Answers
The required factors of the polynomial by grouping are (x-3)(x^2 + 2).
What is grouping to solve cubic polynomial?To factor polynomial equations, a specialized approach is called grouping. It can be applied to polynomials with four terms as well as quadratic equations. Although they differ significantly, the two approaches are comparable.The first two terms and the final two terms are combined: p(x)=(x3 - 4x2) + (3x - 12), and we then identify the shared
factors as follows: p(x) = x2(x - 4) + 3(x - 4). (x - 4).
According to question:x^3 - 3x^2 + 2x -6
(x-3)(x^2 + 2)
Thus, required factors are (x-3)(x^2 + 2).
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Related Questions
Answer to this angle question
Answers
Check the picture below.
HELP FAST
How to find the complex zeroes of [tex]x^2-6x+13[/tex]
Answers
Answer:
There are few possible ways to find the complex zeros
You can find the complex zeros by using quadratic formula
[tex]x^2-6x+13=0[/tex]
[tex]=\frac{-\left(-6\right)\pm \sqrt{\left(-6\right)^2-4\cdot \:1\cdot \:13}}{2\cdot \:1}[/tex]
[tex]x_{1,\:2}=\frac{-\left(-6\right)\pm \:4i}{2\cdot \:1}[/tex]
[tex]x_1=\frac{-\left(-6\right)+4i}{2\cdot \:1},\:x_2=\frac{-\left(-6\right)-4i}{2\cdot \:1}[/tex]
[tex]x=3+2i,\:x=3-2i[/tex]
Understanding the meanings of words and phrases helps translate into algebraic expressions.
Example: 6 multiplied by the absolute value of 7 less than the cube of a number
6 · |n³ – 7|
? Question
What algebraic expression belongs with each verbal description?
the square root of the ____
of the ____ of a ____ and 11 → √x2² - 11 the ____ of __ times a number and -11 → -2x/11
the __ of the ____ ___ of two times a number and 11 → √2x + 11
Answers
The correct statement is- the square root of the __difference__ of a _the polynomial x²_ and 11 → √x² - 11 the __product__ of _-2x_ times a number and reciprocal of -11 → -2x/11 the sum_ of the __square root__ of two times a number and 11 → √2x + 11.
What is a polynomial expression?Polynomial is made up of two terms, namely Poly (meaning “many”) and Nominal (meaning “terms.”). A polynomial is an expression composed of variables, constants, and exponents, combined using mathematical operations such as addition, subtraction, multiplication, and division (No division operation by a variable). Based on the number of terms present in the expression, it is classified as monomial, binomial, and trinomial. For example P(x) = x2-5x+11
Given here, [tex]\sqrt{x^2-11}[/tex] , This in word phrase can be written the square root of the difference between a square of a number and 11.
-2x/11 can be written as twice the number multiplied by the reciprocal of -11
√2x + 11 can be written as sum of square root of twice the number and 11
Hence, The correct statement is- the square root of the __difference__ of a _the polynomial x²_ and 11 → √x² - 11 the __product__ of _-2x_ times a number and reciprocal of -11 → -2x/11 the sum_ of the __square root__ of two times a number and 11 → √2x + 11.
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Solving by Factoring
Please explain in detail the strategy, Solving by Factoring, discussed in the lesson Quadratic in Form Polynomials. Include an example with this explanation to clearly explain the process.
Answers
Answer:
Step-by-step explanation:
Solving by factoring is a strategy for solving a polynomial equation that is in quadratic form. Quadratic form means that the equation is of the form ax^2+bx+c=0, where a,b, and c are real numbers. When factoring, the goal is to express the equation as the product of two simpler equations. To do this, we must factor the quadratic equation into two linear equations, each with a single variable.
For example, consider the equation x^2+3x-4=0. To factor this equation, we can first rewrite it as (x+4)(x-1)=0. This is the same as x+4=0 and x-1=0. We can then solve each of these linear equations to find the solutions. In this case, the solutions are x=-4 and x=1.
