2x² - 5x+1 has roots alpha and beta. Find alpha⁴+beta⁴ without solving the equation.
Please answer fast step by step. I will mark the best answer as brainliest.
Answer:
Step-by-step explanation:
[tex]\alpha+\beta=\dfrac{5}{2} \\\\\alpha*\beta=\dfrac{1}{2} \\\\\alpha^2+\beta^2=\dfrac{21}{4} \ (see\ previous\ post)\\\\(\alpha+\beta)^4=\dfrac{625}{16} \\\\=\alpha^4+\beta^4+4*\alpha^3*\beta+6*\alpha^2*\beta^2+4*\alpha*\beta^3\\\\=\alpha^4+\beta^4+4*(\alpha*\beta)(\alpha^2+\beta^2)+6*\alpha^2*\beta^2\\\\\alpha^4+\beta^4=(\alpha+\beta)^4-4*(\alpha*\beta)(\alpha^2+\beta^2)-6*\alpha^2*\beta^2\\\\= \dfrac{625}{16} -4*\dfrac{1}{2} *\dfrac{21}{4} -6*(\dfrac{1}{2})^2 \\\\[/tex]
[tex]= \dfrac{625}{16}- \dfrac{168}{16}-\dfrac{24}{16}\\\\\\= \dfrac{433}{16}[/tex]
please help fassttttt
Answer:
Step-by-step explanation:
h = 20 + 1.7 + 50 = 71.7 m
What numbers are 3 units from -2 on a number line?
A number line ranging from negative 10 to positive 10
Select from the drop-down menus to correctly complete the statements.
______is 3 units left from -2 on a number line.
______- is 3 units right from -2 on a number line.
The answers are
-1
-5
1
5
please hurry
Answer:
___-5___is 3 units left from -2 on a number line.
___1___- is 3 units right from -2 on a number line
Which option is the correct interpretation of this numerical expression?
55 ÷ 5 − 4
the quotient of 55 divided by 5, decreased by 4
four subtracted from the product of 55 and 5
five less than the quotient of 55 divided by 4
fifty-five divided by the difference of 5 and 4
Answer:
7
Step-by-step explanation:
bc 11×5=55 so you divide it and its 11-4=7 :)
how much time will it take for a bug to travel 5 meters if it is traveling 1 m/s
Answer:
5
Step-by-step explanation:
divide the distance by the rate of speed
5/1=5
Answer:
5 seconds.
Step-by-step explanation:
A number of tourist were interviewed on their
choice of
means
of travell Two-thirds said
they had travel by road, 13 by air. 4
the by
both
air and road. If
20 tourist had not travel
road
Represent the information on
on a Vena
diagram:
by either
air
or road. Represent the information on a venn diagram
Answer:
A number of tourists were interviewed on their choice of means of travel. Two- thirds said that they travelled by road, 1330 by air and 415 by both air and road. If 20 tourists did not travel by either air or road ; (i) represent the information on a Venn diagram ; (ii) how many tourists (1) were interviewed ; (2) travelled by air only?
Help help help help help help help help help help help plss
Answer:
$48.
Step-by-step explanation:
60% off
= 120 - 0.60*120
= 120 - 72
= $48.
p 2 + m; use m = 1, and p = 5
Answer:
26
Step-by-step explanation:
p²+m
=> 5²+1
=> 25 + 1
=> 26
Answer:
26
Step-by-step explanation:
Substitute the given values into the expression
p² + m
= 5² + 1
= 25 + 1
= 26
solve for variable. 3p/5 + 8/5 =1
[tex]\\ \sf\longmapsto \dfrac{3p}{5}+\dfrac{8}{5}=1[/tex]
[tex]\\ \sf\longmapsto \dfrac{3p+8}{5}=1[/tex]
[tex]\\ \sf\longmapsto 3p+8=5[/tex]
[tex]\\ \sf\longmapsto 3p=5-8[/tex]
[tex]\\ \sf\longmapsto 3p=-3[/tex]
[tex]\\ \sf\longmapsto p=\dfrac{-3}{3}[/tex]
[tex]\\ \sf\longmapsto p=-1[/tex]
solve by completing the square pls show work i will mark brainliest
Answer:
[tex]3(x-1)^2 +6[/tex]
Step-by-step explanation:
Write [tex]3x^2-6x+9[/tex] in the form: [tex]x^2 + 2ax + a^2[/tex].
