Identify the center and radius of each. Photo attached.

Answer:

x =(7-√217)/2=-3.865

x =(7+√217)/2=10.865 mark brainliest please

Step-by-step explanation:

   Factoring  x2-7x-42

The first term is,  x2  its coefficient is  1 .

The middle term is,  -7x  its coefficient is  -7 .

The last term, "the constant", is  -42

Step-1 : Multiply the coefficient of the first term by the constant   1 • -42 = -42

Step-2 : Find two factors of  -42  whose sum equals the coefficient of the middle term, which is   -7 .

     -42    +    1    =    -41

     -21    +    2    =    -19

     -14    +    3    =    -11

     -7    +    6    =    -1

     -6    +    7    =    1

     -3    +    14    =    11

     -2    +    21    =    19

     -1    +    42    =    41

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Equation at the end of step  1  :

 x2 - 7x - 42  = 0

Step  2  :

Parabola, Finding the Vertex :

2.1      Find the Vertex of   y = x2-7x-42

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   3.5000  

Plugging into the parabola formula   3.5000  for  x  we can calculate the  y -coordinate :

 y = 1.0 * 3.50 * 3.50 - 7.0 * 3.50 - 42.0

or   y = -54.250

Parabola, Graphing Vertex and X-Intercepts :

Root plot for :  y = x2-7x-42

Axis of Symmetry (dashed)  {x}={ 3.50}

Vertex at  {x,y} = { 3.50,-54.25}

x -Intercepts (Roots) :

Root 1 at  {x,y} = {-3.87, 0.00}

Root 2 at  {x,y} = {10.87, 0.00}

Solve Quadratic Equation by Completing The Square

2.2     Solving   x2-7x-42 = 0 by Completing The Square .

Add  42  to both side of the equation :

  x2-7x = 42

Now the clever bit: Take the coefficient of  x , which is  7 , divide by two, giving  7/2 , and finally square it giving  49/4

Add  49/4  to both sides of the equation :

 On the right hand side we have :

  42  +  49/4    or,  (42/1)+(49/4)

 The common denominator of the two fractions is  4   Adding  (168/4)+(49/4)  gives  217/4

 So adding to both sides we finally get :

  x2-7x+(49/4) = 217/4

Adding  49/4  has completed the left hand side into a perfect square :

  x2-7x+(49/4)  =

  (x-(7/2)) • (x-(7/2))  =

 (x-(7/2))2

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

  x2-7x+(49/4) = 217/4 and

  x2-7x+(49/4) = (x-(7/2))2

then, according to the law of transitivity,

  (x-(7/2))2 = 217/4

We'll refer to this Equation as  Eq. #2.2.1  

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

Note that the square root of

  (x-(7/2))2   is

  (x-(7/2))2/2 =

 (x-(7/2))1 =

  x-(7/2)

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

  x-(7/2) = √ 217/4

Add  7/2  to both sides to obtain:

  x = 7/2 + √ 217/4

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

  x2 - 7x - 42 = 0

  has two solutions:

 x = 7/2 + √ 217/4

  or

 x = 7/2 - √ 217/4

Note that  √ 217/4 can be written as

 √ 217  / √ 4   which is √ 217  / 2

Solve Quadratic Equation using the Quadratic Formula

2.3     Solving    x2-7x-42 = 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   =    -7

                     C   =  -42

Accordingly,  B2  -  4AC   =

                    49 - (-168) =

                    217

Applying the quadratic formula :

              7 ± √ 217

  x  =    —————

                   2

 √ 217   , rounded to 4 decimal digits, is  14.7309

So now we are looking at:

          x  =  ( 7 ±  14.731 ) / 2

Two real solutions:

x =(7+√217)/2=10.865

or:

x =(7-√217)/2=-3.865

Answer:

x^2 - 7x - 42

x^2 - x (21 - 14 ) - 42

x^2 - 21x + 14x -42

7x ( x - 3) + 14 ( x- 3)

(x -3) (7x + 14)

hope this helps you

Answer:

Step-by-step explanation:

18 degrees

Answer:

13

Step-by-step explanation:

use Pythagorean

it is usually, 5, 12, 13

Answer:

You have three card : 3, 4, 5 and 6.

You first pick one card randomly, the probability of picking a 3 is:

P = 1/4

You then pick a second card without putting the first card back, the probability of picking a 3 is:

P = 1/3

=> The probability of picking a 3 and then picking a 3:

P = (1/4) x (1/3) = 1/12

Hope this helps!

:)

Answer:

A

Step-by-step explanation:

Because it's subtracting 2 hours every day, the slope is -2. Also because it's 30 hours, it's 30. Therefore: A.) y=-2x+30 is the answer.

Hopes this Helps!

