The polynomial x³-2x²+x-2 can be completely factorized by applying the technique of grouping and difference of squares, resulting in the complete factorization as (x-2)(x-1)(x+1).
Explanation:The complete factorization of the polynomial x³-2x²+x-2 can be found by first factorizing it into simpler polynomials. The given polynomial can be rewritten as x³-2x²+x-2. It is now possible to apply grouping, pair the terms as (x³-2x²) and (-x²+x-2). This gives us x²(x-1)-1(x-2). Now, you can clearly see that you have a common factor (x-1) that you can take out from each set. This gives you your final answer of (x-2)(x²-1). Then apply further factorization on x²-1 to get (x+1)(x-1), because x²-1 is a difference of two squares. So, the complete factorization is (x-2)(x-1)(x+1).
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The complete factorization of the polynomial x^3 - 2x^2 + x - 2 is (x + 1)(x - 1)(x - 2).
Explanation:The polynomial x^3 - 2x^2 + x - 2 can be factorized completely by using the Rational Root Theorem and synthetic division.
By testing various factors of the constant term -2 (±1 and ±2) and the leading coefficient 1, we find that x = -1 is a root of the polynomial.
Using synthetic division, we can divide the polynomial by (x + 1) to obtain the quotient x^2 - 3x + 2. This quadratic polynomial can be further factorized as (x - 1)(x - 2).
Therefore, the complete factorization of the original polynomial is (x + 1)(x - 1)(x - 2).
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Enter the correct answer in the box.
Solve the inequality for x in terms of a.[tex]ax-8\leq 12[/tex]
Answer:x<=(20)/(a)
Step-by-step explanation:
it cost $270 for 3 people to go on a fishing trip how much does it cost for 10 people to go on a fishing trip
Answer:
$900
Step-by-step explanation:
It cost each person $90 to go on the trip when you divide 270/3. You can find out how much it would cost for 10 people to go on the trip by multiply 10X90.
in the figure L1 L2 and L3 is a traversal what is the value of q-p
Answer:
q=135 degrees
p=45 degrees
Step-by-step explanation:
For q:
q is 135 degrees because alternate exterior angles are congruent when L1 is parallel to L2 intersected by L3.
For p:
p is 45 degrees because L2 is a straight line so it has a measurement of 180 degrees. So to find p you do 180 degrees-q.
Which is 180-135=45 degrees
Identify a pattern in the given list of numbers. Then use this pattern to find the next number 5,9,14,20,27,35,____
Answer:
the answer is 44
Step-by-step explanation:
the pattern is 4,5,6,7,8 so then you would add 9 to get 44
Final answer:
The pattern in the given list of numbers is that each number increases by consecutively larger increments of 1. By continuing this pattern, adding 9 to the last number (35), we determine the next number in the series to be 44.
Explanation:
The given list of numbers is 5, 9, 14, 20, 27, 35, and we are asked to identify the pattern to find the next number in the series.
Let's look at the differences between consecutive terms: 9 - 5 = 4, 14 - 9 = 5, 20 - 14 = 6, 27 - 20 = 7, 35 - 27 = 8.
We can see that with each step, the difference increases by 1. This pattern suggests that the next difference should be 9.
To find the next number, we add 9 to the last number in the series: 35 + 9 = 44. Therefore, the next number in the series is 44.
Find the product of 83 and 3.
Hello!
Answer:
249
Step-by-step explanation:
83
3 x
___
249
Hope this helps! ~Pooch ♥
Please find the Sine, Cosine, and Tangent
Answer:
sin theta = 3/5
cos theta = 4/5
tan theta = 3/4
Step-by-step explanation:
sin = opposite / hypotenuse
cos = adjacent / hypotenuse
tan = opposite / adjacent
sin theta = 18/ 30 = 3/5
cos theta = 24/30 = 4/5
tan theta = 18/24 = 3/4
Answer:
[tex]sin \theta = \frac{3}{5} = 0.6\\\\ cos \theta = \frac{4}{5} = 0.8\\\\tan \theta = \frac{3}{4} = 0.75\\[/tex]
Step-by-step explanation:
Use SOHCAHTOA for reference
[tex]sin = \frac{opposite}{hypotenuse} \\\\cos = \frac{adjacent}{hypotenuse} \\\\tan = \frac{opposite}{adjacent}[/tex]
[tex]sin \theta = \frac{18}{30} = \frac{3}{5} = 0.6\\\\cos \theta = \frac{24}{30} = \frac{4}{5} = 0.8\\\\tan \theta = \frac{18}{24} = \frac{3}{4} = 0.75[/tex]
What is the solution to
-x+3y=2
X+y=-2
Answer:
(-2, 0)
Step-by-step explanation:
Use elimination: add the two systems. Because the left is equal to right, you are adding the same thing and it's legal.
