How many sequences of length 5 can be made when each component of the sequence can take 3 different values?
Faelyn grouped the terms and factored the GCF out of the groups of the polynomial 6x4 – 8x2 + 3x2 + 4. Her work is shown.
Step 1: (6x4 – 8x2) + (3x2 + 4)
Step 2: 2x2(3x2 – 4) + 1(3x2 + 4)
Faelyn noticed that she does not have a common factor. Which accurately describes what Faelyn should do next?
Faelyn should realize that her work shows that the polynomial is prime.
Faelyn should go back and regroup the terms in Step 1 as (6x4 + 3x2) – (8x2 + 4).
In Step 2, Faelyn should factor only 2x out of the first expression.
Falyn should factor out a negative from one of the groups so the binomials will be the same.
Answer:
Faelyn should realize that her work shows that the polynomial is prime.
Explanation:
The only difference between her factors in Step 2 is that the 4 in the first group is negative, while the 4 in the second group is positive.
Rearranging the polynomial to factor it will not change the end result.
Factoring out a negative will make not only one, but both terms, in one of the binomials the opposite sign; this will not make the factors the same.
Factoring only 2x out of the first group will result in having (3x³+4x); this is not the same either.
She should realize that when this happens, her polynomial is prime.
The precision of what Faelyn should do is that Faelyn should realize that her work shows that the polynomial is prime. Hence, the option A is the correct option.
How to find the factors of polynomial?Factors of the polynomial which are multiplied to produce the original polynomial.
The polynomial which can not be factored is known as prime polynomial.
The standard form of the polynomial with highest power of 2 can be given as,
Given information-
The given polynomial equitation in the problem is,
[tex]6x^4 -8x^2 + 3x^2 + 4[/tex]
1) First step of Faelyn is[tex](6x^4- 8x^2) + (3x^2 + 4)[/tex]
2) Second step of Faelyn is[tex]2x^2(3x^2 - 4) + 1(3x^2 + 4)[/tex]
Faelyn noticed that she does not have a common factor. The polynomial which can not be factored is known as prime polynomial.
Thus Faelyn should realize that her work shows that the polynomial is prime. Hence, the option A is the correct option.
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a square has 4 right angle corners. give another shape with 4 right angle corners
A certain lottery has 3434 numbers. in how many different ways can 44 of the numbers beâ selected? (assume that order of selection is notâ important.)
A biologist studied the populations of common guppies and Endler's guppies over a 6-year period. the biologist modeled the populations, in tens of thousands, with the following polynomials where x is time, in years.
common guppies: 3.1x^2+6x+0.3
Endler's guppies: 4.2x^2-5.2x+1
what polynomial models the total number of common and Endler's guppies
what polynomial models the total number of common and Endler's guppies
your answer will be:
7.3x^2+0.8+1.3
Step-by-step explanation:
this answer correct for 2022
Make a comparison between the government’s roles in a capitalist economic system versus a socialist or communist economic system.
A capitalist economic system is built on the respect of private property and competition. Hard work and free enterprise benefit citizens more than the government can. For the most part, government intervention is reduced. However, the government does provide security and some basic services, like infrastructure, to its citizens.
Socialist and communist systems endure more government control. Citizens of these economies have a limited amount of freedom by law. The government controls the market place and the production of most goods and services.
^ My answer from Edge
if m ABC = 116 degrees what is ABC
What are the solutions of the system? Solve by graphing. y=x2-2x-1 y = -2
Ava bought a rectangular rug for her hallway. The rug is 23 yards wide and 234 yards long. What is the area of the rug as a mixed number in simplest form?
The area of Ava's rectangular rug is 5382 square yards, calculated by multiplying the width (23 yards) and the length (234 yards).
To find the area of Ava's rectangular rug, we need to multiply its length and width:
Area = length × width
Using the given dimensions: 23 yards wide and 234 yards long:
Area = 23 × 234
First, let's perform the multiplication:
23 × 234 = 5382 square yards
Thus, the area of the rug is 5382 square yards as an improper fraction, which cannot be simplified further as a mixed number. Since the measurements are whole numbers, converting to a mixed number doesn't apply in this case.
How many possible outcomes exist when Louisa spins the spinner below twice? The spinner is numbered from 1-8.
Answer:
The total number of possible outcomes are:
64
Step-by-step explanation:
It is given that:
Louisa spins the spinner below twice.
The spinner is numbered from 1-8.
