divide 2x³-3x²+5x-7 by x-2
Answer: p(1/2)=11/2p(a)=a.
Step-by-step explanation:
Answer:
2x3 - 5x2 + 2x - 7
——————————————————
x - 2
Step-by-step explanation: 2x3 - 5x2 + 2x - 7
Simplify ——————————————————
x - 2
Checking for a perfect cube :
3.1 2x3 - 5x2 + 2x - 7 is not a perfect cube
Trying to factor by pulling out :
3.2 Factoring: 2x3 - 5x2 + 2x - 7
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: 2x - 7
Group 2: 2x3 - 5x2
Pull out from each group separately :
Group 1: (2x - 7) • (1)
Group 2: (2x - 5) • (x2)
Bad news !! Factoring by pulling out fails :
The groups have no common factor and can not be added up to form a multiplication.
Polynomial Roots Calculator :
3.3 Find roots (zeroes) of : F(x) = 2x3 - 5x2 + 2x - 7
Polynomial Roots Calculator is a set of methods aimed at finding values of x for which F(x)=0
Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers x which can be expressed as the quotient of two integers
The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient
In this case, the Leading Coefficient is 2 and the Trailing Constant is -7.
The factor(s) are:
of the Leading Coefficient : 1,2
of the Trailing Constant : 1 ,7
Let us test ....
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 -16.00
-1 2 -0.50 -9.50
-7 1 -7.00 -952.00
-7 2 -3.50 -161.00
1 1 1.00 -8.00
1 2 0.50 -7.00
7 1 7.00 448.00
7 2 3.50 24.50
Polynomial Roots Calculator found no rational roots
Polynomial Long Division :
3.4 Polynomial Long Division
Dividing : 2x3 - 5x2 + 2x - 7
("Dividend")
By : x - 2 ("Divisor")
dividend 2x3 - 5x2 + 2x - 7
- divisor * 2x2 2x3 - 4x2
remainder - x2 + 2x - 7
- divisor * -x1 - x2 + 2x
remainder - 7
- divisor * 0x0
remainder - 7
Quotient : 2x2 - x
Remainder : -7
so x=-7
Which point lies on the y-axis
Ship has a circular window with a radius of 10 inches find the area of the window in square inches
Enter the correct letter to match each summation expression with the property or formula.
n
Σ
i=1
cai is equal to
. a
n(n + 1)(2n + 1)
6
n
Σ
i=1
i is equal to
. b
n(n + 1)
2
n
Σ
i=1
c is equal to
. c c
n
Σ
i=1
ai
n
Σ
i=1
i3 is equal to
. d cn
n
Σ
i=1
i2 is equal to
. e
n(n + 1)
2
2
The correct letter that match each summation expression are;
[tex]\displaystyle \sum\limits_{i=1}^n[/tex] is equal to c
[tex]\displaystyle {\sum\limits_{i=1}^n i}[/tex] is equal to b
[tex]\displaystyle \sum_{i=1}^n c[/tex] is equal to d
[tex]\displaystyle\sum_{i=1}^n i^3[/tex] is equal to e
[tex]\displaystyle \sum\limits_{i=1}^n i^2[/tex]is equal to a
What is those the summation expression indicates?The summation expression indicates the sum of all values of a series of a function within a specified limit of values.
