Use Multiplication to Check Division Whole numbers are closed under addition because the sum of two whole numbers is always a whole number. Explain how the process of checking polynomial division supports the fact that polynomials are closed under multiplication and addition.
Answers
You multiply the quotient by the divisor to test polynomial division.
The process of checking polynomial division supports the fact that polynomials are closed under multiplication and addition will be as follow:
A polynomial will make up the quotient (with or without a remainder). We obtain a polynomial whose exponents and coefficients have changed by multiplying this one by the polynomial divisor. As a result, polynomials are closed when multiplied.The divisor normally has two or more words. By multiplying the entire quotient by each term in the divisor, we will be able to multiply the quotient by this using the distributive property. After this step is complete, we must sum the polynomials we had after multiplying them. By doing so, we have a polynomial solution whose coefficients have changed. Polynomials are hence closed under addition.Hence we can by this way we can check polynomial division supports the fact that polynomials are closed under multiplication and addition
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Related Questions
Sam road his bike 2/5 of a mile and walked another 3/4 of a mile . How far did he travel ?
Answers
The distance Sam traveled is 1.15 miles.
Given: Sam road his bike 2/5 of a mile and walked another 3/4 of a mile.
To find the total distance Sam traveled,
we need to add the distance he traveled while riding his bike to the distance he traveled on foot.
To do that, we need to find a common denominator for 2/5 and 3/4.
The smallest common multiple of 5 and 4 is 20.
So, we'll rewrite 2/5 and 3/4 with a denominator of 20.2/5 = 8/20 (multiply the numerator and denominator by 4)
3/4 = 15/20 (multiply the numerator and denominator by 5).
Now, we can add these two fractions together: 8/20 + 15/20 = 23/20.
So, Sam traveled 23/20 of a mile, which is equivalent to 1 3/20 miles or 1.15 miles (rounded to the nearest hundredth).
Therefore, the distance Sam traveled is 1.15 miles.
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Can someone help me asap? It’s due tomorrow.
Answers
Answer:
I would say convenience sampling. It's hard to tell. Sampling every other person is like systematic sampling, BUT convenience sampling would be to sample people that are easy to reach.
complete the two-column proof.
pleasee
Answers
∠2 ≅ ∠4 and m∠2 = 110°, and proved m<3 = 70⁰.
The answers of the blank lines are:
A . Vertically opposite angle.
B . Linear angle .
C . Hence proved .
Solution:Given ,
∠2 ≅ ∠4 and m∠2 = 110°.
We have to prove
m<3 = 70⁰
Here ,
m<2 = m<4 => They are vertically opposite angles.
And here ,
m<3 and m<4 are supplementary angles.
m∠3 + m∠4 = 180° => linear angle .
m<4 = 110⁰ => since m<2 = m<4
By substituting m∠4 we get,
m∠3 + m∠4 = 180°
= m∠3 + 110 = 180
= 180 - 110
m∠3 = 70°
Hence proved.
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The hypotenuse, c, of right triangle ABC is 5.0 cm long. Give the trigonometry ratio cosA=0.50 for angle A, what is the area of the triangle to the nearest tenth of a cm?
Answers
Answer:
\(\frac{25\sqrt{3} }{8}\)
Step-by-step explanation:
CosA = \(\frac{1}{2}\) , so <A is 60º
Hypotenuse (c) is 5
Opposite is (b)
Adjascent is (a)
cos A = \(\frac{adjascent}{hypotenuse}\) -----> \(\frac{1}{2} = \frac{a}{5}\) ---------> a = \(\frac{5}{2}\)
Pytagoras
\(5^{2} = (\frac{5}{2}) ^{2} + b^{2}\\ b^{2} = 25 - \frac{25}{4} \\b^{2} = \frac{75}{4} \\\\b = \frac{5\sqrt{3} }{2}\)
A = b . a . 1/2
A = \(\frac{25\sqrt{3} }{8}\)
CosA = , so <A is 60º
Hypotenuse (c) is 5
Opposite is (b)
Adjascent is (a)
cos A = -----> ---------> a =
Pytagoras
A = b . a . 1/2
A =
Step-by-step explanation:
calculate the first order correction to for a particle in a one-dimensional box with walls at and due to the following perturbations
Answers
The first-order correction to the energy of a particle in a one-dimensional box with walls at positions x = 0 and x = L due to perturbations can be calculated using perturbation theory. The perturbations in this case are specified as follows:
In order to determine the first-order correction, we need to calculate the expectation value of the perturbing potential operator, V(x), between the unperturbed eigenstates of the system. Since the particle is confined to a one-dimensional box, the unperturbed eigenstates are given by the stationary states of the particle in the absence of perturbations, which are the standing waves (also known as stationary states) described by the wavefunction ψ_n(x) = √(2/L)sin(nπx/L), where n is the quantum number.
