Let $r$ and $s$ be the roots of $3x^2 + 4x + 12 = 0.$ Find $r^2 + s^2.$

Answers

Answer 1

Use a similar strategy as in your other question, [19925664].

3x² + 4x + 12 = 3 (x - r ) (x - s)

3x² + 4x + 12 = 3 (x² - (r + s) x + rs)

3x² + 4x + 12 = 3x² - 3 (r + s) x + 3rs

so that

r + s = -4/3

rs = 12/3 = 4

Recall that

(r + s)² = r² + 2rs + s²

so that

r² + s² = -2rs = -2(4) = -8


Related Questions

One side of a triangle is 2 times the second side. The third side is 15 feet longer than the second side. The perimeter of a
triangle is 47 feet. Find the length of each side.
Dresdobou

Answers

Answer:

16, 8, 23

Step-by-step explanation:

2x+x+x+15=47

4x+15=47

4x=32

x=8

2x=16

x+15=23

F(x)=4x 2 +2x+6f, left parenthesis, x, right parenthesis, equals, 4, x, squared, plus, 2, x, plus, 6 What is the value of the discriminant of fff? How many distinct real number zeros does fff have?

Answers

Answer:

Discriminant = -92

the equation has no distinct real numbers

Step-by-step explanation:

Given the function f(x) = 4x^2 + 2x + 6 where;

a = 4, b = 2 and c= 6

The discriminant is expessed as D = b^2 - 4ac

Substitute;

D = 2^2 - 4(4)(6)

D = 4 - 96

D = -92

Hence the discriminant is -92.

Since the discriminant is less than zero i.e D< 0, this shows that the zeros of the equation are not real but complex numbers. Hence, the equation has no distinct real numbers

Answer:

-92 is the discriminant

0 real value 0's

Step-by-step explanation:

Solve the system of equations using elimination 2x+y=3 and 3x-y=12

Answers

2x + y = 3
3x - y = 12
Add both equations
5x = 15, x = 3
2(3) + y = 3
6 + y = 3, y = -3
Solution: x = 3, y = -3... or (3,-3)

Lydia gets kicked out of class twice in 20 minutes. How many times will she get kicked out in 6 hours?

Pop Smoke drops 3 new mixtapes per month. How many years has it been if he drops 45 new tapes?

Answers

Answering the Pop Smoke question.
It’ll be 15 years since 45 divided by 3 is 15.

Answer:

for the first answer : 36

for the second answer : 1 year and 3 months

Step-by-step explanation:

first answer :

ahe gets kicked out 2 times in 20 mins

6 hours = 6 × 60 mins = 360 mins

let the number of times she gets kicked out in 6 hours / 360 mins be "n"

therefore ;

n= (360×2) ÷ 20 = 36

therefore answer is 36 times.

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

second answer :

3 new tapes in 1 month

let the number of years be "n"

therefore:

3×12 = tapes per year = 36 tapes per year

so, n = 45÷36 = 1 (as quotient) year and 3 (as remainder) months.

answer : 1 year and 3 months

What is the inverse of the function fx) = 2x + 1?

Answers

Answer:

X=2y+1

X-1/2=y

Please help thank you so much

Answers

Answer:

This is the correct solution for your question

33

6^2 is 36
9 divided by x when x is 3 is 9 divided by 3 which is 3
then 36-3 which is 33
33

graph the inequality y is less than x-3

Answers

Answer:

i do believe that its y<x-3

Step-by-step explanation:

Marion is twice as old as judy. Six years agot Marion was three times as old as judy was then. Find the age of each girl now.

Pls show work, I will give brainliest

Answers

9514 1404 393

Answer:

  Marion is 24, Judy is 12

Step-by-step explanation:

Let j represent Judy's age now. 6 year ago, the relation was ...

  3(j -6) = (2j) -6

  3j -18 = 2j -6 . . . . . eliminate parentheses

  j = 12 . . . . . . . . . . . add 18-2j

  2j = 24 . . . . . . . . . Marion's age now

Judy is 12; Marion is 24.

BRANLIEST TO THE RIGHT ANSWER!! NEED HELP ASAP!

Answers

Answer:

1

Step-by-step explanation:

1

30 POINTS!!!!!!!

A family is taking a trip to the beach 145 miles away. They have 10 gallons of gas in their car’s gas tank and the car is averaging 14 miles per gallon. Explain why estimating to determine if they have enough gas to make the trip is NOT going to be okay in this instance.

