If ∝ and β are the roots of the quadratic equation x² – x – 2 = 0 then ∝² + β² is equal to​

Answers

Answer 1

Answer:

α² + β² = 5

Step-by-step explanation:

Given a quadratic equation in standard form

ax² + bx + c = 0 ( a≠ 0 ) , then

sum of roots = - [tex]\frac{b}{a}[/tex]

product of roots = [tex]\frac{c}{a}[/tex]

x² - x - 2 = 0 ← is in standard form

with a = 1, b = - 1, c = - 2 , then

α + β = - [tex]\frac{-1}{1}[/tex] = 1

αβ = [tex]\frac{-2}{1}[/tex] = - 2

Using the identity

(α + β)² = α² + β² + 2αβ , then

α² + β² = (α + β)² - 2αβ = 1² - 2(- 2) = 1 + 4 = 5

Answer 2
Answer :

[tex] \large \boxed{ \boxed{\mathrm{ \alpha }^{2} + { \beta }^{2} = 5}}[/tex]

Given :

[tex] \alpha + \beta = 1[/tex]

[tex] \alpha \times \beta = - 2[/tex]

let's solve for :

[tex] { \alpha }^{2} + { \beta }^{2} [/tex]

[tex] { \alpha }^{2} + { \beta }^{2} + 2 \alpha \beta - 2 \alpha \beta [/tex]

[tex]( \alpha + \beta ) {}^{2} - 2 \alpha \beta [/tex]

let's plug the values,

[tex](1) {}^{2} -2 \times ( - 2)[/tex]

[tex]1 + 4[/tex]

[tex]5[/tex]

[tex] \mathfrak{best \: \: of \: \: luck \: \: for \: \: your \: \: assignment}[/tex]


Related Questions

Find the slope of a line through (4, 5) and (4, -5). Determine if the line is vertical, horizontal, or neither.

Answers

Answer:

Its a straight line

Step-by-step explanation:

[(4096)⁰]⁻⁴ =
a)1/(4096)⁴
b)-4
c)4096
d)1

Answers

[(4096)⁰]⁻⁴ = (4096)⁰ = 1

OPTION D

A package of cups contain exactly 6 blue cups.The probability of choosing a blue cup from the package is 3/5.How many of the cups in the package are not blue?

Answers

Answer:

There are 4.

Step-by-step explanation:

If there are 6 blue cups, and the blue cups make up 3/5th of the total cups, you can divide 6 by 3/5 to find the total amount of cups, which is 10. Then, you do 10-6 to find how many cups in the package are not blue.

30) Find the sine, cosine, and tangent of

Answers

Answer:

sin < C = c/a

cos < C = b/a

tan < C = c/b

If charlie bikes at an average speed of 7miles per hour how many hours will take to ride 28 miles

Answers

Answer:

It will take him 4 hours.

Step-by-step explanation:

7x4= 28 miles

Help pleaseeeeeeeeeeeeeeeeeeeeee ASAP

Answers

Pretty sure it’s the first one, if not maybe the last one! I hope that helps! :)

There are 1,597 souvenir paperweights that need to be packed in boxes. Each box will hold 16 paperweights. How many boxes will be needed?

Answers

Answer:

99.8125, or 100

Hope that this helps!

what is 0.8 divided by 62 as a decimal please help this is a finals

Answers

0.8 divided by 62 equals 0.80 or 80 percent (%)

Answer:

0.0129032258

Step-by-step explanation:

I simply did long division.

0.8 divided by 62 = 0.0129032258

Helppp me pleaseee ASAP

Answers

Answer:

$856.91  after 7 years

Step-by-step explanation:

Initial investment, P = 500

Interest rate, i = 8% (compounded once a year, i.e. annually)

Number of years, t = 7

Substitute in compound interest formula

Future value,

A = P (1 + 0.08/1) ^(1*7)

= 500 (1.08)^7

= 856.91 (to the nearest cent)

Brainliest goes to whoever answers correctly and explains also if you want extra points answer my other questions

Answers

Answer:

Step-by-step explanation:

126 + 44 = 170 ( total for under 25s)

186 - 56 = 130 (online for 25s - 50s)

154 - 58 = 96 ( in stores for aboves 50s)

314 for ONLINE TOTAL

196 for IN STORES TOTAL

510 for TOTAL TOTAL

A = 170

B = 56

C = 96

D = 96 - 58 = 38

E = 314 - 196 = 118

F = 510

Question 2 : Two lines meet at a point that is also the endpoint of a ray. Set up and solve an equation to find the value of a.

