For what value of c is p(x) = 2x^4 - 5x^2 + cx - 1 divisible by x - 1? Show work.
Answers
Answer:
c = 4
Step-by-step explanation:
if (x - a) is a factor , that is divisible by, of f(x) then f(a) = 0
then for p(x) to be divisible by (x - 1) , p(1) = 0
then
2[tex](1)^{4}[/tex] - 5(1)² + c(1) - 1 = 0
2 - 5 + c - 1 = 0
- 4 + c = 0 ( add 4 to both sides )
c = 4
Related Questions
Given the following definitions: U = {1, 2, 3, 4, 5, 6, 7} A = {1, 2, 4, 5} B = {1, 3, 5, 7} How many elements are in A ∩ B' ?
Answers
Only 1 and 5
I. Need.The.Answer
ASAP
Congratulations! You have been selected to be an emergency substitute teacher. You are given a lesson plan on writing parallel line equations. However the answer key is missing. Opps!
1) Start by writing this equation on the virtual white board: y = 1/2x -3
2) You then need to write an equation of a line using slope-intercept format that is parallel to this line and goes through the point (4,2).
Answers
An equation of a line in a slope-intercept format that is parallel to
y = (1/2)x - 3 line and goes through the point (4, 2) is y = (1/2)x
What are lines and their slopes?We know lines have various types of equations, the general type is
Ax + By + c = 0, and the equation of a line in slope-intercept form is
y = mx + b.
Where slope = m and b = y-intercept.
the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.
We know parallel lines have equal slopes.
The equation of the line given is y = (1/2)x - 3 and our required equation is parallel to it and passes through (4, 2).
So, 2 = (1/2)(4) + b.
2 = 2 + b.
b = 0.
Hence, y = (1/2)x is the required equation of the line.
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Which division problem can be described using this model? Responses 3÷4 , 3 divided by 4, 3÷1/4 3 divided by 1 fourth 1÷1/12 , 1 divided by fraction 1 over 12, 3÷1/12
Answers
The model represent here gives the division problem is 3÷1/4.
What is Fraction?The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.
The number of parts into which the whole has been divided is shown by the denominator. It is positioned in the fraction's lower portion, below the fractional bar.How many sections of the fraction are displayed or chosen is shown in the numerator. It is positioned above the fractional bar in the upper portion of the fraction.Given:
We have three section 1+ 1 + 1= 3.
and, Each section have the fraction
= 4/12
= 1/3
so, the model represent here gives the division problem
3÷1/4.
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given the graph below which statements are true about the graph and the key features. select all that apply.
Answers
Option B: The domain of the function is the set of all real numbers, Option C: the range of the function is the set of all non-negative real numbers, Option D: the graph has an intercept at (0, 0), and option G: the graph is symmetric with respect to the y-axis are correct statements about the graph.
There are only real numbers in the domain, or collection of x-values. This is so because x holds true for all numbers. The set of all non-negative real numbers is known as the range or set of y-values. This is due to the fact that every value we obtain for y is a positive real number. The graph's x-intercept and y-intercept, also known as the intersection point, are located at (0, 0). Instead of the other way around, the graph increases on the interval x>0 and decreases on the interval x<0. Instead of a maximum, the graph shows a minimum at (0, 0). The graph is symmetric with respect to the y-axis because it may be folded in half along that axis.
As per the question, the function described below is an example of a polynomial function since it is a function of a single independent variable that has been raised to an integer power. Adding terms with a numerical coefficient multiplied by a specific power of the independent variables results in polynomial functions.
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a hot air balloon decends 305 feet per minute for 4minutes then ascends at a rate of 215 per minute for another 2 minutes. find the total feet in altitude
Answers
The total feet in altitude is given by the equation A = -790 feet
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the total feet in altitude be represented as A
Now , the equation will be
The hot air balloon descends 305 feet per minute for 4 minutes
So , the total descending will be a negative value , where
The feet in altitude descended = -305 x 4 = -1220 feet
Now , hot air balloon ascends 215 feet per minute for 2 minutes
So , the total ascending will be a positive value , where
The feet in altitude ascended = 215 x 2 = 430 feet
And , the total feet in altitude A = feet in altitude descended + feet in altitude ascended
Substituting the values in the equation , we get
The total feet in altitude A = -1220 + 430
On simplifying the equation , we get
The total feet in altitude A = -790 feet
Hence , the equation is A = -790 feet
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A researcher is studying a group of field mice. the distribution of the weight of the field mice is approximately normal with mean 25 g and standard deviation 4 g. which of the following is closest to the proportion of the field mice with a weight greater than 33 g? A 0.023 B 0.046 С 0.954 D 0.977 E 1.000
Answers
The probability of the field mice having a weight greater than 33 g is 0.977, the field mice have a weight greater than 33 g.
