Answers
Answer/Step-by-step explanation:
Given:
f(x) = 2x + 2
Domain = {-5, -1, 2, 3}
To write the range of f using set notation, substitute each domain value into f(x) = 2x + 2 to get each corresponding range value that will make up the set.
Thus:
✔️f(-5) = 2(-5) + 2
= -10 + 2
f(-5) = -8
✔️f(-1) = 2(-1) + 2
= -2 + 2
f(-1) = 0
✔️f(2) = 2(2) + 2
= 4 + 2
f(-1) = 6
✔️f(3) = 2(3) + 2
= 6 + 2
f(3) = 8
Range of f using set notation = {-8, 0, 6, 8}
✔️Graph f by plotting the domain values on the x-axis against the corresponding range values on the y-axis as shown in the attachment below:
*See attachment for the graph of f
Related Questions
20 and 1/2 feet times 13 and 1/8 feet is what total
Answers
Answer:
269 and 1/16 feet total (or 269.0625 feet to be precise)
Step-by-step explanation:
20 and 1/2 = 20.5
13 and 1/8 = 13.125
20.5 * 13.125 = 269.0625 feet = 269 and 1/16 feet
1). A population of 20 rabbits is released into a wildlife region. The population is growing at a rate of 60% per year.
A) the General Equation from the Video was: P(x) = (blank)
What is the population of rabbits after 5 years?
B) the Evaluated equation I used to get the following answer is (blank)
and After five years there will be(blank)
rabbits.
And What is the population of rabbits after 8 years?
c) the Evaluated equation I used to get the following answer is(blank)
and After eight years there will be(blank)
rabbits.
Answers
Answer:
(a) A = 20(1.6)^t
(b) 210 rabbits
Step-by-step explanation:
Initial number of rabbits = 20
rate of growth, R = 60 % annually
(A) The general equation is
[tex]A = P \left ( 1+\frac{R}{100} \right )^t\\\\A = 20\left ( 1+\frac{60}{100} \right )^t\\\\A = 20 (1.6)^t[/tex]
(B) Let the time, t = 5 years
So, the population after 5 years is
[tex]A = 20 (1.6)^5\\\\A = 209.7 = 210 rabbits[/tex]
What is the inverse of function f?
Answers
9514 1404 393
Answer:
D. f^-1(x) = 3 -7x
Step-by-step explanation:
Solve x = f(y) for y to find the inverse function.
x = f(y)
x = (3 -y)/7 . . . . . . use the function definition
7x = 3 -y . . . . . . . .multiply by 7
y = 3 -7x . . . . . . . add y-7x to both sides
Then the inverse function is ...
[tex]\boxed{f^{-1}(x)=3-7x}[/tex]
Find sin D sin E cos D and cos E
Answers
9514 1404 393
Answer:
sin(D) = cos(E) = (√3)/2
cos(D) = sin(E) = 1/2
Step-by-step explanation:
The mnemonic SOH CAH TOA is intended to remind you of the relationships between trig functions and right triangle sides.
Sin = Opposite/Hypotenuse
Cos = Adjacent/Hypotenuse
For this diagram, this means ...
sin(D) = cos(E) = (13√3)/26 = (√3)/2
cos(D) = sin(E) = 13/26 = 1/2
URGENT
Look at picture to see question
Answers
Answer:
first row you add 4 to get the next term. look at the difference in numbers.
second row the difference is 3 so you add 3 to get the next one.
3rd row the nth term is 3n so the one above would be 2n and the first /top nth term would just be n on its own - meaning one lot of it
4th row add 5 so 7-5= 2 being the 0th term. so just add 5 each time. so it would be 4n
bottom row the difference is 14 or to get that do 26-12
don't let it trick you out- after the third term it goes to the tenth so it would be best getting a piece of paper and working the whole of it out so u don't get confused
Q.1 Determine whether y = (c - e ^ x)/(2x); y^ prime =- 2y+e^ x 2x is a solution for the differential equation Q.2 Solve the Initial value problem ln(y ^ x) * (dy)/(dx) = 3x ^ 2 * y given y(2) = e ^ 3 . Q.3 Find the general solution for the given differential equation. (dy)/(dx) = (2x - y)/(x - 2y)
Answers
(Q.1)
[tex]y = \dfrac{C - e^x}{2x} \implies y' = \dfrac{-2xe^x-2C+2e^x}{4x^2} = \dfrac{-xe^x-C+e^x}{2x^2}[/tex]
Then substituting into the DE gives
[tex]\dfrac{-xe^x-C+e^x}{2x^2} = -\dfrac{2\left(\dfrac{C-e^x}{2x}\right) + e^x}{2x}[/tex]
[tex]\dfrac{-xe^x-C+e^x}{2x^2} = -\dfrac{C-e^x + xe^x}{2x^2}[/tex]
[tex]\dfrac{-xe^x-C+e^x}{2x^2} = \dfrac{-C+e^x - xe^x}{2x^2}[/tex]
and both sides match, so y is indeed a valid solution.