Factor out 3.
[tex]3(x^2 -2x+3)[/tex]
Add and subtract [tex]\left(-1\right)^2\:[/tex].
[tex]3\left(x^2-2x+3+\left(-1\right)^2-\left(-1\right)^2\right)[/tex]
You dont have to write this section down but its for notes:
[tex]x^2+2ax+a^2=\left(x+a\right)^2[/tex]
[tex]x^2-2x+\left(-1\right)^2=\left(x-1\right)^2[/tex]
Continue writing this down to show work:
Complete the square
[tex]3\left(\left(x-1\right)^2+3-\left(-1\right)^2\right)[/tex]
Simplify
[tex]3\left(x-1\right)^2+6[/tex]
A cookie company expanded its standard package of 36 cookies to include 4 extra cookies of a brand new flavor. If all of the cookies from an expanded package were put in a container and one were selected at random, what is the probability that it will be a cookie of the new flavor?
Answer:
1/9 probability
Step-by-step explanation:
The total cookies are 36 and the new flavors are 4, if you simplify 4/36, it equals 1/9
Problem 11
Six friends who enjoy tennis decide to play a game of singles and a game
of doubles every day of the 7-week school holidays.
(a) Show that at least four of the games of singles will be between friends
playing each other for the fourth time.
(b) Show that at least four of the games of doubles will be between pairs
playing the same opposing pair for the second time.
Number combination can be used to find the number of selecting n items from m items
The known parameters are;
Number of days the six friends play a game of tennis = Every day = 7 days
Number of weeks the six friends the friends play for = 7 weeks
Therefore the total number of days = 7 × 7 days = 49 days
Required:
(a) The number of ways the friends can play with each other once is given as follows;
[tex]The \ number \ of \ 2 \ combinations \ in \ 6 \ options, C_6^2 = \dfrac{6!}{2!\times (6-2)!} = 15[/tex]
The number of ways the six friends can play with each other once is 15 ways
Therefore, minimum number of singles games that will be between the same friends playing each other is given as follows;
[tex]\mathbf{Number \ of \ games = \dfrac{7 \times 7}{C_6^2} }=3.2\overline 6[/tex]
Therefore, more than 3 of the games or four games will be between pairs playing the game more than four times together, and when at least four of the games of singles are counted it will be between friends playing each other for the fourth time
(b) The number of ways the friends can play game of doubles is given as follows;
[tex]C_6^4 = \dfrac{6!}{4! \times (6 - 4)!} = 15[/tex]
The number of pairs = ₆C₂ = 15
The number of games of doubles = 49
In 49 games, we have;
The number of times the same opposing will play a game of doubles where a member of the pair can be on either side of the court will given as follows;
[tex]\mathbf{Number \ of \ games \ of \ doubles \ between \ same \ pair} = \dfrac{7 \times 7}{15 } =3.2\overline 6[/tex]
Therefore, at least four of the of the games of doubles will be between the same set of four friends playing for the 4th time, which gives; at least four games of doubles between the same set of four friends, two of which are playing (as a pair) the same opposing pair for the 4/2 = second time
Learn more about combination here:
https://brainly.com/question/22692807
please help me is for my homework
Answer:
35/100 if I remembered correctly, XD
Answer:
[tex]\frac{35}{100}[/tex]
Step-by-step explanation:
if you want to convert decimal to fraction you first have to observe the decimal point
here the decimal point is after 2 numbers so
u will take 100 to be divided with
[tex]\frac{35}{100}[/tex]
Someone help pleasee
Answer:
a horizontal translation 3 units to the right because-3 has been added to the exponent
Given CH with C(2, 1) and H(-2,-15), find
the coordinates of E if E divides CH three
fourths of the way from C to H.