Answers

Answer:

No they don't.

Step-by-step explanation:

I did 14 x 10. Since it's 14 per gallon and they have 10. I got 140. 140 is not enough for the trip. They need 145.

Answer:

6.0

Step-by-step explanation:

common sense

2. There is 3/4 ft of ribbon to go on each of the 3 packages. You decide to divide the ribbon evenly
for each package. How much ribbon does each package get?

1/4 ft
3/12 ft
2 1/4 ft
9/4
WILL GIVE BRAINLIEST

Answers

1/4 ft I’m pretty sure I want to be brainliest

You found a great deal on CDs for gifts! You were
able to buy 12 CDs for $15! What was the cost per
CD?

Answers

Answer:

80 cents per cd

Step-by-step explanation:

when finding that answer you divide 12/15 which equals .8

PLEASE HELPPO I BEFGG

Answers

Answer:

-1.75, -1 1/2, -3/4, 1/4, 0.75

Step-by-step explanation:

I hope this helped and if it did I would appreciate it if you marked me Brainliest. thank you and have a nice day!

Best answer gets brainliest hurry ASAP

Answers

Answer:

42 minutes

Step-by-step explanation:

PLEASE PLEASE HELP MEEEE!!!!

Answers

Answer:

The answer is D) f(x) = 1/3 x^2 -1

Step-by-step explanation:

the key is at the end, the minus 1

Answer:

The answer is D!

Step-by-step explanation:

сатре о
Find the condition that the roots of the quadratic equation
ax2 + cx + C =0
may be in the ratio m:n​

Answers

Answer:

[tex]mnb^2 = ac(m+n)^2[/tex]

Step-by-step explanation:

Given

[tex]ax^2 +bx + c = 0[/tex]

Required

Condition that the roots is in m : n

Let the roots of the equation be represented as: mA and nA

A quadratic equation has the form:

[tex]x^2 + (sum\ of\ roots)x + (product\ of\ roots)=0[/tex]

or

[tex]x^2 - (\frac{b}{a})x + \frac{c}{a} = 0[/tex]

We have the roots to be mA and nA.

So, the sum is represented as:

[tex]Sum = mA + nA[/tex]

[tex]Sum = A(m + n)[/tex]

And the product is represented as:

[tex]Product = mA * nA[/tex]

[tex]Product = mnA^2[/tex]

By comparing:

[tex]x^2 + (sum\ of\ roots)x + (product\ of\ roots)=0[/tex]

with

[tex]x^2 - (\frac{b}{a})x + \frac{c}{a} = 0[/tex]

[tex]Sum = -\frac{b}{a}[/tex]

[tex]Product = \frac{c}{a}[/tex]

So, we have:

[tex]Sum = -\frac{b}{a}[/tex]

[tex]A(m + n) = -\frac{b}{a}[/tex]

Make A the subject:

[tex]A = \frac{-b}{a(m+n)}[/tex]

[tex]Product = \frac{c}{a}[/tex]

[tex]mnA^2 = \frac{c}{a}[/tex]

Substitute [tex]A = \frac{-b}{a(m+n)}[/tex]

[tex]mn(\frac{-b}{a(m+n)})^2 = \frac{c}{a}[/tex]

[tex]mn\frac{b^2}{a^2(m+n)^2} = \frac{c}{a}[/tex]

Multiply both sides by a

[tex]a * mn\frac{b^2}{a^2(m+n)^2} = \frac{c}{a} * a[/tex]

[tex]\frac{mnb^2}{a(m+n)^2} = c[/tex]

Cross Multiply:

[tex]mnb^2 = ac(m+n)^2[/tex]

Hence, the condition that the ratio is in m:n is

[tex]mnb^2 = ac(m+n)^2[/tex]

If 65% of a number is 169 and 15% of the same number is 39, find 80% of that number.

