what is the remainder when a polynomial (x^2-1) is divided by (x-2)
Answers
\(3\)
Step-by-step explanation:According to the Remainder Theorem, if we divide a polynomial, \(P(x)\), by \(x -\blue a\), the remainder is \(P(\blue a)\).
If we let \(P(x) = x^2 -1\), the remainder when we divide \(P(x)\) by \(x -\blue 2\) is \(P(\blue 2)\).
The last thing we need to do now is to evaluate \(P(\blue 2)\).
\(&P(\blue 2) &= &(\blue 2)^2 -1 \\ &P(\blue 2) &= &4 -1 \\ &P(\blue 2) &= &3\)
Related Questions
Consider the matrices.
What is product matrix PQ?
Enter your answer by filling in the boxes.
Answers
The product matrix PQ can be found to be:
\(\left[\begin{array}{ccc}-17\\-3\\-37\\49\end{array}\right]\)
How do you calculate the product matrix PQ?The numbers on the first column of P will be multiplied by the first number of Q and the second column of P, by the second number in Q.
This becomes:
= \(\left[\begin{array}{ccc}1(-1) + &2 (-8)\\3(-1) +&0 (-8)\\5(-1) +&4(-8)\\-1(-1) +&-6(-8)\end{array}\right]\)
The result becomes:
= \(\left[\begin{array}{ccc}-17\\-3\\-37\\49\end{array}\right]\)
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What do we know about a system of linear equations when is has
INFINITELY many solutions? (HINT-SELECT ALL THAT APPLY(3))
They have the same slope(m)
They have different slopes(m)
They have the same line on the graph
They have the same y-intercept(b)
They have different y-intercept's(b)
Pls help!!!!!!
Answers
The value of the expression 3^-4 • 3^-5 is
Answers
Answer:
3^-9
Step-by-step explanation:
3^-4 • 3^-5
We know that a^b * a^c = a^(b+c)
3^-4 • 3^-5 = 3^(-4-5) = 3^ -9
If P(B)=0.3,P(A∣B)=0.5,P(B ′ )=0.7, and P(A∣B ′ )=0.8, find P(B∣A).
Answers
If P(B)=0.3, P(A|B)=0.5, P(B')=0.7and P(A|B')=0.8, then the value of the probability P(B|A)= 0.2113
To find the value of P(B|A), follow these steps:
The probability of B given A can be given by the product of the probability of A given B and the probability of B, divided by the total probability of B. So, the formula for P(B|A) = P(A|B) * P(B) / [P(A|B)*P(B)+P(A|B')*P(B')]. Substituting the values, we get P(B|A) = (0.5) (0.3) / [(0.5) (0.3) + (0.8) (0.7)] ⇒P(B|A) = 0.15 / [0.15 + 0.56] ⇒P(B|A) = 0.15 / 0.71 ⇒P(B|A) = 0.2113. Therefore, P(B|A) = 0.2113.Learn more about probability:
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The histogram below shows the heights, rounded to the nearest inch, of the members of the Oak High School basketball team. A. 1 inch B. 9 inches C. 7 inches D. 5 inches
Answers
Answer:
Range of player's height = 9 inch
Step-by-step explanation:
Given:
Number of players Height range
4 66-67
8 68 -69
14 70-71
9 72-73
1 74-75
Find:
Range of player's height
Computation:
Range = Maximum value - Minimum Value
Range of player's height = Maximum height of a player - height of a player
Range of player's height = 75 inch - 66 inch
Range of player's height = 9 inch
can somone help me please
Answers
Answer:
3 41/50
Step-by-step explanation:
first you would write it as 3 82/100, then you simplify it to 3 41/50. Hope this helped :)
its 3+41/50.........................
for what real values of $x$ is $-4
Answers
This is a simple inequality problem involving absolute values.
The given inequality is: $-4 < |x-3|$.We need to find the range of real values of $x$ that satisfy this inequality.
First, let's consider the case when $x-3$ is positive. In this case, the absolute value of $x-3$ is simply $x-3$. So, we can write the inequality as: $-4 < x-3$
Adding $3$ to both sides, we get: $-1 < x$
This means that all values of $x$ greater than $-1$ satisfy the inequality when $x-3$ is positive.
