Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form.
3, -13, and 5 + 4i
f(x) = x4 - 8x3 - 12x2 + 400x - 1599
f(x) = x4 - 200x2 + 800x - 1599
f(x) = x4 - 98x2 + 800x - 1599
f(x) = x4 - 8x3 + 12x2 - 400x + 1599
Answer:
third option
Step-by-step explanation:
Given f(x) has zeros x = a, x = b, then
the factors are (x - a), (x - b) and the polynomial is the product of the factors.
Complex zeros occur as conjugate pairs, thus
5 + 4i is a zero then 5 - 4i is a zero
The zeros are x = 3, x = - 13, x = 5 + 4i, x = 5 - 4i, thus the factors are
(x - 3), (x - (- 13)), (x - (5 + 4i)), (x - (5 - 4i)), that is
(x - 3), (x + 13), (x - 5 - 4i), (x - 5 + 4i)
= (x - 3), (x + 13), ((x - 5) - 4i), ((x - 5) + 4i)
The polynomial is the product of the factors
f(x) = (x - 3)(x + 13)((x - 5) - 4i)((x - 5) + 4i) ← expand factors in pairs
= (x² + 10x - 39)((x - 5)² - 16i²) → i² = - 1
= (x² + 10x - 39)(x² - 10x + 25 + 16)
= (x² + 10x - 39)(x² - 10x + 41) ← distribute
= [tex]x^{4}[/tex] - 10x³ + 41x² + 10x³ - 100x² + 410x - 39x² + 390x - 1599 ← collect terms
= [tex]x^{4}[/tex] - 98x² + 800x - 1599
Answer:
The third option
Step-by-step explanation:
The circle has an angle of 40° and an area of 8 cm2. Calculate the area of the entire circle.
Step-by-step explanation:
answer it yourself
Jordan is a salesperson at the store. Jordan has a base monthly salary of $1,450 and also earns a commission of 5% on his monthly sales. Jordan would like to earn a monthly salary of $1,800 in July. What amount of sales, in dollars, does Jordan need in order to reach the desired salary goal in July
Answer:
$7,000
Step-by-step explanation:
1800 = 1450 + 0.05X
0.05X = 350
X = 7000
Answer:
7,000
Step-by-step explanation:
because 1450 x 5 is 7250
5 percent of 7250 is 7000
An arithmetic sequence is given below.
14, 21, 28, 35, ...
Write an explicit formula for the nth term an.
can someone please solve this
Answer:
Y-intercept: (0,6)
Multiplier: 3
Equation: y = 3x + 6
4-2y+3=-9
What is y?
y = 8
hope this helps :)
The western and eastern cell towers are 10 miles apart. From the
western cell tower, a phone signal is 10° north of east. From the eastern cell tower, the
signal is 20° west of north. How far away is the cell phone from each of the towers?
Sketch a diagram.
The distance of the cell phone from the western tower is 27.47 miles and from the eastern tower is 1.76 miles
Explanation:
The sketch is attached for the reference.
tan (10) = [tex]\frac{NE}{WE}[/tex]
[tex]0.176 = \frac{NE}{10} \\\\NE = 1.76[/tex]
tan (70) = [tex]\frac{NW}{WE} \\\\[/tex]
[tex]2.747 = \frac{NW}{10} \\\\NW = 27.47[/tex]
Therefore, the distance of the cell phone from the western tower is 27.47 miles and from the eastern tower is 1.76 miles
It takes a jet 2 hours to fly 1,100 miles. At this rate, how far does it fly in 8 hours?
We know that 8(hrs) is 4 times 2(hrs) so now we just need to multiply.
Multiply 1,100 by 4.
1,100 × 4 = 4,400
The jet will fly 4,400 miles in 8 hours.
Answer:
4400miles
Step-by-step explanation:
1,100 divided by 2 = 550
and 550 times 8 is 4400
2x - 4(x + 2) = -2X-8
Answer:
x= 0
Step-by-step explanation:
in order to find the value of x in the 2x - 4(x + 2) = -2X-8
we are going to apply bodmas rule by first opening the bracket
we have,
2x-4x-8 = 2x -8
we proceed to collect the like terms
2x -4x-2x = -8 +8
-4x = 0
divide both sides by -4
-4x/-4 = 0/-4
x= 0
Desiree ran 12 miles in 1 hr, 48 minutes, What was Desiree's average running rate, in minutes per mile
Answer: 1/9
Step-by-step explanation:
60 + 48 = 108 minutes
12 / 108 = 1/9
The sum of two numbers is 141. One number is 37 more than the other. Find the numbers
Answer:
104
Step-by-step explanation:
x+37=141
subtract 37 from both sides
-37=141-37
x= 104
Step-by-step explanation:
x = First number
x + x + 37 = 141 (Because we know that the 2nd number is 37 more than the first, we can just say x + 37.)
