A duck dives underwater and its path is described by the quadratic function y = 2x^2 - 4x, where y represents the position of the duck in meters and x represents the time in seconds. How long was the duck underwater?​

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎ ‎[tex]\bigstar\boxed{\bf\purple{\leadsto b=\dfrac{a+4}{4}}}[/tex]

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➠ On solving the given equation for b :

[tex]\rm{\longrightarrow 6b+2a-4=2b+3a}[/tex]

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎

‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎[tex]\rm{\longrightarrow 6b-2b=3a-2a+4}[/tex]

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎

‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎[tex]\rm{\longrightarrow 4b=a+4}[/tex]

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎

‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎[tex]\rm{\longrightarrow b=\dfrac{a+4}{4}}[/tex]

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎

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Given that :

To Find :

Solution :

[tex]\qquad \sf \: { \dashrightarrow 6b + 2a - 4 = 2b + 3a }[/tex]

[tex]\qquad \sf \: { \dashrightarrow 6b - 2b - 4 = 3a - 2a }[/tex]

[tex]\qquad \sf \: { \dashrightarrow 4b - 4 = a }[/tex]

[tex]\qquad \sf \: { \dashrightarrow 4b = a + 4}[/tex]

[tex]\qquad \bf \: { \dashrightarrow b = \dfrac{a + 4}{4} }[/tex]

Answer: jo mama medicine

Step-by-step explanation: 1st one 2nd two!

Answer: y = -1.5x - 1.5 or y = -3x/2 -3/2

Step-by-step explanation:

Basically you need to know first what slope intercept form is:

y = mx + b

b is the y intercept and m is the slope

so first you have the equation 3x + 2y = -3

you will first subtract 3x from both sides because if you do something to one side of the equal sign, you have to do it to the other side:

3x + 2y - 3x = -3 - 3x

now you have 2y = -3x -3

Then you are going to divide both sides by 2:

2y/2 = -3x/2 -3/2

That gets you to

y = -3x/2 -3/2

or in fraction form, it is

y = -1.5x - 1.5

Answer:

Step-by-step explanation:

The slope intercept form uses y=mx +b where m is the slope. To convert the equation into slope intercept form you just need to isolate y.

3x+2y=-3

subtract 3x from both sides

2y= -3x-3

divide everything by 2 to isolate y

[tex]y=-\frac{3}{2} x-\frac{3}{2}[/tex]

Answer:

1.58113883 i

Step-by-step explanation:

√-2.5 is error

1.58113883 i

i the square root of negative one.

Any number times itself is a positive number (or zero), so you can't ever get to a negative number by squaring. Since square roots undo squaring, negative numbers can't have square roots.

Answer:

[tex]1.58\ i[/tex]

Step-by-step explanation:

Step 1:  Determine the square root of -2.5

The [tex]\sqrt{-1}[/tex] is equal to i so we can say that [tex]\sqrt{(-1)^2}[/tex] is equal to [tex]\sqrt{i^2}[/tex] which is then equal to [tex]i[/tex].  This means that we have [tex]i\sqrt{2.5}[/tex].

We can then take the square root of 2.5 which is rounded to [tex]1.58\ i[/tex]

Answer:  [tex]1.58\ i[/tex]

Answer:

66.5

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

4 or lower means the number stays the same

Answer:

x = 12

Step-by-step explanation:

Answer:

B. 12w + 62 = 242 is the answer  Happy to Help :)

Step-by-step explanation:

Answer:

16m-16

Step-by-step explanation:

Im not sure that’s the correct answer

Answer:

what is the question?

210 people were asked.

Answer:

Step-by-step explanation:

Let H be the number of harcover, and S the number of softcover books.

We know that:

H+S=36

and $8*(H) + $2*(S) = $144

Rearrange the first: H = 36 - S

Use this definition of H in the second equestion:

$8*(H) + $2*(S) = $144

$8*(36-S) + $2*(S) = $144

$288 - 8S + 2S = $144

-6S = -144

S = 24

This means H = 36 - S is:

H = 36 - 24

H = 12

"You" purchased 24 softcover and 12 hardcover books.

Check the results: 24*2 + 12*8 = 48 + 96 = $144 It

works.

    The question gives us two points,  (-1, -1) and (98, 87), from which we can find the slope and later the equation of the line.