Answers

Answer:

you should draw it in your graph sis

give me some points i have question two

Step-by-step explanation:

find the volume of the cone. the radius is 5 and the height is 3

Answers

Answer:

V= 78.54

Step-by-step explanation:

The solution to the system below is (1, -3).
2y + x = -5 and y - 3x = -6
Which graph correctly represents this?

Answers

-17 multiply the -5 by the x after adding 2y and then y-3x = -6 and then you get -17

The graph correctly represents this system is attached below.

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables. A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

We are given system of equation as;

2y + x = -5

y - 3x = -6

The solution to the system of equations is given as (x, y) = (1, -3).

The solution to the system of equations ploted on the graph is the point where the lines intersect.

The coordinates of the point of where the lines cross are (1, 3).

Learn more about equations here;

https://brainly.com/question/25180086

#SPJ2

Which values of a and b make the equation true?

Answers

Answer:

a=3

b=3

Step-by-step explanation:

(2xy)^4

----------------

4xy

Expand the numerator

2^4 x^4 y^4

---------------------

4xy

Simplify

16 x^4 y^4

---------------------

4xy

We know that a^b / a^c = a^(b-c)

16/4 * x^(4-1)  y^(4-1)

4 x^3 y^3

Answer:

a = 3 & b = 3

Step-by-step explanation:

[tex] \small \sf \: \frac{ ( 4 xy )⁴ }{4xy }= 4x {}^{a} y {}^{b} \\ [/tex]

2⁴ x⁴ y ⁴ / 4 xy

simplify

16 x⁴ y⁴ / 4 xy

[tex] \small \sf \frac{a {}^{b} }{a {}^{c} } \: = a {}^{b - c} [/tex]

16 / 4 × x⁴ - x × y⁴ - y

4 x³ y³

Therefore , a = 3 and b = 3

This negative when developed will produce a 4” by 6” photograph. What is the length of each negative, if the width is 24 millimeters

Answers

Anwer: 36 millimeters

If a test consists of ten multiple choice questions with each permitting a possible answers. How many ways are there in which a student give his answer?

Answers

The question isn't correctly given, a possible format is in the comment below, however, the explanation will cover then concept which can be applied to different but similar

Answer:

10048576 ways

Step-by-step explanation:

We are given a question, from which we can choose aby of 4 options, this gives ua 4 possible choices for 1.

This will also apply if we have more than 1 question with the same number of options.

This can be called the product rule, as each possibility is the same of each question given :

Therefore, given 10 questions:

. We have

4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 = 4^10 = 10048576 ways

PLEASE HELP! WAYYY OVERDUE!!!
Look at the box plots and decide whether each team's distribution is symmetric or skewed negatively or positively.

Answers

Answers:

Red = negative skewYellow = symmetricBlue = positive skew

================================================

Explanation:

A symmetric distribution is where we have the left half be a mirror copy of the right half. In other words, we have symmetry going on.

For the yellow team, note the distance between Q1 and the median is 1 unit (47-46 = 1), and so is the distance from the median to Q3  (48-47 = 1). So the box portion has perfect symmetry. You should find that the whiskers are also perfectly symmetric as well using a similar technique of finding the distances and comparing them.

Overall, the entire box-and-whisker plot for the yellow team is perfectly symmetric.

---------------

If a distribution isn't symmetric, then it's skewed in some way. If the right side is pulled longer than the left, then we consider it "skewed to the right" aka "positively skewed". So that applies to the blue team. The red team has negative skew because its left tail is longer than the right tail.

PLZ HELP IF RIGHT THEN YOU'LL GET BRAINLIEST

One year, the population of a city was 346,000. Several years later it was 339,080. Find the percent decrease.

Answers

Answer:

2% decrease

Step-by-step explanation:

Steps to find percent decrease:

- Subtract starting value minus final value

- Divide that amount by the absolute value of the starting value

- Multiply by 100 to get percent decrease

no files just type it in thank you.

Answers

Answer:

True

Step-by-step explanation:

[tex]3[/tex] · 10 = 30

30 = (3 · 5) + (3 · 5)

30 =   (15)   +   (15)

30 = 30

True

Which number could represent point Z

Answers

10 1/2 would be the place u dotted Z down

In 2009, a school population was 1,700. By 2017 the population had grown to 2,500. Assume the population is changing linearly.

Find an equation for the population, P, of the school t years after 2009.