2x + 37 = 141 (Combine like terms.)
2x = 104 (Subtract 37 from both sides.)
x = 52 (Divide 2 from both sides.)
Now we know that the first number is 52. Now we just add the 37 to 52 to find the second number.
37 + 52 = 89 = Second number
Proof: 52 + 89 = 141
If f(x) = 4x2 -3 and g(x)= x+1, find (f -9)(x)
Answer:
4x^2 - x - 4.
Step-by-step explanation:
(f - g)(x) = f(x) - g(x)
= 4x^2 - 3 - (x + 1)
= 4x^2 - 3 - x - 1
= 4x^2 - x - 4.
Ariyonne claims that (6,3) is the point of intersection of the lines y=4x-2 and y=1/2x+5. Is she correct? How do you know ?
construct a polynomial function with the stated properties. third degree with zeros of -2,-1, and 3 and passes through the point (2,12)
Answer:
[tex]f(x) = - (x + 2)(x + 1)(x - 3)[/tex]
Step-by-step explanation:
Let f(x) be the 3rd degree polynomial function.
The roots of this function are:
x=-2, x=-1 and x=3.
The factored form is:
[tex]f(x) = a(x + 2)(x + 1)(x - 3)[/tex]
This equation passes through (2,12)
This implies that;
[tex]a(2 + 2)(2+ 1)(2 - 3) = 12 \\ - 12a = 12 \\ a = - 1[/tex]
The polynomial function is
[tex]f(x) = - (x + 2)(x + 1)(x - 3)[/tex]
The width of a rectangular room is 40% of its length. If the length is 20 feet, what is the area of the room?
Answer:
160 ft^2
Step-by-step explanation:
First you have to find the width, then you find the area. To find the width with a percentage we do Part/ Total = %/100 and we cross multiply. We need to find the part so that is the unknown, we will call it 'w' for width
w/20 = 40/100 Now we cross multiply, the x and the 100 and the 20 and 40
w * 100 = 100w
20 * 40 = 800
Now we have 100w = 800 The next step is to divide both sides by 100 so we just have w
100x/100= w
800/100 = 8
w = 8
The width is 8
Now we find the area which is length x width
20 x 8 = 160
So the area is 160 ft^2
Somebody please help me I only have 46 min ! Please ASAP !
7/-21=7/4.58=350/229=1whole number 121/224
What ratio is equivalent to 20/10
Hello There!
The answer to your problem is 10:5 or 2:1
How to get 10:5
To get 10:5 you divide a number that can go into 20 and 10 which is 2. You divide 20/2 and 10/2 and get 10:5.
How to get 2:1
To get 2:1 you divide a number that can go into 10 and 5 which is 5. You divide 10/5 and 5/5 and get 2:1.
Hope This Helps!
The equivalent ratio of 20 : 10 will be 40/20 or 40 : 20.
What are ratios and proportion?
Ratio is a quantitative relation between two amounts showing the number of times one value contains or is contained within the other. A statement expressing the equality of two ratios A:B and C:D is called a proportion. We can express proportion as -
A : B ∷ C : D
AND
A x D = B x C
Product of extremes equal to product of means.
Given is the ratio 20 : 10
The equivalent ratio of 20 : 10 will be -
20 : 10 = 20/10 = (20 x 2)/(10 x 2) = 40/20 = 40 : 20
Therefore, the equivalent ratio of 20 : 10 will be 40/20 or 40 : 20.
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Please help me I’m terrible at algebra.
Answer:
72 lbs
Step-by-step explanation:
t=tail h=head b=body
t = 9
h = t + .5b
b = h + t
Substitute
b = h + 9
h = 9 + .5b
h = 9 + .5h + 4.5
.5h = 13.5
h = 27
b = 36
TOTAL = t + h + b = 27 + 36 + 9 = 72
Alyssa and Gabriel play the following game. Alyssa rolls a die. If she rolls a 1, 2, or 3, Gabriel gives Alyssa $4. If Alyssa rolls a 4 or 5, Gabriel gives Alyssa $1. However, if Alyssa rolls a 6, she gives Gabriel $12.
a) Determine Alyssa's expectation.
b) Determine Gabriel's expectation.
11.3 #12
Answer:
Part a) Alyssa's expectation is equal to $0.33
Part b) Gabriel's expectation is equal to -$0.33
Step-by-step explanation:
we know that
The expected value is the probability of winning multiplied by the value you get when you win, plus the probability of losing multiplied by the value you get when you lose (which is negative as it is a loss).