The coordinate of E will be (1, -3) if the coordinates of E if E divides CH three -fourths of the way from C to H
Midpoint of a line is a point that divides a line into two equal parts.
If the line is divided in the ratio a:b, then the midpoint formula will be expressed as:
[tex]M(X,Y) =(\frac{ax_1+bx_2}{a+b}, \frac{ay_1+by_2}{a+b})\\[/tex]
Given the coordinate points, C(2, 1) and H(-2, 15) divided in the ratio of 3:4
[tex]X = \frac{3(2)+1(-2)}{3+1}\\X= \frac{6-2}{4}\\X=\frac{4}{4}\\X = 1[/tex]
Get the coordinates Y:
[tex]Y = \frac{3(1)+1(-15)}{3+1}\\Y= \frac{3-15}{7}\\Y=\frac{-12}{4}\\Y= -3[/tex]
This shows that the coordinate of E will be (1, -3)
Learn more here: https://brainly.com/question/3510899
Identify the rule for the following pattern:
4, 24, 144
Answer:
It is being multiplied by 6 each time.
Step-by-step explanation:4x6, 24x6
A gas has a density of 0.824 g/L and occupies a volume of 3.00 liters. What is the mass in grams?
Density is mass per unit volume,
ρ = m/v
Solving for mass gives
m = ρv
so that a gas with density 0.824 g/L that occupies 3.00 L has a mass of
m = (0.824 g/L) (3.00 L) = 2.47 g
If 2x minus 4 equals negative 18 what is x with shown work
Answer:
-7
Step-by-step explanation:
Equation: 2x - 4 = -18
First, add 4 to both sides:
2x = -14
Finally, divide both sides by 2:
x = -7
Check (optional):
2(-7) - 4 = -18
-14 - 4 = -18
-18 = -18 so this is correct
If you're confused about any of these steps, just let me know and I'll try to clear it up for you! :)
Which polynomial is in standard form?
O 2xy + 3x8y4 - 4x4y5 + 9x576
O 8X5 - 5y4 – 2xy + xy
O x3y2–3x2y-9x4y +11x
O 5x?y2 +7x8y5 – 14x3y? +51x2y9
The polynomial in standard form is as follows;
8x⁵ - 5y⁴ - 2xy⁵ + x²y
How to find the standard form of polynomial?A polynomial can have constants, variables and exponents, but never division by a variable. example of a polynomial is as follows:
4xy² + 2y + 5
Polynomial can be named base on the number of terms. For example monomial, binomial and trinomial.
The standard form of a polynomial is expressed by writing the highest degree of terms first then the next degree and so on.
Therefore, the polynomial in standard form is as follows;
8x⁵ - 5y⁴ - 2xy⁵ + x²y
learn more on polynomial here: https://brainly.com/question/27205112
#SPJ1
Answer: its b
8xy5 -5y4 -2xy5 +x2y
Step-by-step explanation:
I got it right on edge
when is it hard to show if a set is closed or not closed?
Simplify: (14^6*15^5)/(35^6*6^5)
Answer:
2/5
Step-by-step explanation:
=(2*7)^6 * (3*5)^5/ (7*5)^6 * (2*3)^5
=(2^6 * 7^6) * ( 3^5 * 5^5) / (7^6 * 5^6) * ( 2^5* 3^5)
=2^5 * 2^1 * 5^5/ 5^5 * 5^1 *2^5
=2/5
The simplified expression of (14^6*15^5)/(35^6*6^5) is 2/5
How to simplify the expression?The expression is given as:
(14^6*15^5)/(35^6*6^5)
Express 14 as 2 * 7, 15 as 3 * 5 and 35 as 5 * 7
[tex]\frac{(2 * 7)^6 * (3 * 5)^5}{(5 * 7)^6 * (2 * 3)^5}[/tex]
Expand the expression
[tex]\frac{2^6 * 7^6 * 3^5 * 5^5}{5^6 * 7^6 * 2^5 * 3^5}[/tex]
Divide the common factors
[tex]\frac{2}{5 }[/tex]
Rewrite as:
2/5
Hence, the simplified expression of (14^6*15^5)/(35^6*6^5) is 2/5
Read more about expressions at:
https://brainly.com/question/4344214
A triangle has three angles. The first angle measures 20 less than a number. The second triangle is three
times the number. The third is the number. What are the measurements of each of the three angles in this
triangle?
