:
Given :-
height of can of milk :- 6cm diameter :- 2 cm , radius :- 1cmTo find:-
Surface area of milk canSolution:-
formula for surface area cylindrical milk can :-
2πr(h+r)
putting the known values ,
2 × 3.14 × 1 (6+1) cm²
Surface area :- 43.96 cm²
Suppose f (x) = x². Find the graph of
y (x+5).
Answers
Step-by-step explanation:
Suppose f (x) = x². Find the graph of
y (x+5).
find the value of 9 and 4
Answers
Evaluate (2 minus 5 i) (p + q) (i) when p = 2 and q = 5 i.
29 i
29 i - 20
- 21 i
29
Answers
Answer:
29 i
Step-by-step explanation:
As the expression given in the question.
= (2 - 5i) (p + q)i
Simplify the above
= (2 - 5i) (pi + qi)
= 2pi + 2qi - 5pi²- 5qi²
As i² = -1
Put in the above
= 2pi + 2qi + 5p +5q
= 2i × 2 + 2i × 5i + 5 × 2 + 5 × 5i
= 4i + 10i² + 10 + 25i
As i² = -1
= 4i - 10 + 10 + 25i
= 29i
Thus the value of the (2 – 5i)(p + q)i is 29i .