Find a polynomial f(x) of degree 5 that has the following zeros.
WILL GIVE BRAINEST!
Answers
The polynomial f(x) with zeros -7 (multiplicity 2), - 2, 5 , 9, is f(x) = x⁵ - 26x⁴ + 234x³ + 49x³ - 736x² - 427x + 4410
What is a polynomial?A polynomial is a mathematical function with the power of the unknown greater than or equal to 2.
To find the polynomial of degree 5 with the following zeros -7 (multiplicity 2), - 2, 5 , 9, we proceed as follow.
Since the polynomial has the zeros of -7 (multiplicity 2), - 2, 5 , 9, then its factors are
(x - 7)²[x - (-2)] = (x + 2)(x - 5) and (x - 9)So, multiplying the factors together, we get the polynomial f(x).
So, f(x) = (x - 7)²(x + 2)(x - 5)(x - 9)
Expanding the brackets, we have
= (x² - 14x + 49)(x + 2)(x - 5)(x - 9)
= (x² - 14x + 49)(x² -5x + 2x - 10)(x - 9)
= (x² - 14x + 49)(x² - 3x - 10)(x - 9)
= (x² - 14x + 49)(x³ - 3x² - 10x - 9x² + 27x + 90)
= (x² - 14x + 49)(x³ - 12x² + 17x + 90)
= (x⁵ - 12x⁴ + 17x³ + 90x² - 14x⁴ + 168x³ - 238x² - 1260x + 49x³ - 588x² + 833x + 4410)
Collecting like terms, we have
= (x⁵ - 12x⁴ - 14x⁴ + 17x³ + 168x³ + 49x³ + 90x² - 588x² - 238x² - 1260x + 833x + 4410)
= x⁵ - 26x⁴ + 234x³ + 49x³ - 736x² - 427x + 4410
So, f(x) = x⁵ - 26x⁴ + 234x³ + 49x³ - 736x² - 427x + 4410
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Related Questions
9 is 60% of what number? 12 45 15 54
Answers
Answer:
15
Step-by-step explanation:
3 is 20% or 1/5 of the number. 3 x 5 = 15
Answer:
The answer is 15.
I need to add more characters
Find the value of x
Answers
The value of x for the intersecting chords is derived to be 14 which makes option C correct.
What is the properties of intersecting chordsThe property of intersecting chords states that in a circle, if two chords intersect, the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord.
x × 32 = 16 × 28
32x = 448
32x/32 = 144/32 {divide through by 32}
x = 14
Therefore, the value of x for the intersecting chords is derived to be 14
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A movie theater has a seating capacity of 253. The theater charges $5.00 for children, $7.00 for students, and $12.00 of adults. There are half as many adults as there are children. If the total ticket sales was $ 1828 on a sold out night, how many children, students, and adults attended?
children attended=
adults attended=
students attended=
Answers
Answer:
children attended= 114
adults attended= 57
students attended= 82
Step-by-step explanation:
children attended= c
adults attended= a
students attended= s
c+s+a = 253
5c + 7s + 12a = 1828
c=2a
2a + s + a =253
5*2a + 7s + 12a = 1828
3a + s = 253
22a + 7s = 1828
s = 253 - 3a
22a + 7(253 - 3a) = 1828
22a - 21a + 7*253 = 1828
a = 1828 - 7*253
a = 57
s = 253 - 3a = 253 - 3*57 = 82
s = 82
c=2a=2*57= 114
c=114
The Venn diagram shows the number of customers who have purchased different types of pets from a pet store, where C represents customers who have purchased cats, D represents customers who have purchased dogs, and F represents customers who have purchased fish.
Circles C, D, and F overlap. Circle C contains 15, circle D contains 21, and circle F contains 12. The overlap of C and F contains 2, the overlap of F and D contains 0, and the overlap of D and C contains 3. The overlap of all 3 circles contains 1. Number 14 is outside of the circles.
How many people are in the set C ∩ D?
4
6
36
38
Answers
The number of people in the set C ∩ D (customers who purchased both cats and dogs) is obtained by adding the overlap of D and C (3) with the overlap of all 3 circles (1), resulting in a total of 4 individuals.
The correct answer is 4.