The proportion of field mice with a weight greater than 33 g can be calculated using the formula for a standard normal distribution. This formula states that the probability of an event with a normal distribution occurring can be calculated by subtracting the area under the normal curve from the mean to the given value and dividing by the standard deviation.
In this case, the mean of the distribution is 25 g, the standard deviation is 4 g and the given value is 33 g.
Therefore, the probability of the field mice having a weight greater than 33 g is 0.977. This means that 0.977, or 97.7%, of the field mice have a weight greater than 33 g.
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The ordered data set is given below. 19 24 27 27 28 31 33 37 We have determined that the 25th percentile of the data is between the second and third observations and the decimal portion of L25 is 0.25. Find the value of the 25th percentile. 25th percentile = second observation + decimal portion of L25(third observation - second observation) = 24 + 0.25 ( ____ – 24) =
Answers
The value of the 25th percentile for this data set is 26.25. This means that 25% of the data is below 26.25 and 75% of the data is above 26.25
The 25th percentile, also known as the lower quartile, is a value that separates the lowest 25% of the data from the rest of the data. To find the 25th percentile of an ordered data set, we first need to determine the position of the 25th percentile, which can be calculated using the formula:
position = (n+1) * p
where n is the number of observations in the data set and p is the percentile (in decimal form). In this case, n = 8 and p = 0.25. Put values:
position = (8+1) * 0.25 = 2.25
Since the position is not a whole number, we know that the 25th percentile falls between the second and third observations in the data set. In this case, the second observation is 24 and the third observation is 27. To find the exact value of the 25th percentile, we use the formula:
value = L + (position - i) * h
where L is the value of the lower observation, i is the integer part of the position, and h is the difference between the two observations. In this case, L = 24, i = 2, and h = 27 - 24 = 3. Put values:
value = 24 + (2.25 - 2) * 3 = 24 + 0.75 * 3 = 24 + 2.25 = 26.25
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Mei is thinking of a 2-digit multiple of 2. Ben is thinking of a 2-digit multiple of 3. Xander is thinking of a 2-digit multiple of 4. Dom is thinking of a 2-digit multiple of 6. Alice is thinking of a 2-digit multiple of 8. They are all thinking of the same number.
Answers
The only 2-digit multiple of 2, 3, 4, 6, and 8 is the number 24.
What is multiple ?Multiple is a term that refers to an amount that is greater than one or a collection of two or more items. It is often used to describe a quantity of objects, people, or events that are distinct from each other. For example, a multiple of five would be five, ten, fifteen, twenty, etc. Similarly, a multiple of three would be three, six, nine, twelve, etc.
Therefore, all five people are thinking of the same number: 24.
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Linear equation that passes through the points of (1,4) and (6,-1)
Answers
Answer:
y = -x+5
Step-by-step explanation:
Use point slope formula to find the equation of the line
First find the slope: (-1-4)/(6-1) = -5/5, slope = -1
Then, use the formula: y - y1 = m(x - x1)
y - 4 = -1(x - 1)
y - 4 = -x+1
y = -x + 5
Frank's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Frank $4.20 per pound, and type B coffee costs $5.60 per pound. This month's blend used four times as many pounds of type B coffee as type A, for a total cost of $984.20. How many pounds of type A coffee were used?
Answers
The quantity of type A coffee will be 37 pounds.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Frank's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Frank $4.20 per pound, and type B coffee costs $5.60 per pound.
The quantity of Type A coffee will be calculated as:-
B = 4A
4.20A + 5.6B = 984.20
4.20A + 4 x 5.6 x A = 984.20
4.20A + 22.4A = 984.22
26.6A = 984.22
A = 37
Therefore, the amount of each type of 37 pounds will equal one coffee.