Answer:
first angle is 20, 2nd is 120, 3rd is 40.
Step-by-step explanation:
with these words, "20 less than a number, Three
times the number, is the number." We can set up the equation x-20+3x+x = 180. combine like terms and we get 5x-20=180. add 20 to both sides to get 5x=200 then divide 200 by 5x to get x = 40. We can then plug 40 into each of the expressions, x-20, 3x, x, to get our angles.
5. Classify the number 15.
O Whole, integer, rational, real
Integer, rational, real
O Natural, whole, integer, rational, real
O rational, real
Answer:
O Natural, whole, integer, rational, real
Step-by-step explanation:
it can be expressed as a fraction of 45/3, which means that it is rational.
it is a whole number because it does not contain a fraction or decimal.
it is a real number because it is a number we normally use such as 1, -0.1, 3/4, etc
it is a natural number because it is a positive integer.
and it is an integer because it does not contain a decimal.
Answer: Natural, whole, integer, rational, real
Solving equations and inequalities.
I’m confused on the subtraction behind the one, am I supposed to turn the one into a negative?
1-(4+3x)<-3
Answer:
x>0
Answer to your question:
Because the subtraction sign is after the negative, it applies to the term in front of it, in this case because there is a parenthesis, it would multiply into that and your equation from there would be 1-4-3x<-3. Then combine like terms from there.
Help me with this math question plss
Answer:
C. 8/17
Step-by-step explanation:
PM = 16+14 = 30 cm
KP= LN = 16×tan45° = 16×1 = 16cm
by using pythagorean theorem, we find :
KM² = PM²+KP²
= 30²+16²
= 900+256
= 1156
=> KM =√1156 = 34cm
so, cos theta = KP/KM = 16/34 = 8/17
Multiply. Write your answer as a fraction in simplest form. −1/4×(−4/3)=
Answer:
[tex]\frac{1}{3}[/tex]
Step-by-step explanation:
Given
- [tex]\frac{1}{4}[/tex] × - [tex]\frac{4}{3}[/tex] ( negative times negative = positive )
= [tex]\frac{1}{4}[/tex] × [tex]\frac{4}{3}[/tex] ( cancel the 4 on the numerator and denominator )
= [tex]\frac{1}{3}[/tex]
Find type of angle and solve for x.Please help.
Step-by-step explanation:
72° and a° is the angle of a straight line so
a+72°=180
a=180-72
a=108°
By using alternate exterior angle definition:
7x+24=180
7x=108-24
7x=84
x=84/7
x=12
Number x is 10% more than number y. Number y is 10% more than number z. How much percent is number z less than number x?
pls step by step
Answer:
i hope it helped U
stay safe stay happy
Prove this
sinx/cosecx-cotx = 1+cosx
Answer:
= sin x
1
−
cos
x
(
1
+
cos
x
1
+
cos
x
)
-multiply by the conjugate
=
sin
x
+
sin
x
cos
x
1
−
cos
2
x
-distribute
=
sin
x
sin
2
x
+
sin
x
cos
x
sin
2
x
-use property
sin
2
x
+
cos
2
x
=
1
=
1
sin
x
+
cos
x
sin
x
-simply
=
csc
x
+
cot
x
=
Right Hand Side
Step-by-step explanation:
help me plzzzzzzzzzzz
Answer:
x = 18°
Step-by-step explanation:
∠AOB and ∠BOD form linear pair of angles, so they are supplementary, i.e., their sum is 180°.
130° + (2x + 14)° = 180°
=> 130° + 2x° + 14° = 180°
=> 2x° = 180° - 130° - 14°
=> 2x° = 36°
=> x = 36°/2°
=> x = 18°