Answers

Answer:

P(t) = 100t + 1900

Step-by-step explanation:

∆P = 2500 - 1700 = 800

∆t = 2017 - 2009 = 8

m = ∆p/∆t = 800/8 = 100

b = initial pop = 1900

using slope intercept form

P(t) = 100t + 1900

Which statement has the same information that is given for the proof below

Answers

Answer:

D. TU is a midsegment

Step-by-step explanation:

Which expression is equivalent to
(3m² + 5m - 2) + (-2m +18)?
Someone answer ASAP

Answers

3m^2 +5m-2-2m+18

3m^2 +3m+16

Answer:

3m² + 3 m + 16

Step-by-step explanation:

( 3 m ² + 5 m - 2 ) + ( - 2m + 18 )

Remove the unnecessary parantheses and rewrite

3 m ² + 5 m - 2 - 2 m + 18

combine like terms

3m² + 5 m - 2 m + 18 - 2

calculate the sum

3m² + 3 m + 16


4. Convert the following fractions to decimals
1. 23/100

Answers

Answer:

0.23

Step-by-step explanation:

Using either long division or a calculator, divide 23 by 100; you will get the result 0.23.

Answer:

0.23 hope tbis helps :)

Step-by-step explanation:

Complete the square of the quadratic equation x^2 - 2x - 35 = 0. What is the vertex of the equation?
( )( )

Answers

Answer:

Step-by-step explanation:

x^2 - 2x - 35 = 0

Solve for x over the real numbers:

x^2 - 2 x - 35 = 0

Add 35 to both sides:

x^2 - 2 x = 35

Add 1 to both sides:

x^2 - 2 x + 1 = 36

Write the left hand side as a square:

(x - 1)^2 = 36

Take the square root of both sides:

x - 1 = 6 or x - 1 = -6

Add 1 to both sides:

x = 7 or x - 1 = -6

Add 1 to both sides:

Answer:  x = 7 or x = -5  as for the vertex plane curve | Cartesian equation x^2 - 2 x - 35 = 0 | vertex (not a possible affine variety)

what is the answer pleaseee

Answers

Answer:

7

Step-by-step explanation:

In most cases the first step is to create an equation to solve for the missing variable

But in this case we are already given the equation

(7.25h + 5 = 6.5h + 10.25)

All we have to do is solve for h

7.25h + 5 = 6.5h + 10.25

Step 1 subtract 5 from both sides

7.25h = 6.5h + 5.25

Step 2 subtract 6.5h from both sides

0.75h = 5.25

Step 3 divide both sides by .75

h = 7

So at 7 hours the cost will be the same for both instructors

Find each product.

1. 2x(x^2-6x+3)

2. 2a^2(5b^2 + 3ab + 6a + 1)

Answers

Given:

The expressions are:

[tex]2x(x^2-6x+3)[/tex]

[tex]2a^2(5b^2+3ab+6a+1)[/tex]

To find:

The product of each expression.

Solution:

According to the distributive property of multiplication over addition, we get

[tex]a(b+c)=ab+ac[/tex]

The first expression is:

[tex]2x(x^2-6x+3)[/tex]

Using distributive property of multiplication over addition, we get

[tex]2x(x^2-6x+3)=(2x)(x^2)+(2x)(-6x)+(2x)(3)[/tex]

[tex]2x(x^2-6x+3)=2x^3-12x^2+6x[/tex]

Therefore, the product of [tex]2x(x^2-6x+3)[/tex] is [tex]2x^3-12x^2+6x[/tex].

The second expression is:

[tex]2a^2(5b^2+3ab+6a+1)[/tex]

Using distributive property of multiplication over addition, we get

[tex]2a^2(5b^2+3ab+6a+1)=(2a^2)(5b^2)+(2a^2)(3ab)+(2a^2)(6a)+(2a^2)(1)[/tex]

[tex]2a^2(5b^2+3ab+6a+1)=10a^2b^2+6a^3b+12a^3+2a^2[/tex]

Therefore, the product of [tex]2a^2(5b^2+3ab+6a+1)[/tex] is [tex]10a^2b^2+6a^3b+12a^3+2a^2[/tex].

Given the function g(x) = 3x² - 5, find the values of t such that g(x) = -7/2t.​

Answers

Answer:

Step-by-step explanation:

-7/2t = 3x^2 - 5

t =  -2(3x^2 - 5)/7

The value of t is given by the equation t = [2/7](5 - 3x²) if the function g(x) = 3x² - 5.

What is a function?

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

It is given that:

The function:

g(x) = 3x² - 5

To find the value of such that g(x) = -(7/2)t

Equate both the equations:

3x² - 5 = -(7/2)t

After simplification:

t = [2/7](5 - 3x²)

The above equation represents the value of t.

