A book rests on a table. The force of gravity pulls down on the book with a force of 25 newtons. What prevents the book from accelerating downward at 9. 8 m/s2?.

Answer:

Step-by-step explanation:

x=(1-sqrt(13))/2=-1.303

x=(1+sqrt(13))/2=2.303

steps

 (2x2 -  2x) -  6  = 0

step 2 pull out like terms

2x2 - 2x - 6  =   2 • (x2 - x - 3)

step 2 continued

3.2     Factoring  x2 - x - 3

The first term is,  x2  its coefficient is  1 .

The middle term is,  -x  its coefficient is  -1 .

The last term, "the constant", is  -3

Step-1 : Multiply the coefficient of the first term by the constant   1 • -3 = -3

Step-2 : Find two factors of  -3  whose sum equals the coefficient of the middle term, which is   -1 .

     -3    +    1    =    -2

     -1    +    3    =    2

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

step 3

 2 • (x2 - x - 3)  = 0

Step 4

4.2      Find the Vertex of   y = x2-x-3

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,Ax2+Bx+C,the  x -coordinate of the vertex is given by  -B/(2A) . In our case the  x  coordinate is   0.5000  

Plugging into the parabola formula   0.5000  for  x  we can calculate the  y -coordinate :

 y = 1.0 * 0.50 * 0.50 - 1.0 * 0.50 - 3.0

or   y = -3.250

step 4

4.4     Solving    x2-x-3 = 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   =    -1

                     C   =   -3

Accordingly,  B2  -  4AC   =

                    1 - (-12) =

                    13

Applying the quadratic formula :

              1 ± √ 13

  x  =    —————

                   2

 √ 13   , rounded to 4 decimal digits, is   3.6056

So now we are looking at:

          x  =  ( 1 ±  3.606 ) / 2

Two real solutions:

x =(1+√13)/2= 2.303

or:

x =(1-√13)/2=-1.303

concluision

x =(1-√13)/2=-1.303

x =(1+√13)/2= 2.303

Answer:

the LCM is 6x^2(x-1)^2(x+2)

Answer:

720

Step-by-step explanation:

For the first wedge, you have 6 numbers to choose from .

For the second wedge , you have 5 numbers to choose from . 

For the 3rd wedge , you have 4 numbers to choose from . 

For the 4th wedge , you have 3 numbers to choose from . 

For the 5th wedge , you have 2 numbers to choose from . 

For the 6th wedge , you have 1 number to choose from . 

Conclusion: this numbering can be done in:

6×5×4×3×2×1 = 720

Note :

Generally ,we write 6×5×4×3×2×1 as 6! and we read it 6 factorial.

Answer:

5.69

Step-by-step explanation:

22.76/4 = 5.69

Answer:

4√13 or 14.422

Step-by-step explanation:

we can use the pythag theorem to figure out the length of a. Since a is the hypotenuse it would be 12 squared + 8 squared = a squared

144+64=208

the square root of 208 is 4√13 or 14.422

The probability that a student chosen at random will play an instrument other than drums is 31/36.

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

The formula of probability can be defined as the ratio of a number of favorable outcomes to the total number of outcomes.

P(E) = Number of favorable outcomes / total number of outcomes

Total number of elements of sample space is 36.

Based on these results, express the probability that a student chosen at random will play an instrument other than drums as;

31/36

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Answer:

4ln 2+ln 5

Step-by-step explanation:

An angle is formed from the intersection of two lines. Types of angles are acute, obtuse and right angled.

An equation is an expression that shows the relationship  between two or more numbers and variables.

An angle is formed from the intersection of two lines. Types of angles are acute, obtuse and right angled.

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Answer:

A. -180

Step-by-step explanation:

Edge2022

Answer:

Part A: total pizza cost = 2.50s + 2.25t + 18

Part B: 30 dollars

Step-by-step explanation:

I hope this helped! If it did, please click "Thanks"!

Answer:

Part A: 18 + 2.25t + 2.50s

Part B: $30

Step-by-step explanation:

Let t= each additional topping

Let s=each side

First we add the cost of one pizza ($18)

Then we add each additional topping (t) multiplied by its cost (2.25 dollars)

Finally we add each side (s) multplied (2.50 dollars)

Part B:

Plug in 2 for t and 3 for s into the expression from earlier and simplify:

Expression: 18 + 2.25(2) + 2.50(3)

=18+ 4.50 + 7.50

=30

And there you have it- the total cost is $30.

Hope this helps and good luck in your studies :)

The given information is,

→ a = -8

→ b = -7

→ c = 6

Let's verify the problem,

→ (a+b) + c = a+ (b+c)

→ (-8 - 7) + 6 = -8 + (-7 + 6)

→ -15 + 6 = -8 - 1

→ -9 = -9

→ [ LHS = RHS ]

Hence, it is equal and verified.