To determine the number of people in the set C ∩ D (customers who have purchased both cats and dogs), we need to analyze the overlapping regions in the Venn diagram.
Given information:
- Circle C (cats): 15
- Circle D (dogs): 21
- Circle F (fish): 12
- Overlap of C and F: 2
- Overlap of F and D: 0
- Overlap of D and C: 3
- Overlap of all 3 circles: 1
- Number outside of circles: 14
To determine the number of people in the set C ∩ D (customers who have purchased both cats and dogs), we need to consider the overlapping region between circles C and D.
From the information given, we know that the overlap of D and C is 3. Additionally, we have the overlap of all 3 circles, which is 1. The overlap of all 3 circles includes the region where customers have purchased cats, dogs, and fish.
To calculate the number of people in the set C ∩ D, we add the overlap of D and C (3) to the overlap of all 3 circles (1). This gives us 3 + 1 = 4.
Therefore, from the options given correct one is 4.
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Answer: 4
Step-by-step explanation:
trust me bro
Kisha can play 3 games of pool in 45 minutes. If kisha plays 5 games, predict how much time Kisha plays
Answers
Answer: 75 minutes ( 1 hour 15 minutes )
Step-by-step explanation:
3 games = 45 minutes
45 divided by 3 = 15
1 game = 15
15 x 5 = 75
5 games = 75 minutes
Complete this sequence of numbers such that the difference between any two adjacent numbers is the same : 3/k, _, _, 9/2k.
Answers
The completed sequence is: 3/k, 3/k, 3/k, 9/2k.To complete the sequence of numbers with a constant difference between adjacent numbers, we can calculate the common difference by subtracting the first term from the second term.
Let's denote the missing terms as A and B.
The given sequence is: 3/k, A, B, 9/2k.
The common difference can be found by subtracting 3/k from A or B. Therefore:
A - 3/k = B - A = 9/2k - B.
To simplify, we can equate the two expressions for the common difference:
A - 3/k = 9/2k - B.
Next, we can solve for A and B using this equation.
Adding 3/k to both sides gives:
A = 3/k + 9/2k - B.
Now, we can substitute the value of A into the equation:
3/k + 9/2k - B - 3/k = 9/2k - B.
Simplifying further, we have:
9/2k - 3/k = 9/2k - B.
Cancelling out the common terms, we find:
-3/k = -B.
Multiplying both sides by -1, we get:
3/k = B.
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Name the Inequalities
Answers
Kevin has completed 36% of his running marathon. he has ran 9 miles. How long is the marathon?
Answers
Answer:
25 miles
pls tell if I'm wrong
The marks obtained by a student in Business, Science and History were 60, 68 and 50 respectively. Find the appropriate average if weights of 6, 5, 4 are assigned to these marks (7 mks)
Answers
Answer:
60
Step-by-step explanation:
To find the appropriate average with weights assigned, we need to use the weighted average formula:
Weighted average = (w1 * x1 + w2 * x2 + w3 * x3) / (w1 + w2 + w3)
where
x1, x2, x3 are the marks obtained in Business, Science, and History respectively
w1, w2, w3 are the weights assigned to each subject
Substituting the given values, we get:
Weighted average = (660 + 568 + 4*50) / (6 + 5 + 4)
= (360 + 340 + 200) / 15
= 900 / 15
= 60
Therefore, the appropriate weighted average is 60.
Answer:To find the appropriate average, we need to calculate the weighted mean, which takes into account the different weights assigned to each mark.
The formula for the weighted mean is:
weighted mean = (w1x1 + w2x2 + w3x3) / (w1 + w2 + w3)
where w1, w2, w3 are the weights assigned to each mark, and x1, x2, x3 are the corresponding marks obtained by the student.
Plugging in the values given in the problem, we get:
weighted mean = (6 x 60 + 5 x 68 + 4 x 50) / (6 + 5 + 4)
weighted mean = (360 + 340 + 200) / 15
weighted mean = 900 / 15
weighted mean = 60
Therefore, the appropriate average of the marks obtained by the student is 60.
Step-by-step explanation:
Find the perimeter of this shape
Answers
The perimeter of the given shape as represented in the task content is; 29 cm.