Answers

Answer:

208

Step-by-step explanation:

169/65%=260= the original number

260 x 80% = 208

Answer:

208 is 80% of that number

Step-by-step explanation:

to find the number, take 65/100 (or 65%), and set it equal to 169/x (because x is the number that 169 is 65% of, so we need to find x)=> 65/100=169/x

Next, cross multiply to get 16900=65x

Divide both sides of the equation by 65 to get 260=x, which means that 260 is the mystery number that the question speaks of. Then, to get 80% of 260, set 80/100 equal to x/260=> 80/100=x/260

cross multiply to get 20800=100x

divide both sides by 100 to get 208

Therefore, the answer is 208

Solve the quadratic function using square root X+10x+25 =18

Answers

Answer:

= − 7 /1 1  in fraction form

Step-by-step explanation:

STEP 1: Multiply by 1

1 + 1 0 + 2 5 = 1 8

+ 1 0 + 2 5 = 1 8                                                                                                                               STEP 2: Combine like terms

+ 1 0 + 2 5 = 1 8

1 1 + 2 5 = 1 8                                                                                                                       STEP 3: Subtract  2 5   from both sides of the equation

11x+25=18

1 1 + 2 5 − 2 5 = 1 8 − 2 5

STEP 4: Simplify  by subtracting the numbers

1 1 + 2 5 − 2 5 = 1 8 − 2 5

11x+25−25=18−25                                                                                                   1 1 = 1 8 − 2 5                                                                                                                                   1 1 =  -7

STEP 5: Divide both sides of the equation by the same term                                                     1 1 = − 7                                                                                                                         11x/ 11x = −7/ 1 1 (set up as a fraction)                                                                       STEP 6: Cancel terms that are in both the numerator and denominator

=  − 7 /1 1                                                                                                                      SOLUTION

=  − 7 /1 1

choose a number between 67 and 113 as a multiple of 3, 5 and 10

Answers

Answer: 90

Step-by-step explanation:

90 / 3 = 30

90 / 5 = 14

90 / 10 = 9

Therefore, 90 is between 67 and 113. It is also a multiple of 3, 5, and 10.

What is the slope given: y= -x + 5

Options:
1
5
-1
0

Answers

-1 because of X is on its own it will usually be considered one and if it is negative then -1

Answer:

5

Step-by-step explanation:

shasta claimed that the equation x^2+25=0 can be solved by using its factored form of (x+5i)^2=0, and that -5i is the only zero for this function. which statement is true?

Answers

Answer:

The given equation will have two roots as +5i and -5i

Step-by-step explanation:

Shasta claimed that the equation x^2+25=0 can be solved by using its factored form of (x+5i)^2=0, and that -5i is the only zero for this function

The given equation is [tex]x^2+25 =0[/tex]

This clearly shows it will have complex roots, and since it is a quadratic equation it will have 2 complex roots

[tex]x^2 = -25 \\x = \sqrt{-25} \\x= \sqrt{-1}* \sqrt{25}\\[/tex]

[tex]x = i\sqrt{25}[/tex]

x = ± 5i

It will be false to say that -5i will be the only complex root to this equation.

The given equation will have +5i and -5i as its roots.

Lets verify

x = +5i

[tex](5i)^2 + 25 \\25i^2 + 25 \\25(-1) + 25\\-25 + 25 = 0[/tex]

x = -5i

[tex](-5i)^2 + 25 \\25i^2 + 25 \\25(-1) + 25 \\-25 + 25 \\ = 0[/tex]

I have a coupon to save 30% off of my bill. If my bill is originally $45.00
how much will I pay?*

Answers

$31.50 is the correct answer

Answer:

$31.50

Step-by-step explanation:

the decrease will be $13.50

Which choice is equivalent to the expression below? (V= square root)
V -125

A. 5iV-5
B. -5i
C. 5i V5
D. 5i
E. V125​

Answers

The answer is exactly c

Answer:

C

Step-by-step explanation:

i = [tex]\sqrt{-1}[/tex]

[tex]\sqrt{125}[/tex] is equal to 5[tex]\sqrt{5}[/tex]

Since it is [tex]\sqrt{-125}[/tex], then you must have i as well

5i[tex]\sqrt{5}[/tex]

please give a heart to give thanks :)

a crown would be nice too :)

A sequence is defined by the recursive formula f (n + 1) = f(n) – 2. If f(1) = 18, what is f(5)?

Answers

Step-by-step explanation:

f(2)=18-2=16

f(3)=16-2=14

f(4)=14-2=12

Then,

f(5)=12-2=10

the answer is 10

A rectangular page is to contain 36 square inches of print. The margins on each side are 1 inch. Find the dimensions of the page such that the least amount of paper is used.

