We are given the polynomial:
2x³ - 3x² + 4x - 1 = 0
We need to find the value of r² + s² + t² where r,s,t are the solutions.
Simplifying r² + s² + t²:
r² + s² + t² = (r + s + t)² - 2(rs + st + rt)
[since a²+b²+c² = (a+b+c)² - 2(ab + bc + ca)]
Using the Vieta's formulae:
Above, we can see that in order to find the value of r² + s² + t², we need to find the value of the sum of solutions and sum of solutions taken 2 at a time.
Sum of roots:
We know that the Vieta's formula to find the sum of roots is:
Sum of roots = [tex]-\frac{b}{a}[/tex]
Where b and a are the coefficients from the general form: ax³ + bx² + cx - d
We notice that for the given equation, b = -3 ; a = 2
Sum of roots = [tex]-(\frac{-3}{2})[/tex]
Sum of roots = [tex]\frac{3}{2}[/tex]
Hence, the sum of roots (r + s + t) = 3/2
Sum of roots taken two at a time:
We know that the Vieta's formula to find the sum of roots taken 2 at a time is: Sum of roots taken 2 at a time = [tex]\frac{c}{a}[/tex]
Where c and a are the coefficients from the general form: ax³ + bx² + cx - d
for the given equation, c = 4 ; a = 2
Sum of roots taken 2 at a time = [tex]\frac{4}{2}[/tex]
Sum of roots taken 2 at a time = 2
Hence, the sum of roots taken 2 at a time (rs + st + rt) = 2
Finding the value of r² + s² + t²:
We proved before that:
r² + s² + t² = (r + s + t)² - 2(rs + st + rt)
now that we know the values of (r + s + t) and (rs + st + rt), we can plug those values to get our answer
r² + s² + t² = ([tex]\frac{3}{2}[/tex])² - 2(2)
r² + s² + t² = ([tex]\frac{9}{4\\}[/tex]) - 4
r² + s² + t² = [tex]\frac{9 - 16}{4\\}[/tex]
r² + s² + t² = [tex]\frac{-7}{4}[/tex] = -1.75
Hence, the value of r² + s² + t² is -1.75
0540-0058= ???
In military time
Answer:
0442 (4:42 normal time)
btw plz give brainliest
show all your work?
and please help me out ASAP!!
Answer:
EF = 36
Step-by-step explanation:
On a rhombus, all sides are equal because its a parallelogram so,
EF = FG
we first have to find what x equals so . . .
let's plug in the numbers
4x - 20 = 2x + 8
Now we combine like terms
we add 20 to both sides
so now it would be
4x = 2x +28
Now we subtract 2x from both sides because we want x by itself
this would equal
2x = 28
now we divide two from both sides this equals
x = 14
now we insert the numbers in the equation
4 x 14 - 20 = 36
if you have any questions feel free to ask - Mark
Can someone help me?
What's 4/5 of 55?
Answer:
44 is 4/5 out of 55 (44/55 = 4/5)
Step-by-step explanation:
55 can be divided into fifths.
1/5 = 11 or 11/55
11 x 4 = 44
Hopefully this helps :3 Sorry if wrong :( Plz mark brainiest if correct :D Your bootiful/handsome! Have a great day luv <3
-Bee~
rhombus and a square have one and the same side of 6 cm. The area of the rhombus is 4/5 of the area of the square. Find the height of the rhombus.
Answer:
1.8 is the h of the rhombus
Answer:
4.8 cm
Step-by-step explanation:
What is 273x 346 I need help like asp
Answer:
94458
Step-by-step explanation:
273 x 346 =94458
Answer:
just use a calculator
Step-by-step explanation:
94458
that is the answer
ADD two expressions
-3t-1 and 6t + 10
A small radio station can broadcast in a circular range with a radius of 20 miles. About how many square miles is the area covered by this range? Use 3.14 for π.
The requried range of the radio station is given as 1256 square miles.
What is an area circle?The area of the circle is given by the pie times square of the radius.
A = πr², where r is the radius of the circle.
Here,
A small radio station can broadcast in a circular range with a radius of 20 miles.
The range is given by the area of the circle with given radius,
Area of the circle = πr²
Area of the circle = 3.14 × 20²
area of the circle = 1256 square miles
Thus, the requried range of the radio station is given as 1256 square miles.
Learn more about circle here:
brainly.com/question/11833983
#SPJ2
Determine the y intercept
Answer:
-9
Step-by-step explanation:
What is (are) the solution(s) to the equation 23x−3=−13x−6?
Find the Volume please help
Solve the inequality for x: 1/2(2x + 4) = 3x -6
Please help me...will mark brainiest
Answer:
x-121
Step-by-step explanation:
Answer:
x² - 22x + 121
Step-by-step explanation:
(x-11)² is the same as (x-11)(x-11)
multiply the x in the first parentheses by x and -11 in the other parentheses and multiply the -11 in the first parentheses by x and -11 in the other parentheses and add all together
x²- 11x - 11x + 121
x² - 22x + 121
+-√-49=+-
please help
Answer: 0 if I am not mistaken
The increased demand for vegetarian meals has caused an increase in the price of tofu. If the current cost of $2.99 per pound is increasing 6% per year, what will it cost in 5 years?
Answer:
R90,70
Step-by-step explanation:
[tex]2.99 \times \frac{6}{100} \times 5 = [/tex]
Answer:
y=4, or $4
Step-by-step explanation:
a=initial amount
b=growth
+6%=growth
100+6=106
106/6=1.06
equation: y=2.99(1.06)^x
2.99(1.06)^5
around 4
Find the measures of the numbered angles in each rhombus
Answer:
2=41 1=49 3=49
Step-by-step explanation:
Angle 2 = 41 because it is directly across the given angle.