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How many times does 1/2 go into 3/4
Answers
Answer:
1/2 goes into 3/4 1 1/2 or 1.5 times
Step-by-step explanation:
Read the following problem carefully! The amount of work, W, required to move a particle of mass M a vertical distance d above its starting height is given by the formula,W=Mgdwhere g is the acceleration due to gravity. A heavy rope is 15 m long and has a constant (linear) density of rho=2 kg/m. The rope hangs over the edge of a 25 m building, as shown below: The work required to pull the rope to the top of the building cannot be computed using the above formula because the distance each part of the rope must be moved is different! Answer the following questions and put your final answer for each part in the box. I. (The Approximate Work) A. On the figure above, the rope has been divided into three segments of equal length,Δy. Calculate Δy.Δy=B. Find the mass, M2, of the middle segment of the rope.M2 =C. The y values of the bottom of each segment of rope are indicated above. Find the valuesy0, y1, and y2 and label them on the figure (No justification is necessary). By approximating that the middle segment is a particle located at y2: D. Find the distance d2 the middle segment must be moved to reach the top of the building.d2 =
Answers
A. The length of each segment of the rope is 5 m.
B. The mass of the middle segment is the length of the segment 10 kg.
C. The y values of the bottom of each segment are y₀ = 0, y₁ = 5 m, and y₂ = 10 m.
D. The distance d₂ the middle segment must be moved is 15,
What do you mean by acceleration?Acceleration is a measure of the change in velocity over time. In physics, acceleration is defined as the rate of change of velocity, or the second derivative of position with respect to time. Acceleration is a vector quantity that has both magnitude and direction, and its unit is meters per second squared (m/s²).
A positive acceleration indicates an increase in speed, while a negative acceleration indicates a decrease in speed or a change in direction. In everyday life, we encounter examples of acceleration in movements such as starting a car, stopping a car, or changing direction while driving.
A. The length of each segment of the rope is 15 m / 3 = 5 m.
B. The mass of the middle segment is the length of the segment multiplied by the density of the rope: M2 = 5 m × 2 kg/m = 10 kg.
C. The y values of the bottom of each segment are y0 = 0, y1 = 5 m, and y2 = 10 m.
D. The distance d2 the middle segment must be moved is 25 m - 10 m = 15 m.
Therefore, the work required to move the middle segment can be approximated using the formula W = M2 × g × d2, where g is the acceleration due to gravity. The exact value of the work required to move the entire rope would need to take into account the different distances that each segment must be moved.
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Let X be a continuous random variable taking values between 0 and 2 with probability density function p(x) = 0.5. Find E(X) and Var(X). Plot its Cumulative Distribution Function.
Answers
E(X) = 2 and Var(X) = 4/3.
And then, Here's a plot of the CDF of X:
[Plot of the CDF of X with x on the x-axis and F(x) on the y-axis, showing a line with slope 0.5 for x in [0,2]]
Continuous Random Variable ExpectationsThe expected value (mean) of a continuous random variable X with probability density function p(x) is given by:E(X) = ∫x*p(x)dx, where the integral is taken over the range of X.
In this case, since p(x) = 0.5 for all x in [0,2], we have:E(X) = ∫x*0.5dx = 0.5∫xdx = 0.5(x²/2)|0 to 2 = (2²/2 - 0²/2)*0.5 = 2.
The variance of X is given by:Var(X) = E((X - E(X))²) = E(X²) - (E(X))².
We have to calculate E(X²), which can be found as:E(X²) = ∫x²*p(x)dx = 0.5∫x²dx = 0.5(x²/3)|0 to 2 = (2²/3 - 0³/3)*0.5 = 8/3.
So, Var(X) = E(X²) - (E(X))² = 8/3 - (2)² = 8/3 - 4 = 4/3.
The cumulative distribution function (CDF) of a continuous random variable X is given by:F(x) = P(X <= x) = ∫p(t)dt for all t <= x.
In this case, since p(x) = 0.5 for all x in [0,2], we have:F(x) = 0.5x for x in [0,2].
The CDF of X is a monotonically increasing function, and it tells us the probability that X takes a value less than or equal to x.
Now, Here's a plot of the CDF of X:
[Plot of the CDF of X with x on the x-axis and F(x) on the y-axis, showing a line with slope 0.5 for x in [0,2]]
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Find the distance between the following numbers on the real number line a=12, b=3
Answers
Answer: 9
Step-by-step explanation:
12-3=9 or count up from 3 until you get too 12
(2) Melissa and Ron entered a competition as a team Ron's score was 4/9 of Melissa's score. Melissa scored 50 more points than Ron. How many points did Melissa score?