Answer:

cos(θ) = 3/4

Step-by-step explanation:

Since cos=adj/hyp, the Hypotenous is 24, and the adjacent is 18. We write cos(θ)=18/24, which can be simplified to cos(θ)=3/4.

Answer:

The chances of landing on red are 1 in 4, or one fourth. This problem asked us to find some probabilities involving a spinner

Answer:

A = Z

B = X

C = Y

AB = ZX

AC = ZY

BC = XY

CAB = YZX

Step-by-step explanation:

Flip the second triangle so the longest line is on the bottom

after you do that it looks exactly like the other one

Answer:

Step-by-step explanation:

    diameter = 12 cm

                  r =  12 ÷ 2 = 6 cm

                 h = 6 cm

      [tex]\sf \boxed{\text{\bf Volume of cone = $\dfrac{1}{3} \pi r^2h$ }}[/tex]

                                    [tex]\sf = \dfrac{1}{3}*3.14*6*6*6\\\\ = 226.08 \ cm^3[/tex]

To find the surface area, we need to find the slant 'l'

       [tex]\sf l = \sqrt{h^2+r^2}\\\\ =\sqrt{6^2+6^2}\\\\ = \sqrt{36+36}\\\\ =\sqrt{72}\\\\= 8.49 \ cm[/tex]

       [tex]\sf \boxed{\text{\bf Total surface area of cone = $\pi r(r+l)$}}[/tex]

                                                         = 3.14 * 6 * (6 + 8.49)

                                                        = 3.14 * 6 * 14.49

                                                        = 273 cm²

Answer:

b. more money

Step-by-step explanation:

Randy's original position lets him make:

50*500 = $25,000

The new position will let him make:

$27,500

Therefore,

original position < new position = $25,000 < $27,500

Answer: The number of miles increases as time increases.

The number of hours causes a change in the number of miles ridden.

The variable h is the independent variable.

The variable m is the dependent variable.

Step-by-step explanation:

Answer: (3,3)

Step-by-step explanation:

Answer:

No.

Step-by-step explanation:

To find the y value, one must replace x value, meaning that it's a multi step problem and it's not direct because y=exact value is not given

Answer:

An exponential function is a Mathematical function in the form f (x) = ax, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.

The expression (-0.3)⁴ is an exponential expression and the value of the expression is 0.0081

The expression is given as:

(-0.3)⁴

Expand the expression

(-0.3)⁴ = (-0.3) * (-0.3) * (-0.3) * (-0.3)

Evaluate the product

(-0.3)⁴ = 0.0081

Hence, the value of the expression is 0.0081

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Answer:B

count 2 and ~1/4 back and you get b

Answer:

r = 3.95

Explanation:

A = [tex]\pi {r}^{2} [/tex]

3.14r² = 15.6 (3.14)

Divide by 3.14

r² = 15.6

r = [tex] \sqrt{15.6} [/tex]

r ≈ 3.95

Answer:

C) 312 cm^2

Step-by-step explanation:

To find the total area of the composite figure, you must sum the individual components of the figure.

First, we find the area of the rectange, which is A = l x w = 16 x 12 = 192

Second, we find the area of the first triangle which is also equal to the area of the second triangle, so instead of finding the base times height and dividing by 2, we will simply find the area of base times height and it will work for both trianges.

A = b x h x 1/2 x 2 = 10 x 12 = 120

120 + 192 = 312 cm^2

Answer: the answer would be 8.94

Step-by-step explanation:

I hope this helps! :)

Im  sorry if it turns out to be wrong!

Have a good rest of your day!

If the cost of the party supplies was $316. Then the amount of money spent by each of them is $158.

Division means the separation of something into different parts, sharing of something among different people, places, etc.

Keri and Samantha are equally splitting the cost of party supplies for their mom's surprise birthday party.

The total cost of the party supplies was $316.

Then the money spent by each of them will be

[tex]\rightarrow \dfrac{316}{2}\\\\\rightarrow 158[/tex]

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Answer: The median is 6

Step-by-step explanation:

Answer:

5x + 3x = 28x
8x = 28x
x must be 0

Answer:

8 pints

Step-by-step explanation:

A pint is 16 ounces = 2 cups

8 pints is then 16 cups

Answer:

[tex]y = x^2 - 8x + 38[/tex]

Step-by-step explanation:

Hello!

The standard form of a quadratic is [tex]ax^2 + bx + c[/tex].

To convert the vertex form to standard form, we have to expand the parenthesis and add the constant.

Convert:

The standard form is [tex]y = x^2 - 8x + 38[/tex]