Therefore, the strategy of solving by factoring is to rewrite a polynomial equation in quadratic form as the product of two simpler equations, and then solve each of these equations. The solutions to the original equation can then be found by solving each of the linear equations.
The sum of the page numbers on the facing pages of a book is 553. Find the smaller page number.
Answers
Answer: To solve this problem, we can use algebra. Let x be the smaller page number. Then, the larger page number is x + 1, since the pages are facing each other. We know that the sum of these two numbers is 553, so we can set up the equation:
x + (x+1) = 553
Next, we will solve for x by combining like terms:
2x + 1 = 553
Now we will subtract 1 from both sides of the equation:
2x = 552
Finally, we will divide both sides by 2:
x = 276
So the smaller page number is 276.
Step-by-step explanation:
The ratio of 1.2 to 32 is the same as the ratio of 4.8 to ———-.
Answers
Answer:
128
Step-by-step explanation:
1.2*4 =4.8
so 32*4 = 128
Triangle FYJ is congruent to triangle HYJ using the
Triangle Congruence Theorem. Therefore, segment
FJ is congruent to segment
Figure FJHW
JW 1 FH, FY≈ HY, JY WY
W
H
Answers
Triangle FYJ is congruent to triangle HYJ using the RHS congruency theorem.
FJ is congruent to segment HJ.
What is congruency?We know two similar planer figures are congruent when we have sides or angles or both that are the same as the corresponding sides or angles or both.
We know right angle hypotenuse congruency, which states two right angle triangles are congruent if one of the legs and hypotenuse corresponding to the other right angle triangle is equal in measure.
Triangle FYJ is congruent to triangle HYJ as FY is congruent to HY and JH is congruent to JH.
So, Their hypotenuses are also equal in measure.
Hence, FJ is congruent to JH.
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Pleaseeeeew i beg you
Answers
0.
A woman on a billboard is 8
3
8
feet tall. If the
scale of the billboard is 1 foot = 8 inches,
what is her actual height?
Answers
Answer: The scale of the billboard is 1 foot = 8 inches, so to find the actual height of the woman, we need to multiply the height on the billboard by 8.
8 3/8 feet x 8 inches/foot = 66 inches (8 x 8) + (3 x 8) = 66
So the woman's actual height is 66 inches.
Step-by-step explanation:
In interest rate 6% in 2500$ in year when go to investment at the end how many amount of 3 yrs and 5 months in simple interest ?
Answers
Answer: So, after 3 years and 5 months, the total amount of simple interest earned on an investment of $2500 at a 6% interest rate would be $525.
Step-by-step explanation:
To calculate the simple interest on an investment of $2500 at a 6% interest rate for 3 years and 5 months, you would use the formula:
Simple Interest = (Principal x Interest Rate x Time in Years)
In this case, the time in years would be 3.5 (3 years and 5 months)
Simple Interest = (2500 x 0.06 x 3.5) = $525
So, after 3 years and 5 months, the total amount of simple interest earned on an investment of $2500 at a 6% interest rate would be $525.
4. The 92 million Americans of age 50 and over control 50% of all discretionary income. AARP estimates that the average annual expenditure on restaurants and carryout food was $1,873 for individuals in the age group. Suppose this estimate is based on a sample of 80 persons and that the sample standard deviation is $550. a. At 95% confidence, what is the margin of error? b. What is the 95% confidence interval for the population mean amount spent on restaurants and carryout food? c. What is your estimate of the total amount spent by Americans of age 50 and over on restaurants and carryout food? d. If the amount spent on restaurants and carryout food is skewed to the right, would you expect the median amount spent to be greater than or less than$1,873?
Answers
a) The margin of error for the 95% confidence interval is given as follows: $122.4.
b) The 95% confidence interval for the population mean amount spent on restaurants and carryout food is given as follows: ($1,750.6, $1,995.4).
c) The estimate of the total amount spent by Americans of age 50 and over on restaurants and carryout food is between $161,055,200,000 and $183,576,800,000.
d) As the distribution os skewed to the right, the median would be expected to be less than the mean.