Now, let's consider the case when $x-3$ is negative. In this case, the absolute value of $x-3$ is $-(x-3)$. So, we can write the inequality as: $-4 < -(x-3)$. Expanding the right-hand side, we get: $-4 < -x + 3$
Subtracting $3$ from both sides, we get: $-7 < -x$. Multiplying both sides by $-1$ (which reverses the inequality), we get: $x < 7$.This means that all values of $x$ less than $7$ satisfy the inequality when $x-3$ is negative. Putting both cases together, we have:$x < 7$ or $x > -1$
This is the final answer. We can express it more concisely as:
$-1 < x < 7$
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Jane bought 5 hot dogs at h dollars each 3 soft drink at s dollars each what is the total cost in dollars of the hot dogs and the software drinks
Answers
Answer:
Total cost = $5h + $3s
Step-by-step explanation:
total cost of hot dog = price of hot dog x quantity of hot dog = 5 x $h
total cost of softdrink = price of softdrink x quantity of softdrink = $3s
total cost = $5h x $3s
3. in triangle , point is the incenter. sketch segments to represent the distance from point to the sides of the triangle. how must these distances compare?
Answers
The incenter is the intersection of the angle bisectors, the distances from the incenter to the sides are proportional to the lengths of the adjacent sides, which gives the desired proportionality.
What is proportion?
The size, number, or amount of one thing or group as compared to the size, number, or amount of another. The proportion of boys to girls in our class is three to one.
To sketch the segments representing the distance from the incenter to the sides of a triangle, we draw perpendiculars from the incenter to each of the sides, as shown in the attached image.
The segments representing the distances from the incenter P to the sides of the triangle are the inradii.
Let r1, r2, and r3 be the lengths of the inradii corresponding to sides AB, BC, and AC, respectively.
Then, we have:
r1 = distance from P to AB
r2 = distance from P to BC
r3 = distance from P to AC
To compare these distances, we use the fact that the incenter is the intersection of the angle bisectors of the triangle.
Therefore, the distance from the incenter to each side is proportional to the length of the corresponding side. More precisely, we have:
r1 : r2 : r3 = AB : BC : AC
This proportionality can be proved using the angle bisector theorem, which states that the length of the segment of an angle bisector in a triangle is proportional to the lengths of the adjacent sides.
Hence, the incenter is the intersection of the angle bisectors, the distances from the incenter to the sides are proportional to the lengths of the adjacent sides, which gives the desired proportionality.
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8. (8 points) Solve the following system of linear equations. 2x - 5y + z = -9 x + 4y - 6z = 2 3x – 4y – 2z = -10
Answers
Therefore, the solution to the given system of linear equations is: x = 2y - 4 = 2(5/3) - 4 = -2/3 y = 5/3 z = 8/3
The given system of linear equations is, 2x - 5y + z = -9 (i) x + 4y - 6z = 2 (ii)
3x - 4y - 2z = -10 (iii)
Let's solve this system using the elimination method. From equations (i) and (iii), we have:
2x - 5y + z = -9 ........(i)
3x - 4y - 2z = -10.......(iii)
We can eliminate z from these equations by multiplying equation (i) by 2 and adding it to equation (iii) as shown:4x - 10y + 2z = -18 (2i)3x - 4y - 2z = -10........(iii)
7x - 14y = -28............(iv)
Divide equation (iv) by 7, and we get
x - 2y = -4....................(v)
Now let's eliminate z from equations (ii) and (iii). We can do this by multiplying equation (ii) by 2 and adding it to equation (iii) as shown:
x + 4y - 6z = 2.......(ii)
3x - 4y - 2z = -10.......(iii)
2x + 8y - 12z = 4.......(ii)
3x - 4y - 2z = -10.......(iii)
5x + 4y - 14z = -6.......(vi)
Now, let's eliminate y from equations (v) and (vi). To do this, we can multiply equation (v) by 4 and add it to equation (vi) as shown:
4x - 8y = -16..........(v)
5x + 4y - 14z = -6.......(vi)
9x - 14z = -22.........(vii)
We can now solve for z by substituting equation (vii) into equation (iv). Therefore:
9x - 14z = -22 (vii)
x - 2y = -4 (v)
Solve equation (v) for x as follows:x = 2y - 4Substitute this into equation (vii) to get:
9(2y - 4) - 14z = -22
Simplify and solve for z as follows:
18y - 36 - 14z = -22 18y - 14z = 14 9y - 7z = 7
Now, we can substitute the values we have obtained for x and z into equation (ii) to solve for y as follows:
x + 4y - 6z = 2 (ii)2y - 4 + 4y - 6z = 2 6y - 7z = 3 6y - 7(1) = 3 6y - 7 = 3 6y = 10 y = 5/3
Now we can substitute x = 2y - 4 and y = 5/3 into any of the three original equations to solve for z. Using equation (i), we get:
2x - 5y + z = -9 2(2y - 4) - 5y + z = -9 4y - 8 - 5y + z = -9 -y + z = 1 z = y + 1 = 5/3 + 1 = 8/3.