Angles 1 and 3 are equal, and the total number of degrees in the rombus are 180.
41+41=82
180-82=98
98 / 2 = 49
Angles and 3 both equal 49
Answer:
2=41°(Alternate Interior angles)
1=41°(diagonal of rhombus bisects the interior angles)
3=49°(180-82/2)
Step-by-step explanation:
what is the Radical of 125?
Answer:
5√5
Step-by-step explanation:
:))))))))))))))))))
Simplify the following expressions. Assume all variables are positive.
Exponents in simplified form should all be positive.
(81)
1.
493 · 494
2.
3
(81)
3.(16x24)
Write the mixed number as a percent.
[tex]1 \frac{1}{4} [/tex]
What is the solution given the expression 7x^-2 when x=3 and y=9 ?
Answer:
252
Step-by-step explanation:
If u can help please do
Answer:
the first one is 240
the second one is 280
the third one is 200
The answers that would be discarded would be 220, 360 and 500
Step-by-step explanation:
Hey There!
So for this problem all we have to do is plug in the hours worked and drones sold into the expression 10h+40d
For the first one we just plug in 8 for hours (because he worked 8 hours) and 4 for drones ( because he sold 4 drones )
so we would have 10(8) + 40(4)
10x8=80
40x4=160
160+80=240 So 240 would go with the first one
For the second one we plug in 4 for hours ( because he worked 4 hours) and 6 for drones ( because he sold 6 drones)
so we would have 10(4)+40(6)
10x4=40
40x6=240
240+40=280
So 280 would go with the second one
For the third one we plug in 12 for hours ( because he worked 12 hours) and 2 for drones ( because he sold 2 drones)
so we would have
12(10)+2(40)
12x10=120
2x40=80
120+80=200
so 200 would go with the third one
hope this helps :)
It takes 45 min for Faucet A to fill a tank, and it takes Faucet B 63 min. How many minutes will it take the two faucets to fill the tank together?
Answer:
the total minutes taken together is 26.25 minutes
Step-by-step explanation:
The computation of the number of minutes that required to fill the tank together is shown below:
[tex]\frac{1}{45} + \frac{1}{63} = \frac{1}{x}\\\\\frac{7 + 5 }{315} = \frac{1}{x} \\\\\frac{12}{315} = \frac{1}{x} \\\\12x = 315\\x = 26.25[/tex]minutes
Hence, the total minutes taken together is 26.25 minutes
I really need help with thing I am in math class help this is due today
Answer:
C
Step-by-step explanation:
The triangle is doubled
what is the scientific notation of 0.0000003
Answer:
This is ur answer.
Hope.it helps!!!
15,19,23,__,31 find the number sequence
Answer:
27
Step-by-step explanation:
yes.
are you trying to find the missing number bc if so then its 27
15,19,23,27,31
what are some ratios equivalent to 7:6
Answer:
14 : 12 , 21 : 18 and 28 : 24
Step-by-step explanation:
simplify:
2⁴ x 10³
(-5)³ x (-2)
Answer:
hope this helps
Step-by-step explanation:
An auditorium has 21 rows of seats. The first row has 18 seats and each succeeding row has 2 more seats than the previous row. How many seats are in the auditorium?
Answer:
798
Step-by-step explanation:
So, 21*{2*18 + (21-1)*2}/2
= 21*{36 + 20*2}/2
= 21*{36+40}/2
= 21*76/2
= 1596/2
= 798
Total number of seats is 798
Given that;Number of seats in first row = 18
Number of rows = 21
Each row added number of seats then previous = 2
Find:Total number of seats
Computation:Total number of seats = Sn = (n/2)[2a + (n-1)d]
Total number of seats = Sn = (21/2)[2(18) + (21-1)2]
Total number of seats = (21/2)[36 + (20)2]
Total number of seats = (21/2)[36 + 40]
Total number of seats = (21/2)[76]
Total number of seats = (21)(38)
Total number of seats = 798
Learn more:https://brainly.com/question/16668552?referrer=searchResults
What is the slope of the line through (-9,6) and (-3, 9)?
Answer:
1/2 think it is bc -9,6 and -3,9 are 1/2
subtract 9 from 16 as an expression pls help
Answer:
16 - 9 = x
i thonk :0
or 16 - 9 = 7
Step-by-step explanation:
Jack has $500 in a bank account that will earn 3% interest every year. Diane has $100 in an investment account that will earn 12% every year. How many years will it take for Diane's account balance to overtake Jack’s?
Answer:
20 years
Step-by-step explanation:
A=500(1+.03)^20
$903
A=100(1+.12)^20
$964
It took her 20 years to overtake.
Answer:
Simple interest = NeverCompound interest = 19 years and 4 monthsStep-by-step explanation:
Jack
Initial amount = $500Interest rate = 3% = 0.03Yearly interest = 0.03*500 = $15
Diane
Initial amount = $100Interest rate = 12% = 0.12Yearly interest = 0.12*100 = $12
Diane's initial amount and yearly interest amount are both less than of Jack's.
It means her balance will never overtake Jack's.
=======================
It is not mentioned in the question but let's assume it is compound interest which is annually compounded.
Then after x years their balance will be:
Jack
500(1 + 0.03)^x = 500*1.03^xDiane
100(1 + 0.12)^x = 100*1.12^xSolve inequality below:
100*1.12^x ≥ 500*1.03^x(1.12/1.03)^x ≥ 51.087^x ≥ 5x log 1.087 ≥ log 5x ≥ log 5 / log 1.087x ≥ 19.29 years = 19 years and 4 months