The equation for the sum of a constant c and the ith term of an of a sequence of numbers is equivalent to the product of the constant and the sum of the terms of the sequence as follows;
[tex]\sum\limits_{i=1} ^n {c\cdot a_i} = c\cdot \sum\limits_{i=1} ^n {a_i}[/tex] the correct option is c
The sum of ith terms from i = 1 to i = n is an arithmetic series with the formula;
Sₙ = (n/2)·[2·a + (n - 1)·d]
Where; a = The first term = 1
d = The common difference = 1
Therefore;
Sₙ = (n/2)·[2 + (n - 1)] = n + n·(n - 1)/2 = (2·n + n² - n)/2
(2·n + n² - n)/2 = (n² + n)/2 = n·(n + 1)/2
Therefore;
[tex]\sum\limits_{i=1}^n i = \dfrac{n\cdot (n + 1)}{2}[/tex] The correct option is b
The sum of n number of a constant, c is c·n, therefore;
[tex]\sum\limits_{i = 1}^n c = c\cdot n[/tex] The correct option is d
[tex]\sum\limits_{i=1}^n [(1 + i)^3-i^3[/tex] = (2³ - 1³) + (3³ - 2³) + ... + ((n + 1)³ - n³) = (n + 1)³ - 1³
(n + 1)³ - 1³ = n³ + 3·n² + 3·n
[tex]\sum\limits_{i=1}^n [(1 + i)^3-i^3[/tex] = n³ + 3·n² + 3·n
However, we get;'
[tex]\sum\limits_{i=1}^n [(1 + i)^3-i^3[/tex] = [tex]\sum\limits_{i=1}^n [ i^3 + 3\cdot i^2 + 3\cdot i+ 1-i^3][/tex]
[tex]\sum\limits_{i=1}^n [ i^3 + 3\cdot i^2 + 3\cdot i+ 1-i^3][/tex] = [tex]\sum\limits_{i=1}^n [ 3\cdot i^2 + 3\cdot i+ 1][/tex] = 3·S₂ + 3·S₁ + n
Where;
[tex]S_2 = \sum\limits_{i=1}^n i^2[/tex]
[tex]S_1 = \sum\limits_{i=1}^n i[/tex] = n·(n + 1)/2
[tex]\sum\limits_{i=1}^n [ 3\cdot i^2 + 3\cdot i+ 1][/tex] = n³ + 3·n² + 3·n = 3·S₂ + 3·S₁ + n
3·S₂ = n³ + 3·n² + 3·n - (3·S₁ + n) = n³ + 3·n² + 3·n - (3·(n·(n + 1)/2) + n)
n³ + 3·n² + 3·n - (3·(n·(n + 1)/2) + n) = n³ + 3·n²/2 + n/2
3·S₂ = n³ + 3·n²/2 + n/2
S₂ = n³/3 + 3·n²/6 + n/6 = (2·n³ + 3·n² + n)/6
S₂ = (2·n³ + 3·n² + n)/6 = n·(2·n² + 3·n + 1)/6
S₂ = n·(2·n² + 3·n + 1)/6 = n·(2·n + 1)·(n + 1)/6
S₂ = n·(2·n + 1)·(n + 1)/6
[tex]S_2 = \sum\limits_{i=1}^n i^2 = \dfrac{n\cdot (2\cdot n + 1)\cdot (n + 1)}{6}[/tex] The correct option is; a
(n + 1)⁴ - n⁴ = 4·n³ + 6·n² + 4·n + 1
Therefore;
(n + 1)⁴ - 1⁴ = 4·S₃ + 6·S₂ + 4·S₁ + n
4·S₃ = (n + 1)⁴ - 1⁴ - (6·S₂ + 4·S₁ + n)
(n + 1)⁴ - 1⁴- (6·(n·(2·n + 1)·(n + 2)/6) + 4·(n·(n + 1)/2) + n) = (n + 1)·(3·n² - n + 1)
4·S₃ = n²·(n + 1)²
S₃ = n²·(n + 1)²/4
[tex]S_3 = \sum\limits_{i=1}^n i^3 = \dfrac{n^2\cdot (n+1)^2}{4}[/tex] The correct option is e
Learn more about the sum of a series of values here: https://brainly.com/question/28586583
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Solve the system of equations x+2y=-16 and x+6y=-28 by combining the equations.
Answer:
x= -18 y=-5/3
Step-by-step explanation:
Answer:
x = -10
y = -3
Step-by-step explanation:
When combining the equations, we must ensure that one of the two variables will cancel out. The easiest way to do this will be to multiply one of the equations by -1, such that the x will cancel out once they are added together. This can be done with either equation, but I will do it for the first one.
This gives us the system:
[tex]\left \{ {{-x-2y=16} \atop {x+6y=-28}} \right.[/tex]
We can then add the two equations by combining each of the terms:
[tex](x - x) + (6y - 2y) = (-28 + 16)\\(0) + (4y) = (-12)\\4y = -12\\y = -3[/tex]
Now that we have the value for y, we substitute it back into any of the original equations and solve for x:
[tex]x + 2y = -16\\x + 2(-3) = -16\\x - 6 = -16\\x = -10[/tex]
To check our work, we substitute both x and y into the other original equation:
[tex]x + 6y = -28\\(-10) + 6(-3) = -28\\-10 - 18 = -28\\-28 = -28[/tex]
answer for 30 points and brainilest
answer choices are : $168 , 9 , 158 , 10 , 30 , 157 , $100 , 32, $4 , 85 , $167 , 84 , $99 , $46 , $45 , $3
Answer:
1.10 2.158 3.157 4.100. 5.32 6. 168 7.99 8.46 9.3
Step-by-step explanation:
Answer:
9, 84, 30, 10, 157, 45, 168, 3, 100, 99
Step-by-step explanation:
find the value of the variable and the length of each chord. round your answers to the nearest tenth
Answer:
x = 3, JL = 17, MN = 13
Step-by-step explanation:
Given 2 intersecting chords in a circle , then
The product of the parts of one chord is equal to the product of the parts of the other chord, that is
14x = 7 × 6 = 42 ( divide both sides by 14 )
x = 3
Then
JL = x + 14 = 3 + 14 = 17
MN = 6 + 7 = 13
Find the center and radius of the circle:
x2 + y2 + 14x – 2y + 25 = 0
Solve for x and y. show your work please
Answer:
I think it's c.