Now, on spinning the spinner twice we obtain the sample space as:
(1,1) (1,2)....................(1,8)
(2,1) (2,2)...................(2,8)
(3,1) (3,2)..................(3,8)
(4,1) (4,2)..................(4,8)
(5,1) (5,2)..................(5,8)
(6,1) (6,2)..................(6,8)
(7,1) (7,2)..................(7,8)
(8,1) (8,2)..................(8,8)
Hence, the total number of outcomes is equal to the number of elements in sample space.
Hence, the total number of possible outcomes are:
64
Which describes the slope of this line?
Number graph ranging from negative five to five on the x and y axes. A line is drawn on the graph that passes through (zero, negative three) and (two, one).
negative slope
positive slope
undefined slope
zero slope
Find the banker's interest to the nearest cent. Principal: $2,500; Rate: 9%; Time: 180 days: Interest: ? (based on a 365 day year).
Final answer:
The banker's interest rounded to the nearest cent is approximately $110.60.
Explanation:
To calculate the banker's interest on a principal of $2,500 at a rate of 9% for 180 days, you would apply the formula for simple interest:
Interest = Principal × rate × time
Since time needs to be expressed in years and the rate as a decimal, convert 180 days into a fraction of a year by dividing by 365:
Time (in years) = 180 / 365 ≈ 0.4932
Convert the rate to a decimal:
Rate (as a decimal) = 9% = 0.09
Now calculate the interest:
Interest = $2,500 × 0.09 × 0.4932 ≈ $110.595
Thus, the banker's interest rounded to the nearest cent is approximately $110.60.
Identify the pair of alternate interior angles.
Question options:
A.) 2 and 8
B.) 1 and 8
C.)2 and 7
D.) 4 and 6
The mean of people in the sample of households of 7th-grade students is 4.3. The mean of people in the sample of households for 8th-grade students is 4.5. What might Principal Coleman infer or predict about the entire population based on the data?
Answer:
The mean of something is the "average"
For example, if the mean of people in the households of 7th-grade students is 4.3, this means that if you go to a random house of a 7th-grade student, you can expect around 4 people in there.
Now, for the 7th-grade students, the mean is 4.5, just a 0.2 bigger. (This means that, on average, there is more people in the 8th-grade student's households)
So Principal Coleman can infer that the amount of people in the households of 7th-grade students and 8th-grade students is almost the same, wherein the 8th-grade students there is a small chance of finding more people, but this difference is almost depreciable.
Use signed numbers to solve. A helicopter descended 1200 feet, rose 800 feet, and then descended 450 feet. What was the net gain or loss in altitude? A. lost 2450 ft B. lost 850 ft C. gained 850 ft D. gained 2450 ft
Given: KLMN is a parallelogram, KA − angle bisector of ∠K LA − angle bisector of ∠L Prove: m∠KAL = 90°
Final answer:
This answer explains how to prove that angle KAL is 90 degrees in a parallelogram using angle bisectors.
Explanation:
To prove: m∠KAL = 90°
Given: KLMN is a parallelogram, KA - angle bisector of ∠K, LA - angle bisector of ∠L.
Proof:
Since KA and LA are angle bisectors in parallelogram KLMN, m∠K = m∠L.In a parallelogram, consecutive angles are supplementary, so m∠K + m∠L = 180°.Substitute m∠K for m∠L in the above equation: m∠K + m∠K = 180°, which simplifies to 2m∠K = 180°, giving m∠K = 90°.Proved that the measure of angle KAL is 90 degrees, which means that angle KAL is a right angle.
To prove that [tex]\( m\angle KAL = 90^\circ \)[/tex], we need to use the properties of angle bisectors and parallelograms.
Step 1: Identify the properties of a parallelogram.
In a parallelogram, opposite sides are equal in length, and opposite angles are equal. Also, adjacent angles are supplementary, meaning they add up to 180 degrees.
Step 2: Apply the properties to parallelogram KLMN.
Since KLMN is a parallelogram, we have:
[tex]\[ m\angle K + m\angle L = 180^\circ \][/tex]
[tex]\[ m\angle K = m\angle M \][/tex]
[tex]\[ m\angle L = m\angle N \][/tex]
Step 3: Use the properties of angle bisectors.
An angle bisector divides an angle into two equal parts. Therefore, we have:
[tex]\[ m\angle KAK = m\angle KAA \][/tex]
[tex]\[ m\angle LAL = m\angle LAA \][/tex]
Step 4: Express the angles in terms of the bisected angles.