Hence, the main answer is
x = -2/3, y = 5/3, z = 8/3.
Therefore, the solution to the given system of linear equations is: x = 2y - 4 = 2(5/3) - 4 = -2/3 y = 5/3 z = 8/3.
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Please helpppp please I will mark branlyist and 50 point please Question 13 (5 points)
(02.02 MC)
Which of the following rational numbers is equal to 34 ? (5 points)
32
33
34
31
9
9
9
1) 31
9
2) 32
9
3) 33
9
4) 34
9
Answers
Which of the following rational number is equal to 3,4?
Answer:31
9
Step-by-step explanation:
That's my opinion and I hope it helps^_^
#CARRYONLEARNING #STUDYWELLlet be a differentiable function where 9 and 4 and 3. if we change by -0.7 and we change by 0.3 then we can expect the value of to change by approximately what amount
Answers
If we change x by -0.7, we can expect the value of f(x) to decrease by approximately 2.1 units.
Assuming you meant to say "let f be a differentiable function where f(9) = 4 and f'(9) = 3. If we change x by -0.7 and we change y by 0.3, then we can expect the value of f(x) to change by approximately what amount?"
Using the linear approximation formula, we have:
\(Δf(x) ≈ f'(9) Δx\)
where Δx = -0.7 and we want to find Δf(x) when Δy = 0.3.
We can rearrange the formula to solve for Δf(x):
\(Δf(x) ≈ f'(9) Δx\)
Δf(x) ≈ 3(-0.7)
Δf(x) ≈ -2.1
This means that if we change x by -0.7, we can expect the value of f(x) to decrease by approximately 2.1 units. However, this is only an approximation based on the linear behavior of the function near x = 9, so it may not be exactly accurate for large changes in x.
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Determine whether each ordered pair is a solution or not a solution to this system of inequalities.
y< −x
2x+y>2
Answers
The ordered pair that is the solution of the given system of inequalities is (2, -2)
What is inequality?A relationship between two expressions or values that are not equal to each other is called inequality.
Given is a system of inequalities, y < -x and 2x+y > 2, we need to determine solution set of the given system of inequalities,
The inequalities are,
y < -x....(i)
2x+y > 2
y < 2-2x...(ii)
To find the ordered pair, put y = -x in equation Eq(ii) and replace < by =
-x = 2 - 2x
x = 2
y = -2
Therefore, the ordered pair, is (2, -2) {look at the graph attached}
Hence, the ordered pair that is the solution of the given system of inequalities is (2, -2)
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Given v =(-12,-4), what are the magnitude and direction of v? Round the magnitude to the thousandths place and the direction to the nearest degree.
11.314; 18°
11.314; 198°
12.649; 18°
12.649, 198°
Answers
Step-by-step explanation:
Magnitude = sqrt ( (-12)^2 + (-4)^2 ) = sqrt 160 = 12.649
Angle = arctan(-4/-12) = 198 degrees
The Magnitude: 12.649 and Direction: 18° (option c).
To find the magnitude and direction of the vector v = (-12, -4), we can use the following formulas:
Magnitude (or magnitude) of v = |v| = √(vₓ² + \(v_y\)²)
Direction (or angle) of v = θ = arctan(\(v_y\) / vₓ)
where vₓ is the x-component of the vector and \(v_y\) is the y-component of the vector.
Let's calculate:
Magnitude of v = √((-12)² + (-4)²) = √(144 + 16) = √160 ≈ 12.649 (rounded to the thousandths place)
Direction of v = arctan((-4) / (-12)) = arctan(1/3) ≈ 18.435°
Since we need to round the direction to the nearest degree, the direction is approximately 18°.