What is a t-distribution confidence interval?The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the following rule:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
The margin of error is then defined as follows:
[tex]M = t\frac{s}{\sqrt{n}}[/tex]
In which the variables of the equation are presented as follows:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 80 - 1 = 79 df, is t = 1.9905.
The parameters for this problem are given as follows:
[tex]\overline{x} = 1873, s = 550, n = 80[/tex]
Hence the margin of error is of:
[tex]M = 1.9905 \times \frac{550}{\sqrt{80}} = 122.40[/tex]
Considering the sample mean and the margin of error, the bounds of the confidence interval are given as follows:
Lower bound: 1873 - 122.40 = $1,750.6.Upper bound: 1873 + 122.40 = $1,995.4.Considering the bounds of the confidence interval and the population of 92 million, the bounds of the estimate of the total amount are given as follows:
Lower bound: 92,000,000 x 1,750.6 = 161,055,200,000.Upper bound: 92,000,000 x 1,995.4 = 183,576,800,000.The relation between mean, median and skewness is given as follows:
Mean greater than median: Positively(right) skewed.Mean less than the median: Negatively(left) skewed.More can be learned about the t-distribution at https://brainly.com/question/17073112
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20 POINTS PLEASE I NEED THIS RIGHT NOW!!!!!!!
A system of equations is given.
Equation 1: 5x − 2y = 10
Equation 2: 4x − 3y = 15
Explain how to eliminate x in the system of equations.
Answers
Hope it helps.
Please send your query through comment section.
Step-by-step explanation:
the funny thing with equations is we can transform them (as long as we do every operation in both sides), and we can even add them up or subtract from each other to get new equations that are maybe simpler to solve.
to eliminate x i would recommend to multiply the first equation by 4, and the second equation by 5 and then subtract equation 2 from equation 1 (comparable term by comparable term).
5x - 2y = 10
4x - 3y = 15
would then turn into
20x - 8y = 40
- 20x - 15y = 75
------------------------
0 7y = -35
y = -35/7 = -5
now we can pick any original equation to solve for x.
e.g.
5x - 2×-5 = 10
5x + 10 = 10
5x = 0
x = 0
solve the equation
(x + 2)(x + 6) = 0
Answers
Answer:
The zeroes of the equation are -2 and -6.
Step-by-step explanation:
(x + 2)(x + 6) = 0
=> x = -2, -6
Hope it helps.
Find the missing length.
Answers
Answer:
125
Step-by-step explanation:
2^2+11^2=c^2
4+121=c^2
125=c^2
c=125 square root
What’s the answer Question 43
Answers
Answer:
90
Step-by-step explanation:
15 to first 20
so 120 = 6*20
so 6*15 =90
What is the product?
(4s+2)(5s²+10s+3)
20s²+20s+6
20s³ +40s²+12s
20s^3 +10s^2 +32s+6
20s³ +50s²+32s+6
Answers
Answer:
Answer
Step-by-step explanation:
20s³ +50s²+32s+6
Ill give brainiest to who ever answers
Answers
Answer:
Angle EBC = 88
because of the angle bisector theorem
44 + 44 = 88
Answer:88°
Step-by-step explanation:
EBD is equal to 44°, while DBC is also equal to 44° if you see it well.
So EBD and DBC together is 88°.
44°+44°=88°
v+w=7
v+w=1
helpppppppppppppp
Answers
Answer:
4+3=7
-2+3=7
Step-by-step explanation:
Write 8,400,000 m3 as a fraction of 0.012 km3. Give your answer in its simplest form.
Answers
8,400,000 m^3 / 10^9 = 0.0084 km^3
So, 8,400,000 m^3 is equal to 0.0084 km^3.
Next, divide 0.0084 km^3 by 0.012 km^3 to get the fraction:
0.0084 km^3 / 0.012 km^3 = 0.07.
The answer is 0.07 in its simplest form.
A factory that produces toy wheels finds that they must discard 3 out of 100 wheels because they are defective. How many wheels would they expect to discard everyday if the factory produces 1200 wheels per hour in each 8 hr day.