Since KA is the angle bisector of [tex]\( \angle K \)[/tex], we can express [tex]\( m\angle KAK \)[/tex]and [tex]\( m\angle KAA \)[/tex] as half of [tex]\( m\angle K \)[/tex]:
[tex]\[ m\angle KAK = m\angle KAA = \frac{1}{2}m\angle K \][/tex]
Similarly, since LA is the angle bisector of [tex]\( \angle L \)[/tex], we can express [tex]\( m\angle LAL \)[/tex] and [tex]\( m\angle LAA \)[/tex] as half of [tex]\( m\angle L \)[/tex]:
[tex]\[ m\angle LAL = m\angle LAA = \frac{1}{2}m\angle L \][/tex]
Step 5: Use the supplementary angle relationship.
Since [tex]\( \angle K \)[/tex] and [tex]\( \angle L \)[/tex] are supplementary, we have:
[tex]\[ m\angle K + m\angle L = 180^\circ \][/tex]
Dividing both sides by 2, we get:
[tex]\[ \frac{1}{2}m\angle K + \frac{1}{2}m\angle L = 90^\circ \][/tex]
Step 6: Substitute the expressions for the bisected angles.
[tex]\[ m\angle KAK + m\angle LAL = 90^\circ \][/tex]
[tex]\[ \frac{1}{2}m\angle K + \frac{1}{2}m\angle L = 90^\circ \][/tex]
Step 7: Recognize that [tex]\( m\angle KAL \)[/tex] is the sum of [tex]\( m\angle KAK \)[/tex]and[tex]\( m\angle LAL \)[/tex].
[tex]\[ m\angle KAL = m\angle KAK + m\angle LAL \][/tex]
Step 8: Substitute the values from Step 6 into the equation from Step 7.
[tex]\[ m\angle KAL = \frac{1}{2}m\angle K + \frac{1}{2}m\angle L \][/tex]
[tex]\[ m\angle KAL = 90^\circ \][/tex]
share 747 pound in the ratio 2:7 betwen tom and ben
Find the equation of the plane in xyzxyz-space through the point p=(5,5,3)p=(5,5,3) and perpendicular to the vector n=(1,2,5)
The equation of the plane in xyz-space that passes through the point p=(5,5,3) and is perpendicular to the vector n=(1,2,5) is x + 2y + 5z = 30.
Explanation:In mathematics, the equation of the plane can be found using the plane equation Ax + By + Cz = D. Given that the plane goes through point p=(5,5,3) and is perpendicular to vector n=(1,2,5). The vector n actually gives us the coefficients A, B, and C. Meaning A=1, B=2, and C=5. We get D by substituting the given point into the equation (Ax + By + Cz = D) as follows D = Ax + By + Cz = (1*5) + (2*5) + (5*3) = 5 + 10 + 15 = 30. Thus, the equation of the plane is x + 2y + 5z = 30.
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Deposit $400 into an account that pays simple interest at rate of 4% per year how much interest will she be paid in the first 6 years
Solve for X.
x - 7.9 = 2.23
for this job , Hayden earns an hourly rate of $30. For each hour he works over 40 hours, he earns 1.5 times his regular hourly rate. In a two-week period, Hayden earns $2175 by working 40 regular hours, plus overtime. How many overtime hours did Hayden work?
anyone free to help with this?
Mildred Lost bought two (2) radial tires at $49.95 each and two (2) seat cushions at $16.99 each. The sales tax where she lives is 6 percent. What was the total amount of the purchase?
PLEASE ANSWER FAST PLEASE!!!!!!
1. Beatrice decides she wants to babysit a few children at the same time to earn the money faster. She tells parents that if they allow her to babysit their children at her house, she will eliminate her automatic $5 tip and will give them an additional $5 discount.
(a) Write an equation showing the total cost for each client. Identify all variables.
(b) Four parents bring their children to Beatrice’s house at the same time for babysitting. Beatrice wants to find out how many hours she must babysit the 4 children to earn exactly the $100 she needs in order to buy the present for her mother. Write and solve an equation to find the number of hours. Justify each step in the solution.
(c) One parent decides not to drop off her child. The remaining 3 parents drop their children off at 9 a.m. Two of the parents say they will be back at 1 p.m. The third parent says she will pick up her child at 2 p.m. At noon, Beatrice realizes she needs help feeding the 3 children at the same time. She tells her little sister that she will pay her if she helps feed the children. How much can Beatrice pay her little sister and still make sure she has enough money to buy her mother a $100 present? Show your work and justify your answer.