So, the correct answer is:
Magnitude: 12.649 (rounded to the thousandths place)
Direction: 18° (rounded to the nearest degree)
The correct option is: 12.649; 18°
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The expression, 20(4x) + 500, represents the cost in dollars of the materials and labor needed to build a square fence with side length x feet around a playground. What is the meaning of the coefficient 20?
Answers
Answer:
20 represent the cost per variable inputs
Step-by-step explanation:
C(x) = 20(4x) + 500
Total cost is the addition of variable cost and fixed cost
Fixed cost are cost that do not change during the production process such as machinery, furnitures and fittings.
Variable cost are cost of production that changes with production process such as cost of labor, cost of raw materials.
C(x) = 20(4x) + 500
C(x) represent the total cost
20(4x) represent the variable cost
500 represent the fixed cost
From the variable cost 20(4x)
20 represent the cost per variable inputs
a group of 4 pupils can take 2 weeks to do a certain job.how long will 12 pupils take to complete the job if they work at the same rate
Answers
Answer:
6 weeks
Step-by-step explanation:
Set up a proportion where x is the amount of time with 12 pupils:
\(\frac{4}{2}\) = \(\frac{12}{x}\)
Cross multiply and solve for x:
4x = 24
x = 6
So, it will take 12 pupils 6 weeks to complete the job.
since apparently NOBODY has asked this exact question.
The basket of golf balls at a miniature golf course contains 16 golf balls, of which 6 are green.
What is the probability that a randomly selected golf ball will be green?
Answers
Answer:
6/16
.375
Step-by-step explanation:
Answer:
37.5%
Step-by-step explanation:
what is the expected number of wins for the month of november? (round your answer to two decimal places.)
Answers
the expected number of wins for the month of November is approximately 4.55.
To find the expected number of wins for the month of November, we first need to calculate the mean or expected value of the binomial distribution. We know that the probability of winning any given game is 0.3789, and there are 12 games in November.
Let X be the number of games won in November, then X follows a binomial distribution with parameters n = 12 and p = 0.3789.
The expected value of a binomial distribution is given by E(X) = np, where n is the number of trials and p is the probability of success in each trial. So, in this case, the expected number of wins for the month of November is:
E(X) = np = 12 x 0.3789 = 4.547
This means that, on average, we can expect the hockey team to win about 4 or 5 games in November, based on their historical win rate. However, it's important to note that this is just an average and there is always variability in the number of wins in any given month or season.
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Complete question is:
The probability that a certain hockey team will win any given game is 0.3789based on their 13 year win history of 391 wins out of 1032 games played (as of a certain date). Their schedule for November contains 12 games. Let X = number of games won in November.
What is the expected number of wins for the month of November? (Round your answer to two decimal places.)
Melanie's dance class was 100 minutes long. If 1/8 of the time was spent
stretching, how many minutes were spent stretching?
Answers
Answer:
12.5 minutes
Step-by-step explanation:
Multiply 1/8 by 100. Convert 25/2 to a decimal by dividing 25 by 2. The answer is 12.5 minutes.
PLS HELP I DONT UNDERSTAND THIS-
Which types of classification does e fall under? Select all the different classifications.
A) Natural numbers
B) Whole numbers
C) Integers
D) Rational numbers
E) Irrational numbers
F) Real numbers
Answers
1.15=
2.30=
3.12=
mrs.torres's class has 28 students the class includes 12 boys what is the ratio of girls and boys
Answers
Answer:
4:3.
Step-by-step explanation:
Number of boys = 12 and number girls = 16.
Ratio girls to boys = 16:12
= 4:3.
Need help! Writing System of Equations from Context
Let x be:
Let y be:
and in need of 2 equations
Answers
A rental car company charges $77. 50 per day to rent a car and $0. 14 for every mile
driven. Juan wants to rent a car, knowing that:
• He plans to drive 425 miles.
• He has at most $230 to spend.
Write and solve an inequality which can be used to determine d, the number of days
Juan can afford to rent while staying within his budget.
Answers
77.5d + .14m
m = 425
.14 * 425 = 59.5
77.5d + 59.5 ≤ 230
77.5d ≤ 170.5
d ≤ 170.5/77.5
d ≤ 2.2
if they only take payment for whole days, he has 2 whole days
Ravi's mass is 31 kg. His brother, Rajar, is 10 kg heavier than Ravi.
