if 2x+1 is a factor of 2x³ +x²-kx-1, find the value of k
Answers
Answer:
k=2
Step-by-step explanation:
Find the zeros of the factor
2x+1=0
x=-½
Plug x=-½ into the function and equate to 0
2(-½)³+(-½)²-k(-½)-1=0
2(-1/8)+¼+½k-1=0
-¼-1+¼+½k=0
-1+½k=0
½k=1
k=2
Step-by-step explanation:
2x+1=0
x=-1/2
Now p(x)= 2x^3 + x^2 -kx-1
subtitute value of x:
p(-1/2)= 2(-1/2)^3 + (-1/2)^2 -k(-1/2)-1
p(-1/2)=2*-1/8+1/4+k/2-1
p(-1/2)=-1/4+1/4+k/2-1
p(-1/2)=k/2-1
2x+1 is the factor of p(x) so
k/2-1=0
k/2=1
k= 2
Related Questions
Look at the data under PURCHASE BEHAVIOR. How often do consumers in this segment purchase a backpack? Purchase behavior last quarter - 23% : a. Once every 6 years b. Once every 3 years c. Once every year d. Once every 2 years e. Once every 5 yrs
Answers
By looking at the data under PURCHASE BEHAVIOR, we can see that the consumers in this segment purchase a backpack at a range of purchase every five years. The Option E is correct.
What determines a Consumer purchase interval?We have several factors that can determine a consumer's purchase interval, including:
Product usage: How frequently a product is used or consumed can influence the consumer's purchase interval. If a product is used frequently, the consumer may need to purchase it more often.Product durability: The durability of a product can impact the purchase interval. If a product is durable and lasts a long time, the consumer may not need to purchase it as frequently.Price: The price of a product can also determine the purchase interval. If a product is expensive, the consumer may wait longer before making another purchase.Consumer behavior: Consumer behavior, such as brand loyalty or habit, can also influence the purchase interval. Consumers who are loyal to a particular brand may purchase that brand more frequently, while others may be more open to trying different brands and products etc.Read more about Consumer
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Answer:
Step-by-step explanation:
answer is c. once every year
is an altitude in triangle wxz. if δywz ~ δyxw, what is true about xwz?
Answers
What is true about ΔXWZ is that the ratio of its altitude to the corresponding altitude in ΔYWZ is equal to the ratio of the length of XW to the length of YZ.
If ΔYWZ is similar to ΔYXW, it means that these two triangles have corresponding angles that are equal and corresponding sides that are proportional. In this case, we are specifically interested in the altitude of ΔWXZ, which we will denote as h.
Since ΔYWZ is similar to ΔYXW, we can establish the following proportion based on their corresponding sides:
YZ/YX = YW/YW
Let's denote the length of YZ as a and the length of YW as b. We can rewrite the proportion as:
a/YX = b/YW
Now, let's consider ΔXWZ. Since XW is common to both triangles, we can conclude that the altitude of ΔXWZ, which we will denote as k, is also proportional to the altitude of ΔYWZ (h). Therefore, we can express this proportion as:
k/h = XZ/YZ
To establish a relationship between k and h, we need to find a way to relate XZ to YZ. Using the proportion established earlier, we can substitute a for YZ:
k/h = XZ/a
To relate XZ to YZ, we need to find a relationship between XZ and YX. Again, using the similarity of the triangles, we have:
XZ/YZ = XW/YW
Substituting the value of YZ (a) from the earlier proportion, we have:
XZ/a = XW/YW
Now, we can combine the two proportions to find the relationship between k and h:
k/h = (XW/YW) * (YW/a)
Simplifying further, we get:
k/h = (XW/a)
From this equation, we can conclude that the ratio of the altitudes k/h in ΔXWZ and h in ΔYWZ is equal to the ratio of XW to YZ. In other words, the ratio of the altitudes is equal to the ratio of the corresponding sides in the similar triangles.
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Age(years) Total( frequency)
15-20 2
20-25 6
25-30 24
30-35 45
35-40 78
40-45 89
45-50 92
50-55 98
55-60 100
Find The Median.
Answers
Answer:
40
Step-by-step explanation:
given tan(x)=24/25 (in quadrant 1), find sin(2x)
Answers
Given tan(x)=24/25 (in quadrant 1), the value of sin(2x) is 2352 / 15625.
