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Divide x^3 -3x^2 by x-2
. Step 1 - Fill in the missing number:
To divide x^3 - 3x^2 by x - 2, use long division. The quotient is x^2 - x - 4.
Explanation:To divide x^3 - 3x^2 by x - 2, we can use long division. Here are the steps:
Start by dividing the first term of the numerator, x^3, by the denominator, x. This gives us x^2.Multiply the entire denominator, x - 2, by the quotient we found in the previous step, x^2. This gives us x^2(x - 2) which simplifies to x^3 - 2x^2.Subtract this product from the numerator, x^3 - 3x^2 - (x^3 - 2x^2) = -x^2.Bring down the next term from the numerator, which is 0x.Divide this new term, -x^2, by the denominator, x, to get -x.Multiply the entire denominator, x - 2, by the quotient we found in the previous step, -x. This gives us -x(x - 2) which simplifies to -x^2 + 2x.Subtract this product from the previous result, -x^2 - (-x^2 + 2x) = -4x.Bring down the final term from the numerator, which is -6x^2.Divide this term, -4x, by the denominator, x, to get -4.Multiply the entire denominator, x - 2, by the quotient we found in the previous step, -4. This gives us -4(x - 2) which simplifies to -4x + 8.Subtract this product from the previous result, -4x - (-4x + 8) = -8.Therefore, the quotient of x^3 - 3x^2 divided by x - 2 is x^2 - x - 4.
The value of [tex]\( k \)[/tex] is 2.
Which gives a remainder of 0, indicating [tex]\( x - 2 \)[/tex] is a factor of the polynomial [tex]\( x^3 - 3x^2 - 10x + 24 \)[/tex]. The complete synthetic division process for [tex]\( k = 2 \)[/tex] would then be:
2 | 1 -3 -10 24
| 2 -2 -24
---------------------
1 -1 -12 0
The quotient of the division is [tex]\( x^2 - x - 12 \)[/tex] with a remainder of 0.
complete question given below:
Simplify the expression. Write your answer as a power. (2/3)^2⋅(2/3)^6
The expression simplifies to[tex]\( \left(\frac{2}{3}\right)^8 \), representing \( \frac{2^8}{3^8} \), or \( \frac{256}{6561} \).[/tex]
Sure, here's a detailed stepwise solution with explanation:
1. **Understand the problem**: We're asked to simplify the expression [tex]\( \left(\frac{2}{3}\right)^2 \cdot \left(\frac{2}{3}\right)^6 \).[/tex]
2. **Apply the exponent property**: According to the exponent property [tex]\(a^m \cdot a^n = a^{m+n}\),[/tex] when multiplying two expressions with the same base, we add their exponents.
3. **Calculate the exponents**:
- The first expression [tex]\( \left(\frac{2}{3}\right)^2 \) has an exponent of 2. - The second expression \( \left(\frac{2}{3}\right)^6 \)[/tex] has an exponent of 6.
4. **Add the exponents**:
[tex]- \(2 + 6 = 8\).[/tex]
5. **Combine the expressions**:
- By applying the exponent property, we get [tex]\( \left(\frac{2}{3}\right)^{2+6} = \left(\frac{2}{3}\right)^8 \).[/tex]
6. **Final result**:
- The simplified expression is [tex]\( \left(\frac{2}{3}\right)^8 \), which represents \( \frac{2^8}{3^8} \).[/tex]
- This can also be expressed as [tex]\frac{256}{656\1} \),[/tex] where 256 is the numerator and 6561 is the denominator.
7. **Explanation of the result**:
- The simplified expression represents the result of raising [tex]\( \frac{2}{3} \)[/tex] to the power of 8, which is obtained by multiplying the expression by itself 8 times.
- It can be interpreted as the fraction [tex]\( \frac{256}{6561} \)[/tex] , which is the result of raising 2 to the 8th power in the numerator and 3 to the 8th power in the denominator.
In 2005, 24.8% of all Americans
were under 18 years old. Rhonda
conducts a survey of the ages of
students in eleventh grade at her school.
On November 1, she finds the average
age is 200 months. She also finds that
two-thirds of the students are within
6 months of the average age. Write and
solve an equation to determine the age
limits for this group of students. How
many months will it be until the first of
these students turn 18?
Let's assume
x is the age of 11th grade student
we are given
Rhonda conducts a survey of the ages of students in eleventh grade at her school.