Finding the Slope  

The slope of the line (m)   = (y₂ - y₁) ÷ (x₂ - x₁)  

                                            = (87 - (-1)) ÷ (98 - (-1))        

                                            =  (88) ÷ (99)    

                                            =   ⁸/₉  

Checking my answer visually:  

Finding the Equation

We can now use the point-slope form (y - y₁) = m(x - x₁)) to write the equation for this line. Once we have that equation, we can graph it to see if it passes through the two points. If it does, then we calculated the slope correctly.

                               ⇒  y - (-1) = ⁸/₉ (x - (-1)              [using the point (-1, -1)]

                                      y + 1  = ⁸/₉ (x + 1)  

To test my answer, I have included a Desmos Graph that I graphed using the information provided in the question and my answer.  

Answer:

33

Step-by-step explanation:

33 appears most.

Answer:

the answer is C

Step-by-step explanation:

yeah-ya.... right?

Answer:

6x^6..........................

Answer:

9.  A: 3:00 A.M.

10. C: 6.535 kg

11. D: Php 1,600.00

12. D: 217,500

13. A: P450.00

14. A: 7  

15. D: 5.48 x 10^4

The equation of the line passing through the points (0,0) and (2, -3) is y = (-3/2)x. Option D.

To find the equation of the line passing through the points (0,0) and (2, -3), we can use the point-slope form of a linear equation: y - y1 = m(x - x1), where (x1, y1) are the coordinates of one point on the line, and m is the slope of the line.

Given the points (0,0) and (2, -3), we can calculate the slope as follows:

slope (m) = (change in y) / (change in x)

= (-3 - 0) / (2 - 0)

= -3/2

Now that we have the slope, we can substitute one of the given points and the slope into the point-slope form to find the equation of the line. Let's use the point (0,0):

y - y1 = m(x - x1)

y - 0 = (-3/2)(x - 0)

y = (-3/2)x Option D is correct.

For more such question on equation. visit :

https://brainly.com/question/22688504

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Answer: A) √35

Step-by-step explanation:

Answer:

(2^2)3 = 2^6

(2^3)2 = 2^6

Step-by-step explanation:

There are various exponent rules. The problems that you were assigned must follow the power of a power rule:

(x^a)^b = x^a*b

Exponents must be multiplied according to this rule. Hope this helps.

Answer:

A. 17

Step-by-step explanation:

Answer:

256

Step-by-step explanation:

Answer:

x=10

x=-4

Step-by-step explanation:

Quadratic Equation:  (x – 3)^2 = 4

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    (x-3)^2-(49)=0

Step 1:

valuate :  (x-3)²   =    x²-6x+9

Factoring x²-6x-40  

The first term is, x²its coefficient is  1 .

The middle term is,  -6x  its coefficient is  -6 .

The last term, "the constant", is  -40  

Step-1 : Multiply the coefficient of the first term by the constant   1 • -40 = -40  

Step-2 : Find two factors of  -40  whose sum equals the coefficient of the middle term, which is   -6 .

     -40    +    1    =    -39  

     -20    +    2    =    -18  

     -10    +    4    =    -6    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -10  and  4

x²- 10x + 4x - 40

Step-4 : Add up the first 2 terms, pulling out like factors :

                   x • (x-10)

             Add up the last 2 terms, pulling out common factors :

                   4 • (x-10)

Step-5 : Add up the four terms of step 4 :

                   (x+4)  •  (x-10)

            Which is the desired factorization

Equation at the end of step

1

:

 (x + 4) • (x - 10)  = 0  

STEP

2 :

Theory - Roots of a product

A product of several terms equals zero.  

When a product of two or more terms equals zero, then at least one of the terms must be zero.  

We shall now solve each term = 0 separately  

In other words, we are going to solve as many equations as there are terms in the product  

Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation:

Solve  :    x+4 = 0  

Subtract  4  from both sides of the equation :  

                     x = -4

Solving a Single Variable Equation:

Solve  :    x-10 = 0  

Add  10  to both sides of the equation :  

                     x = 10

Supplement : Solving Quadratic Equation Directly

Solving x²-6x-40  = 0   directly  

Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula

Parabola, Finding the Vertex:

Find the Vertex of   y =x²-6x-40

For any parabola,Ax²+Bx+C,the  x -coordinate of the vertex is given by  -B/(2A) . In our case the  x  coordinate is   3.0000  

