Find a third-degree polynomial equation with rational coefficients that has roots –5 and 6 + i.
Answers
The coefficients of the polynomial are rational, which means that any non-real roots occur alongside their complex conjugates. In this case, 6+i is a root, so 6-i is also a root.
So the simplest polynomial you can build with these roots is
(x - (-5)) (x - (6 + i )) (x - (6 - i )) = x ^3 - 7x ^2 - 23x + 185
(first choice)
Related Questions
6. A super-bouncy-ball is thrown 25m into the air. The ball falls, rebounds to 70% of the height of the previous bounce and falls again. If the ball continues to rebound and fall in this manner, find the total distance the ball has travelled after it hits the ground the 5th time. This may be answered in decimal form. Round your answer to 2 decimal places.
Answers
Answer:
The total distance the ball has travelled after it hits the ground the 5th time is of 48.53m.
Step-by-step explanation:
Geometric sequence:
In a geometric sequence, the quotient of consecutive terms is the same. The nth term of a geometric sequence is given by:
[tex]a_n = a_1q^{n-1}[/tex]
In which [tex]a_1[/tex] is the first term and [tex]q[/tex] is the common ratio.
A super-bouncy-ball is thrown 25m into the air. The ball falls, rebounds to 70% of the height of the previous bounce and falls again.
This means that:
[tex]q = 0.7, a_1 = 25*0.7 = 17.5[/tex]
Then
[tex]a_n = a_1q^{n-1}[/tex]
[tex]a_n = 17.5(0.7)^{n-1}[/tex]
First 5 terms:
[tex]a_1 = 17.5[/tex]
[tex]a_2 = 17.5(0.7)^{2-1} = 12.25[/tex]
[tex]a_3 = 17.5(0.7)^{3-1} = 8.58[/tex]
[tex]a_4 = 17.5(0.7)^{4-1} = 6[/tex]
[tex]a_5 = 17.5(0.7)^{5-1} = 4.2[/tex]
Find the total distance the ball has travelled after it hits the ground the 5th time.
[tex]T = 17.5 + 12.25 + 8.58 + 6 + 4.2 = 48.53[/tex]
The total distance the ball has travelled after it hits the ground the 5th time is of 48.53m.
n is an integer
Write the values of n such that [tex]-8\leq 4n\ \textless \ 12[/tex]
Answers
Answer:
-2, -1, 0, 1, 2,
Step-by-step explanation
Divide the whole thing by 4.
You will have -2 [tex]\leq[/tex] n < 3
The only values that fit range from -2 to 2.
How many quarters are there in 5 3/4?
Answers
Answer:
One quarter= 1/4
5 3/4= 23/4
Number of quarters in 5 3/4= 23/4 divided by 1/4
23/4 ÷ 1/4
= 23/4 × 4
=23
I hope this helps!
Answer:
23
Step-by-step explanation:
5x4 + 3
5 x 4 = 20
20 + 3 (3 Is the fraction part)
show the solution 3×(2÷3)^3+(2÷3)^2−20×2÷3+12
Answers
Answer with Step-by-step explanation:
We are given that
[tex]3\times (2\div 3)^2+(2\div 3)^2-20\times 2\div 3+12[/tex]
[tex]3\times (\frac{2}{3})^3+(\frac{2}{3})^2-20\times \frac{2}{3}+12[/tex]
[tex]3\times \frac{8}{27}+\frac{4}{9}-\frac{40}{3}+12[/tex]
[tex]\frac{24}{27}+\frac{4}{9}-\frac{40}{3}+12[/tex]
[tex]\frac{24+12}{27}-\frac{40}{3}+12[/tex]
[tex]\frac{36}{27}-\frac{40}{3}+12[/tex]
[tex]\frac{4}{3}-\frac{40}{3}+12[/tex]
[tex]\frac{4-40}{3}+12[/tex]
[tex]-\frac{36}{3}+12[/tex]
[tex]-12+12[/tex]
[tex]=0[/tex]
Line CD passes through points C(1,3) and D(4,-3). What is the equation of line CD in standard form?