Answers

Given :

A rectangular page is to contain 36 square inches of print.

The margins on each side are 1 inch.

To Find :

The dimensions of the page such that the least amount of paper is used.

Solution :

Let, length and breadth of paper are x and y respectively.

Area is given by :

Area = xy    ....1)

xy = 36 inch²

Now, it is given than the margins on each side is 1 inch.

So, area of paper is :

A = ( x + 2 )( y + 2 )

We want area to be minimum.

Putting value of x from 1 , we get :

A = ( 36/y + 2 )( y + 2 )

Now, differentiating above equation and equating with 0 :

[tex]3 - \dfrac{108}{y^2}=0\\\\y = \pm 6[/tex]

Now, we know dimension cannot be negative.

So, y = 6 and x = 6 .

Therefore, length and breadth are 6 and 6 inch respectively.

The length are breadth is x = 6 and y = 6 inch respectively.

Given;

Each rectangular page is to contain 36 square inches of print.

The margins on each side are 1 inch.

We have to find ;

The dimensions of the page such that the least amount of paper is used.

 Therefore,

Let, length and breadth of paper are x and y respectively.

Area is given by :

Area = xy    

xy = 36 inch²

Now, it is given than the margins on each side is 1 inch.

So, Area of paper is :  A = ( x + 2 )( y + 2 )

We want area to be minimum.

Putting value of x from 1 , we get :

A = ( [tex]\frac{36}{y}[/tex] + 2 )( y + 2 )

Now, Differentiating above equation and equating with 0 :

[tex]3 -\frac{108}{y^{2} } = 0[/tex]

[tex]\frac{3y^{2} - 108 }{y^{2} } = 0[/tex]

[tex]3y^{2} - 108 = 0 \\3y^{2} = 108\\y^{2} = \frac{108}{3} \\y^{2} = 36\\y = 6[/tex]

then;  xy = 36

        6x = 36

         x =[tex]\frac{36}{6}[/tex]  

         x = 6inches

Now, we know dimension cannot be negative.

So, y = 6 and x = 6 .

Therefore, length and breadth are 6 and 6 inch respectively.

For more information about the Area of dimension click the link given below.

https://brainly.in/question/12894735

Find 1000% of 99 pls help

Answers

Step-by-step explanation:

1000% of 99 = 10 * 99 = 990.

Algebra 1 help, please!! ............................................................................

Answers

Answer:

D

Step-by-step explanation:

(f-g)(x) = 3ˣ  + 10x - (5x - 3)

          = 3ˣ + 10x - 5x  + 3    {Combine like terms}  

          = 3ˣ + 5x + 3

Answer:

d

Step-by-step explanation:

Anyone please help me to do 4 ) f

Answers

i think your missing one which is G

A scientist is working with 15 meters of gold wire. How long is the wire in millimeters

Answers

The answer is 15000 millimeters! If you convert meters to MMs you will multiply by 1000! Hope this helps!

Please give brainliest❤️

The length of the gold wire that is 15 metres in millimetres is 15000 mm

How to convert the length of the wire?

The scientist is working with 15 metres of gold wire.

The wire is in metres.

Therefore, let's convert it millimetres.

1 m = 1000 mm

15 m = ?

cross multiply

length(mm) = 15 × 1000

length(mm) = 15000 mm

learn more on length here: https://brainly.com/question/308075

#SPJ2

Write an equation for the nth term of the arithmetic sequence.
2, 5, 8, 11, ...

Answers

Answer:

An equation for the nth term of the arithmetic sequence.

[tex]a_n=3n-1[/tex]

Step-by-step explanation:

Given the sequence

2,5,8,11,...

An arithmetic sequence has a constant difference 'd' and is defined by  

[tex]a_n=a_1+\left(n-1\right)d[/tex]

here

a₁ = 2

computing the differences of all the adjacent terms

d = 5-2 = 3, d = 8-5=3, d=11-8=3

Using the nth term formula

[tex]a_n=a_1+\left(n-1\right)d[/tex]

substituting a₁ = 2, d = 3

[tex]a_n=2+\left(n-1\right)3[/tex]

     [tex]=2+3n-3[/tex]

     [tex]=3n-1[/tex]

Thus, an equation for the nth term of the arithmetic sequence.

[tex]a_n=3n-1[/tex]

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