Answers
The number of points that Melissa scored would be = 89 points.
How to calculate the number of point scores by Melissa?The competition was carried out by these two individuals that had different scores such as follows:
The total number of scores for Melissa = 50 point + Ron's score. That is , y = 50+X. ---> eq 1
The total number of Ron's score X = 4/9 × y --> 2
substitute y into equation 2.
X = 4/9× (50+X)
X= 22 + 0.44x
0.56x= 22
X= 22/0.56
X= 39.
substitute X into equation 1;
y= 50+39
y = 89
Therefore, the total number of points for Melissa = 89 point.
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A shirt was originally priced at $30. The store is having a 30% off sale. How much will you pay for the shirt after the discount (not including tax)? Round your answer to the nearest cent
A $30 shirt marked 30% off will cost $
Answers
Answer:
$21
Step-by-step explanation:
Answer:
21
Step-by-step explanation:
$30 subtracted by 30% is equal to $21
9 × 3 = 27 +10% (3) = $30
find the value of x in 2/3 (2x+4) +6=10
Answers
Answer:
x = 1
Step-by-step explanation:
2/3 (2x + 4) + 6 = 10
2/3 (2x + 4) = 10 - 6
1⅓x + 2⅔ = 4
1⅓x = 4 - 2⅔
1⅓x = 1⅓
x = 1
Turning yards into feet
Answers
To convert yards to feet we multiply the given value by 3.
How is this determined?A yard is one linear yard. "Yd" is the yard symbol. It is equivalent to 36 inches or 3 feet. 1 yard equals 0.9144 metres in metres when measured in metres. Both the imperial and US customary systems of measuring use this unit. The most common use of yards is to measure the length of a field, such a sports field.
A foot can also be used to measure length. The letter "ft" stands for the foot. Twelve inches and one third of a yard make up one foot. Additionally, one foot is equal to 0.3048 metres. We must divide the provided value by 3.281 to translate the given value from feet to metres. In aviation and elevation, the foot is typically used to measure height or altitude. The height of a person is also expressed in feet and inches.
Hence, to convert yards to feet we multiply the given value by 3.
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The triangle below is equilateral. Find the length of side x in simplest radical form with a rational denominator.
Answers
The length of side x is √3 units.
How to find the value of x?We know that the larger triangle is an equilateral triangle, and it is divided into two equal right triangles.
Now, let's analyze these, we can see that the catheti are:
x and 3.
And the hypotenuse must have a length of 2x (if the triangle is equilateral).
Now we can use Pythagorean's theorem.
Then we will get:
(2x)^2 = x^2 + 3^2
4x^2 = x^2 + 9
4x^2 - x^2 = 9
3x^2 = 9
x^2 = 9/3 = 3
x = ± √3
We only care for the positive value, then:
x = √3
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Solve the triangle:
Answers
Answer:
Step-by-step explanation:
we will find the first angle in the larger triangle;
180⁰-60⁰= 120⁰
120⁰
the second angle will be;
120⁰+30⁰=150⁰
180⁰-150⁰=30⁰
30⁰ this means that the second triangle is isosceles triangle, when we find the hypotenuse of the smaller triangle it will be equal to x since the sides are equal
88/sin60⁰=x/sin90⁰
88sin 90⁰=xsin60⁰
88/0.8660=0.8660x/0.8660
x=101.62
I need help………………………
Answers
Step-by-step explanation:
could you answer to my question
I'll need more than I need help in a picture to answer your question
please answer to this with what you need help with I am only seeing a question which I do not know and what I need to focus
thank you for cooperating - yuri
The probability that a baseball player hits a home run is greater than the probability that he gets a successful hit. (Select all that apply.) A.) A home run is the only type of successful hit, so the probabilities of each must be equal. B.)The probability that he hits a home run and the probability that he gets a successful hit must add up to 1. C.)The probability that he gets a successful hit must be 1, since a successful hit is always possible, and therefore the probability that he hits a home run cannot be greater. D.)A home run by definition is a successful hit, so the probability that he gets a successful hit must be greater than, or at least equal to, the probability that he hits a home run. E.)These probabilities cannot be calculated, so it is impossible to say which one is greater.
