(i) Factorise the expression x^3 + 3x - x^2 - 3 completely.
(ii) Hence, express (x^2 – 3)^3 - (2 - x^2)^2 + 3(x^2- 3) in the form (x^4+Ax^2+B)(x^2+ C), where A, B and C are integers.
Step-by-step explanation:
Answer 1 put all like terms then solve
hope it helps....
a) The value of the equation is A = ( x - 1 ) ( x² + 3 )
b) The value of the equation is B = ( x⁴ - 6x² + 10 ) ( x² - 4 )
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
a)
The equation is A = x³ + 3x - x² - 3
On simplifying the equation , we get
A = x³ - x² + 3x - 3
A = x² ( x - 1 ) + 3 ( x - 1 )
On factorizing the equation , we get
A = ( x² + 3 ) ( x - 1 )
b)
The equation is B = ( x² - 3 )³ - ( 2 - x² )² + 3 ( x² - 3 )
On simplifying the equation , we get
B = ( x² - 3 )³ - ( x⁴ - 2x² - 2x² + 4 ) + 3 ( x² - 3 )
On further simplification , we get
B = ( x² - 3 )³ - x⁴ + 4x² - 4 + 3x² - 9
B = ( x² - 3 )³ - x⁴ + 7x² - 13
On factorizing the equation , we get
B = ( x - 2 ) ( x⁵ + 2x⁴ - 6x³ - 12x² + 10x + 20 )
B = ( x - 2 ) ( x + 2 ) ( x⁴ - 6x² + 10 )
And , on further simplification , we get
B = ( x² - 4 ) ( x⁴ - 6x² + 10 )
Hence , the equation is B = ( x² - 4 ) ( x⁴ - 6x² + 10 )
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What is the sum of the two fractions below in simplest form.
3 3/8 and 2 1/4
Answer:
5 5/8
Step-by-step explanation:
This is in the simplest form
If ε = {whole numbers less than 50 but greater than 20} and X = {perfect squares}, Y = {factors of 12}, Z = {prime numbers}; find the following:
a) X ∪ Y
b) X ∩ Y
c) X ′
d) X′ ∩ Y ∩ Z
Answer:
A. X∪Y = {25, 36, 49}
B. X∩Y = ∅ i.e empty set
C. X' = {21, 22, 23, 24, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48}
D. X′∩Y∩Z = ∅
Step-by-step explanation:
We'll begin by determining the universal set (ε), set X, set Y and set Z.
This can be obtained as follow:
ε = {whole numbers less than 50 but greater than 20}
ε = {21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49}
X = {perfect squares}
X = {25, 36, 49}
Y = {factors of 12}
Y = ∅ i.e empty
Z = {prime numbers}
Z = {23, 29, 31, 37, 41, 43, 47}
A. Determination of X∪Y
X = {25, 36, 49}
Y = ∅
X∪Y =?
X∪Y => combination of elements in set X and Y without repeating any element in both X and Y.
X∪Y = {25, 36, 49}
B. Determination of X∩Y
X = {25, 36, 49}
Y = ∅
X∩Y =?
X∩Y => elements common to both set X and Y
X∩Y = ∅ i.e empty
C. Determination of X′
ε = {21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49}
X = {25, 36, 49}
X' =?
X' => elements in the universal set but not found in set X.
X' = {21, 22, 23, 24, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48}
D. Determination of X′∩Y∩Z
X' = {21, 22, 23, 24, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48}
Y = ∅
Z = {23, 29, 31, 37, 41, 43, 47}
X′∩Y∩Z =?
X′∩Y∩Z => elements common to set X', Y and Z
X′∩Y∩Z = ∅
please help me please
Answer:
the answer is 70
Step-by-step explanation:
Because I'm in collage I know this stuff just trust me here
Could you please solve these? I will give five stars if correct.
9x−17=3x+7 Solve for x
−7b−1=−5(b+3) Solve for b
Answer:
x=4 b=-4/3
Step-by-step explanation:
for b you simplify both sides of the equation, and then you get -7b - 1 = 5B + 15 then you subtract 5 from both sides which gets you to -12b - 1 = 15 then you divide both sides by negative 12 which would be negative 12 b - -12 = 16-12 which gives you the answer of -4/3.
for x you would subtract 3x from both sides which gets you to 6x - 17 = 7 and then you would add 17 to both sides which would give you 6X = 24 and then you would divide both sides by 6 which would give you x = 4
!!!!?HELP WILL MARK BRAINLIST ANSWER PLEASE HELP!!!! !!ALSO I ADDED THE PICTURE!!!
The pressure in the Hartford Dam is building because of all the
melted snow from the winter. The lake behind the dam is as high
as it gets all year. The managers have decided to open three
floodgates on the dam. Each one is a different size, and that means
a different amount of water comes out of each one. The table below
shows the gallons per second coming out of each gate.
Answer:
I believe it's 20 seconds.
PLS HELP ME I WILL GIVE BRAINLIEST TO THE BEST ANSWER
Answer:
Step-by-step explanation:
S= 180 - ( 62 + 90)
=180-152
=80
So S = 80
Answer:
28°
Step-by-step explanation:
none needed
The volume of a Toblerone candy bar is 275 cm3. If the candy bar is 11 cm long, what is the area of the base?
Answer:
275 - 11=264
Step-by-step explanation:
You and your friends are at the local ice cream shop. You get a cone that has a diameter of 12 cm and a height of 12 cm that is full of ice cream, and has a sphere of ice cream on top with the same diameter. What is the total volume of your ice cream cone? Show your work in terms of π.