Part a) Determine Alyssa's expectation
we know that
1) If Alyssa rolls a 1, 2, or 3, Gabriel gives Alyssa $4
The probability is 3/6
so
we have
[tex]\frac{3}{6}(4)=\$2[/tex]
2) If Alyssa rolls a 4, or 5, Gabriel gives Alyssa $1
The probability is 2/6
so
we have
[tex]\frac{2}{6}(1)=\$0.33[/tex]
3) if Alyssa rolls a 6, she gives Gabriel $12
The probability is 1/6
so
we have
[tex]-\frac{1}{6}(12)=-\$2[/tex] ---> is negative because is a loss
therefore
Alyssa's expectation is equal to
[tex]\$2+\$0.33-\$2=\$0.33[/tex]
Part b) Determine Gabriel's expectation
we know that
1) If Alyssa rolls a 1, 2, or 3, Gabriel gives Alyssa $4
Is a loss for Gabriel
The probability is 3/6
so
we have
[tex]-\frac{3}{6}(4)=-\$2[/tex] ---> is negative because is a loss
2) If Alyssa rolls a 4, or 5, Gabriel gives Alyssa $1
Is a loss for Gabriel
The probability is 2/6
so
we have
[tex]-\frac{2}{6}(1)=-\$0.33[/tex] ---> is negative because is a loss
3) if Alyssa rolls a 6, she gives Gabriel $12
Is a win for Gabriel
The probability is 1/6
so
we have
[tex]\frac{1}{6}(12)=\$2[/tex]
therefore
Gabriel's expectation is equal to
[tex]-\$2-\$0.33+\$2=-\$0.33[/tex]
The expected outcomes for both Alyssa and Gabriel from the game are $0. This is calculated using the probabilities of each outcome and their respective gains or losses.
Explanation:In the game between Alyssa and Gabriel, we are to calculate the expected outcomes for both players. To calculate the expectation, we will weigh the possible outcomes ($4, $1, -$12 for Alyssa and -$4, -$1, $12 for Gabriel) by their probabilities.
The dice has six faces, so the probability for each outcome is determined by the number of corresponding faces divided by six. Let's calculate the expectation for both:
Alyssa's expectation: (1/2 * $4) + (1/3 * $1) - (1/6 * $12) = $2 - $2 = $0. Gabriel's expectation: -(1/2 * $4) - (1/3 * $1) + (1/6 * $12) = -$2 + $2 = $0.
So, both Alyssa and Gabriel have an expected gain of $0 from this game.
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A swimming pool is shown below.
Two maintenance workers correctly found the total area of the pool by adding the areas of 3 rectangles. But each worker wrote a different expression for the area.
Which could be the expressions the two workers wrote?
Answer:
the answer is c
Step-by-step explanation
Answer:
c
Step-by-step explanation:
The polynomial is a difference of perfect squares. Use the formula a2 – b2 = (a + b)(a – b) to factor completely.
81x2 – 49
The value of a is .
The value of b is .
The product of the prime factors is
Answer:
a=9x
b=7
(9x-7)(9x+7)
Step-by-step explanation:
81x^2-49=(9x)^2 - 7^2=(9x-7)(9x+7)
Answer:
1: 9x
2: 7
3: (9x-7)(9x+7)
OR
1: 3rd option
2: 2nd option
3: 4th option
Step-by-step explanation:
got it right on Edge
have a great day!!!
PLZ MARK BRAINLIEST
table A
x y
4 1
8 2
12 3
16 4
Compare the table of Object A and the equation y = 5x of Object B. Which of the two moving objects has greater speed and by what factor? (round to nearest hundredth)
A) Object A by a factor of 1.05
B) Object B by a factor of 1.05
C) Object A by a factor of 1.25
D) Object B by a factor of 1.25
Answer:
D
Step-by-step explanation:
1. Find the rate of change of the graph. Which is 4.
2. Because 5 is greater of 4, Object B has the greater speed.
3. To find the factor you must divide 4 from 5. 5 ÷ 4
4. 5 ÷ 4 = 1.25
5. The correct answer is D
Answer:C)Object A by a factor of 1.25
Step-by-step explanation:this is the answer for USA test prep.
Which number is a factor of 22 , but not a multiple of 2?
Answer:
11
Step-by-step explanation:
i think.............
The Equation C = 2D shows how the cost of a car ride depends on the distance in miles. The Variable D Represents the number of miles driven, and the Variable C represents the cost in dollars. If a Car ride is 10 miles long, how much will it cost?
A)15
B)30
C)20
D)25
$ 20
Step-by-step explanation:
Step 1:
Equation is given by C = 2D
Here D is equal to 10 miles
Variable C costs twice the distance traveled.
Step 2:
Here D= 10 Miles.
Hence, C= 2*10 = 20
Hence $20 will be the cost.