Let B be the amount Beatrice charges per hour per child
Let x be the number of hours
Let n be the number of children
a)total amount Beatrice charges = T = B*x*n - 10
b)n =4 and T = 100
100 = B*x*4 -40
x = 35/B
c)Let S be the amount she has t o pay to her sister
n = 3 and x = (4+4+5) = 13
so, 13*B*3 -30 -S = 100
S = 39B - 130
In a circle with a radius of 26.9 m, an arc is intercepted by a central angle of 9π5 radians.
What is the arc length?
Use 3.14 for π and round your final answer to the nearest hundredth.
Make sure to show your calculations.
152.04 is right i just took the test
your welcome ;)
What fraction is equivalent to the fraction 0/6
Juno deposited $750 in a savings account that earns 4% interest compounded annually. If she does not deposit or withdraw any more money, how much money will there be in the account after 13 years? Round your answer to the nearest dollar. A. $1249 B. $1360 C. $1427 D. $1140
Answer:
A. $1249.
Step-by-step explanation:
We have been given that Juno deposited $750 in a savings account that earns 4% interest compounded annually. We are asked to find the amount of money in the account after 13 years.
To solve our given problem, we will use compound interest formula. [tex]A=P(1+\frac{r}{n})^{nt}[/tex], where,
A = Amount after t years,
P = Principal amount,
r = Interest rate in decimal form,
n = Number of times interest is compounded per year,
t = Time in years.
Let us convert our given interest rate in decimal form.
[tex]4\%=\frac{4}{100}=0.04[/tex]
Upon substituting our given values in compound interest formula we will get,
[tex]A=\$750(1+\frac{0.04}{1})^{1\cdot 13}[/tex]
[tex]A=\$750(1+0.04)^{13}[/tex]
[tex]A=\$750(1.04)^{13}[/tex]
[tex]A=\$750\times 1.665073507310388[/tex]
[tex]A=\$1248.805130482791\approx \$1249[/tex]
Therefore, there will be $1249 in Juno's account after 13 years and option A is the correct choice.
Complete the factorization of 3x2 – 5x + 2.
Which two factors can be multiplied together to make this trinomial?
(x – 2)
(x – 1)
(x + 1)
(3x – 2)
(3x + 2)
the answers are (x-1) and (3x-2)
You borrow $6,730 to buy a car. the terms of the loan call for monthly payments for 5 years a rate of interest of 6 percent. what is the amount of each payment?
glenn raced his motorcycle 30 times last season. he finished first 12 times, second 5 times and crashed in 9 races. what percent of races did he crash? set up a proportion and solve.
Final answer:
Glenn crashed in 30% of the races.
Explanation:
To find the percentage of races Glenn crashed, you can set up a proportion. A proportion is an equation that states that two ratios are equivalent. Since Glenn raced 30 times and crashed 9 times, the ratio of crashes to total races is 9 crashes out of 30 races.
You can set up the proportion as follows:
Crashes / Total Races = Percentage of Crashes / 100
Plugging in the known values gives us this:
9 / 30 = Percentage of Crashes / 100
To solve for the percentage of crashes, you multiply both sides of the equation by 100:
(9 / 30)
100 = Percentage of Crashes
Simplifying gives us:
(9/3) 10 = Percentage of Crashes
Hence, the percentage of races that Glenn crashed is 30%.
4j-2/2=4j+5
4j minus 2 divided by 2 equals 4j plus 5 ?
The solution to the equation (4j - 2) / 2 = 4j + 5 is j = -3. The equation was simplified by eliminating fractions and isolating the variable j through algebraic steps.
To solve the equation (4j - 2) / 2 = 4j + 5 for the variable j, you can follow these steps:
1. First, simplify both sides of the equation:
(4j - 2) / 2 = 4j + 5
2. Multiply both sides of the equation by 2 to eliminate the fraction:
4j - 2 = 2 * (4j + 5)
3. Distribute the 2 on the right side:
4j - 2 = 8j + 10
4. Move the variable terms to one side of the equation and the constants to the other side. You can do this by subtracting 8j from both sides:
4j - 8j - 2 = 10
5. Combine like terms:
-4j - 2 = 10
6. Add 2 to both sides to isolate the variable term:
-4j = 10 + 2
-4j = 12
7. Finally, divide both sides by -4 to solve for j:
j = 12 / -4
j = -3
So, the solution to the equation is j = -3.
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