Answer:
the answer is 24 centimeters
Find the perimeter P of the figure shown. Simplify your answer
Answer:
C) 26x + 3
Step-by-step explanation:
Perimeter = 7x + 2 + 5x - 3 + 9x + 7 + 5x - 3
combine like terms:
Perimeter = 26x + 3
divide .072 by 345.00 and round to the nearest tenth
Answer:
.072 / 345.00 = 0.0002086956
the tenth place is the fist digit to the right of the decimal point
so it would round to 0.0
Step-by-step explanation:
One morning at a zoo, there were 165 adults and children who paid to enter. The zoo collected $1,440 from admission fees. The price of admission is $10 for an adult and $7 for a child. How many children were admitted to the zoo?
Answer:
number of children admitted to the zoo=70
let adult =a
let children=c
a+c=165........equation 1
10a+7c=1440.......equation 2
a=165-c........equation 3
substitute equation 3 in equation 2
10a+7c=1440
10(165-c)+7c=1440
1650-10c+7c=1440
-10c+7c=-210
-3c=-210
c=70
Therefore children =70
A right circular cylinder has a volume of 1296 cubic inches if the radius of the cylinder is divided by 12 what be the volume in cubic inches of the smaller cylinder
Answer:
Step-by-step explanation:
A right circular cylinder has a volume of 1296 cubic inches
The volume of a cylinder = πr²h
Step 1
We find the radius
1296 inches = πr²h
r² = 1296/π ×>h
if the radius of the cylinder is divided by 12 what be the volume in cubic inches of the smaller cylinder
Complete the set of data with one value so that the mean of the data is 24. 26, 35, 10, 18, 15, 37, 25, 20, 15,
Answer:
39
Step-by-step explanation:
So there are 9 values. (1 to be added). First we add them all up. And we need to add another value. So the mean is all of the values added up, divided by the number of numbers. If we add another value, then there'll be 10 values. 24x10 is, of course, 240. If you add all of the given values, you get 201. And we can easily create the equation, x+201=240, and x, or the missing value, is obviously 39.
What is the volume of a cylinder,in cubic feet,with a high of 5 feet in a base diameter of 10 feet?Round to the nearest tenth place
Answer:
390.7ft³ is the answer
eu preciso de ajuda pfvr:(
please helpppp!!!will mark brainlyist
hey cutie i need help :(
select all that apply !
Of the students who prefer science, 70% are female.
The number of students who prefer science is 130
Of the students who prefer math, 21 are male.
Of the students who prefer math, 17% are male.
Of the students who prefer science, 54% are female.
Of the students who prefer math, 14% are male.
Answer:
wrong right right wrong right wrong
Step-by-step explanation:
70/ 130= 53.8%
4th row 3rd one to the right
2nd row, 2nd one to the right.
21/156 = 13.4%
70/130 = 53.8% round to get 54%
21/156 = 13.4%
so 2nd 3rd 5th apply
Can someone plsss help mee :(
Answer:I think it is 89
Step-by-step explanation:
Plz help I am bad at this
find the value of x plz help
Answer:
29 degrees
Step-by-step explanation:
Both angles are the same.
15 of 20 answer
You and your friend fill 20 bags with leaves. The ratio of bags you filled to bags your friend filled is 2 to 3. Use the tape diagram to find how many bags
you filled
You
Your friend
You filled
bags
Answer:
8 bags
Step-by-step explanation:
You divided them by 20 which gives you 4. So you take the 3 and multiply by 4 which is 12 bags. And then you do the same for your bags which makes you do 2 times 4 which gives you 8. You take 20 - 12 and that leaves you with 8.
The average area of a bedroom in a home is 219 square feet with a standard deviation of 32.5 square feet. What is the largest a bedroom can be and be among the smallest 25% of bedrooms in a home?
Answer:
197.095
Step-by-step explanation:
Mean, m = 219 ft²
Standard deviation, s = 32.5 ft²
For a bedroom to be among the smallest 25%
P(x < Z) = 0.25
From Z probability calculator, this corresponds to a Zscore of - 0.674
Recall :
Zscore = (x - m) / s
x = bedroom size
-0.674 = (x - 219) / 32.5
-0.674 * 32.5 = x - 219
-21.905 = x - 219
x = - 21.905 + 219
x = 197.095
Hence, the largest a bedroom can be and still be among the smallest 25% is 197.095
Chapter 7 need help ASAP
Answer:
The answer should be that Q is (-3,-2)
Step-by-step explanation:
when f(x) is replaced with
f(x)+k, the graph that results is shown below
K=__?
Answer:
k = 6
Step-by-step explanation:
Parent function of the given graph → f(x) = (x - 1)²
If the parent function is shifted 6 units up.
Equation of the translated function will be → g(x) = (x - 1)² + 6
g(x) = f(x) + 6
Therefore, k = 6 will be the answer.
Solve the equation for X+15 =X+30
Answer:
i'm pretty sure there's no solution
Answer:
Step-by-step explanation:
Points that you can have! :)
Answer:
Thank youuu !
Step-by-step explanation:
Answer:
Thank you
Step-by-step explanation:
Find the area of a circle with diameter 14 mm. Use the value 3.14 for π, and do not round your answer. Be sure to include the correct unit in your answer.
Answer:
153.86 mm²
Step-by-step explanation:
Radius of circle = diameter/2 = 14/2 = 7mm
Area of circle = πr² = (3.14)(7mm)²
= 3.14 x 49 mm²
= 153.86 mm²
Can anyone plz answer this question, i will give brainliest
Answer:
C.6
Step-by-step explanation:
Remember, a constant term is a term that keeps repeating. Also, it's the only term that doesn't contain a variable. In this equation, 6 is the constant.
Hope I helped!!!
I will give BRAINLIEST
Answer:
D.
Step-by-step explanation:
the factors are (x-1)(x+4)(x-4)