How to calculate the valueIt should be noted that tan(x) = sin(x) / cos(x)
Given tan(x) = 24/25, we can represent it as:
24/25 = sin(x) / cos(x)
cos²(x) + sin²(x) = 1
Since we're in quadrant 1, both sin(x) and cos(x) are positive. Let's solve for cos(x):
cos²(x) + (24/25)² = 1
cos²(x) + 576/625 = 1
cos²(x) = 1 - 576/625
cos²(x) = 49/625
Taking the square root of both sides:
cos(x) = sqrt(49/625)
cos(x) = 7/25
Now that we have cos(x), we can find sin(x) using the given equation:
24/25 = sin(x) / (7/25)
Multiplying both sides by (7/25):
(7/25) * (24/25) = sin(x)
168/625 = sin(x)
Now, we have sin(x) and cos(x), and we can use double angle formula to find sin(2x):
sin(2x) = 2 * sin(x) * cos(x)
Substituting the values we found:
sin(2x) = 2 * (168/625) * (7/25)
sin(2x) = (2 * 168 * 7) / (625 * 25)
sin(2x) = 2352 / 15625
Therefore, sin(2x) = 2352/15625.
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1. The Fibonacci sequence In the 13th century, the Italian mathematician Leonardo Fibonacci-as a way to explain the geometic growth of a population of rabbits-devised a mathematical sequence that now bears his name. The first two terms in this sequence, Fib(0) and Fib(1), are 0 and 1, and every subsequent term is the sum of the preceding two. Thus, the first several terms in the Fibonacci sequence look like this: Fib(0) = 0 Fib(1) = 1 Fib(2) = 1 (0+1) Fib(3) = 2 (1+1) Fib(4)= 3 (1+2) Fib(5)=5 (2+3) Write a program that displays the terms in the Fibonacci sequence, starting with Fib(0) and continuing as long as the terms are less than 10,000. Thus, your program should produce the following numbers: 0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 This program continues as long as the value of the term is less than the maximum value, so that the loop construct you need is a while, presumably with a header line that looks like this: while term
Answers
To display the terms in the Fibonacci sequence, starting with Fib(0) and continuing as long as the terms are less than 10,000, a program is written with a loop construct. This loop is implemented using a `while` loop with a header line that looks like this: `while term < 10000:`.
Fibonacci sequence is named after the Italian mathematician Leonardo Fibonacci who developed a mathematical sequence in the 13th century to explain the geometric growth of a population of rabbits.
The first two terms in this sequence, Fib(0) and Fib(1), are 0 and 1, and every subsequent term is the sum of the preceding two.
The first several terms in the Fibonacci sequence are:
Fib(0) = 0, Fib(1) = 1, Fib(2) = 1, Fib(3) = 2, Fib(4)= 3, Fib(5)=5.
This program continues as long as the value of the term is less than the maximum
The output is as follows:
```1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765```
The while loop could also be used to achieve the same goal.
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What is irrational statement?
Answers
An irrational statement is a kind of genuine number that can't be addressed as a basic portion. It can't be communicated in that frame of mind of a proportion. If N is silly, N isn't equivalent to p/q where p and q are numbers and q isn't equivalent to 0. Model: √2, √3, √5, √11, √21, π(Pi) are nonsensical.
A number can't be communicated as a portion of any numbers and. . Unreasonable numbers have decimal developments that neither end nor become occasional. Each supernatural number is irrational.
If a square root is not an ideal square, then it is viewed as an unreasonable number. These numbers can't be composed as a portion because the decimal doesn't end (non-terminating) and doesn't rehash an example (non-repeating).
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A polynomial P has zeros when x=0, x=-1/6 and x=-3 Whats could be the equation p?
Answers
Answer:
P(x) = \(x^{3}\) + \(\frac{19}{6} x^{2}\) + \(\frac{1}{2} x\)
Step-by-step explanation:
x(x + 1/6)(x + 3) = P
x(\(x^{2}\) + 3x + 1/6(x) + 1/2) = P
x (\(x^{2}\) + 19/6(x) + 1/2) = P
\(x^{3}\) + \(\frac{19}{6} x^{2}\) + \(\frac{1}{2} x\) = P(x)
find an acute angle theta that satisfies the equation sin theta =cos (2 theta + 27 degrees)
Answers
An acute angle theta that satisfies the equation sin θ =cos (2 theta + 27 degrees) is 45 degrees.
To find an acute angle theta that satisfies the equation sin theta =cos (2 theta + 27 degrees), we can use the identity cos (90 - theta) = sin theta.