-x+3y=2
+ (x+y=-2)
Add each term
-x+x + 3y+y = 2+ -2
4y=0
y=0
x+y=-2
x+0=-2
x=-2
Answer:
x=-2, y=0
Step-by-step explanation:
-x+3y=2
X+y=-2
We can add these two equations together to eliminate x
-x+3y=2
x+y=-2
--------------
4y = 0
Divide each side by 4
4y/4 = 0/4
y=0
Now we still need to find x
x+y = -2
Substitute x=0
0+y = -2
y= -2
The Gonzalez family has three children on summer break they want to an amusement park they bought three child tickets for $18.50 and two adult tickets if they spent a total of $104.50 how much was the price of each adult ticket
Answer:
Each adult ticket was $43
Step-by-step explanation:
2x+18.5 = 104.5
Simplify
2x = 86
x = $43
The manager of a store orders balance beams that cost $550 and sells them for $704. What percentage is the mark-up?
Answer:
28%
Step-by-step explanation:
Percentage mark up = (new - original) / original * 100 %
new = 704
original = 550
Substituting these values in
Percentage mark up = (704 - 550) / 550 * 100 %
=154/550 * 100%
=.28*100%
28%
What is the equation of the line passing through the points (2, –1) and (5, –10) in slope-intercept form?
A)
Y=3x-5
B)
Y=3x+5
C)
Y=3x-5
D)
Y=3+5
Answer:
y = -3x+5 This has a negative slope
Step-by-step explanation:
The first step is to find the slope. We can use the formula
slope = (y2-y1)/(x2-x1)
= (-10--1)/(5-2)
= (-10+1)/3
= -9/3
=-3
Next we will use the point slope form of the equation of a line
y-y1 = m(x-x1)
y--1 = -3(x-2)
y+1 = -3(x-2)
Distribute the -3
y+1 = -3x -3*(-2)
y+1 = -3x+6
Subtract 1 from each side
y+1-1 = -3x+6-1
y = -3x+5
This is in the slope intercept form of the equation.
My answer differs from the options because I have a negative slope
The number in the middle of a data set best describes
Out of 25 students in Mrs. Green’s class, 12 have a pet. What percent of the students in Mrs. Green’s class have a pet?
Answer by YourHope:
Hi! :)
Out of 25 students in Mrs. Green’s class, 12 have a pet. What percent of the students in Mrs. Green’s class have a pet?
76% of the students in Mrs. Green’s class have a pet!
I also love your profile pic! :)
-4/40c+12/30 factor each expression completely
Answer:
[tex]\frac{4}{10}(-\frac{1}{4} c+1)[/tex]
Step-by-step explanation:
To factor the expression [tex]\frac{-4}{40}c+\frac{12}{30}[/tex] we use the GCF or greatest common factor. The greatest common factor is the greatest number that will divide into the values. We start to find it by factoring each term's coefficient:
[tex]\frac{2*2}{2*2*2*5}[/tex]
[tex]\frac{2*2*3}{2*3*5}[/tex]
We notice both have 2*2 in the numerator and 2*5 in the denominator. This is our GCF.
[tex]\frac{2*2}{2*5}=\frac{4}{10}[/tex]
We now write the expression 4/10(____+_____). We find the inside of the parenthesis by dividing the coefficients by the GCF. This is also the remaining factors which are not part of the GCF.
[tex]\frac{1}{2*2}=\frac{1}{4}[/tex]
[tex]\frac{3}{3}=1[/tex]
So the answer is [tex]\frac{4}{10}(-\frac{1}{4} c+1)[/tex]
The wholesale price of a lamp is $44 and will be marked up by 40 percent. What is the retail price of the lamp?
Answer:
61.60
Step-by-step explanation:
Answer:
The answer is $61.60
Step-by-step explanation
The wholesale price is 44$, but it will be marked up 40% which in decimal form is .40. You multiply that by 44 to get 17.6, and since its mark up you add that number to 44 to get $61.6
I need help with his problem.
which of the binomials below is a factor of this trinomial 5x^2-18x+9
Answer:
5x-3 or x-3
Step-by-step explanation:
I don't know what are the choices, so I'll just factor the whole thing. Choose the ones that fit.
-3 + -15 = -18
-3 * -15 = 9*5
5x^2-15x-3x+9
5x(x-3)-3(x-3)
(5x-3)(x-3)
Answer:
5x - 3
Step-by-step explanation:
APEX
Mario made six batches of cookies. His friends asked him to make an extra batch. He used 15 3/4 cups of sugar and needs another 5/8 cup for the extra batch. How many cups of sugar will Mario use altogether? Show work.
The cups of sugar mario use would be 16 3/8 cup
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.
We are given that Mario made six batches of cookies. His friends asked him to make an extra batch.
He used 15 3/4 cups of sugar
15 3/4 cup = 126/8 cup
then he needs another 5/8 cup for the extra batch.