On November 1, she finds the average age is 200 months.
and
She also finds that two-thirds of the students are within 6 months of the average age.
so, we can set up equation as
[tex]|x-200|=3[/tex]
now, we can solve for x
[tex]x-200=3, x-200=-3[/tex]
[tex]x-200=3[/tex]
[tex]x-200+200=3+200[/tex]
[tex]x=203[/tex]
[tex]x-200=-3[/tex]
[tex]x-200+200=-3+200[/tex]
[tex]x=197[/tex]
So, the minimum age of 11th grade student is 197 months
So, the maximum age of 11th grade student is 203 months
now, we are given age is 18 years
we will change into months
[tex]18 years=12*18 months[/tex]
[tex]18 years=216 months[/tex]
So, first of these students turn 18 is
[tex]=216 -203[/tex]
[tex]=13[/tex] months...........Answer
Simplify |2.35 - 4.89| + | 8.39 - 3.72 |
The answer to this equation would be 7.21
the answer is 7.21.
please solve
|q-8|=14
The population of a town y years after 1970 is 31,787 + 1,735y.
Which statement is correct?
A.
The population increased by 1,735 people each year after 1970.
B.
The population decreased by 1,735 people each year after 1970.
C.
The population decreased by 31,787 people each year after 1970.
D.
The population increased by 31,787 people each year after 1970.
The population of a town y years after 1970 is;
31,787 + 1,735y.
From the results above;
y represents the number years
So the population increased by 1,735 people each year after 1970.
Population after y years = 31,787 + 1,735y
The correct choice is 'A.'
need help with this math problem
is 20 over 5 a rational number
Answer:
Yes
Step-by-step explanation:
It is rational because it isnt a decimal or fraction
Pls rate me 5 stars and thank me :D
Some help me please
I think the answer is 2 (D) Hope this helps :D
Answer:
6
Step-by-step explanation:
paper clips costs $7.20 what is the unit price of the paper clips
What is 2−b3=−52 thanks
Answer: 18
Step-by-step explanation:
a woman has $28,000. part is invested for one year in a certificate of deposit paying 7% interest, and the remaining amount in cash management fund paying 9%. after 1 year, the total interest on the two investments is $2,200. how much is invested at each rate
Answer:
Amount invested at 7% = 16000
Amount invested at 9% = 12000
Step-by-step explanation:
Let x be the amount invested at 7% and y be the amount invested at 9%.
Since the total amount invested is $28000, therefore, we can set up the first equation as:
[tex]x+y=28000[/tex]
Secondly, we are give that sum of two investments is $2200. Therefore, we can write the second equation as:
[tex]0.07x+0.09y=2200[/tex]
Now we need to solve these two equations to get the values of x and y.
First of all, we multiply the second equation with 100 in order to get rid of decimal values.
[tex](0.07x+0.09y)*100=2200*100\\7x+9y=220000[/tex]
Let us use substitution method here. First of all we will solve for y from first equation and plug that into second equation.
[tex]y=28000-x[/tex]
[tex]7x+9(28000-x)=220000\\7x+252000-9x=220000\\-2x=-32000\\x=16000[/tex]
Therefore, amount invested at 7% is $16000 and amount invested at 9% is 28000-16000=$12000.
Find the product of 20 x 9 x 5. Tell which property you use?
The answer to 20 x 9 x 5 is 900. You use multiplication property.
Hope this helps! :)
What is the value for y?
Enter your answer in the box.
y =
The given triangle has two sides marked equal and hence is an isosceles triangle.In isosceles triangle base angles are equal <A=<B=50.
Sum of angles in any triangle is 180 degrees.
<A+<B+<C=180°
50+50+5y+10=180
Adding like terms :
110+5y=180
Subtracting 110 on both sides:
5y=70
Dividing both sides by 5:
y=14.
The isosceles triangle, with base angles both at 50 degrees, is solved for the variable y, resulting in y = 14. This value, when substituted, gives angle C as 65 degrees.
The triangle in question is an isosceles triangle, meaning that two of its sides are of equal length. Consequently, the base angles, denoted as angle A and angle B, are also equal, and both are given as 50 degrees. In any triangle, the sum of its angles equals 180 degrees, so for this isosceles triangle:
[tex]\[ \angle A + \angle B + \angle C = 180^\circ \][/tex]
Substituting the known values:
50 + 50 + 5y + 10 = 180
Combining like terms:
110 + 5y = 180
To isolate the variable term, subtract 110 from both sides:
5y = 70
Now, divide both sides by 5 to find the value of y:
y = 14
In conclusion, the value of y is determined to be 14. This signifies that in the given isosceles triangle, angle C is represented as 5y + 10, which becomes 65 degrees. Therefore, the solution provides a comprehensive understanding of the triangle's angle distribution.
For more such information on: angles
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What is the sum of 4 8/10 and 1 1/2
A 35-inch board is to be cut into three pieces so that the second piece is twice as long as the first piece and the third piece is 4 times as long as the first piece. If x represents the length of the first piece, find the lengths of all three pieces.