Substituting 90 - theta for 2 theta + 27 degrees, we get:
sin theta = cos (90 - theta)
Using the identity cos (90 - theta) = sin theta, we can simplify the equation to:
sin theta = sin (90 - theta)
Since sin θ = sin (90 - theta), we can conclude that theta = 90 - theta.
Solving for theta, we get:
2 theta = 90
theta = 45 degrees
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What was her speed?
0. 1 mile per minute
0. 5 mile per minute
5 miles per minute
10 miles per minute
Answers
Question :
The graph shows the relationship between the number of minutes Maria spent jogging on a treadmill and the distance she jogged. what was her speed?
Answer:
The Answer is A. 0.1 mile per minute
expressions is equal to 2(40 - p)?
Answers
You use the distributive property
NEED HELP ASAP 10 POINTS BRAINLY IF CORRECT
Answers
Answer:
can u just post a question pls
2. A computer programmer earns a regular hourly rate of P50. 0. If he
worked 42. 75 hours in a week, how much did he earn?
pls answer this with solution a really need the solution
Answers
Answer:
b
Step-by-step explanation:
42.75+4=6
“Find the slope and y-intercept of the linear graph” please help I’ll mark brainliest!!
Answers
Slope: 2/-3
(Im sorry if im wrong)
calculate using multiplication method 145×188
Answers
Answer:
27260
Step-by-step explanation:
145
x188
1160
11600
+14500
27260
The slope of the line shown on the
graph below is
Answers
simplified 1/3 is the slope
Which statement best describes f(6) = 12?
When the input is 6, the output must be 12.
O When the input is 12, the output must be 6.
O When the output is 6, the input must be 12.
O When the output is 12, the input must be 6.
Answers
Answer:
When the input is 6, the output must be 12.
Step-by-step explanation:
f(6) = 12
The input to the function is x which is 6 and the output is what f(6) equals which is 12
Answer:
When the input is 6, the output must be 12
Step-by-step explanation:
If you put in 6 into the equation it must equal or output 12
Find the 6th term of the geometric sequence whose common ratio is 2/3 and whose first term is 8.
Answers
To solve this question, we need to find the formula for the nth term of the geometric sequence. The formula is:
\(a_n=a_1r^{n-1}\)Where:
a_n is the nth term of the sequence
a_1 is the first term of the sequence
r is the common ratio
In this case:
a_1 8
r = 2/3
\(a_6=8\cdot(\frac{2}{3})^{6-1}=8\cdot(\frac{2}{3})^5=8\cdot\frac{32}{243}=\frac{256}{243}\)The answer is:
256/243
Given a∥b , and c is not parallel to a or b, which statements must be true? Select each correct answer. Responses m∠1=m∠5 the measure of angle 1 equals the measure of angle 5 m∠7=m∠11 the measure of angle 7 equals the measure of angle 11 m∠5=m∠12 the measure of angle 5 equals the measure of angle 12 m∠4=m∠5 the measure of angle 4 equals the measure of angle 5 three lines a, b, and c that look somewhat horizontal. they are cut by a transversal forming 12 angles. line a intersects the transversal for form angles 1, 2, 4, 3 clockwise starting from the top left. line b intersects with the transversal to form angles 5, 6, 8, 7 clockwise starting from top left. line c intersects with the transversal to form angles 9, 10, 12, and 11 clockwise starting from top left. Skip to navigation
Answers
By using the properties of parallel lines, the result obtained is-
The correct options are first, second and fourth
What are parallel lines?
Two lines are said to be parallel if on extending them indefinitely, they will never intersect
Here,
From the figure,
For the first option,
m∠1=m∠5 [Corrosponding angles are equal]
First option is correct
For the second option,
m∠7=m∠11 [Corrosponding angles are equal]
Second option is correct
For the third option,
m∠5 ≠ m∠12 [ c is not parallel to b]
Third option is wrong
For the fourth option,
m∠4 = m∠5 [Alternate interior angle are equal]
Fourth option is correct
So the correct option are first, second and fourth
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Complete Question
The diagram has been attached
Answer: The answer is below
Step-by-step explanation:
To evaluate 8^2/3 find
Answers
To evaluate \(8^{\frac{2}{3} }\) first find the square of 8 and then take the cube root.
What are exponents?The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself.
Depending on the powers they possess, many rules of exponents are given.
Law of Multiplication: Exponents should be added while keeping the base constant when multiplying like bases.
Exponents should be multiplied while bases are kept constant when bases are raised by a power of two or more.
Division Rule: When dividing like bases, maintain the base constant and deduct the exponent of the denominator from the exponent of the numerator.