Find the ratio of Rajar's mass to their total mass.
Answers
Answer:
31 : 41
Step-by-step explanation:
Given that Ravi's mass is 31kg . And his brother is 10 kg heavier than him . So his weight will be 31kg + 10kg = 41kg. So we have ,
\(\begin{cases}Mass \ of \ Ravi = 31kg \\ Mass of Brother \ = \ 41kg \end{cases}\)
Therefore their total mass = 31 + 41 = 72 kg .
Therefore the ratio will be 41:72 .
The ratio of Rajar's mass to their total mass is 41:72.
What is the ratio?The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.
Given that, Ravi's mass is 31 kg.
His brother, Rajar, is 10 kg heavier than Ravi.
Weight of Rajar is 31+10=41 kg
Total weight =31+41
= 72 kg
The ratio of weights = 41:72
Therefore, the ratio of Rajar's mass to their total mass is 41:72.
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Mae Ling earns a weekly salary of $365 plus a 5.0% commission on sales at a gift shop. How much she make in a workweek if she sold $4,800 worth of merchandise?
Answers
The amount that she make in a workweek if she sold $4,800 worth of merchandise will be $605.
How to calculate the value?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.
Here, Mae Ling earns a weekly salary of $365 plus a 5.0% commission on sales at a gift shop.
The amount that she make in a workweek if she sold $4,800 worth of merchandise will be:
= $365 + (5% × $4800)
= $605
The amount is $605.
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2x- 6y = - 12x + 2y = 14
Answers
Answer:
Step-by-step explanation:
add your x and y together first
21.Bill and Sam are playing a game where they roll a die and draw a card from a deck. What is the probability of rolling a 5 and then drawing a 5 from the deck of cards? Write your answer as a fraction in lowest terms.
Answers
So we must find the probability that two independent events happen at once. These events are rolling a 5 and drawing a 5 from the deck. Since they are independent events because the result of one of them doesn't depend on the result of the other the probability that both happen is given by the product of their individual probabilities.
The probability of rolling a 5 is given by the quotient between the number of 5's in the die and the total number of faces in the die. There's only one 5 in the die and it has 6 faces so the probability of rolling a 5 is:
\(P(r5)=\frac{1}{6}\)A standard deck has 52 cards and four of those cards are fives. Then the probability of drawing a 5 is given by the quotient between the number of fives in the deck and the total number of cards in it. Then we get:
\(P(d5)=\frac{4}{52}=\frac{1}{13}\)Then the probability of rolling a 5 and then drawing a 5 from the deck is given by the product of the two probabilities that we found before:
\(P=\frac{1}{6}\cdot\frac{1}{13}=\frac{1}{78}\)AnswerThen the answer is 1/78.
When computing the control limits for the p-chart, what value is used when the population proportion of defective items is not known
Answers
Answer:
sample proportion of defective items
Step-by-step explanation:
The p-chart is a type of chart in which the sample is taken periodically from the production process, so as to determine if the population proportion of defective items in the sample falls within the control limits on the chart.
For a P-chart, as the sample size gets larger it turns more into a normal distribution making it possible to approximate the distribution of the proportion defective.
If principal=p,rate of interest=R and time=T,then write the formula to find the compound amount
Answers
It is given that P = principal, R = rate of interest and T = time
Formula to find compound interest is:
A = P(1 + R/100)^T
where A = amount received after n years
P = principal amount invested
R = rate of interest
T = time for which the amount is invested
The interest earned on savings that are computed using both the original principal and the interest accrued over time is known as compound interest.
It is thought that Italy in the 17th century is where the concept of "interest on interest" or compound interest first appeared. It will accelerate the growth of a total more quickly than simple interest, which is solely calculated on the principal sum.
Money multiplies more quickly thanks to compounding, and the more compounding periods there are, the higher the compound interest will be.
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jasmine bought three tickets for a concert for a $55 each. The two family members she bought them for can no longer go to the concert so Jasmine decides to sell the tickets for a 15% markup to two of her friends. How much total money will she receive after selling the tickets to her friends?
Answers
Answer:
$126.5
Step-by-step explanation:
Find how much 15% is in 55, then add it to 55 and multiply by 2!