The first-order correction to the energy is given by the expression ΔE^(1) = ⟨ψ_n|V|ψ_n⟩, where ⟨ψ_n|V|ψ_n⟩ represents the expectation value of the potential operator V(x) between the unperturbed eigenstates. We can evaluate this expectation value by integrating the product of the perturbing potential and the square of the unperturbed eigenstate wavefunction over the entire range of the box.
In summary, to calculate the first-order correction to the energy of a particle in a one-dimensional box due to perturbations, we evaluate the expectation value of the perturbing potential operator between the unperturbed eigenstates. This correction accounts for the effects of the perturbations on the system's energy levels and provides insight into the behavior of the particle in the presence of the perturbing potential.
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"write an equation of the perpendicular bisector or the segment with endpoints Q(-2,0) and R(6,12). what does y equal?
Answers
Answer:
The equation of perpendicular bisector of QR is:
y = -\frac{2}{3}x+\frac{22}{3}y=−32x+322
Step-by-step explanation:
Given points are:
Q(-2,0)\ and\ R(6,12)Q(−2,0) and R(6,12)
First of all, we have to find the slope of the given line
So,
m = \frac{y_2-y_1}{x_2-x_1}m=x2−x1y2−y1
Here
(x1,y1) = (-2,0)
(x2,y2) = (6,12)
Let m1 be the slope of QR:
Then
\begin{gathered}m_1 = \frac{12-0}{6+2}\\= \frac{12}{8}\\= \frac{3}{2}\end{gathered}m1=6+212−0=812=23
Let m2 be the slope of perpendicular bisector
We know that the product of slopes of two perpendicular lines is -1
\begin{gathered}m_1.m_2 = -1\\\frac{3}{2}.m_2 = -1\\m_2 = -1 * \frac{2}{3}\\m_2 = -\frac{2}{3}\end{gathered}m1.m2=−123.m2=−1m2=−1∗32m2=−32
The bisector will pass through the mid-point of QR
\begin{gathered}M = (\frac{x_1+x_2}{2} , \frac{y_1+y_2}{2})\\M = (\frac{-2+6}{2}, \frac{0+12}{2})\\M = (\frac{4}{2}, \frac{12}{2})\\M = (2,6)\end{gathered}M=(2x1+x2,2y1+y2)M=(2−2+6,20+12)M=(24,212)M=(2,6)
Slope-intercept form of equation is:
y = m_2x+by=m2x+b
Putting the value of slope
y = -\frac{2}{3}x+by=−32x+b
Putting (2,6) in the equation
\begin{gathered}6 = -\frac{2}{3}(2)+b\\6 = -\frac{4}{3}+b\\b = 6+\frac{4}{3}\\b = \frac{18+4}{3}\\b = \frac{22}{3}\end{gathered}6=−32(2)+b6=−34+bb=6+34b=318+4b=322
So,
y = -\frac{2}{3}x+\frac{22}{3}y=−32x+322
Hence,
The equation of perpendicular bisector of QR is:
y = -\frac{2}{3}x+\frac{22}{3}y=−32x+322
A farmer saved $250 in four months. Which unit rate represents the farmer's savings? $1000 per year $1000 per month $750 per year $750 per month
Answers
Answer:
$750 per year
Step-by-step explanation:
The farmer saves $250 in four months. You need to find out how much he makes in a year. There are 12 months in a year. Multiply the amount he saves by 3.
$250 × 3 = $750
The farmer saves $750 per year.
please help me on this asap
Answers
3x² + 22x + 35
Factor the trinomial
Help guys asp!!
Answers
Answer:
(x + 5)(3x + 7)
Step-by-step explanation:
Given
3x² + 22x + 35
Consider the factors of the product of the x² term and the constant which sum to give the coefficient of the x- term
product = 3 × 35 = 105 and sum = 22
The factors are + 15 and + 7
Use these factors to split the x- term
= 3x² + 15x + 7x + 35 ( factor the first/second and third/fourth terms )
= 3x(x + 5) + 7(x + 5) ← factor out (x + 5) from each term
= (x + 5)(3x + 7) ← in factored form
Tracy has a long weekend coming up, and she wants to spend all 3 days camping at Moose Hill Forest. She
checked the weather and found that there is a 25% chance of rain each day. How likely is it that the weather will
stay dry the entire time?
Answers
Answer:
a 75% chance the weather will stay dry
Step-by-step explanation:
3/4
2) 4x - y = 7
-4x + y = -7
I need helpppp
Answers
Answer:
(0,-7)
Step-by-step explanation:
4x - y = 7
-y = -4x + 7
y = 4x - 7
-4x + (4x - 7) = -7
-4x + 4x - 7 = -7
x = 0
4(0) - y = 7
-y = 7
y = -7
Dynamically complete models Consider the following model where the expected value of y, conditional on all current and past values of z and y, is equal to Ely,IZ): y= Bo + Bızı + Bazi-1 + $3Zt-2 + $4Z1-3 + up Which of the following variables must be contained in Z for the model to be dynamically complete? Check all that apply. 0 Y:-1 Zt-2 O Zt-1 21-3 O Zt O yt-2
Answers
The variables that must be contained in Z for the model to be dynamically complete are as follows:Zt-2Zt-1Ztyt-2 Thus, the correct answer is (a), (b), (c), and (g). Hence, this is the required solution.
The following variables must be included in Z for the model to be dynamically complete: Zt-2, Zt-1, Zt, yt-2. Thus, the correct answer is (a), (b), (c), and (g).Explanation:According to the given information and model, for the model to be dynamically complete, it needs to include some variables in Z. To be precise, for a model to be considered as dynamically complete, all the past values should be included in Z. The given model is:y
= Bo + Bızı + Bazi-1 + $3Zt-2 + $4Z1-3 + up .Expected value of y, conditional on all current and past values of z and y, is equal to Ely,IZ.The variables that must be contained in Z for the model to be dynamically complete are as follows:Zt-2Zt-1Ztyt-2 Thus, the correct answer is (a), (b), (c), and (g). Hence, this is the required solution.
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At a company meeting, there were 100 people in attendence. 25% of them are managers. How many managers were in the meeting.
Answers
Answer:
25 managers
Step-by-step explanation:
25% percent of the people are managers.
So 25% of 100 is 25 because 25% means 25/100. So there are 25 managers.
You want to put a 2 inch thick layer of topsoil for a new 15 ft by 12 ft garden. The dirt store sells by the cubic yards. How many cubic yards will you need to order
Answers
The order approximately 1.1111 cubic yards of topsoil from the dirt store.
The volume of topsoil required in cubic feet.
The area of the garden is:
The area of the garden is found by multiplying the length and width of the garden. In this case, the garden is 15 feet by 12 feet, so the area is 15 ft x 12 ft = 180 sq ft.
Since we want a 2 inch thick layer of topsoil, we need to convert the thickness to feet:
2 inches = 2/12 feet = 0.1667 feet
The volume of topsoil required in cubic feet is therefore:
180 sq ft × 0.1667 ft = 30 cubic feet
To convert this to cubic yards, we divide by 27 (since there are 27 cubic feet in a cubic yard):
The dirt store sells topsoil by the cubic yard, so we need to convert our answer from cubic feet to cubic yards. Since there are 27 cubic feet in a cubic yard (3 feet x 3 feet x 3 feet)
30 cubic feet ÷ 27 = 1.1111 cubic yards
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If m< EBC = 3y+10 and m< ABE = 2y-20, find m< EBF.
Answers
By applying the supplementary angle theorem, the magnitude of angle EBF (m<EBF) is equal to 60°.