Answer:
Step-by-step explanation:
name all the number sets the number 0 belongs to
The number zero (0) belongs to the following sets:
Integers - which are all whole numbers. Zero (0) is a whole number and thus an integer.Real numbers - which are all rational and irrational numbers. Zero (0) is a rational number and thus a real number.Mrs. Sheppard cuts 1/2 of a piece of construction paper. She uses 1/6 of the piece to make a flower. What fraction of the sheet of paper does she use to make the flower?
she uses 1/12 of the paper
She uses ¹/₁₂ of the sheet of paper to make the flower
Further explanationOrder of Operations in Mathematics follow this following rule :
ParenthesesExponentsMultiplication and DivisionAddition and SubtractionThis rule is known as the PEMDAS method.
In working on a mathematical problem, we first calculate operation that is in parentheses, follow by exponentiation, then multiplication or division, and finally addition or subtraction.
Let us tackle the problem!
Let :
Total Area of Paper = X
Given:
Mrs. Sheppard cuts 1/2 of a piece of construction paper
[tex]\texttt{Cutting Piece Area of Paper} = \frac{1}{2} \times \texttt{Total Area of Paper}[/tex]
[tex]\texttt{Cutting Piece Area of Paper} = \frac{1}{2} \times X[/tex]
[tex]\texttt{Cutting Piece Area of Paper} = \boxed {\frac{1}{2} X}[/tex]
She uses 1/6 of the piece to make a flower
[tex]\texttt{Area of Paper for Making Flower} = \frac{1}{6} \times \texttt{Cutting Piece Area of Paper}[/tex]
[tex]\texttt{Area of Paper for Making Flower} = \frac{1}{6} \times \frac{1}{2} X[/tex]
[tex]\texttt{Area of Paper for Making Flower} = \frac{1 \times 1}{2 \times 6}X[/tex]
[tex]\texttt{Area of Paper for Making Flower} = \boxed {\frac{1}{12}X}[/tex]
Learn morePerimeter of Rectangle : https://brainly.com/question/12826246Elimination Method : https://brainly.com/question/11233927Sum of The Ages : https://brainly.com/question/11240586Answer detailsGrade: Middle School
Subject: Mathematics
Chapter: Percentage
Keywords: Linear , Equations , 1 , Variable , Line , Gradient , Point , Multiplication , Division , Exponent , PEMDAS , percentange , percent
Raphael went to the store and bought 2 1/2 pounds of chicken breasts for $9.00 what was the cost per pound of chicken breasts? Round your answer to the nearest cent
You have to divide 9 by 2.5, which is 3.6
The answer is $3.60 per pound of chicken breasts
Simplify the expression.
(6g)^3
Well, the exponent is distributed to the 6 and g.
g cannot be changed and therefore remains as [tex]g^3[/tex]
[tex]6^3[/tex] can be simplified even further and into the number 216
Therefore, your answer should be:
[tex]216g^3[/tex]
When the highest exponent of any variable is three, then the the expression is termed as cubic expression.
Thus,the given expression is a cubic expression and the answer to the given expression is [tex]216g^3[/tex].
Given expression has two components, a whole number and a variable.
Variables cannot be solved with powers and remain same. Whole number needs to be multiplied by the times its power is.Calculations:
Solving the expression [tex][6\rm g]^3[/tex] :
[tex](6\times\ 6 \times6) g^3 = 216g^3[/tex]
Thus, the final value of the expression is [tex]216g^3[/tex].
Learn more about the topic here:
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A wheel has 16 spokes. How many spaces are there between the spokes?
The distance between the spokes of the wheel will be πr / 8 units.
What is the arc length of the sector?Let r is the radius of the sector and θ be the angle subtended by the sector at the center. Then the arc length of the sector of the circle will be
Arc = (θ/2π) 2πr
A wheel has 16 spokes. Then the angle between the two spokes is calculated as,
θ = 2π / 16
Let 'r' be the radius of the wheel. Then the distance between the spokes will be given as,
Arc = ((2π / 16)/2π) 2πr
Arc = 2πr / 16
Arc = πr / 8
The distance between the spokes of the wheel will be πr / 8 units.
More about the arc length of the sector link is given below.
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If RS = 3x + 1, ST = 2x – 2, and RT = 64, find the value of x.
S+ST = RT
3x+1 + 2x-2 = 64
5x = 65
x = 13
Seven less than one-fourth of a number is -1 (Write this as an equation) HELP FAST!!!!!
1/4n - 7 = -1
Hope this helps and was fast enough!
The phrase 'Seven less than one-fourth of a number is -1' translates into the mathematical equation: 1/4x - 7 = -1.
Explanation:The subject of your question is Mathematics, and based on the content, it seems like it's geared toward a Middle School level. 'Seven less than one-fourth of a number is -1' can be translated into the equation: 1/4 x - 7 = -1, where 'x' represents the number in question.
To achieve this, the phrase 'one-fourth of a number' translates into 1/4x in mathematics and 'seven less' means you subtract seven from that quantity (hence, -7). Hence, the equation becomes '1/4x - 7'. This equals -1, according to your statement, so the final equation is 1/4x - 7 = -1.