Plugging into the parabola formula   3.0000  for  x  we can calculate the  y -coordinate :  

 y = 1.0 * 3.00 * 3.00 - 6.0 * 3.00 - 40.0

or   y = -49.000

Parabola, Graphing Vertex and X-Intercepts :

Root plot for :  y = x²-6x-40

Axis of Symmetry (dashed)  {x}={ 3.00}  

Vertex at  {x,y} = { 3.00,-49.00}  

x -Intercepts (Roots) :

Root 1 at  {x,y} = {-4.00, 0.00}  

Root 2 at  {x,y} = {10.00, 0.00}

Solve Quadratic Equation by Completing The Square

Solving   x²-6x-40 = 0 by Completing The Square .

Add  40  to both side of the equation :

  x2-6x = 40

Now the clever bit: Take the coefficient of  x , which is  6 , divide by two, giving  3 , and finally square it giving  9  

Add  9  to both sides of the equation :

 On the right hand side we have :

  40  +  9    or,  (40/1)+(9/1)  

 The common denominator of the two fractions is  1   Adding  (40/1)+(9/1)  gives  49/1  

 So adding to both sides we finally get :

  x2-6x+9 = 49

Adding  9  has completed the left hand side into a perfect square :

  x2-6x+9  =

  (x-3) • (x-3)  =

 (x-3)2

Things which are equal to the same thing are also equal to one another. Since

  x2-6x+9 = 49 and

  x2-6x+9 = (x-3)2

then, according to the law of transitivity,

  (x-3)2 = 49

We'll refer to this Equation as  Eq. #3.2.1  

The Square Root Principle says that When two things are equal, their square roots are equal.

Note that the square root of

  (x-3)2   is

  (x-3)2/2 =

 (x-3)1 =

  x-3

Now, applying the Square Root Principle to  Eq. #3.2.1  we get:

  x-3 = √ 49

Add  3  to both sides to obtain:

  x = 3 + √ 49

Since a square root has two values, one positive and the other negative

  x2 - 6x - 40 = 0

  has two solutions:

 x = 3 + √ 49

  or

 x = 3 - √ 49

Solve Quadratic Equation using the Quadratic Formula

3.3     Solving    x2-6x-40 = 0 by the Quadratic Formula .

According to the Quadratic Formula,  x  , the solution for   Ax2+Bx+C  = 0  , where  A, B  and  C  are numbers, often called coefficients, is given by :

           - B  ±  √ B2-4AC

 x =   ————————

                     2A

 In our case,  A   =     1

                     B   =    -6

                     C   =  -40

Accordingly,  B2  -  4AC   =

                    36 - (-160) =

                    196

Applying the quadratic formula :

              6 ± √ 196

  x  =    —————

                   2

Can  √ 196 be simplified ?

Yes!   The prime factorization of  196   is

  2•2•7•7  

To be able to remove something from under the radical, there have to be  2  instances of it (because we are taking a square i.e. second root).

√ 196   =  √ 2•2•7•7   =2•7•√ 1   =

               ±  14 • √ 1   =

               ±  14

So now we are looking at:

          x  =  ( 6 ± 14) / 2

Two real solutions:

x =(6+√196)/2=3+7= 10.000

or:

x =(6-√196)/2=3-7= -4.000

Two solutions were found :

x = 10

x= -4

Answer:

The first 3 student spend $8 per person

Step-by-step explanation:

1. $24=3x (divide both sides by 3)

2. $8=x

Hopefully I understood the question correctly

Answer:

False

Step-by-step explanation:

a>b

Let c> 0 then ac>bc because we are multiplying by a positive number

if c<0  then ac < bc because we are multiplying by a negative number we have to flip the inequality symbol

Since we do not know the value of c, we have to go with false

Answer:

Check explanation

Step-by-step explanation:

Answer:

390

Step-by-step explanation:

5 or more, means round up.

So 385 ( 5 or above ) - round to the nearest tenths place...

= 390

Answer:

390

Step-by-step explanation:

The number in the tenth place is 80 so you look on the right, the number is 5. If the number is 5 or above, that means you go up. SO it's 390

Answer:

9.30232558

Step-by-step explanation:

Set up an equation to solve for it. For instance, the following:

[tex]10.75*x=100[/tex]

[tex]x=9.30232558[/tex]