What is a supplementary angle?A supplementary angle can be defined as two (2) angles or arc whose sum is equal to 180 degrees.
Mathematically, a supplementary angle can be calculated by using this formula:
Q + R = 180
Where:
Q and R are measure of the angles subtended.
Substituting the given parameters into the formula, we have;
m<EBC + m<ABE = 180
3y + 10 + 2y - 20 = 180
5y - 20 = 180
5y = 180 + 20
5y = 200
y = 200/5
y = 40
Now, we can determine the magnitude of angle EBF (m<EBF) based on the given diagram:
m<ABE = m<EBF
m<EBF = 2y - 20
m<EBF = 2(40) - 20
m<EBF = 80 - 20
m<EBF = 60°
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What is 160.5cm to feet
Answers
Answer:
5.265748
Step-by-step explanation:
i did a cm to feet calcu-lator
have good day
The correct answer is 4 feet 17 inches is 160.5 c.m.
How to convert c.m. to feet?The process to convert cm to feet is simple. 1 cm. is equal to 0.025 feet. So you must multiple the unit by 0.025.
Given:
1 feet = 38.48 cm.
1 cm. = 0.025 feet.
160.5 cm = (0.025/1) * 160.5
160.5 cm = 4.1709 feet
4.1709 feet
4.1709 feet = 4 feet + 1709 inches.
We can 4.1709 feet which is equal to 4 feet 17 inches.
Therefore, 160.5 cm is equal to 4 feet 17 inches.
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The volume of a sphere with a diameter of 6cm, rounded to the nearest tenth
Answers
V = (4/3) * π * (d/2)^3
where d is the diameter of the sphere and π is the mathematical constant pi (approximately equal to 3.14159).
Substituting the given value, we get:
V = (4/3) * π * (6 cm/2)^3
V = (4/3) * π * (3 cm)^3
V = 113.0973355 cubic centimeters
Rounding to the nearest tenth, we get:
V ≈ 113.1 cubic centimeters.
Answer:
113.1 cm³
Step-by-step explanation:
diameter = 2 X radius
Volume of sphere = (4/3) X π X r ³
= (4/3) π (3)³
= 36π
= 113.1 cm³ to nearest tenth
HELP? is this easy or am i ?? HELP
Answers
Answer:
6960
Step-by-step explanation:
PLEASE help me solve this question
Answers
Answer:
Step-by-step explanation:
from08:15 to 12:15=4hour
from1300 to 1730=4 and half hour
altogether # of hours worked=8 and half hour
8 and half hour x $12/hr=$102
A line passes through the point (8,-9) and has a slope of -5/4.
Write an equation in point-slope form.
Answers
Answer:
y=-5/4x-19
Step-by-step explanation:
y=-5/4(x(-8))-9
y=-5/4x-10-9
y=-5/4x-19
M = -5/4
2. Y- intercept
Y = mx + b
-9 = (-5/4)(8) + b
-9 = -10 + b
-9 + 10 = -10 + 10 + b (the ten cancels out and we are just left with our b)
1 = b
So, therefore, the equation is:
Y = -5/4x + 1
Help asap please show your work
Answers
Answer:
false
Step-by-step explanation:-3 in the () means -3 x -3 which is positive 9, where as without () it's -3x3 which is -9. Positive 9 is bigger than -9.
Answer:
False
Step-by-step explanation:
-3^2 = -(3^2) = -(3 × 3) = -9
(-3)^2 = -3 × -3 = 9
-9 < 9
In the case of Confidence Intervals and Two-Tailed Hypothesis Tests, the decision rule states that: Reject H0 if the confidence interval ______ contain the value of the hypothesized mean mu0.
Answers
Answer: Reject \(H_0\) if the confidence interval does not contain the value of the hypothesized mean \(\mu_0\).
Step-by-step explanation:
In the case of Confidence Intervals and Two-Tailed Hypothesis Tests,
Null hypothesis : \(H_0:\mu=\mu_0\) [There is no change in mean.]
Alternative hypothesis: \(H_a:\mu\neq\mu_0\) [There is some difference.]
Since confidence intervals contain the true population parameter ( mean).