126/8 + 5/8 = 131/8 cup
Mario use altogether;
131/8 = 16 3/8 cup
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4.25•0.6=2.04•1.25 true or false
Answer:
True
Step-by-step explanation:
Find the length of segment AD.
Someone please help! I’m not the smartest when it comes to math lol.
Answer:
Since AG = GC then AD must equal DC
2x -3 = x +2
x = 5
Step-by-step explanation:
Point Y is the midpoint of segment XZ. If XY = 2(3x +1) and YZ = 5x + 22, find the value of x. x = 20 x = 24 x = 18 x =11
Answer:x=20
Step-by-step explanation:
2(3x+1) = 6x+2
since xy and yz are the parts of a midpoint they are equal to eachother
so 6x+2=5x+22
if you subtract 5x from both sides you get x+2 = 22 then you subtract 2 from both sides so you have x=20
enrico buys 3/8 pound of cheddar cheese and 4/8 pound swiss cheese how many cheese does enrico buy in all
Answer:
They buy [tex]\frac{7}{8}[/tex] of cheese.
Step-by-step explanation:
When adding two fractions with the same denominator, you simply add the two numerators (numbers on top):
[tex]\frac{3}{8} + \frac{4}{8} = \frac{7}{8}[/tex]
So they buy [tex]\frac{7}{8}[/tex] of cheese.
Write an equation for the line that is parallel to the given line and passes through the given point.
Given line: y= 2x + 4 Given Point: (3, 8)
A.) y = 2x + 2
B.) y = 2x + 6
C.) y = -2x + 6
D.) y = - 1/2x + 2
Parallel lines have the same slope.
If y = 2x + 4, then parallel line has equal y = 2x + b.
The line passes throught the point (3, 8). Put the coordinates of the point to the equation of a line:
8 = 2(3) + b
8 = 6 + b subtract 6 from both sides
2 = b
Answer: A) y = 2x + 2Please help with my math homework :(
Answer:
8x-12=6x-2 x=5
Step-by-step explanation:
Select the best estimate for the diameter of a quarter
Answer:
20 Centimeters
Step-by-step explanation:
did it on edge
Apply the Pythagorean Theorem to find the distance between points A and B.
A)
11
units
B)
50
units
C)
61
units
D)
72
units
Answer:
c 61 units but it should be under a square root
Step-by-step explanation:
CA=6
CB=5
5^2+6^2=AB^2
61=AB^2
The Option C is partially correct , the answer must be under a square root as [tex]\;\sqrt {61} {\text{ units}}[/tex].
Further explanation:
The pythagorean theorem is used in the right angle triangle and it states that the square of the hypotenuse is equal to the sum of the squares of the perpendicular and base.
It can be mathematically expressed as,
[tex]{h^2} = {p^2} + {b^2}[/tex]
Here, [tex]h[/tex] is the hypotenuse, [tex]p[/tex] is the perpendicular and [tex]b[/tex] is the base.
Step by step explanation:
Step 1:
It is observed from given figure that after joining the points [tex]A,B{\text{ and C}}[/tex] it is established as right angle triangle.
First determine the perpendicular and the base of the triangle.
It can be seen that there are 5 boxes between the point [tex]A{\text{ and }}C[/tex] and 6 boxes between the point [tex]{\text{B and C}}[/tex].
Therefore, the perpendicular of the triangle [tex]AC[/tex] is [tex]{\text{6 units}}[/tex] and the perpendicular of the triangle [tex]AB[/tex] is .
Step 2:
Now use the Pythagoras theorem to find the distance between [tex]B{\text{ and }}A[/tex].
The distance between [tex]B{\text{ and }}A[/tex] is the length of the hypotenuse of the triangle [tex]ABC[/tex].
The length of the hypotenuse [tex]AB[/tex] can be calculated as,
[tex]\begin{aligned}{h^2}&= {p^2} + {b^2}\\{h^2} &= {6^2} + {5^2}\\{h^2} &= 61\\h &= \sqrt {61}\\\end{aligned}[/tex]
Therefore, the distance between [tex]B{\text{ and }}C[/tex] is [tex]\sqrt {61}[/tex] units.
Thus, option C is partially correct , the answer must be under a square root as [tex]\sqrt {61}[/tex] units.
Learn more:
Learn more about the distance between two points on the number linehttps://brainly.com/question/6278187 Learn more about the distance between two coordinates of the linehttps://brainly.com/question/10135690 Learn more about midpoint of the segment https://brainly.com/question/3269852Answer details:
Grade: Junior school
Subject: Mathematics
Chapter: Pythagoras theorem.