The given value can be written as:
\(8^{\frac{2}{3} } = \sqrt[3]{8^{2} }\)
Hence, to evaluate \(8^{\frac{2}{3} }\) first find the square of 8 and then take the cube root.
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The difference of two numbers is 16. The greater number is 4 times the smaller
number minus 5. Find the numbers.
Answers
After using the linear equation - The smaller number is 7, and the greater number will be 23.
what is the substitution method?
Mathematicians frequently use the substitution method to resolve an equation system. With this method, you solve the equation for the first variable first, and then plug the answer into the second equation.
what is a linear equation in two variables?
When an equation is written in the form axe + by + c=0 and the coefficients of x and y, i.e., a and b, respectively, are not equal to zero and the greater of the two numbers is four times the smaller number minus 5, that equation is said to be linear in two variables.
Let's assume that "x" is the smaller number, making "4x-5" the greater number. The requirement that the difference between the two numbers be 16 is also included.
thus,
4x - 5 - x = 16
3x -5 = 16
3x = 16 +5
3x =21
x = 21/3
x = 7
for the second number
4x-5
=4(7)-5
=28-5
=23
hence the smaller number is 7, and the greater number will be 23.
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Please help I'm very confused, Will give Brainliest
Fred wants to buy some feeder mice for $1.25 each and some goldfish for $0.50 each for his pet lizard, but he can spend no more than
$10.
Which inequality represents the situation?
1.25x+0.50y≤10
1.25x+0.50y<10
1.25x+0.50y≥10
1.25x+0.50y>10
Answers
Answer:
1.25x+0.50y<10 is the correct answer
Step-by-step explanation:
this is because 1.25+0.50 is less than 10 so in other words 10 is greater than 1.25+0.50
hope this helps
Answer:
I believe the answer is b if not then a
Step-by-step explanation:
Identify values of coefficients in the quadratic equation x^2-2x+7=0a=b=c=7x^2=10-13xa=b=c=5x^2=4x+7a=b=c=-11x+3=-4x^2a=b=c=
Answers
a = 7
b = 13
c = -10
Explanantion:\(7x^{2}\text{ = 10 - 13x}\)Re-writing the expression above in the form: ax² + bx + c = 0
7x² = 10 - 13x
7x² + 13x - 10 = 0
From 7x² + 13x - 10 = 0
a = 7
b = 13
c = -10
Please help! 15 points!
Answers
Answer:
b
Step-by-step explanation:
the 80 degrees one and y are the same
Answer:
y=80 degrees
Step-by-step explanation:
The corresponding angles and opposite angles are equal to each other because of the parallel lines.
4,022 + x = 7,565=?????????
Answers
Answer:
x = 3,543
Step-by-step explanation:
4,022 + x = 7,565
-4,022 -4,022
_______________
x = 3,543
Answer:
x = 3,543
Step-by-step explanation:
4,022 + x = 7,565
Since 4,022 is being added to x, subtract 4,022 from both sides.
4,022 + x - 4,022 = 7,565 - 4,022
x = 3,543
A box has dimensions of 2.5 cm by 3.0 cm by 4.0 cm. The volume of the box in milliliters and liters is:
Answers
Answer:
30000 milliliters
0.03 liters
Step-by-step explanation:
The volume of the box is 2.5 x 3.0 x 4.0 = 30 cc
There are 1000 ml in 1 cc so 30cc = 30 x 1000 = 30000 ml
There are 1000 cc in 1 liter so 30 cc = 30/1000 = 0.03 liters
The volume of the box is 30 mL or 0.03 L.
What is volume?Volume is a metric magnitude that is defined as the extension in three dimensions of a region of space. Volume is defined as the amount of space occupied by the object or figure in three-dimensional space. Volume is measured in cubic units.
The volume of this prism depends on its three dimensions and is calculated as the multiplication of these dimensions,
Volume= Dimension 1× Dimension 2× Dimension 3
The volume of the box = 2.5 x 3.0 x 4.0 = 30 cc
There are 1000 ml in 1 cc so 30cc = 30 x 1000 = 30000 ml
There are 1000 cc in 1 liter so 30 cc = 30/1000 = 0.03 liters
Hence, the volume of the box is 30 mL or 0.03 L.
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1) back at basketball practice, Haley's coach is impressed with the improvement in her scoring ability over the past month. She went from scoring 12 points per game last month to scoring 18 points per game this month. He exclaims, "Haley, you have made a 100% improvement in your average points per game!"
a. If Haley increased her average points per game by 100%, how many points per game would she be scoring this month?
b. If she had increased her average points per game by 25%, how many points would she be scoring this month?
d. What portion of her points per game for last month does that increase represent? By what percent did Haley improve her average points per game?
P.S I did c
Answers
Answer:
A: It would be 24 points per game.
B: It would be 15 points per game
C: 33.33%
Step-by-step explanation:
A explanation:
100% of 12 is 24
12 + 12 = 24
B explanation:
25% of 12 = 3
12 + 3 = 15
C explanation:
12/18 = 66.66%
100 - 66.66 = 33.33%
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We want to select a random sample of five dealers. The random numbers are: 30, 96, 45, 1, 69, 77, 16, 25, 20, 87, 71, and 20. Which dealers would be included in the sample
Answers
Based on the provided random numbers, the dealers that would be included in the sample are Dealer 1, Dealer 16, Dealer 20, Dealer 20, and Dealer 25. It's worth noting that Dealer 20 appears twice in the sample, which could be a result of duplicate entries or a coincidence in the random number generation.
The dealers that would be included in the sample are: Dealer 30, Dealer 96, Dealer 45, Dealer 1, and Dealer 69.
To select a random sample of five dealers from the given list, we can use the random numbers provided. Let's sort the random numbers in ascending order: 1, 16, 20, 20, 25, 30, 45, 69, 71, 77, 87, 96.
The first five numbers in the sorted list correspond to the dealers that would be included in the sample. Therefore, Dealer 1, Dealer 16, Dealer 20, Dealer 20, and Dealer 25 would be selected.
If duplicates are not desired in the sample, the selection process could be repeated, or one of the instances of Dealer 20 could be replaced with the next number in the sorted list, which would be Dealer 30.
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Consider the basis of . Let be the linear transformation such thatSet. Compute .Consider the basis B = ([ 0 ] , [ 0 ] , [ 1 ] of R^3. [ 0 ] [ -1 ] [ -2 ][ 1 ] [ -1 ] [ 1 ]Let T:R^3→R^2 be the linear transformation such that T( [0] ) = [1] , T ([ 0 ]) = [3] , T([ 1 ]) = [ 0][0] [1] [ -1] [2] [ -2] [-1][1] [ -1] [ 1 ]Set v = [ -1 ] Compute T(v).[ 1 ][ -2 ]T(v) = [ .... ]
Answers
The value of T(v), express v as linear combination in the basis B and the matrix representation of T obtain is T(v) = [4, -4].
To find T(v), we need to express v as a linear combination of the basis vectors of R^3 with respect to B:
v = (-1)[0] + (-1)[0] + (1)[1]
This means that the coordinate vector of v with respect to B is [-1, -1, 1].
To find the matrix representation of T with respect to the standard bases of R^3 and R^2, we can apply T to each of the basis vectors:
T([1, 0, 0]) = [1, 3]
T([0, 1, 0]) = [-1, 1]
T([0, 0, 1]) = [2, -2]
We can arrange the results in a matrix:
[1 -1 2]
[3 1 -2]
The matrix [1 -1 2; 3 1 -2] represents T with respect to the standard bases of R^3 and R^2.
To find T(v), we can multiply the matrix representation of T with the coordinate vector of v with respect to B:
T(v) = [1 -1 2; 3 1 -2] * [-1; -1; 1] = [4; -4]
Therefore, T(v) = [4, -4].
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Kaylee is working two summer jobs, making $6 per hour walking dogs and $13 per hour landscaping. Last week Kaylee worked a total of 8 hours and earned a total of $83. Determine the number of hours Kaylee worked walking dogs last week and the number of hours she worked landscaping last week.
Kaylee worked
hours walking dogs and
hours landscaping.
Answers
Answer:
3 hours walking dogs and 5 hours landscaping
Step-by-step explanation:
Answer 65$ 5 hours landscaping 18$ 3 hours walking dogs
Step-by-step explanation:
Please help
Thank you!
Answers
Answer:
B. point S
Step-by-step explanation:
The point between 0 and -5 is -2.5.
The point between -5 and -10 is -7.5.
We need a point to the right of -7.5 and to the left of -2.5.
Answer: B. point S
Answer:
-2.5>R>-7.5
Step-by-step explanation:
Look at the left of the graph. The first tick to the left of 0 is -2.5. The third tick to the left of zero is -7.5
R is the only point that is less then -2.5 but greather then -7.5