Delia had several packages of jellybeans. She opened them all and had 684 jellybeans. If each package has 76 jellybeans, how many packages of jellybeans did she open?

Answer:

2 solutions:

1) m =(4-√52)/2=2-√ 13 = -1.606

2) m =(4+√52)/2=2+√ 13 = 5.606

Step-by-step explanation

The first term is,  m2  its coefficient is  1 .

The middle term is,  -4m  its coefficient is  -4 .

The last term, "the constant", is  -9

Step-1 : Multiply the coefficient of the first term by the constant   1 • -9 = -9

Step-2 : Find two factors of  -9  whose sum equals the coefficient of the middle term, which is   -4 .

     -9    +    1    =    -8

     -3    +    3    =    0

     -1    +    9    =    8

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Equation at the end of step 1:

 m2 - 4m - 9  = 0  

STEP 2:

Parabola, Finding the Vertex:

2.1      Find the Vertex of   y = m2-4m-9

Parabolas have a highest or a lowest point called the Vertex .   Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) .   We know this even before plotting  "y"  because the coefficient of the first term, 1 , is positive (greater than zero).

Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two  x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.

Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.

For any parabola,Am2+Bm+C,the  m -coordinate of the vertex is given by  -B/(2A) . In our case the  m  coordinate is   2.0000  

Plugging into the parabola formula   2.0000  for  m  we can calculate the  y -coordinate :

 y = 1.0 * 2.00 * 2.00 - 4.0 * 2.00 - 9.0

or   y = -13.000

Parabola, Graphing Vertex and X-Intercepts :

Root plot for :  y = m2-4m-9

Axis of Symmetry (dashed)  {m}={ 2.00}

Vertex at  {m,y} = { 2.00,-13.00}

m -Intercepts (Roots) :

Root 1 at  {m,y} = {-1.61, 0.00}

Root 2 at  {m,y} = { 5.61, 0.00}

Add  9  to both side of the equation :

  m2-4m = 9

Now the clever bit: Take the coefficient of  m , which is  4 , divide by two, giving  2 , and finally square it giving  4

Add  4  to both sides of the equation :

 On the right hand side we have :

  9  +  4    or,  (9/1)+(4/1)

 The common denominator of the two fractions is  1   Adding  (9/1)+(4/1)  gives  13/1

 So adding to both sides we finally get :

  m2-4m+4 = 13

Adding  4  has completed the left hand side into a perfect square :

  m2-4m+4  =

  (m-2) • (m-2)  =

 (m-2)2

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

  m2-4m+4 = 13 and

  m2-4m+4 = (m-2)2

then, according to the law of transitivity,

  (m-2)2 = 13

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

Note that the square root of

  (m-2)2   is

  (m-2)2/2 =

 (m-2)1 =

  m-2

Now, applying the Square Root Principle to  Eq. #2.2.1  we get:

  m-2 = √ 13

Add  2  to both sides to obtain:

  m = 2 + √ 13

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

  m2 - 4m - 9 = 0

  has two solutions:

 m = 2 + √ 13

  or

 m = 2 - √ 13

Solving    m2-4m-9 = 0 by the Quadratic Formula .

According to the Quadratic Formula,  m  , the solution for   Am2+Bm+C  = 0  , where  A, B  and  C  are numbers, often called coefficients, is given by :

           - B  ±  √ B2-4AC

 m =   ————————

                     2A

 In our case,  A   =     1

                     B   =    -4

                     C   =   -9

Accordingly,  B2  -  4AC   =

                    16 - (-36) =

                    52

Applying the quadratic formula :

              4 ± √ 52

  m  =    —————

                   2

Can  √ 52 be simplified ?

Yes!   The prime factorization of  52   is

  2•2•13

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).