El horario y el minutero de un reloj miden respectivamente 0.7 y 1.2cm. Determinar la distancia entre los extremos de dichas manecillas a las 13:30 horas
Answer:
1.5887 cm
Step-by-step explanation:
If the time is 13:30, The hour pointer will be between the numbers 1 and 2.
Each number of the 12 number clock is separated by 30 degrees, so the hour pointer is at 45 degrees.
The minute pointer is at 30 minutes, so it is in number 6, being therefore at angle 180.
The angle formed by the pointers will be 180 - 45 = 135 degrees.
We can draw a triangle with both pointers and this angle (image attached)
So, we can calculate the distance between the tip of the pointers (let's call it "d") using law of cosines:
d^2 = 0.7^2 + 1.2^2 - 0.7*1.2*cos(135)
d^2 = 0.49 + 1.44 - (-0.5940) = 2.524
d = 1.5887 cm
The distance between the tip of the pointers (let's call it "d") using law of cosines is 1.5887 cm.
If the time is 13:30, The hour pointer will be between the numbers 1 and 2.
Each number of the 12 number clock is separated by 30 degrees, so the hour pointer is at 45 degrees.
The minute pointer is at 30 minutes, so it is in number 6, being therefore at angle 180.
The angle formed by the pointers will be 180 - 45 = 135 degrees.
We can draw a triangle with both pointers and this angle (image attached)
So, we can calculate the distance between the tip of the pointers (let's call it "d") using law of cosines:
d^2 = 0.7^2 + 1.2^2 - 0.7*1.2*cos(135)
d^2 = 0.49 + 1.44 - (-0.5940) = 2.524
d = 1.5887 cm
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When plotting point on the coordinate plane below, which point would lie on the y-axis?
Answer:
The attached picture shows the location of each of the coordinates on the Cartesian plane. Hence, (0, 1) is the coordinate that lies on the y- axis.
Step-by-step explanation:
The solution to the question above is answered thus:
Note that the first value in each bracket is for x while the other is for y. Hence; 0, 7, 6 and 8 are value of x while 1, 0, 8 and 2 are values of y.
Thus:
Coordinate (0, 1) lies on the y - axis.
Coordinate (7, 0) lies on the x - axis.
Coordinates (6, 8) and (8, 2) lie on the 1st quadrant of the Cartesian plane
Coordinates.
Therefore, coordinate (0, 1) is the answer because it lies on the y- axis.
The answer is (0,1)
What is the co-ordinate system?In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.
Given here: The points (0,1), (7,0), (6,8), (8,2)
For the point to lie on the y-axis its x-coordinate or abscissa must be zero
Only (0,1) satisfies this.
Hence, The answer is (0,1)
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If one factor of x2 + 2x - 24 is (x+6), what is the other factor?
(x+8)
(x-8)
(x+4)
(x-4)
Answer:
( x - 4)
Step-by-step explanation:
x² + 2x - 24
From here, you must find the two factors of -24 (the first and third terms' coefficients multiplied together) that add up to 2 (the middle terms coefficient)
( x - 4) ( x + 6)
Other factor of x² + 2x - 24 is (x - 4).
What is factor?Factors and multiples are two related concepts in math. A factor is a number that divides the given number exactly with 0 as the remainder.
Given expression
x² + 2x - 24 has factor (x + 6)
So, the expression should be divisible by (x + 6)
(x² + 2x - 24)/(x + 6)
It can be written as
(x² + 6x - 4x -24)/(x + 6)
Factoring out common factor
(x (x + 6) - 4 (x + 6))/(x + 6)
factoring out common factor
(x + 6)(x - 4)/(x + 6)
Simplifying
= (x - 4).
Hence, (x - 4) is other factor of x² + 2x - 24.
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What is the range of the given function
4,139 divided by 14 equals what?
Answer:
that would be 57,946
Answer: 295.642 (Work is shown below in the image)
Step-by-step explanation:
a middle school wants to have its students see a movie at a loccal theater. the total cost of the theater and movie rental is $1500. what equation show how the cost per student depends on the nuber of students
Answer:
Since I don't know the number of students, I think the equation would be 1500=x*n, with x being the cost and n being the number of students.
Step-by-step explanation:
Final answer:
The equation that shows how the cost per student depends on the number of students is: Cost per student = Total cost / Number of students. For example, if there are 30 students, the cost per student would be $50.
Explanation:
The equation that shows how the cost per student depends on the number of students can be expressed as:
Cost per student = Total cost / Number of students
In this case, the total cost is $1500, so the equation becomes:
Cost per student = $1500 / Number of students
For example, if there are 30 students, the cost per student would be:
Cost per student = $1500 / 30 = $50