Answers
(4,-3) means x2 = 4 and y2 = -3
To find slope:
(y2-y1) / (x2-x1)
(-3-3) / (4-1)
-6 / 3
Slope is -2
To find intercept:
y-y1 = m(x - x1)
y - 3 = -2(x - 1)
y - 3 = -2x + 2
y = -2x + 5 :)
Answer:
2x + y = 5
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = C (1, 3) and (x₂, y₂ ) = D (4, - 3)
m = [tex]\frac{-3-3}{4-1}[/tex] = [tex]\frac{-6}{3}[/tex] = - 2 , then
y = - 2x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
Using (1, 3 )
3 = - 2 + c ⇒ c = 3 + 2 = 5
y = - 2x + 5 ← equation in slope- intercept form
Add 2x to both sides
2x + y = 5 ← equation in standard form
simplify and find the absolute value
Answers
Step-by-step explanation:
Explanation is in the attachmenthope it is helpful to you
Step-by-step explanation:
{(-10)-(-15)÷5}
-10+15÷5
-10+3
= -7
Can somebody pls help !!
Answers
Hope this helps!!
Answer:
$26.84
Step-by-step explanation:
We have to find 10% of 268.40. To do that, we multiply it by 0.10:
268.40 * 0.1 = 26.840, or $26.84
Determine if the product of 2/18 • 3/3 is rational or irrational?
Explain your answer.
Answers
Answer:
Rational.
Step-by-step explanation:
2/18=0.1 repeating.
3/3 = 1
Multiplying these together get you 0.1 repeating.
There is only one rule that makes a number irrational.
This is a number that is not divisiable by two integers, and is not capable of being expressed as a fraction.
0.1, as we know, can be written as 2/18, or 1/9.
So it must be a rational number.
Something you may not know - Rational numbers CAN be infinitly repeating numbers.
For instance, 0.111 like shown above is repeating, and its rational.
However, pi is a repeating number...but its irrational.
This is not because its infinitly repeating, this is actually becuase it is not divisiable by two numbers, and cannot be put into fraction form.
Some people think infinitly repeating numbers are irrational, however this is not correct, for some fractions are actually repeating.
Hope this helps!
What is the average rate of change of f
over the interval (-5,0]?
Give an exact number.
Answers
Answer:
Average rate of change = 0.6
Step-by-step explanation:
Average rate of change of a function between x = a and x = b is given by,
Average rate of change = [tex]\frac{f(b)-f(a)}{b-a}[/tex]
From the graph attached,
f(-5) = 0
f(0) = 3
Average rate of change of the graph between x = -5 and x = 0,
Average rate of change = [tex]\frac{3-0}{0-(-5)}[/tex]
= [tex]\frac{3}{5}[/tex]
= 0.6
Therefore, average rate of change of the given function between x = -5 and x = 0 is 0.6.
Second Number Cube
1
2.
3
4
5
6
First Number Cube
locN-
1,1 1,2 1,3 1,4 1,5 1,6
2,1 2,2 2,3 2,4 2,5 2,6
3,1 3,2 3,3 3,4 3,5 3,6
4,1 4,2 4,3 4,4 4,5 4,6
5,1 5,2 5,3 5,4 5,5 5,6
6,1 6,2 6,3 6,4 6,5 6,6
How many possible outcomes are there?
O 6
12
Answers
Answer:
36
Step-by-step explanation:
summation of all the outcome
There are 36 possible outcomes is shows in table for rolling two six - sided number cubes.
What is mean by Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
We have to given that;
The table shows all the possible outcomes for rolling two six - sided number cubes.
Now, We know that;
For rolling one six - sided number cubes,
There is 6 possible outcomes.
Hence, For two six - sided number cubes.
Number of possible outcomes = 6 × 6
= 36
Thus, There are 36 possible outcomes is shows in table for rolling two six - sided number cubes.
Learn more about the multiplication visit:
https://brainly.com/question/10873737
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Mary is making a recipe that calls for 3/4 teaspoon of cinnamon. Her only
measuring spoon holds 4/8 teaspoon. How many times will she need to fill
her measuring spoon to get enough cinnamon for the recipe?
Answers
Answer:
She will need to fill her spoon twice, once adding in the full amount, and the second adding half the amount.
3/4 ÷ 4/8
=3/4 * 2/1
=6/4
=1.5
So, that much amount would be needed o be added to the recipe during the two times
doe anyone know this
Answers
In order for the parallelogram to be a
rhombus, x = [?].
(5x - 8°
(2x + 16)°
Answers
Answer:
8
Step-by-step explanation:
5x-8 = 2x+16
Move 2x to the left side and you get 3x-8 = 16
Move -8 to the right side and you get 3x = 24
Divide 3 on both sides and you get x = 8
If f(1) = 2 and f(n) = f(n − 1)2 + 3 then find the value of f(3).