Learn more about Equation Translation here:https://brainly.com/question/35166334
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Negative three times a number increased by seven less than -11
If there isn't any parenthesis it would be
-3n + 7 < 11
-3n < 4
n > 4 divided by 3
With parenthesis
-3(n+7) < 11
-3n - 21 < 11
-3n < 10
n > - 10 over 3
The difference between consecutive perfect square numbers is always odd. True or false?
Answer:
True.
Step-by-step explanation:
Consecutive square numbers can be written as:
1^2, 2^2, 3^2, 4^2, 5^2 ...
The sequence of the numbers being squared in odd, even, odd, even...
Squaring an odd number yields an odd. Squaring an even yields an even. The difference between an odd and even number is always odd. Since consecutive perfect squares are odd, even, odd... then the difference is always odd.
Answer:
The answer is: True.
Step-by-step explanation:
A perfect square number in math is an integer that can be expressed as the product of a number by itself.
The difference between each square and consecutive number, if it starts with 0, is all odd numbers, in ascending order.
The answer is: True.
What is the common difference between the elements of the arithmetic sequence below?
–18, –22.5, –27, –31.5, –36
I need help D: (The question is on the image!)
I am sprry bit I am not sure if I got it right but 560 centimeters if you group the sum of each side and multiply it like 2(2+12)*2(4+6), maybe I switched the multiplications around
Remark
You have to make an assumption here. I know of no other way to do the problem than by making the assumption that 10 * 14 figure is a rectangle. If that is not true, the problem is not solvable.
Step One
Find the length of the shaded area.
The length will be the length of the hypotenuse of a right triangle formed by the two smaller sides = the hypotenuse.
a = 4
b = 12
c = ????
Length
L = square root (a^2 + b^2)
L = √(4^2 + 12^2)
L = √(16 + 144)
L = √160 = √(4*4 * 10)
L = 4√(10)
Width
The width is done the same way.
a = 6
b = 2
w = c = ??
w = √(6^2 + 2^2)
w = √(36 + 4)
w = √40
w = √(2 * 2 * 10)
w = 2 √ 10
Area
Area = L * W
Area = 4√10 * 2√10
Area = 8 * 10
Area = 80
which of these is not included in the set of rational numbers? all integers, all whole numbers, all repeating decimals, or all non-terminating decimals
Answer: non-terminating decimals
Integers and whole numbers can be converted to fraction form. Example, the whole number 3 can be written as 3/1 which is rational. A rational number is any fraction of whole numbers (eg: 7/19). The denominator can never be zero.
All repeating decimals can be converted into a fraction. A number like 0.8888 with the 8s repeating forever converts to the fraction 8/9, which is rational
Non-terminating decimals are decimals that go on forever. If there is no pattern to the decimal sequence, then the decimals don't repeat and the number cannot be converted to a rational number. Something like pi = 3.14159... has no pattern to the decimal sequence. Therefore, a number like pi is irrational, which literally means "not rational", so numbers like pi aren't rational and are not part of the set of rational numbers.
Non terminating and non repeating decimals cannot be written in fraction from . So they are not included in set of rational numbers.
Given :
Lets take set of rational numbers that can written as a fraction of two numbers.
All integers are positive and negative numbers.
Rational numbers includes integers
Whole numbers starts from 0,1,2..........
Whole numbers are included in rational numbers
Repeating decimals can be written in fraction form .
Non terminating and non repeating decimals cannot be written in fraction from . So they are not included in set of rational numbers.
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Geo: Worth 50 points and I will give brainliest to right answer! #24
1. ∠1 ≅ ∠3 1. given
∠1 and ∠6 are supplementary angles
∠3, ∠4, and ∠5 are supplementary angles
2. m∠1 = m∠3 2. definition of congruency
3. m∠1 + m∠6 = 180° 3. definition of supplementary angles
m∠3 + m∠4 + m∠5 = 180°
4. m∠3 + m∠4 + m∠5 = m∠1 + m∠6 4. transitive property
5. m∠3 + m∠4 + m∠5 = m∠3 + m∠6 5. substitution property
6. m∠4 + m∠5 = m∠6 6. subtraction property of equality
Add. 5/6+2 3/4 Enter the sum in the box as a mixed number in the simplest form.
5/6+2 3/4
= 10/12 + 2 9/12
= 2 19/12
= 3 7/12
Hope that helps
Mixed Number Form:[tex]3\frac{7}{12}[/tex]
Step by step: [tex]\frac{5}{6} + 2\frac{3}{4}[/tex]
= [tex]\frac{5}{6} + \frac{11}{4}[/tex]
= [tex]\frac{43}{12}[/tex]
Answer: [tex]3\frac{7}{12}[/tex]