(Q.2)
[tex]\ln\left(y^x\right)\dfrac{\mathrm dy}{\mathrm dx} = 3x^2y[/tex]
This DE is separable, since you can write [tex]\ln\left(y^x\right)=x\ln(y)[/tex]. So you have
[tex]x\ln(y)\dfrac{\mathrm dy}{\mathrm dx} = 3x^2y[/tex]
[tex]\dfrac{\ln(y)}y\,\mathrm dy = 3x\,\mathrm dx[/tex]
Integrate both sides (on the left, the numerator suggests a substitution):
[tex]\dfrac12 \ln^2(y) = \dfrac32 x^2 + C[/tex]
Given y (2) = e ³, we find
[tex]\dfrac12 \ln^2(e^3) = 6 + C[/tex]
[tex]C = \dfrac12 \times3^2 - 6 = -\dfrac32[/tex]
so that the particular solution is
[tex]\dfrac12 \ln^2(y) = \dfrac32 x^2 - \dfrac32[/tex]
[tex]\ln(y) = \pm\sqrt{3x^2 - 3}[/tex]
[tex]\boxed{y = e^{\pm\sqrt{3x^2-3}}}[/tex]
(Q.3) I believe I've already covered in another question you posted.
write the following numbers in scientific notation. 0.0009. 12. 1000. 0.03. 1.12. 120
Answers
Answer:
Step-by-step explanation:
Take the first real number and keep a decimal point to the right of it. Write the number after it.
Put a multiplication symbol and then 10.
Now count the number places to the right of the first real number and the number of place will be the power of 10.
If , number of place are before the first real number, then the power of 10 will be negative.
0.0009 = 9 * 10⁻⁴
12 = 1.2 *10
1000 = 1* 10³
0.03 = 3 *10⁻²
120 = 1.2 * 10²
1.12 = 1.12 *10⁰
if the smaller side of a rectangle was increased by 7 cm, it would be exactly 55% of the 110 cm longer side. Find the area of the rectangle
Answers
Answer:
5886 cm
Step-by-step explanation:
start by finding 55% of 110 which is 60.5. then subtract by 7 and then you get 53.5
then multiply 53.5 by 110 = 5885 cm
Each of these extreme value problems has a solution with both a maximum value and a minimum value. Use Lagrange multipliers to find the extreme values of the function subject to the given constraint.
(a) f (x, y) = x^2 - y^2; x^2 + y^2 = 1
Max of 1 at (plusminus 1, 0), min of - 1 at (0, plusminus l)
(b) f (x, y) = 3x + y; x^2 + y^2 = 10
Max of 10 at (3, 1), min of - 10 at (- 3, - 1)
(c) f (x, y) = xy; 4x^2 + y^2 = 8
Max of 2 at plusminus (1, 2), min of - 2 at plusminus (l, - 2)
Answers
Answer:
a) f(x,y) = - 1 minimum at P ( 0 ; -1 )
b) f (x,y) = 10 maximum at P ( 3 , 1 ) and f (x,y) = - 10 minimum at Q ( - 3 , - 1 )
c) Max f ( x , y ) = 2 for points P ( 1, 2 ) and T ( -1 , -2 )
Min f ( x , y ) = -2 for points Q ( 1 , - 2 ) and R ( -1 , 2 )
Step-by-step explanation:
A) f(x,y) = x² - y² subject to x² + y² = 1 g(x,y) = x² + y²- 1
δf(x,y)/ δx = 2*x δg(x,y)/ δx = 2*x
δf(x,y)/ δy = - 2*y δg(x,y)/ δy = 2*y
δf(x,y)/ δx = λ* δg(x,y)/ δx
2*x = λ*2*x
δf(x,y)/ δy = λ* δg(x,y)/ δy
- 2*y = λ*2*y
Then, solving
2*x = λ*2*x x = λ*x λ = 1
- 2*y = λ*2*y y = - 1
x² + y²- 1 = 0 x² + ( -1)² - 1 = 0 x = 0
Point P ( 0 ; -1 ) ; then at that point
f(x,y) = x² - y² f(x,y) = 0 - ( -1)² f(x,y) = - 1 minimum