Answers
they expect to discard everyday 288.
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
here, given that,
they must discard 3 out of 100 wheels because they are defective.
the factory produces 1200 wheels per hour in each 8 hr day.
total per day = 9600
so, they expect to discard everyday =9600 * 3%
=288
hence, they expect to discard everyday 288.
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one fctor of the function f(x)= x^3 -9x^2 +20x -12 is (x-6) describe how to find the x-intercepts and the y-intercept
Answers
The x-intercepts and the y-intercept of the cubic function f(x) = x³ - 9·x² + 20·x - 12 for which (x - 6) is a factor are;
The x-intercepts are; (6, 0), (2, 0), and (1, 0)The y-intercepts of the function is the point (0, -12)What is a function?A function is a rule that uniquely maps each value from the set of input variables to exactly one value in the set of the output variables.
The specified cubic function is; f(x) = x³ - 9·x² + 20·x - 12
A factor of f(x) = x - 6
The x-intercepts are the points on the graph of the function, where the value of the function, f(x) = 0, which are found as follows;
At the x-intercept, f(x) = x³ - 9·x² + 20·x - 12 = 0
x³ - 9·x² + 20·x - 12
Dividing the cubic function by the factor (x - 6), we get;
x² - 3·x + 2
(x - 6) | x³ - 9·x² + 20·x - 12
[tex]{}[/tex] x³ - 6·x²
[tex]{}[/tex] -3·x²
[tex]{}[/tex] -3·x² + 18·x
[tex]{}[/tex] 2·x
[tex]{}[/tex] 2·x - 12
[tex]{}[/tex] 0
The other factor of the cubic function is; x² - 3·x + 2
x² - 3·x + 2 = (x -2)·(x - 1)
Therefore;
f(x) = x³ - 9·x² + 20·x - 12 = (x - 6)·(x - 2)·(x - 1)
From which at the x-intercepts, we get;
f(x) = (x - 6)·(x - 2)·(x - 1) = 0
x = 6, x = 2, and x = 1
The x-intercepts are the points (6, 0), (2, 0), and (1, 0)The y-intercept are the points the x-values is zero, therefore, at the y-intercepts, we get;
f(0) = 0³ - 9·0² + 20·0 - 12 = -12
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Suppose A = {2, 5, 7, 9, 13, 25, 26}.
(a) Find n(A).
n(A) =
(b) T/F: 20 A
True
False
Answers
Part (a)
Answer: 7Reason:
There are 7 items inside set A. The notation n(A) counts the number of elements in a set.
==========================================
Part (b)
It's not clear what your teacher is asking. It seems this part is incomplete. Please revise.
To order tickets online to a hockey game, there is a processing fee plus the cost per ticket. The cost for 5 tickets is $174.45. The cost for 8 tickets is $271.95. Write and solve a linnear equation to find the total cost to order 12 tickets.
Answers
The linear equation for this situation is ax + y = Total cost, where is no. of ticket, x = $32.5, is cost of ticket and y = $11.9 is processing fee.
What is linear equation?A linear equation is an algebraic equation where the highest exponent of the variable is one. There are linear equations with one, two, or three variables, but not all linear systems have three equations. Typically, a system of linear equations has a single solution, but occasionally there is no solution or an infinite number of solutions.
A relationship in which the value of one variable, say "x," depends on the value of the other variable, say "y," is described by a two variables linear equation. A linear equation's graph will be a straight line if there are only two variables.
Given that cost for 5 tickets is $174.45
Let x be the cost of each ticket and y be the processing fee
5x + y = 174.45
And for the cost for 8 tickets is $271.95
8x + y = 271.95
Subtract the terms
8x + y = 271.95
- 5x + y = 174.45
3x + 0 = 97.5
If 3x = 97.5
Then,
x = 97.5/3
x = 32.5
Each ticket costs $32.5 then processing fees
5(32.5) + y = 174.45
y = 174.45 - 162.5
y = 11.95
8(32.5) + y = 271.95
y = 271.95 - 260
y = 11.95
Thus, The linear equation for this situation is ax + y = Total cost, where is no. of ticket, x = $32.5, is cost of ticket and y = $11.9 is processing fee.