Thus, the value of t is given by the equation t = [2/7](5 - 3x²) if the function g(x) = 3x² - 5.

Learn more about the function here:

brainly.com/question/5245372

#SPJ2

Helpppppppppppp..!!!!!’nnnnmmmm


Answers

Step-by-step explanation:

heyYYYYYYYY I HAVE AGREAT APP FOE U. it's called algebrator use that and it'll help ya

What is the value of u?

Answers

Answer:

you on the games

Step-by-step explanation:

Answer:

I think its 58

Step-by-step explanation:

Other Questions
Help please !! Thank u In a group of five students, there are two boys and three girls. The instructor randomly selects one student to record for the group and another student to spy on the other groups. Find P(boy first and girl second), the probability of selecting one of the boys first, and then selecting a girl for the second role which of the following elements are more reactive than the others. A. calcium (Ca)B. Magnesium (Mg) C. potassium (K) D. Sodium (Na) for private goods allocated in markets, a. prices guide the decisions of buyers and sellers and these decisions lead to an inefficient allocation of resources. b. the government guides the decisions of buyers and sellers and these decisions lead to an efficient allocation of resources. c. prices guide the decisions of buyers and sellers and these decisions lead to an efficient allocation of resources. d. the government guides the decisions of buyers and sellers and these decisions lead to an inefficient allocation of resources simplify 16 + 15 - 5 Find the length x Plz help ASAP 40 POINTS!!!All integers are either odd or even. Conceptually, an integer is odd if it has a remainder of 1 when dividing by 2. And an integer is even if it has a remainder of 0 when dividing by 2.But when proving something rigorously, mathematicians use more precise definitions, like these: an integer is odd if it can be written in the form 2k + 1, where k is some integer. An integer is even if it can be written in the form 2k, where k is some integer. For example, 13 is odd because 13 can be written as 2(6) + 1.With these definitions, use complete sentences to explain why zero is an even number. Which line uses alliteration?Line 2Line 3Line 4Line 5 Is segment ST tangent to circle P1 Hay alguien del coro de la iglesia aqu?RCul opcin contesta correctamente la pregunta?o s, todo nios del coro estn aqu.O S, cualquier nio del coro est aqu.S, alguien nio del coro est aqu.S, algunos nios del coro estn aqu.< Previous You have chosen an Experimental designfor your study. This means you need toset up experimental and controlconditions.How would you do this? Question 9 of 30Which of the following statements most accurately describes how watermoves through Earth and its atmosphere?A. Liquid water falls to Earth as rain.B. Gaseous water moves from the atmosphere to Earth's rivers andoceans.C. Liquid water enters the atmosphere from Earth's rivers andoceans.O D. Gaseous water falls to Earth from the clouds.SUBMIT What is the answer to this question we have so many natural resources in our country,we are not able to use them well.what is the main resources list? Read the excerpt from The Scarlet Ibis.That winter we didnt make much progress, for I was in school and Doodle suffered from one bad cold after another. But when spring came, rich and warm, we raised our sights again. Success lay at the end of summer like a pot of gold, and our campaign got off to a good start. On hot days, Doodle and I went down to Horsehead Landing and I gave him swimming lessons or showed him how to row a boat. Sometimes we descended into the cool greenness of Old Woman Swamp and climbed the rope vines or boxed scientifically beneath the pine where he had learned to walk. Promise hung about us like the leaves, and wherever we looked, ferns unfurled and birds broke into song.Which sentences from the excerpt most emphasize that spring has become a symbol of hope for the boys? Check all that apply.That winter we didnt make much progress, for I was in school and Doodle suffered from one bad cold after another.But when spring came, rich and warm, we raised our sights again.Success lay at the end of summer like a pot of gold, and our campaign got off to a good start.Sometimes we descended into the cool greenness of Old Woman Swamp and climbed the rope vines or boxed scientifically beneath the pine where he had learned to walk.Promise hung about us like the leaves, and wherever we looked, ferns unfurled and birds broke into song What is the approximate area covered by the label? When the surface of a metal is exposed to blue light, electrons are emitted. If the intensity of the blue light is increased (so the light is just brighter), what value will also increase?A. the maximum kinetic energy of the ejected electronsB. the number of electrons ejected per secondC. the time lag between the onset of the absorption of light and the ejection of electrons please help!!! how do you do the probability section? Interpret When describing how he paid his child tutors, Douglass says, "This bread I used to bestow upon the hungry little urchins, who, in return, would give me that more valuable bread of knowledge." ? Genotypes are the genes of an organism with alleles represented by letters of the alphabet. Phenotypes are an organism's observable inherited characteristics.True or False?