Answers
Answer:
52
Step-by-step explanation:
f(n) is purely based on the previous value of f(n), or f(n-1), so we can start with f(1) and work our way up. We know f(1) = 2, so to find f(2), we plug f(1) into
f(n-1)²+3 to get
f(1)²+3 = 2²+3 = 4+3=7
Thus, f(2) =7. Similarly,
f(3) = f(3-1)²+3 = f(2)² + 3 -= 7² + 3= 52
3
2
In the diagram above, Z3 = 40°.
Find the measure of Z2.
L2 = [?]°
Answers
Select the fraction greater than 7/9. a)4/5 b)2/3 c)13/18 d)3/5
Answers
Answer:
A)4/5
Step-by-step explanation:
7/9=0.778
so you need to convert the other fractions into decimals as well. The one that's greater than 0.778 will be your answer.
a)4/5=0.8
b)2/3=0.667
c)13/18=0.722
d)3/5=0.6
The decimal that's greater than 0.778 is A=0.8 so that's the answer.
Write the equation in slope-intercept form from the graph
Answers
Answer:
[tex]1) y=\frac{1}{2} x+1[/tex]
[tex]2)y=-x-1[/tex]
[tex]3)y=-\frac{1}{2} -3[/tex]
Step-by-step explanation:
Hope this helps
(x+1)^2 . (x^2+1) = 0
Answers
Answer:
[tex]x^4+2x^3+2x^2+2x+1[/tex]
Step-by-step explanation:
Given that,
[tex](x+1)^2 . (x^2+1) = 0[/tex]
We know that, [tex](a+b)^2=a^2+b^2+2ab[/tex]
So,
[tex](x+1)^2=x^2+1+2x[/tex]
So,
[tex](x+1)^2 . (x^2+1) = (x^2+1+2x)(x^2+1)\\\\=x^2\times x^2+x^2+2x^3+x^2+1+2x\\\\=x^4+2x^3+2x^2+2x+1[/tex]
So, the value of the given expression is equal to[tex]x^4+2x^3+2x^2+2x+1[/tex]
help help help help help
Answers
Answer:
y = 45
Step-by-step explanation:
y = 9x
input = 5
y = 9(5)
9(5) = 45
y = 45
Based on given information for each of the following, which lines cannot be parallel?
b) Angle 69 degrees, angle 7=71 degrees
c) Angle 1=103 degrees, angle 4=105 degrees
PLSSS HELP THANKS!!
Answers
Answer:
Step-by-step explanation:
C
Answer:
c
Step-by-step explanation:
(5+6b^3)^2 expand and combine like terms
Answers
Answer:
[tex]( 5 + 6b^3)^2 = 36b^6 + 60b^3 + 25[/tex]
Step-by-step explanation:
[tex](a + b)^2 = a^2 + b^2 + 2ab[/tex]
So,
[tex](5 + 6b^3)^2 = (5)^2 + (6b^3)^2 + 2 (5)(6b^3)[/tex]
[tex]= 25 + 36b^6 + 60b^3[/tex]
What is the difference of the rational expressions below? 4/x^3 - 2x-1/3x
Answers
Answer:
C
Step-by-step explanation:
Given
[tex]\frac{4}{x^3}[/tex] - [tex]\frac{2x-1}{3x}[/tex]
Multiplying the numerator/ denominator of the first fraction by 3 and the numerator/denominator of the second fraction by x² will ensure that the fractions have a common denominator.
= [tex]\frac{3(4)}{3x^3}[/tex] - [tex]\frac{x^2(2x-1)}{3x^3}[/tex]
= [tex]\frac{12}{3x^3}[/tex] - [tex]\frac{2x^3-x^2}{3x^3}[/tex] ← combine terms on numerator
= [tex]\frac{12-2x^3+x^2}{3x^3}[/tex]
= [tex]\frac{-2x^3+x^2+12}{3x^3}[/tex] → C
HELP? I WILL MARK BRAINIEST!!! Yuson must complete 15 hours of community service. She does 3 hours each day. Which linear equation represents the hours Yuson still has to work after x days?
Answer: y = 3x – 15
For the graph of the equation you wrote in Part A, what does the y-intercept represent?