b) f( x, y ) = 3*x + y g ( x , y ) = x² + y² = 10
δf(x,y)/ δx = 3 δg(x,y)/ δx = 2*x
δf(x,y)/ δy = 1 δg(x,y)/ δy = 2*y
δf(x,y)/ δx = λ * δg(x,y)/ δx ⇒ 3 = 2* λ *x (1)
δf(x,y)/ δy = λ * δg(x,y)/ δy ⇒ 1 = 2*λ * y (2)
x² + y² - 10 = 0 (3)
Solving that system
From ec (1) λ = 3/2*x From ec (2) λ = 1/2*y
Then (3/2*x ) = 1/2*y 3*y = x
x² + y² = 10 ⇒ 9y² + y² = 10 10*y² = 10
y² = 1 y ± 1 and
y = 1 x = 3 P ( 3 , 1 ) y = - 1 x = -3 Q ( - 3 , - 1 )
Value of f( x , y ) at P f (x,y) = 3*x + y f (x,y) = 3*(3) +1
f (x,y) = 10 maximum at P ( 3 , 1 )
Value of f( x , y ) at Q f (x,y) = 3*x + y f (x,y) = 3*(- 3) + ( - 1 )
f (x,y) = - 10 minimum at Q ( - 3 , - 1 )
c) f( x, y ) = xy g ( x , y ) = 4*x² + y² - 8
δf(x,y)/ δx = y δg(x,y)/ δx = 8*x
δf(x,y)/ δy = x δg(x,y)/ δy = 2*y
δf(x,y)/ δx = λ * δg(x,y)/ δx ⇒ y = λ *8*x (1)
δf(x,y)/ δy = λ * δg(x,y)/ δy ⇒ x = λ *2*y (2)
4*x² + y² - 8 = 0 (3)
Solving the system
From ec (1) λ = y/8*x and From ec (2) λ = x/2*y Then y/8*x = x/2*y
2*y² = 8*x² y² = 4*x²
Plugging that value in ec (3)
4*x² + 4*x² - 8 = 0
8*x² = 8 x² = 1 x ± 1 And y² = 4*x²
Then:
for x = 1 y² = 4 y = ± 2
for x = -1 y² = 4 y = ± 2
Then we get P ( 1 ; 2 ) Q ( 1 ; - 2)
R ( - 1 ; 2 ) T ( -1 ; -2)
Plugging that values in f( x , y ) = xy
P ( 1 ; 2 ) f( x , y ) = 2 R ( - 1 ; 2 ) f( x , y ) = - 2
Q ( 1 ; - 2) f( x , y ) = -2 T ( -1 ; -2 ) f( x , y ) = 2
Max f ( x , y ) = 2 for points P and T
Min f ( x , y ) = -2 for points Q and R
A grinding stone completes 175 revolutions before coming to a stop. How many radians did the stone complete
Answers
Answer:
175 * 2 * [tex]\pi[/tex]
350[tex]\pi[/tex] radians
Step-by-step explanation:
The number of radians completed by the stone will be 350 radians.
What is an angle in radians?The angle subtended from a circle's centre that intercepts an arc with a length equal to the circle's radius is known as a radian.
Given that a grinding stone completes 175 revolutions before coming to a stop.
The number of the revolutions in radians will be calculated as:-
Multiply the number by 2π to convert it into the radians.
Number of revolutions = 175 x 2 x π
Number of revolutions = 350 radians
Therefore, the number of radians completed by the stone will be 350 radians.
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Children arrive at a house to do Halloween trick-or- treating according to a Poisson process at the unlucky rate of 13/hour. What is the probability that the time between the 15th and 16th arrivals will be more than 4 minutes ? (Hint: Think exponential.)
a) e e-2 = 0.1353
b) e-13/15 = 0.4204
c) e-1 = 0.3679
d) 1-2-1 = 0.6321
Answers
Answer:
0.4204 probability, option b.
Step-by-step explanation:
Exponential distribution:
The exponential probability distribution, with mean m, is described by the following equation:
[tex]f(x) = \mu e^{-\mu x}[/tex]
In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.
The probability that x is lower or equal to a is given by:
[tex]P(X \leq x) = \int\limits^a_0 {f(x)} \, dx[/tex]
Which has the following solution:
[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]
The probability of finding a value higher than x is:
[tex]P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}[/tex]
Children arrive at a house to do Halloween trick-or- treating according to a Poisson process at the unlucky rate of 13/hour
13 arrivals during an hour, which means that the mean time between arrivals, in minutes is of [tex]\mu = \frac{13}{60} = 0.2167[/tex]
What is the probability that the time between the 15th and 16th arrivals will be more than 4 minutes ?
This is P(X > 4). So
[tex]P(X > 4) = e^{-0.2167*4} = 0.4204[/tex]
So the correct answer is given by option b.
I’m having trouble solving this. What’s the answer?
Answers
What is the growth factor that corresponds to a product that increases its value first by 2%, and then increases by 5% of
its value, and finally increases by 12% of its value? Round to the tenths place.
a. 1.20
C. 1.19
b. 3.19
d. 1
Answers
Answer:
1.19
Step-by-step explanation:
1+0.02+0.05+0.12 = 1.19
Determine the measure of the interior angle at vertex C.
Answers
Answer:
The ANSWER is 18*3= 54
Step-by-step explanation:
total angle inside pentagon = 540 degrees so 3(8x)+2(3x)=540 and that is 30x=540
Answer:
C = 144
Step-by-step explanation:
A 5 sided figure has the interior angle sum of 540 degrees
8x+8x+8x+3x+3x = 540
Combine like terms
30x= 540
30x/30 = 540/30
x = 18
<C = 8*18 = 144
Find m angle TUV if m angle TUN=1+38 pi m angle NUV=66^ m angle TUV=105x
Answers
Answer:
m∠TUV = 105
Step-by-step explanation:
From the question given above, the following data were obtained:
m∠TUN = 1 + 38x
m∠NUV = 66°
m∠TUV = 105x
m∠TUV =?
Next, we shall determine the value of x. This can be obtained as illustrated below:
m∠TUV = m∠TUN + m∠NUV
105x = (1 + 38x) + 66
105x = 1 + 38x + 66
Collect like terms
105x – 38x = 1 + 66
67x = 67
Divide both side by 67
x = 67 / 67
x = 1
Finally, we shall determine the value of m∠TUV. This can be obtained as shown below:
m∠TUV = 105x
x = 1
m∠TUV = 105(1)
m∠TUV = 105
Write the quadratic equation in standard form:
3x2 – 3x = 11
Answers
Answer:
[tex]3x^{2} -3x-11 = 0[/tex]
Step-by-step explanation:
Is this a function? Yes or no?
Answers
Answer:
NO
Step-by-step explanation:
NO
A certain list of movies were chosen from lists of recent Academy Award Best Picture winners, highest grossing movies, series movies (e.g. the Harry Potter series, the Spiderman series), and from the Sundance Film Festival and are being analyzed. The mean box office gross was $138.64 million with a standard deviation of $11.2526 million. Given this information, 98.49% of movies grossed greater than how much money (in millions)
Answers
Use the values in 9 = 2.2 and In 200 – 5.3 to find the approximate value of log, 200.
Answers
Answer:
2.409
Step-by-step explanation:
㏑ 9 = 2.2
ln 200 = 5.3
[tex]ln 9 = log_{e}9\\ln 200 = log_{e}200[/tex]
[tex]log_{9}200 = \frac{log_{e}200}{log_{e}9}[/tex]
= [tex]\frac{ln 200}{ln 9}[/tex]= [tex]\frac{5.3}{2.2}[/tex]
= 2.409
The approximate value of log 200 would be; 2.409
What is a logarithm?When we raise a number with an exponent, there comes a result.
Let's say you get a^b = c Then, you can write 'b' in terms of 'a' and 'c' using logarithm as follows [tex]b = \log_a(c)[/tex]'a' is called the base of this log function. We say that 'b' is the logarithm of 'c' to base 'a'
We have given the values in 9 = 2.2 and 200 – 5.3
We need to find the approximate value of log, 200.
Therefore,
㏑ 9 = 2.2
ln 200 = 5.3
[tex]ln 9 = log_{e}9\\\\ln 200 = log_{e}200[/tex]
Using the logarithm property;
[tex]log_{9}200 = \dfrac{log_{e}200}{log_{e}9}\\ = \dfrac{ln 200}{ln 9}\\ = \dfrac{5.3}{2.2}[/tex]
= 2.409
Hence, the approximate value of log, 200 would be; 2.409
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Mac is about to sue his contractor who promised to install a water tank that holds 260 gallons of water. Mac knows that 260 gallons is the capacity of a tank that
holds 35 cubic feet. The cylindrical tank has a radius of 2 feet and height of 2 feet 6 inches. Does the evidence indicate Mac can win the case against the contractor
if it goes to court
Does the evidence indicate Mac can win the case against the contractor if it goes to court?
Please hello :)
Answers
Answer:
Yes
Step-by-step explanation:
volume of cylinder = πr²h
volume = (3.14)(2 ft)²(2.5 ft)
volume = 31.4 ft³
The volume of the cylinder that was built is 31.4 ft³. It should have been 35 ft³. The evidence helps Mac in court.
Which choice correctly shows the line y = -x?
А
B
NOW
-
1 2 3 4
NH
-4 -3 -2 -1 1 2 3 4
UN
С
2
1 2 3 4
-4-3-2/4 1 2 3 4
-4 -3 -2 -3
NA
2
At
2
Answers
Answer:
The answer is A
Step-by-step explanation:
Hope this helps
Jane has earned a 91, 85, and 84 on her first three quizzes of the semester. If she hopes to have an A quiz average (90 or above), what is the lowest score Jane can make on her fourth and final quiz?
She cannot earn an A quiz average*****
100
97
95
Answers
Answer:
100
Step-by-step explanation:
CalculationLet mark to be scored in fourth =x
but since the total will be more or above we will have the sign
[tex] \geqslant [/tex]
[tex]91 + 85 + 84 + x \div 4 \geqslant 90[/tex]
[tex]260 + x \div 4 \geqslant 90[/tex]
L.c.m =4 ( cross multiplying)
260+xtex 90*4
260+xtex 360
x tex 360-260
x tex 100
The value of the lowest score Jane can make on her fourth and final quiz is, 100
What is Addition?The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.
We have to given that;
Jane has earned a 91, 85, and 84 on her first three quizzes of the semester.
And, she hopes to have an A quiz average (90 or above).
Let us assume that;
her fourth and final quiz = x
Hence, We get;
(91 + 85 + 84 + x) / 4 = 90
260 + x = 360
x = 360 - 260
x = 100
Thus, the lowest score Jane can make on her fourth and final quiz is,
x = 100
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which of the following function shows the absolute value parent function FX=lxl shifted up
Answers
Answer:
The answer is C.
as for C . the value of f(x) increases by 7 and so the graph goes up by units 7.
OR
g(x) = |x| + 7
we know that |x| is f(x), so :-
g(x) = f(x) + 7
and since f(x) is plot on y- axis the graph climbs the y axis by 7 units
*The graph shifts right or left for the other functions*
give me answer please don't skip
If a^2+b^2 = 58 and a-b = 4 then what is the value of ab
Answers
Answer:
ab = 21
Step-by-step explanation:
[tex](a - b)^2 = (a^2 + b^2 ) - 2ab\\\\4^2 = 58 - 2ab\\\\16 - 58 = - 2ab\\\\- 42 = - 2ab\\\\ab = \frac{-42}{-2} = 21[/tex]
Step-by-step explanation:
Th value of ab is 21
Explanation is in the attachment
hope it is helpful to you ☺️
thank you for giving me a chance to answer your question
A farmer picks pumpkins from a large field. The farmer makes samples of 260 pumpkins and inspects them. If one in fifty pumpkins are not fit to market and will be saved for seeds, what is the standard deviation of the mean of the sampling distribution of sample proportions?
Answers
Answer:
[tex]\mu = 5.2[/tex]
[tex]\sigma = 2.257[/tex]
Step-by-step explanation:
Given
[tex]n = 260[/tex] -- samples
[tex]p = \frac{1}{50}[/tex] --- one in 50
Solving (a): The mean
This is calculated as:
[tex]\mu = np[/tex]
[tex]\mu = 260 * \frac{1}{50}[/tex]
[tex]\mu = 5.2[/tex]
Solving (b): The standard deviation
This is calculated as:
[tex]\sigma = \sqrt{\mu * (1-p)}[/tex]
[tex]\sigma = \sqrt{5.2 * (1-1/50)}[/tex]
[tex]\sigma = \sqrt{5.2 * 0.98}[/tex]
[tex]\sigma = \sqrt{5.096}[/tex]
[tex]\sigma = 2.257[/tex]
There are two numbers. The sum of 4 times the first number and 3 times the second number is 34 the difference between 2 times the first number and 3 times the second number is 12 . Find the two numbers
Answers
Answer:
10/9
23/3
Step-by-step explanation:
4x + 3y = 34
2x - 3y = 12
2x = 12 + 3y
2×(12 + 3y) + 3y = 34
24 + 6y + 3y = 34
24 + 9y = 34
9y = 10
y = 10/9
3×10/9 + 4x = 34
10/3 + 4x = 34
4x = (102 - 10)/3 = 92/3
x = (92/3)/4 = (92/3)/(4/1) = 92/(4×3) = 23/3
Answer pls:) I would really appreciate it
Answers
Answer:
1. C
2. B
3 A
4. A
Step-by-step explanation:
#1
Brady starts off with 12 coins
And buys 6 more coins every year
So add 6 to find number of coins he will have the next year until we've done it five times ( because we want to find how many he will have after 5 years )
12 ( 1st year )
Add 6
12 + 6 = 18 ( 2nd year )
Add 6
18 + 6 = 24 ( 3rd year )
Add 6
24 + 6 = 30 ( 4th year )
Add 6
30 + 6 = 36 ( 5th year )
By the fifth year he will have 36 coins and the sequence would be
12, 18, 24, 30, 36
Which corresponds with answer choice C
2
15, 19, 23, 27, ?
We want to find the next term
To do so we must find the common difference
We can do this by subtracting the last given term by the term before it
27 - 23 = 4
Just to clarify we can do the terms before those
19 - 15 = 4
So the common difference is 4
Now to find the next term we simply add 4 to the last given term
27 + 4 = 31
The next term would be 31
3. Cumulative property of addition states that you can add any 3 numbers in a different order and they will be the same
a + b + 2 = 2 + a + b
Same variables and numbers just different order
Therefore this is an example of cumulative property of addition
4. The GCF ( greatest common factor ) is the greatest number that the two numbers can be divided by
18a and 24ab
Factors of 18
2 , 9 , 6, 3 , 1 and 18
Factors of 24
24, 1, 2, 12, 6, 4, 3 and 8
The greatest factor that both 18 and 24 have is 6
The GCF would be 6a ( not 6 ) because both numbers share a common variable (a) ( 18a , 24ab )
Please help me i will give you brainly please
Answers
Answer:
19. 3x+5/2x+7 =5
or, 3x+5=5×(2x + 7)
or, 3x + 5 = 10x + 35
or, 5 - 35 = 10x - 3x
or, -30 = 7x
or, -30/7 = x
21. let x be the other number
we know,
or, x × 1/7 =2
or, x/7 =2
or, x = 14
therefore, the other number is 14.
One root of a third degree polynomial function f(x) is -5 + 2i. Which statement describes the number and nature of all
roots for this function?
f(x) has two real roots and one imaginary root.
f(x) has two imaginary roots and one real root.
f(x) has three imaginary roots.
f(x) has three real roots.
Answers
Answer:
f(x) has two imaginary roots and one real root.
Step-by-step explanation:
Complex roots:
I a complex number [tex]a + bi[/tex] is a root of a polynomial, it's conjugate [tex]a - bi[/tex] is also a root.
One root of a third degree polynomial function f(x) is -5 + 2i.
This means that -5 - 2i is another root of the polynomial, and thus, 2 of the roots are complex.
Third degree, so it has three roots, which means that the third root is real(not possible to have a complex root without it's conjugate), and thus, the correct answer is:
f(x) has two imaginary roots and one real root.
Answer:
B!
Step-by-step explanation:
just did it
The coordinate plane below represents a city. Points A through F are schools in the city.
graph of coordinate plane. Point A is at negative 5, 5. Point B is at negative 4, negative 2. Point C is at 2, 1. Point D is at negative 2, 4. Point E is at 2, 4. Point F is at 3, negative 4.
Part A: Using the graph above, create a system of inequalities that only contains points D and E in the overlapping shaded regions. Explain how the lines will be graphed and shaded on the coordinate grid above. (5 points)
Part B: Explain how to verify that the points D and E are solutions to the system of inequalities created in Part A. (3 points)
Part C: Timothy can only attend a school in his designated zone. Timothy's zone is defined by y < 3x − 3. Explain how you can identify the schools that Timothy is allowed to attend