Step-by-step explanation:
hiii please help i’ll give brainliest:)
Answer:
Disjointed
Step-by-step explanation:
Their economy and a lot of structures were destroyed which left them struggling to recover.
In the figure, lines a, b, and c are parallel and m24 = 48
Drag and drop the correct angle measure for each angle
m21=
m22=
m23=
m24=
42
48
132
312
Answer:
m<1 = 48°
m<2 = 132°
m<3 = 132°
m<5 = 48°
Step-by-step explanation:
Given:
m<4 = 48°
Required:
m<1, m<2, m<3, and m<5
Solution:
m<1 = m<4 (alternate exterior angles are congruent)
m<1 = 48° (substitution)
m<2 = 180° - (m<1) (linear pair theorem)
m<2 = 180° - 48° (substitution)
m<2 = 132°
m<3 = m<2 (alternate interior angles are congruent)
m<3 = 132° (substitution)
m<5 = m<4 (corresponding angles are congruent)
m<5 = 48° (substitution)
Thank for help find a volume
Answer:
117π=367.38
Step-by-step explanation:
r=d/2=3
V=πr2h=π·3²·13=117π=367.38
Problem A fruit stand has to decide what to charge for their produce. They need \$10$10dollar sign, 10 for 444 apples and 444 oranges. They also need \$12$12dollar sign, 12 for 666 apples and 666 oranges. We put this information into a system of linear equations.
Answer:
4a + 4b = 10
6a + 6b = 12
Step-by-step explanation:
Putting the equation in a system of linear equation :
We donate, apples and oranges using any preffered letter or alphabet
Let :
Apples = a ; oranges = b
4 apples and 4 oranges equals $10
4a + 4b = 10
6 Apples and 6 oranges equals $12
6a + 6b = 12
Hence, the system of linear equation :
4a + 4b = 10
6a + 6b = 12
Answer:
No Solution
Step-by-step explanation:
It would require different amounts of dollars to fulfill eah equation.
find the domain of the function
x → √x − 1
Answer:
The domain of √x - 1 is x ≥ 0
Step-by-step explanation:
The function f(x) = √x has real outputs only for x ≥ 0. The constant -1 is defned for all x.
The domain of √x - 1 is x ≥ 0.
if f(x)=2x+1 and g(x)=x2 find fg(3)
Given:
The functions are:
[tex]f(x)=2x+1[/tex]
[tex]g(x)=x^2[/tex]
To find:
The value of [tex]fg(3)[/tex].
Solution:
We have,
[tex]f(x)=2x+1[/tex]
[tex]g(x)=x^2[/tex]
Substitute [tex]x=3[/tex] in each function.
[tex]f(3)=2(3)+1[/tex]
[tex]f(3)=6+1[/tex]
[tex]f(3)=7[/tex]
And,
[tex]g(3)=(3)^2[/tex]
[tex]g(3)=9[/tex]
We know that, product of two functions is defined as:
[tex]fg(x)=f(x)\times g(x)[/tex]
Using this rule, we get
[tex]fg(3)=f(3)\times g(3)[/tex]
[tex]fg(3)=7\times 9[/tex]
[tex]fg(3)=63[/tex]
Therefore, the value of [tex]fg(3)[/tex] is 63.
Solve for x:
[tex]5x + 5x = 100[/tex]
Answer: X=10
Step-by-step explanation:
HELP ME PLSSSS!!!!!
If the diameter of the circle above is 16 mm, what is the area of the circle?
A.
16 mm2
B.
64 mm2
C.
8 mm2
D.
256 mm2
Answer:
64[tex]\pi[/tex] mm² or approximately 201.06 mm²
Step-by-step explanation:
If the diameter is 16 mm, the radius will be 8 mm.