A. Hours of community service completed each day
B. Hours of community service still to complete
C. Total hours of community service that must be completed
D. Days it takes to complete 15 hours of community service
Answers
Answer: C
Step-by-step explanation:
Select all the correct answers.
Which expressions are equivalent to the given expression?
Answers
Answer:
6√7=15.874507866387543=√252
Step-by-step explanation:
hope this is helpful
The expression that are equivalent to √252 are [tex]252^{\frac{1}{2} }[/tex] and 6√7.
How to find equivalent expression?
Applying the surd rule,
√a = [tex]a^{\frac{1}{2} }[/tex]
Hence,
[tex]\sqrt{252}=252^{\frac{1}{2} }[/tex]
using surd rule, we can also decompose √252
Therefore,
√252 = √36 × 7 = 6√7
Hence, the equivalent expression of √252 are as follows:
[tex]252^{\frac{1}{2} }[/tex]6√7learn more on expression here: https://brainly.com/question/27768447
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In a class test.containing 15 questions 4 marks are given for every correct answer and -2 marks are given for every wrong answer james attempt all the question but only 9 of his answers correct .What is his total score
Answers
Answer:
48
Step-by-step explanation:
(9*4) + (6*2)
36 + 12
= 48
Step-by-step explanation:
no:questions=15
correct questions =9
marks for correct answers =9×4=36
incorrect answers=6
marks for incorrect answers =(-2)×6=(-12)
full marks =36 - (-12)
=36 + 12
=48
Solve for X
I’ll give BRAINLIEST to the correct answer
Answers
Answer: x = 19
Hi! I was studying for the NYC SHSAT when this exact problem came up a year ago. I will do my best to try to answer it correctly!
Step-by-step explanation:
To start, we have to notice the similar properties of the angles. They are alternate exterior angles (?). Therefore, I think that you just have to put the angles on opposite sides of the equation!
(6x + 6) = 120
-6 -6
6x/6 = 114/6
x = 19
I don't really understand it's due soon can someone please help me
Answers
Answer:
60
Step-by-step explanation:
Given: 1/2a + 2/3b =50
(Since b is equal to 30 we will automatically replace b with 30)
Step 1: Simplify both sides of the equation.
1/2a+20=50
Step 2: Subtract 20 from both sides.
1/2a=50-20
1/2a=30
Step 3: Multiply both sides by 2.
2(1/2a) 2(30)
a=60
Hope this helps and if it does, don't be afraid to give my answer a "Thanks" and maybe a Brainliest if it's correct?
Answer:
a = 15
Step-by-step explanation:
1/2(a) + (2/3 x 30) = 50
2/3 x 30 = 20
1/2(a) + 20 = 50
Rearrange > 20 to -20
-20 + 50 = 30
1/2(a) = 30
Rearrange 1/2 to 2
2 > 30/2
30/2 = 15
a = 15
Hope this helps, and please let me know if it is correct or isn't.
Have a nice day
Given: x+y=10
If x= -21, what is y?
Type a numerical answer in the space provided. Do not type spaces in your answer
Answers
Answer:31
Step-by-step explanation:
Answer:
y=31
Step-by-step explanation:
-21 + y= 10
-21 + y + 21 =10 + 21
y = 10+21
y = 31
HOPE THIS ANSWER HELPS YOU :)))
Are the two triangles similar? How do you know? Explain your reasoning thoroughly.
Answers
Answer:
Yes, the triangles are similar ([tex]\triangle HMG \sim \triangle KMJ[/tex]).
Step-by-step explanation:
We're given that the two triangles share at least one angle, angles H and K. The two angles in the triangles at point M, [tex]\angle HMG[/tex] and [tex]\angle KMJ[/tex] are vertical angles, meaning they are on opposite sides of a point of intersection between two lines. Since vertical angles are always equal, these two angles are also equal.
If two triangles share two angles, they must share all three, because all triangles have a total sum of interior angles of 180 degrees. Therefore, the triangles share all 3 angles. AAA (Angle-Angle-Angle) is a proof of similarity, where two triangles share all three of their angles. Thus, the two triangles are similar.
Similarity statement (vertices should correspond):
[tex]\triangle HMG \sim \triangle KMJ[/tex]
There were 7200 cars involved in a survey. 17% were driven by women. a What percentage were driven by men? b How many were driven by men?
Answers
Answer:
83%
Step-by-step explanation:
Percentage of cars driven by man = total percentage - percentage of car driven by women
= 100-17
= 83%