Answers
The correct statement regarding the probability in this problem is given as follows:
D.) A home run by definition is a successful hit, so the probability that he gets a successful hit must be greater than, or at least equal to, the probability that he hits a home run.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes.
For each at bat, there are two possible outcomes:
Elimination.Successful hit.There are four types of hits, which are given as follows:
Single.Double.Triple.Home run.Hence only statement D is correct, as the player can either be eliminated or get one of the four types of hits.
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Which of the following is NOT an impact of American consumerism?
A. Exorbitant personal debts
B. Lack of unemployment and homelessness
C. Cash generators for several nations
D. Stress
Answers
The terms which is not an impact of American consumerism is -
Option C: Cash generators for several nations.
What is consumerism?
The tendency to continuously consume is known as consumerism. It is the need to acquire more possessions and establish one's identity via them. Consumer spending and GDP growth are seen as benefits of consumerism by economists.
The American consumerism includes -
Debts : Due to introduction of credit cards the consumers have ore and more debt on their credit cards whilst they spend on materialistic goods.
Lack of Unemployment : Economists point out that a decline in product demand causes an economic downturn or even depression, which is accompanied by high unemployment.
Stress: Due to debt, recession and unemployment people are constantly under stress for surviving.
Since, consumerism helps in GDP growth of a country it does not help generate cash for other nations.
Therefore, " Cash generators for several nations" is not an impact.
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find the absolute value!! Need asap!!
Answers
Answer:
|-1/7| = 1/7 or approx .14
If 7x-43=5x+43 what is x equal to?
Answers
Answer:
7x-43=5x+43
7x-5x=43+43
2x=86
x=86/2
x=43
new flat screen tv are measured diagonally. if the dimensions of a new tv are 28 inches by 15.7 inches, what is the exact length of the diagonal?
Answers
Because it just is
Graph all vertical and horizontal asymptotes of the Rational function.
f(x)= -7/x^2+4
Answers
The function has no vertical asymptotes and horizontal asymptotes are at y = 0.
What are Asymptotes?A straight line that continuously approaches a certain curve without ever meeting it is an asymptote. In other words, an asymptote is a line that a curve travels toward as it approaches infinity.
A straight line that serves as the asymptote of the curve y = f(x) or, in its implicit form, f(x,y) = 0, where the distance between the two lends to zero as the points on the curve approach infinity.
Given function,
f(x) = -7/(x² + 4)
in the given function the degree of the denominator is more than the numerator so The horizontal asymptote lies at y = 0 because, as we can see, the degree of the numerator is less than the denominator.
and there will be no vertical asymptote.
The graph of the equation is attached.
Hence horizontal asymptote lies at y = 0 and ni vertical asymptote.
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The students in Class 6 vote to pick a class captain. The choice is Anton, Eva, Kofi or Petra. Anton gets 0.2 of the votes. Eva gets 10% of the votes. Petra gets of the votes. Kofi gets 9 votes. How many students are in class 6?
Answers
Answer:
Step-by-step explanation:
Let's say there are "x" students in class 6.
Since Anton got 0.2 of the votes, he got 0.2 * x votes.
Eva got 10% of the votes, which is equal to 0.1 * x votes.
Petra got 0.3 of the votes, which is equal to 0.3 * x votes.
Kofi got 9 votes.
So, the total number of votes in class 6 is x.
By adding up the number of votes each candidate received, we can write an equation:
0.2x + 0.1x + 0.3x + 9 = x
Simplifying the equation:
0.6x + 9 = x
Subtracting 0.6x from both sides:
9 = 0.4x
Dividing both sides by 0.4:
x = 22.5
Since the number of students must be a whole number, we round up to the nearest whole number:
x = 23
So there are 23 students in Class 6.
What is the answer to 19-6(-k-2)?
Answers
Answer: 6k + 31
Step-by-step explanation:
19 - (-6k - 2(6))
19 - (-6k - 12)
19 + 6k + 12
6k + 31
Answer: 6k + 31
Step-by-step explanation:
= 19-6(-k-2)
= 19+6k +12
= 6k + 31
Add −13 1/4 + 4 3/4 . Write your answer as a mixed number in simplest form.
Answers
Answer:
- 8.5
Step-by-step explanation: