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The function below has at least one rational zero. Use this fact to find ALL zeros of the function.
g(x)=5x^3+x^2-20^x-4
If there is more than one zero, separate them with commas. Write exact values, not decimal approximations.
Answers
Answer:
If you want to use the Rational Zeros Theorem, as instructed, you need to use synthetic division to find zeros until you get a quadratic remainder.
P: ±1, ±2, ±3, ±6 (all prime factors of constant term)
Q: ±1, ±7 (all prime factors of the leading coefficient)
P/Q: ±1, ±2, ±3, ±6, ±1/7, ±2/7, ±3/7, ±6/7 (all possible values of P/Q)
Now, start testing your values of P/Q in your polynomial:
f(x)=7x4-9x3-41x2+13x+6
You can tell f(1) and f(-1) are not zeros since they're not = 0Now try f(2) and f(-2):
f(2)=7(16)-9(8)-41(4)+13(2)+6
112-72-164+26+6 ≠ 0
f(-2)=7(16)-9(-8)-41(4)+13(-2)+6
112+72-164-26+6 = 0 OK!! There is a zero at x=-2
This means (x+2) is a factor of the polynomial.
Now, do synthetic division to find the polynomial that results from
(7x4-9x3-41x2+13x+6)÷(x+2):
-2⊥ 7 -9 -41 13 6
-14 46 -10 -6
7 -23 5 3 0 The remainder is 0, as expected
The quotient is a polynomial of degree 3:
7x3-23x2+5x+3
Now, continue testing the P/Q values with this new polynomial. Try f(3):
f(3)=7(27)-23(9)+5(3)+3
189-207+15+3 = 0 OK!! we found another zero at x=3
Now, another synthetic division:
3⊥ 7 -23 5 3
21 -6 -3_
7 -2 -1 0
The quotient is a quadratic polynomial:
7x2-2x-1 This is not factorable, you need to apply the quadratic formula to find the 3rd and 4th zeros:
x= (1±2√2)÷7
The polynomial has 4 zeros at x=-2, 3, (1±2√2)÷7
Step-by-step explanation:
Related Questions
how many turning points will a quartic fumction with four real zeros have?
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upto four roots or zero......
-9=2x-5
Please help me now.....
Answers
Add 5 to both sides
-4= 2x
Divide by 2
-2=x or x=-2
Plot a point on the coordinate plane to represent each of the ratio values in the table.
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Answer:
Please check the explanation.
Step-by-step explanation:
Given the table
Time (h) Distance (km)
1 2
3 6
6 12
9 18
As the time (h) is represented on the x-axis and the distance (km) is represented on the y-axis.
We know that the first coordinate of an ordered pair or point (x, y) is called the x-coordinate and the second coordinate is called the y-coordinate.
Thus, from the table, we get the following points:
(1, 2), (3, 6), (6, 12), and (9, 18)
The given points are plotted on the graph attached below.
From the graph, it is clear that:
Point (1, 2)
Point (1, 2) is represented at x = 1 and y = 2.
Thus, at the point (1, 2):
Speed = Distance / Time = 2/1 = 2km per hour
Point (3, 6)
Point (3, 6) is represented at x = 3 and y = 6.
Thus, at the point (3, 6):
Speed = Distance / Time = 6/3= 2km per hour
Point (6, 12)
Point (6, 12) is represented at x = 6 and y = 12.
Thus, at the point (6, 12):
Speed = Distance / Time = 12/6= 2km per hour
Point (9, 18)
Point (9, 18) is represented at x = 9 and y = 18.
Thus, at the point (9, 18):
Speed = Distance / Time = 18/9= 2km per hour
Please check the attached graph.
What is the answer to this ?
Answers
Answer:
B shows a translation of three units to the right
75=0.25 X 1.33N
How do you solve for N
Answers
Answer:
N=625/3
Step-by-step explanation:
1) 0.25 ⋅ 1.44N=75
2) 0.36N=75
3) 0.36N/0.36 = 75/0.36
4) N= 625/3
Hope that helps
Have a good day
Step 2: Flip the equation.
Step 3: Divide both sides by 0.3325.
N = 225.56391
Type the given number as a product of prime numbers. 135
Answers
Answer:
the guy on top is Wright hdjdbzudvsjahdjsvdhhdusvs
What adaptations allow the same bacteria that live on Earth to live on the International Space Station (ISS)? (Select all that apply.)
living in an environment with increased carbon dioxide levels
living in an environment with increased radiation levels
living in an environment with increased water levels
living in an environment with increased oxygen levels
WILL GIVE BRAINLY
Answers
Answer:
living in an environment with increased carbon dioxide levels.
Step-by-step explanation:
International Space Station have higher carbon dioxide levels as compared to the earth. The earth's atmosphere has now changed due to increased carbon emission by vehicles and factories. The environmental pollution has increased and the trees are being cut which has created an environment less of oxygen and more of carbon dioxide. Bacteria's find it easy to live on earth because of increase carbon dioxide levels.
Answer:
living in an environment with increased radiation levels and living in an environment with increased carbon dioxide levels.
Step-by-step explanation:
Hope you get it right!! :))
NEED AN ANSWER QUICKK Ayo and Ria are both travelling by train.
Ayo's train travels 90 km in 50 minutes.
Ria's train travels 476 km.
It leaves at 14:05 and arrives at 17:35.
Work out the difference, in km/h, between the average speed of their trains.
Answers
Answer:
28
Step-by-step explanation:
I guessed it right on hegarty maths and this was the answer
Which triangle is a translation of the gray triangle?
O ΔDEF
Ο ΔABC
O Neither
Answers
Answer:
abc
Step-by-step explanation:
The cylinder has a surface area of 972cm. Find x. Round to the nearest whole number.
diameter: 2x
height: 5x
Answers
Answer:
A= 2pirh +2pir^2
972=2 x pi x x x 5x + 2 x pi x x^2
972= 31.4x^2 + 6.28x^2
972=37.68x^2
x^2= 972/37.68
x^2=25.796
x= 25.796 square root
x= 5
The value of x is 5 cm.
What is a cylinder?A cylinder is a three-dimensional figure that has a radius and a height.
The volume of a cylinder is given as
Example:
The volume of a cup with a height of 5 cm and a radius of 2 cm is
Volume = 3.14 x 2 x 2 x 5 = 62.8 cubic cm
We have,
The surface area of a cylinder = 972 cm²
The surface area of a cylinder.
= 2πrh + 2πr²
Diameter = 2x
Radius = x
Height = 5x
Now,
2πrh + 2πr² = 972
2π (rh + r²) = 972
2π (5x² + x²) = 972
2π x 6x² = 972
6x² = 972/(2 x 3.14)
6x² = 154.78
x² = 25.79
x = √25.79
x = 5.08
x = 5
Thus,
x value is 5.
Learn more about cylinder here:
https://brainly.com/question/15891031
#SPJ2
A company prints contest codes on its fun-size bags of
candy. Each 6-character code consists of the letter A
followed by the letter H followed by 4 of the digits 0
through 9. The digits may repeat. Which of the
following expressions gives the number of different
6-character codes that are possible?
F. 1(1)(10)(10)(10) (10)
G. 2(1)(10)(9)(8)(7)
H. 2(1)(10)(10)(10)(10)
J. 2(2)(10)(9)(8)(7)
K. 2(2)(10)(10)(10)(10)
Answers
Using the Fundamental Counting Theorem, it is found that the expression that gives the number of different 6 -character codes that are possible is:
F. 1(1)(10)(10)(10) (10)
Fundamental counting theorem:
States that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
In this problem:
For the first two digits, there is only one outcome, A and H, respectively, hence [tex]n_1 = n_2 = 1[/tex].For the next four digits, as the digits may repeat, there are ten possible outcomes for each, hence [tex]n_3 = n_4 = n_5 = n_6[/tex].Hence:
[tex]N = 1 \times 1 \times 10 \times 10 \times 10 \times 10[/tex]
And option F is correct.
To learn more about the Fundamental Counting Theorem, you can take a look at https://brainly.com/question/24314866
I need to know what this is
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Answer:
[tex]★\:\: \frac{3 {x}^{3} - 18 {x}^{2} + 27x}{2 {x}^{2} + 2x - 12}\:when\:x≠2,\:3 \\ = \frac{3x( {x}^{2} - 6x + 9) }{2( {x}^{2} + x - 6) } \\ = \frac{3x( {(x)}^{2} - 2 \times (3) \times (x) + {(3)}^{2} ) }{2( {x}^{2} + 3x - 2x - 6) } \\ = \frac{3x {(x - 3)}(x - 3) }{2(x(x + 3) - 2(x + 3))} \\ = \boxed{‡ \frac{3x {(x - 3)}^{2} }{2(x + 3)(x - 2)}‡}✓[/tex]
3x(x-3)²/2(x+3)(x-2) is the right answer.Tn=n^2+bn+c. Find the values of b and c if the sequences starts with - 1,2,7,14,..
Answers
Answer:
no
Step-by-step explanation:
no
The graph below shows the number of points each team scored how many more points did the marlins have than the torpedoes?
A 250
B 300
C 350
D 450
Answers
Answer:
300
Step-by-step explanation:
Given the endpoint of (-5, - 3) and midpoint of
of (-0.5,0)
find the coordinate point of the other endpoint
Answers
Answer:
You have to plot these points on the graph and find out what the slope is that way or find the slope using the slope form. (below) Then using the slope add the y-coordinate and x-coordinate to the appropriate places in the ordered pair (-0.5,0) this will give you your answer of ordered pair.
Step-by-step explanation:
SLOPE FORMULA-
y2-y1 / x2-x1
Find the solution of the system of equations.
6x – 3y = -30
3x – 6y = 12
Answers
Answer:
Step-by-step explanation:
6x – 3y = -30
3x – 6y = 12
Multiply the top equation by 2 and write the bottom equation under it.
12x - 6y = - 60
3x - 6y = 12 Subtract
9x = - 72 Divide by 9
x = - 72/9
x = - 8
6x - 3y = - 30
6*-8 - 3y = -30
-48 - 3y = - 30 Add 48 to both sides.
-3y = - 30 + 48
-3y = 18 Divide by -3
y = -18/-3
y = -6
What is 3 meters converted to potential energy
Answers
Answer:
4 meters
Step-by-step explanation:
5, 80, 1280, 20480, 327680, ...
Answers
Answer:
It's multiplying by 16 every time... so the next answer is 5242880
Step-by-step explanation:
327680 x 16 = 5242880
The surface is frictionless,Two blocks in contact with each other move
to the right across a horizontal surface by the two forces shown
Determine the magnitude of the force exerted on the block with mass 1.4 kg by the block with mass 6.4 kg.
Answer in units of N
Answers
9514 1404 393
Answer:
55 8/39 N ≈ 55 N
Step-by-step explanation:
The net force on the 1.4 kg block is proportional to its mass. That is, the ratio of net force on that block to the net force on the total mass is the same as the ratio of the block's mass to the total mass.
net force on 1.4 kg = (1.4 kg)/(1.4 +6.4 kg) × (64 N -15 N) = (7/39)(49 N)
net force on 1.4 kg = 8 31/39 N
Then the force applied by the 6.4 kg mass is ...
64 N - 8 31/39 N = 55 8/39 N ≈ 55 N . . . . applied by 6.4 kg mass
A total of 31 microphones are to be purchased. Each microphone costs $249 estimate the total purchase price by using round numbers
Answers
Answer:
The answer is 7,500
Step-by-step explanation:
31 rounds to 30 and 249 rounds to 250. 30 times 250 is 7,500. I hope this helps.
what does equal (+3) * (+9)=
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Answer:
27, we know that +3 and +9 are just the same without the signs. And 3 * 9 = 27.
Solve -15 =p+2.
Enter your answer in the box.
-15 = p + 2
-15 – 2 = p + 2 – 2
___ =P
Answers
Answer:
the answer is -17.......
A university conducted a study of whether running is healthy for men and women over age 50. During the first eight years of the study, 1.4% of the 458 members of a fitness association died. We are interested in the proportion of people over 50 who ran and died in the same eight-year period.
Define the Random Variables X and P', in words. which of the following?
a. X is the proportion of people who ran and died in the eight-year period, and P' is the number of people who ran and died in the eight-year period.
b. X is the proportion of all runners that die, and P' is the number of all runners that die.
c. X is the number of people who ran and died in the eight-year period, and P' is the proportion of people who ran and died in the eight-year period.
d. X is the number of all runners that die, and P' is the proportion of all runners that die.
Answers
Answer:
The correct answer is c.
Step-by-step explanation:
x represents the number of the data variable that is being studied and from this data we obtain P, that is, the proportion
P is the proportion that is equal to x / n that is, x is equal to 6.41 that when divided by 458 which is equal to n and multiplied by 100 gives a proportion of 1.4%
P= 6.41÷458×100=1.4%
The measures of the three angles whose sum is 120° are in the extended ratio 2:5:8 find the exact angle measures
Answers
Answer:
ans is 16°,40°and64°
let ratio be 2x,5xand 8x
Step-by-step explanation:
their sum=120°
2x+5x+8x=120
15x=120
x=120/15=8°
2x=2×8=16°
5x=5×8=40°
8x=8×8=64°
You complete two events of a triathlon. Your goal is to finish with an overall time of less than 100 minutes. a. Select an inequality that represents how many minutes x you can take to finish the running event and still meet your goal. Then solve the inequality. swimming-18.2 biking-45.5
Answers
The projected sales volume of a video game cartridge is given by the function s(p) = 3000 / (2p + a), where s is the number of cartridges sold, in thousands; p is the price per cartridge, in dollars; and a is a constant. If according to the projections, 100000 cartridges are sold at 10 dollars per cartridge, how many cartridges will be sold at 20 dollars per cartridge?
Answers
Answer: 149 cartridges will be sold at 20 dollars per cartridge.
Step-by-step explanation:
Given: The projected sales volume of a video game cartridge is given by the function [tex]s(p)=\dfrac{3000}{2p+a}[/tex], where s is the number of cartridges sold, in thousands; p is the price per cartridge, in dollars; and a is a constant.
Put s(p)=100000, p= 10, we get
[tex]100000=\dfrac{3000}{2(10)+a}\\\\\Rightarrow\ 100=\dfrac{3}{20+a}\\\\\Rightarrow\ 100(20+a)=3\\\\\Rightarrow\ 2000+100a=3\\\\\Rightarrow\ 100a=-1997\\\\\Rightarrow\ a=-19.97[/tex]
i.e. [tex]s(p)=\dfrac{3000}{2p-19.97}[/tex]
Put p=20, we get
[tex]s(20)=\dfrac{3000}{2(20)-19.97}\\\\=\dfrac{3000}{40-19.97}\\\\=\dfrac{3000}{20.03}\approx149[/tex]
Hence, 149 cartridges will be sold at 20 dollars per cartridge.
In a regular polygon, all the angles have the same measure. Martin drew a regular polygon in which the sum of the interior angles was 540°. What is the measure of each angle in Martin’s drawing?
Answers
Answer:
108°
Step-by-step explanation:
Answer:
108°
Step-by-step explanation:
I got 100%
I need help please.
Answers
Answer:
0.1 is 5% of 2.
Step-by-step explanation:
Steps:
0.1 ÷ 5% = 2%
Answer:
2
Step-by-step explanation:
5% of 2 is 0.1
50% is 1
5% is 0.1
What is the equation of the line that passes through the point (4,11) and is perpendicular to the line with the following equation? Y=4/3x+7
Answers
Answer:
Step-by-step explanation:
y = (4/3)x+7
Slope of the line is 4/3.
Slope of any perpendicular to the line is -¾.
Point-slope equation for line of slope -¾ that passes through (4,11):
y-11 = -¾(x-4)
Of course, you may want to rearrange it to slope-intercept form or standard form.
y = -¾x+15 slope-intercept
x+4y = 60 standard
What is the answer 2/3 + 5/12 =
Answers
Answer:
then answer is 13/12
Step-by-step explanation:
(8+5)/12
13/12