What is the perimeter of the given shape?It follows from the task content that the perimeter of the given shape on the centimeter grid as required is to be determined.
Since each grid line has 1cm as it's length;
The perimeter of the shape is the sum of all side lengths of the shape;
Perimeter, P = 6+2+3+2+2+1+3+2+2+2+2+1
P = 29 cm
Hence, the perimeter of the shape is; 29 cm.
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I'm having problems with Algebraic thinking, evaluating expressions with parentheses.
Answers
We have to check which options gives as result 2.
We can apply the order of operations to check them.
We start with option A:
\(\begin{gathered} 32\/(4+3*4) \\ 32\/(4+12) \\ 32\/16 \\ 2 \end{gathered}\)We can check option B also:
\(\begin{gathered} (32\/4)+(3*4) \\ 8+12 \\ 20 \end{gathered}\)Answer: Option A gives the result of 2.
HELP 20 POINTS
Kelsey’s school can be represented by Point A (9, 9). Point A can be translated 6 units left and 5 units down to create A’, the location of Kelsey’s house. Find the d, the diagonal distance between Point A and Point A’ on the grid? Round to the nearest tenth.
Answers
Answer:
6^2 + 5^2 = d^2
Step-by-step explanation:
I hope this helps!!
Simplify by combining like terms and then FACTOR the expression -3+5y+5+3y by picking any fraction less that is not a whole number as the factor outside the parentheses while remaining equivalent.
Answers
Answer:
8y + 2
Step-by-step explanation:
Hope this helps (^-^)
The table shows a function.
ху
2 20
3 10
40
Part A: Is the function linear or nonlinear?
Part B: How did you determine if the function was linear or nonlinear?
Answers
Part A: The function is nonlinear.
Part B: We determined the function to be nonlinear because the corresponding y-values do not change by a constant rate as the x-values increase, indicating a lack of a linear relationship.
Part A: The given function is nonlinear.
Part B: To determine whether the function is linear or nonlinear, we need to examine the relationship between the x-values and the corresponding y-values in the table.
In a linear function, there is a constant rate of change between the x and y values.
This means that for every increase in x by a fixed amount, the corresponding y value will change by a constant amount.
If we look at the x-values in the given table (2, 3, 4), we can see that they are increasing by a fixed amount of 1 each time.
However, when we examine the corresponding y-values (20, 10, 40), we don't see a constant rate of change.
The y-values are not changing by the same amount for each increase in x.
For instance, when x increases from 2 to 3, the y-value decreases from 20 to 10.
This indicates a non-linear relationship as the change in y is not constant for each unit increase in x.
Additionally, when x increases from 3 to 4, the y-value jumps significantly from 10 to 40, which further confirms the nonlinear nature of the function.
Based on these observations, we can conclude that the given function is nonlinear.
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please assist with these questions thanks
Answers
1a. The percentage total return is -19.56%
1b. The dividend yield is 2.42%.
1c. The capital gains yield is -21.98%.
2a. The arithmetic average annual return on large-company stocks in nominal terms is 14.5%.
2b. The arithmetic average annual return on large-company stocks in real terms is 9.67%.
3a. The real return on long-term government bonds is 3.195%
3b. The real return on long-term corporate bonds is 3.291%
How to calculate the percentage total return?In Financial accounting, the percentage total return (P) can be calculated by using this formula;
P = [(Ending price - Initial price) + Dividend] ÷ Initial price
P = [(71 - 91) + 2.20] ÷ 91
P = -0.1956 or -19.56%
1b. For the dividend yield, we have:
Dividend yield = Dividend ÷ Initial price
Dividend yield = 2.20 ÷ 91
Dividend yield = 0.0242 or 2.42%
1c. For capital gains yield, we have:
Capital gains yield = (Ending price - Initial price) ÷ Initial price
Capital gains yield = (71 - 91) ÷ 91
Capital gains yield = -0.2198 or -21.98%.
Part 2.
a. The arithmetic average of annual return on large-company stocks in nominal terms is equal to 14.5%.
b. For arithmetic average annual return in real terms, we have:
(1 + 0.145) = (1 + r)(1 + 0.044)
r = (1.145/1.044) - 1
r = 9.67%
Part 3.
a. For real return on the long-term government bonds, we would apply Fisher equation:
(1 + i) = (1 + r)(1 + h)
Where:
i is the nominal interest rate.r is the real interest rate.h is the inflation rate.(1 + 0.066) = (1 + r)(1 + 0.033)
1 + r = 1.066/1.033
r = 3.195%
b. For real return on long-term corporate bonds:
(1 + 0.067) = (1 + r)(1 + 0.033)
1 + r = 1.067/1.033
r = 3.291%
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Question 6 Which of the following is the graph of f(x) = x² = 5x + 4?
Answers
Given: The equation x² = 5x + 4
We have to draw the the graph for the given equation.
Consider the given equation,
x^2 - 5x - 4 = 0
The vertex of the parabola of the form f(x) = ax^2 + bx + c is given by x = -b/2a
Here,
a= 1
b= -5
c= -4
vertex = x = 5/2= 2.5
Also, the y coordinate at x = 2.5 is,
y = (2.5)^2 -5(2.5)-4
y = -10.25
Thus the vertex of parabola is (2.5 , -10.25)
y - intercept is the point where x = 0
put x = 0 in given equation
f(x) = 0 - 0 -4
f(x) = -4
hence y intercept is at (0, -4).
Now, we calculate x- intercept
x- intercept is where y is equal to 0.
Put f(x) = 0
We have,
x^2 - 5x - 4 = 0
by using quadratic formula,
x = -b ±√b² - 4ac/2a
x=5 ±√-5² - 4 (1)(-4)/2
x= 5±√41/2.
Hence with the obtained values the graph of the equation is obtained.
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Jason charges $18 plus $4 per hour to mow lawns. Andrew charges $7 per hour with a $12 dollar up front cost. In what situation does Jason charge more than Andrew.
Answers
18 +4x = 12+7x solves to 2, meaning they would cost the same at 2 hours of mowing. So anything larger than 2 hours means Andrew gets $3 more an hour than Jason
8. Choose all decimals that are equivalent to (7 x 100) + (5 × 1) + (8 × 7) + X 10 (1 × 100). 75.081 705.810 705.801 75.810 705.81 705.081
Answers
Answer:
705.81 and 705.810
Step-by-step explanation:
700 + 5 + 0.8 + 0.01 = 705.81
Answers:
705.810
705.81
Help me asap and need the answer quick
Answers
Answer:20 m/s
Step-by-step explanation:
Answer:
20 m/s
Step-by-step explanation:
700 ÷ 35 = 20 m/s
In the number 725.78, how does the value of the 7 in the tenths place compare to the value of the 7 in the hundreds place?
Answers
Answer:
C. 1/1,000
Step-by-step explanation:
yes or no ?
help please I beg you
Answers
Answer:1
Step-by-step explanation:
Number selected, =10
Double it=20
Minus 2= 20-2=18
Triple the Total =18×3=54
Add a dozen=54+12=66
Divide by 6=66÷6=11
Subtract the number you stated with =11-10=1
Answer =1
Number 13
I’ll reward you brainiest!!
Answers
100 POINTS PLEASE HELP FAST
Select the correct answer.
The weight of a radioactive isotope was 96 grams at the start of an experiment. After one hour, the weight of the isotope was half of its initial weight. After two hours, the weight of the isotope was half of its weight the previous hour. If this pattern continues, which of the following graphs represents the weight of the radioactive isotope over time?
Answers
The top left graph represents the weight of the radioactive isotope over time.
How to define an exponential function?An exponential function has the definition presented according to the equation as follows:
\(y = ab^x\)
In which the parameters are given as follows:
a is the value of y when x = 0.b is the rate of change.The parameter values for the function in this problem are given as follows:
a = 96, b = 0.5.
Hence the function is given as follows:
\(y = 96(0.5)^x\)
Two points on the graph of the function are given as follows:
(1,48) and (2, 24).
Hence the top left graph represents the weight of the radioactive isotope over time.
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Answer:
Graph W
Step-by-step explanation:
The given information describes a radioactive decay process, where the weight of the isotope decreases by half at regular intervals. This type of decay is characteristic of exponential decay.
Based on the description, the graph that represents the weight of the radioactive isotope over time would be a decreasing exponential curve, where the y-axis represents the weight of the isotope (in grams), and the x-axis represents time (in hours).
The initial weight of the isotope is 96 grams, and after each subsequent hour, the weight becomes half of what it was in the previous hour. Therefore, the correct graph would start at 96 grams (the initial weight when x = 0) and then decrease by half every hour. It would be a curve that gets closer and closer to zero but never quite reaches it.
Initial weight: 96 grams
After 1 hour: 96 / 2 = 48 grams
After 2 hours: 48 / 2 = 24 grams
After 3 hours: 24 / 2 = 12 grams
After 4 hours: 12 / 2 = 6 grams
After 5 hours: 6 / 2 = 3 grams
So, the points on the graph would be:
(0, 96), (1, 48), (2, 24), (3, 12), (4, 6), (5, 3)Therefore, the graph that represents the weight of the radioactive isotope over time is Graph W.
Answers for the practice test on the 1980s-early twenty-first century.
Answers
Answer:
the answer would be look at the test from one year earlier than that year (1979)
Step-by-step explanation:
that's correct answer.
3) The average age of students at XYZ University is 24 years with a standard deviation of 8 years. Number of students at the university is 7500. A random sample of 36 students is selected. What is the probability that the sample mean will be between 25.5 and 27 years
Answers
Answer:
0.1875
Step-by-step explanation:
σM=σ/√N
=8/√7500
=8/86.608
=0.092
Z=(x-μ)/σ/√N
=(25.5-36)/8/√7500
=-10.5/0.0092=-1141.304
Z score = -1.3125
=(27-36)/8/√7500 =
=9/0.0092=978.261
Z score= -1.125
-1.125-(-1.3125)=-1.125+1.3125)= 0.1875
The probability that the sample mean will be between 25.5 and 27 years
P(between 25.5 and 27) = 0.1875
A circle has a radius of 4 ft.
What is the area of the sector formed by a central angle measuring 270 degrees
Use 3.14 for pi and round the decimal to the nearest tenth.
42.8 ft
37.7 ft
12 ft
9.4 ft
Answers
The area of the sector is 37.7 ft.
What is sector:
A sector is a region of a circle that is bounded by two radii and the arc of the circle that lies between the endpoints of those radii.
The formula for the area of a sector is given by
A = (θ/360)πr²Where θ is the central angle in degrees, and r is the radius of the circle
Here we have
A circle has a radius of 4 ft.
The central angle of sector formed = 270°
Using the formula, Area of sector = (θ/360°) × π r²
Area of the given sector = [ 270/360] × 3.14 × (4)²
= [0.75 ] × [50.24]
= 37.68 ft
= 37.7 ft
Therefore,
The area of the sector is 37.7 ft.
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Find the missing length. Round to the nearest tenth if necessary. Find the missing side.
Answers
Given:
a = 4
b = 5
c = unknown
Let's find the length of c.
Here, we are given a right triangle, where c is the longest side.
The longest side of a right triangle is called the hypotenuse.
To find the hypotenuse, apply Pythagorean Theorem:
\(c^2=a^2+b^2\)Input values into the equation above:
\(\begin{gathered} c^2=4^2+5^2 \\ \\ c^2=16+25 \\ \\ c^2=41 \end{gathered}\)Take the square root of both sides:
\(\begin{gathered} \sqrt[]{c^2}=\sqrt[]{41} \\ \\ c=6.4 \end{gathered}\)Therefore, the length of the missing side, c =
HELP PLEASE whats the number for this answer?
ASAP
Answers
Answer:
68°
Step-by-step explanation:
Total angle in a quadrant = 90°
x + 22° = 90°
x = 90 - 22
x = 68°
square 1 is equal to
Answers
Answer:
1
Step-by-step explanation:
Answer:
4sides
Step-by-step explanation:
these is answer 4 sided
What would be the Median Of 6, 8, 1, 4, 6, 0, 4, 3
Answers
Answer:
4
Step-by-step explanation:
0, 1, 3, 4, 4, 6, 6, 8
Cross off each side until you get to the middle
1, 3, 4, 4, 6, 6
3, 4, 4, 6
4, 4
You add the 4 and 4 together
8
then divide by 2
8/2=4
Your answer is 4, hope this helped!!!!