Keywords: Distance, Pythagoras theorem, points, base, perpendicular, hypotenuse, right angle triangle, boxes, units, squares, sum
help me to solve this question...easier
Answer:
x = - 3 and x = - 4
Step-by-step explanation:
(a)
The denominator of f(x) cannot be zero as this would make f(x) undefined. Equating the denominator to zero and solving gives the value that x cannot be.
solve x + 3 = 0 ⇒ x = - 3
(b)
Equate f(x) to 5, that is
[tex]\frac{2x+3}{x+3}[/tex] = 5 ( cross- multiply )
5(x + 3) = 2x + 3 ( distribute left side )
5x + 15 = 2x + 3 ( subtract 2x from both sides )
3x + 15 = 3 ( subtract 15 from both sides )
3x = - 12 ( divide both sides by 3 )
x = - 4
Jackson deposited $5,000 at 3.8% interest, compounded continuously, when he was 18 years old. How much will be in the account when he is 40 years old if he made no other deposits or withdrawals?
With a principal of $5,000, an interest rate of 3.8%, over 22 years, Jackson's principal will grow to $11,535
Given: principal is $5000, interest rate is 3.8% and it is compounded continuously
To find: amount when Jackson is 40 years old
To solve this problem, we use the formula for continuous compounding interest:
[tex]A = P \times e^{rt}[/tex]
where:
A is the total amount of money
P is the principal
r is the annual interest rate (decimal form, so 3.8% becomes 0.038)
t is the time in years
Time here will be 22 years as Jackson deposited the money when he was 18 years old. So, the difference of 40 and 18 gives us 22 years.
Now we can find the total amount by plugging in the values:
[tex]A = 5000 \times e^{0.038 \times 22}\\[/tex]
[tex]A= 5000 \times e^{0.836}\\[/tex]
[tex]A= 5000 \times 2.307\\[/tex]
[tex]A = 11535[/tex]
Therefore, Jackson's account will have $11,535 when he is 40 years old.
The surface area of a cube is 18 3/8 m square. Find its volume.
Answer:
[tex]5\frac{23}{64}\approx 5.36 [/tex] cubic meters.
Step-by-step explanation:
We have been given that the surface area of a cube is [tex]18\frac{3}{8}[/tex] square meters and we are asked to find the volume of the cube.
Since we know that surface area of a cube with each edge equals a units is:
[tex]\text{Total surface area of cube}=6a^2[/tex]
Let us find length of each edge using surface area formula.
[tex]18\frac{3}{8}=6a^2[/tex]
Let us convert our given area into mixed fraction.
[tex]\frac{147}{8}=6a^2[/tex]
Upon dividing both sides of our equation by 6 we will get,
[tex]\frac{147}{8*6}=a^2[/tex]
[tex]\frac{147}{48}=a^2[/tex]
Upon taking square root of both sides we will get,
[tex]\frac{7\sqrt{3}}{4\sqrt{3}}=a[/tex]
[tex]\frac{7}{4}=a[/tex]
Now we will use volume of cube formula with each side length 'a'.
[tex]\text{Volume of cube}=a^3[/tex]
[tex]\text{Volume of cube}=(\frac{7}{4})^3[/tex]
[tex]\text{Volume of cube}=\frac{343}{64}[/tex]
[tex]\text{Volume of cube}=5\frac{23}{64}[/tex]
[tex]\text{Volume of cube}=5.359375\approx 5.36[/tex]
Therefore, the volume of cube will be [tex]5\frac{23}{64}[/tex] cubic meters.
The larger of two numbers exceeds twice the smaller by one. Three times the smaller exceeds the larger by six. If y is the larger number, which of the following systems of equations represents the word problem? y = 2x + 1 and 3x + 6 = y y = 2x + 1 and y + 6 = 3x y = 2(x + 1) and y + 6 = 3x
Step-by-step explanation:
larger number = y
smaller number=x
y>2x+1
y<3x+6
Probably the first one, if I did this right.
To do this problem, you need to know how to read math, literally. The problem says that y is the larger number, so assume the smaller is x. So, y exceeds 2x by 1 (so, y>2x+1). then, it says 3x exceeds y by 6; therefore, 3x+6>y. I may have interpreted it wrong, though, so tell me if I made a mistake :))
Answer:
first one
A. y = 2x + 1 and 3x + 6 = y
factor trinomial 28x^3+27x^2+5x
Answer:
Hello, Gayleayers!! The answer is x(4x+1)(7x+5)
Step-by-step explanation:
To check your answer, use the box method or foil, whichever you prefer. When you use it, leave out the x in front of the parenthesis. The answer will come to x(28x^2+27x+5), then distribute the x. You will get your original answer.
Have a great night and Happy New Year!!
Answer: x(7x + 5)(4x + 1)
Step-by-step explanation:
28x³ + 27x² + 5x
= x(28x² + 27x + 5)
= x(28x² + 7x + 20x + 5)
= x[7x(4x + 1) + 5(4x + 1)]
= x(7x + 5)(4x + 1)