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Please can someone help me on this question i will give out 30 points and brainly if you give me the right answer
Answers
Answer: A irregular
b. irregular
c neither
d. Regular
e. regular
Step-by-step explanation: Regular polygons have all sides equal in length but an irregular polygon does not have all sides equal.
Answer:
A: Irregular polygon
B: Irregular polygon
C: Neither
D: Regular polygon
E: Regular polygon
Step-by-step explanation:
To start off with, we can eliminate C for being a polygon (neither), because being a polygon states the shape must be closed with a finite number of line segments (a circle has an infinite amount of line segments).
A regular polygon states that it must have an equal distance on all sides. We can find this by looking at what shapes have a line (which represents that it has the same length) on all sides. The only polygons that fit this requirement are D and E.
From here we can see that the remaining polygons of A and B are in fact irregular polygons by process of elimination.
A smoke-detector system uses three devices, A, B and C. If smoke is present, the probability that it will be detected by device A is 0.92; by device B is 0.98; and by device C is 0.93. If smoke is present, find the probability that the smoke will be detected by the three devices. Round your answer to 4 decimal places.
Answers
Answer:
Step-by-step explanation:
17. Assessment Focus Students baked
cookies for a charity bake sale.
Elsa baked 2 dozen cookies.
Layton baked 2 times as many
cookies as Elsa. Meghan and Josh
together baked 5 times the number of
cookies that Elsa baked.
a) Estimate. About how many dozen
cookies did Layton bake? About
how many dozen cookies did
Meghan and Josh bake altogether?
b) Calculate how many dozen cookies
Layton baked.
c) Calculate how many dozen cookies
Meghan and Josh baked.
d) How many dozen cookies did these
4 students bake altogether?
e) How many cookies did these
4 students bake altogether?
Show your work.
Answers
Answer:
Step-by-step explanation:
a)24
b)4
c)10
d)16
e)172
A boat can travel 370 miles in 185 gallons. How much gasoline it needs to travel 444 miles. [tex]370:185[/tex]
Answers
Answer: 222 gallons of gasoline to travel 444 miles.
Step-by-step explanation: To find how much gasoline the boat needs to travel 444 miles, we need to use the formula:
distance = rate x time
Where distance is the total distance to be traveled, rate is the distance per unit of fuel (370 miles/185 gallons) and time is the amount of fuel required to travel 444 miles.
So we can calculate the fuel required as:
Fuel = (distance) / (rate)
Fuel = (444 miles) / (370 miles/185 gallons) = 444/ (370/185) = 444/2 = 222 gallons.
So the boat needs 222 gallons of gasoline to travel 444 miles.
A trader sold 1.6 lot EURUSD. How many units of Euros did he sell?
Answers
Answer:
let's see jssjsjnsjsjsjsjsjsjsjsjsjs
Let p be you are a baby. Let Q be you are logical. Let r be you can manage a crocodile. Let S be you are despised. Translate the following Statement into symbolic form. Babies are illogical
A.) Q ➡️~P
B.) ~P ➡️~Q
C.) P➡️~Q
D.) Q➡️P
Answers
Translating the statement "Babies are illogical" into symbolic form willoll be C. P➡️~Q
What is a symbolic form?Symbols and logical connectors are used in symbolic sentences to represent the sentence's logic.
A letter, such as p, can represent an entire statement in symbolic logic.
In symbolic form, the argument is p → q ~p ∴ ~q It is in the form of the fallacy of the inverse and it is a fallacy, or invalid
In this case, it should be noted that since p is that you are a baby and Q be you are logical. The symbolic form will be C.
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18712−9412 i dont know what the final product would be
Answers
18712-9412= 9,000
Answer:
Step-by-step explanation:
Solution:- this is question of subtraction , so 18712-9412=9300(Answer)