So, Decision rule states that
Reject \(H_0\) if the confidence interval does not contain the value of the hypothesized mean \(\mu_0\).We do not reject \(H_0\) if the confidence interval contains the value of the hypothesized mean \(\mu_0\).Five friends share 3 pizzas equally.How much pizza does each friend get?
Answers
Answer:
Each friend gets 3 slices each.
Step-by-step explanation:
A screwdriver is a simple machine called a?
Answers
Answer:
Wheel & axle
Step-by-step explanation:
Answer: it is called a
wheel and axle
Step-by-step explanation:
sheeeeeeeeeeeeeeeeeeeeeeeeeeeesh
Nicole is a wedding organiser. The guests sit at a circular table with a diameter of 180cm each guest needs 7cm around the cicumference of the table. Their are 18 tables at the venu. There is a toptal of 145 guests. Are their enoughb tables
Answers
From the given data of Nicole's wedding organization, 18 tables at the venue is sufficient for the total 145 arriving guest.
To determine whether there are enough tables for the guests, we need to calculate the total circumference required for all the guests and compare it to the total circumference of the available tables. The circumference of a circle is given by the formula C = πd, where C is the circumference, d is the diameter, and π is the constant pi, approximately equal to 3.14.
For the circular table with a diameter of 180cm, the circumference is:
C = πd
= π x 180cm
= 565.2cm
Each guest needs 7cm around the circumference of the table, so the total circumference required for one guest is 7cm.
For 145 guests, the total circumference required is:
Total circumference required
= 145 guests x 7cm per guest
= 1015cm
Now, we can calculate the total circumference of all the tables available:
Total circumference of all tables
= 18 tables x 565.2cm per table
= 10,174.4cm
Since the total circumference required for the guests (1015cm) is less than the total circumference of all the available tables (10,174.4cm), we can conclude that there are enough tables for the guests. Therefore, there are enough tables at the venue for the 145 guests.
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Suki has placed $800 in an account that pays 4 percent interest compounded quarterly. at the end of two years (eight quarters), the balance in the account will be $ 0.08 . that means suki will have earned $ in interest during that time. (round your answers to the nearest cent.) what will be the balance in the account at the end of two years (eight quarters)? how much interest will suki have earned during that time? (round your answers to the nearest cent.)
Answers
The balance in the account at the end of two years is $864.
The interest earned by Suki during that time is $64.
The initial principal amount "P" is $800.
The interest rate "R" is 4%.
The interest is compounded quarterly.
This means the value of "n" is 4.
The time period for which the interest is earned is 2 years.
The formula for compound interest is :
A = P*[1 + (R/n)]^(n*t)
A = 800*[1 + (0.04/4)]^(4*2)
A = 800*[1 + 0.01]^(4*2)
A = 800*[1.01]^(8)
A = 800*1.08
A = 864
The total interest earned is the final amount minus the principal amount.
The total interest earned is $864 - $800.
The total interest earned is $64.
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PLEASE HELP I’ll give brainlest
Answers
Answer:
x = 10
Step-by-step explanation:
∡BDC = ∡ABD
ΔDBC = 20 + 5x - 2 + 112
180 = 20 + 5x - 2 + 112
180 = 5x + 130
50 = 5x
10 = x
A store sells jump ropes each jump rope cost the same amount during the sale of the store reduces the price of each jump rope by $1.90 Mark Spence $12.78 on the two jump ropes at the sale price what was the price of one jump rope before the sale?
Answers
The final answer is that the original price of one jump rope before the sale was $8.29.
Let's start by using algebra to solve this problem.
If the original price of one jump rope is "x", then the sale price is "x - 1.90". We can set up an equation to relate the sale price and the original price:
2(x - 1.90) = 12.78
Simplifying and solving for "x", we get:
2x - 3.80 = 12.78
2x = 16.58
x = 8.29
Therefore, the original price of one jump rope was $8.29.
To check our answer, we can verify that the sale price of one jump rope is $6.39 ($8.29 - $1.90), and that two jump ropes at this price cost $12.78.
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what is the measure of angle OAC
Answers
Answer:
60
Step-by-step explanation:
What expression is equivalent to -16-9
A. 16+(-9)
B. 16+9
C. -16+(-9)
D.-16+8