Use the circle area formula, A = [tex]\pi[/tex]r², where r is the radius. Plug in 8 as r:
A = [tex]\pi[/tex]r²
A = [tex]\pi[/tex](8²)
A = 64[tex]\pi[/tex]
So, the area of the circle is 64[tex]\pi[/tex] mm² or approximately 201.06 mm²
If the diameter of the circle above is 16 mm, what is the area of the circle ?
Solution:-Diameter of the circle = 16 mm. (Given)
Radius (r) of the circle = 16/2 = 8 mm.
[tex] \bigstar [/tex] To Find the area of the circle.
Since we know,
[tex] \dag [/tex] Area of circle is πr².
So, Area of the circle = 3.14 × (8)²
Area of the circle = 3.14 × 8 × 8
Area of the circle = 200.96 = 201 mm².
The area of the circle is 201 mm². [Answer]if b > 1 the function will..
Step-by-step explanation:
Since bx can be defined for all real numbers r, the domain of an exponential function is all real numbers. The range of bx is all real numbers greater than 0. ... If b > 1, then f is an increasing function. I.e. f(x) increases in value as x increases.
what is the equivalent expression for the exponential expression below? x^1/2
Answer:
B. √x.
Step-by-step explanation:
That would be B - the square root of x.
plz help asap what is -20.4 as a mixed number 31 points if u answer
Answer:
-20 2/5 (2/5 as fraction)
If a point at random, what is the probability that it will be in the shaded section. Give your answer as a fraction or a percentage to the hundredths
The diagram isn't attached. However, a rated diagram has been found and attached below.
Answer:
0.8611
Step-by-step explanation:
The probability of an event involves taking the ratio of the required measurement and the entire measurement.
Based on information on the attached circle, the shaded region of the circle takes 310° of the entire 360°
Choosing a point at random from which nside the circle ;
P(shaded portion) = shaded section / total measure of circle
P(shaded point) = 310 / 360 = 0.8611
What is the probability that you will roll a dice and get 3, then get an ace from a deck, then (without replacing the other card) draw a black 2?
Answer:
que pasa parsero deja de esta mostrando el manda aquí vale
Can someone turn this into y=ax+b form with your work?
Step-by-step explanation:
given
2x + y = 13
turning to y = ax + b we get
y = - 2x + 13
hope it helps :)❤
A trampoline is on sale for 50% off. What was the original price if the sale price is $31?
Answer:
$62
Step-by-step explanation:
Hello it's $62 because 31 x 2 = 62 and it was half off so that is why its $62
Answer:
The original price is 62 dollars.
Which is the area of triangle LMN? Group of answer choices 24 square units 27 square units 54 square units 48 square units
Answer:
√65/2 square units
Step-by-step explanation:
Find the diagram attached
Area of the triangle = 1/2 * base * height
To get the base and height, we will use the distance formula;
Area of the triangle LMN = 1/2 * LM * MN
For MN
Given the coordinate M(3, 2) and N(1, 3)
MN = √(3-2)²+(1-3)²
MN = √1²+(-2)²
MN = √1+4
MN = √5
For LM;
Given the coordinate L(1, -1) and M(3, 2)
LM = √(2-(-1))²+(3-1)²
LM = √(2+1)²+(2)²
LM = √3²+(2)²
LM = √9+4
LM = √13
Area of the triangle LMN = 1/2 * √13 * √5
Area of the triangle LMN = √65/2 square units
1) Find the length of AB
2)Find the length of A’B’
3) Find the scale factor.
Answer: Find the length of A
3) Find the scale factor.
Step-by-step explanation:
what is the measure of angle pos
The answer is 104°.
.. .. ..
Answer:
Step-by-step explanation:
A line is always equal to 180. So if angle POR is 76, you would do 180-76 which equals 104.
i'll really appreciate some help! thank you! ln(4x-9)=-5
Answer:
Step-by-step explanation:
The answer is x= 7/2
decimal form 3.5
Evaluate [12 -5 x 9] = 3
Answer:
-33.
Step-by-step explanation:
[12 -5 x 9]
= 12 - 45
= -33.
Answer:
-36
Step-by-step explanation:
[12-45]=3
-33=3
-33-3=-36
Find the area. Round to the nearest tenth.
Answer:
YOU DONT KNOW HOW TO ROUND SMH
Step-by-step explanation:
LEARN KID LEARN CMON ITS EASY