√ 52   =  √ 2•2•13   =

               ±  2 • √ 13

 √ 13   , rounded to 4 decimal digits, is   3.6056

So now we are looking at:

          m  =  ( 4 ± 2 •  3.606 ) / 2

Two real solutions:

m =(4+√52)/2=2+√ 13 = 5.606

or:

m =(4-√52)/2=2-√ 13 = -1.606

Answer: Because the domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x-axis. The range is the set of possible output values, which are shown on the y-axis.

Answer:

Leaf is 8

Pumpkin is 0

Coffee is 16

Step-by-step explanation:

let

width = w

length = 4w + 11

2(length) + 2(width) = perimeter

2(4w + 11) + 2(w) = 162

8w + 22 + 2w = 162

10w + 22 = 162

10w = 140

w = 14 cm (WIDTH)

length = 4w + 11

length = 4(14) + 11

length = 56 + 11

LENGTH = 67 cm

The length is 4(14)+ 11 = 67 cm and width is 14 cm.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values. We frequently observe constant change in specific values in our day-to-day situations.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

Perimeter of rectangle = 162 cm

let the width be x .

then, the length is 4x+ 11

Thus, Perimeter of rectangle= 2(l + w)

162 = 2( 4x + 11 + x)

162 = 2( 5x +11)

81 = 5x+ 11

5x= 70

x= 14

Hence, the length is 4(14)+ 11 = 67 cm and width is 14 cm.

Learn more about algebra here:

https://brainly.com/question/24875240

#SPJ5

Answer:

x=12

Step-by-step:

Square root both sides to get

x-3=9

Then take 3 to the other side

x=9+3

x=12

Answer:

B 66x+206=636

It maybe C since the cube is labeled 1-6 and the coin can land on either heads or tails.

Answer:

240

Step-by-step explanation:

2*8*3*5

Answer:

160

Step-by-step explanation:

a P e X

Answer: 1.8 cans

Step-by-step explanation:

Answer:

1.85 cans of dog food.

Step-by-step explanation:

You need to divide 13 cans by 7 dogs.

Answer:

2.0356 × 1016

Step-by-step explanation:

Answer:

9.875

Step-by-step explanation:

Answer:

9.875

Step-by-step explanation:

get a calculator

Answer:

0.4 mL

Step-by-step explanation:

I was able to do this in my head, but...

If you just take the fraction of 2000 units/5000 units/mL, then the units will cancel out and you're essentially left with 2000/5000 mL. 2000/5000 can be reduced to 2/5, and as a decimal, 2/5 comes out to 0.4 or 40%.

So, 0.4 mL (about half) would be administered to the patient.

Answer:

Step-by-step explanation:

t+t+10+t+20=180

3t+30=180

3t=180-30=150

t=150/3=50

t+20=50+20=70

exterior angle=180-70=110°

Answer:

24y-48

btw just downloaded a app called YHomework it shows the steps

Answer:

find ity yourself          -_______________-

Step-by-step explanation:

Answer:

13 so yeah it correect

Answer:

1)(6,4)

11+1=12/2 =6

6+2=8/2=4

[tex]7p + 6q - 2p + q \\ = (7p - 2p) + (6q + q) \\ = 5p + 7q[/tex]

Answer:

5p+7q is the answer

Step-by-step explanation:

Answer:

thank you

Step-by-step explanation:

thanks for the pts i need them sowwy

Answer:

Step-by-step explanation:

perimeter of the given trapezoid = 7 + 4 + 4 + 5

                                                      = 20 units

                                             (see image below)

Answer:

0.002704

Step-by-step explanation:

You just multiply 0.052 by itself

then divide the answer by 0.052

Answer:

We have 3 boys and 2 girls. This gives a total count of 5. So we need to see how many lots of 5 will fit into 25. 5 lots of 5 gives 25. So we have 5 lots of the ratio

Answer:

55

Step-by-step explanation:530 would be rounded to 550 and 9 would be rounded to 10

550 divided by 10 is 55

Pls give me brainliest if this helps

Answer: B I believe

Step-by-step explanation:

Answer:

Isosceles becuase there are 2 equal sides but 1 side is different.