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

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.

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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

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

Answer:

80 cents per cd

Step-by-step explanation:

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

Answer:

X=2y+1

X-1/2=y

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:

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]

Answer:

This is the correct solution for your question

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

Answer:

1

Step-by-step explanation:

1

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:

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:

Answer:

i do believe that its y<x-3

Step-by-step explanation:

Step-by-step explanation:

1000% of 99 = 10 * 99 = 990.

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!

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 :)

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

Answer:

5

Step-by-step explanation:

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.

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

computing the differences of all the adjacent terms

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]

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

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

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

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

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.

Answer:

42 minutes

Step-by-step explanation:

Answer:

$31.50

Step-by-step explanation:

the decrease will be $13.50

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]

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