Answer:

8:24

Step-by-step explanation:

dont ask me

Answer:

x=-60/24 or -5/2

Step-by-step explanation:

u have to find X

2/4x - 1/2 = 1/3 + 5/6x

subtract 2/4x from both sides

to do that u need to have common denominator

2/4= 6/12

5/6=10/12

-1/2=1/3+4/12x

subtract 1/3 on both sides and u need common denominator

-1/2=-3/6

1/3=2/6

-5/6=4/12x

multiply 12/4 on both sides

x=-60/24

Answer:

x=-5/2

Step-by-step explanation:

2/4x-1/2=1/3+5/6x

-5/6x           -5/6x

2/4x-5/6x-1/2 =1/3

+1/2                  +1/2

6/12x-10/12x=2/6+3/6

-4/12x=5/6

x=5/6:(-4/12)=5/6*(-12/4)=-5/2

x=-5/2

Answer:

u = -4w+9

Step-by-step explanation:

u - 5 = -4(w-1)

Distribute

u - 5 = -4w +4

Add 5 to each side

u -5+5 = -4w +4+5

u = -4w+9

Answer:

Slope (m) =0

Slope (m) =  

ΔY

ΔX

= 0

θ =  

arctan( ΔY )

ΔX

= 0°

ΔX = 3 – 13 = -10

ΔY = -2 – -2 = 0

Distance (d) = √ΔX2 + ΔY2 = √100 = 10

Answer:

18-6×10=-42

Step-by-step explanation:

all i did was put it in my calculator

Answer:

The answer is 2,142.

Step-by-step explanation:

Mark me brialianist of its right

Answer:

Cylinder B has a greater volume

Step-by-step explanation:

Volume of a cylinder[tex]=\pi r^2h[/tex]

Cylinder A

h=5m, r=3m

Volume

[tex]=3.14 *3^2*5\\=141.3m^3[/tex]

Cylinder B

h=3m, r=5m

Volume

[tex]=3.14 *5^2*3\\=235.5m^3[/tex]

Cylinder B has a greater volume.

Answer:

B. to show the general tendency of the points in a scatterplot

Step-by-step explanation:

Answer:

The answer is 364. There are 364 ways of choosing a recorder, a facilitator and a questioner froma club containing 14 members.

This is a Combination problem.  

Combination is a branch of mathematics that deals with the problem relating to the number of iterations which allows one to select a sample of elements which we can term "r" from a collection or a group of distinct objects which we can name "n". The rules here are that replacements are not allowed and sample elements may be chosen in any order.

Step-by-step explanation:

Step I

The formula is given as

[tex]C (n,r) = \frac{n}{r} = \frac{n!}{(r!(n-r)!)}[/tex]

n (objects) = 14

r (sample) = 3

Step 2 - Insert Figures

C (14, 3) = [tex](\frac{14}{3})[/tex] = [tex]\frac{14!}{(3!(14-3)!)}[/tex]

= [tex]\frac{87178291200}{(6 X 39916800)}[/tex]

= [tex]\frac{87178291200}{239500800}[/tex]

= 364

Step 3

The total number of ways a recorder, a facilitator and a questioner can be chosen in a club containing 14 members therefore is 364.

Cheers!

Answer:

d= 5.2

[][][]-[][][]

P = √5.2 ^3

P = √5.2 × 5.2 × 5.2

P = √140.608 (plug into calculator)

P = 11.857824421

P = 11.86

The orbital period of Jupiter is 11.86 Earth years.

Answer:

C many solutions

Answer: 458

Simplify

8³=8×8×8

Multiply

8×8×8=512

10×5=50

Subtract

512-50=462

462-4=458

Answer:

458

Step-by-step explanation:

8×8×8=512

10×5=50

512- 50 = 462

462-4= 458

Answer:

5.83

Step-by-step explanation:

[tex]c=\sqrt{a^2+b^2\\} =\sqrt{3^2+5^2}\\=5.83[/tex]

Answer:

5.83

Step-by-step explanation:

rs²=3²+5²

rs²=9+25

rs²=34

rs=5.83

Answer:

1/2

Step-by-step explanation:

When you find the sine of an angle, it is the opposite side / hypotenuse. This means that the hypotenuse of this triangle is 2 and the side opposite to 60° is √3. This means that the side adjacent to 60° is 1 (Pythagorean Theorem). When you find the cosine of an angle, it is the adjacent side / hypotenuse, which in this case will be 1 / 2. Hope this helps!

Answer:

1/2.

Step-by-step explanation:

Sine = opposite side / hypotenuse.

The side opposite 60 degrees has length√3 and the hypotenuse = 2.

By Pythagoras the side adjacent to the angle 60 = √( 2^2 - 3)

= 1 unit.

So cos 60 = adjacent / hypotenuse = 1/2.

Answer:

5/16 and 3/8 are two

Step-by-step explanation:

idk a third

Answer:

2989.12

Step-by-step explanation:

238.00+232.50+54.88+236.00= 760.88

3750-760.88=2989.12

Answer: The price of the stock yesterday was $78.59

Step-by-step explanation:

p - 6.28=72.31

   +6.28   + 6.28

p= 78.59

Answer:

78.59$

Step-by-step explanation:

p-6.28=72.31

p=72.31+6.28

p=78.59$

Answer:

to find volume you multiply length x width x height

Step-by-step explanation:

5 x 3.5 x 6= 105

Answer:

5 x 3.5 x 6= 105

Step-by-step explanation:

PLZZZ give me brainliest

Answer:

this answer is attached to the picture

Radical function or values are values inside the square root. This shows that the cube root of the given value is 3

Radical function or values are values inside the square root. For instance;

√a is a radical function.

According to the law of indices

a^1/3 = ∛a

Given the expression

27^1/3 = ∛27

∛27 = 3

This shows that the cube root of the given value is 3

Learn more on radical function here:https://brainly.com/question/13430746

[tex]\text{You would use the distributive property to get your answer} \\\\\text{This means that you would distribute the 5 to the numbers inside the}\\\text{parenthesis}\\\\\text{When you distribute, you would multiply}\\\\\text{Distribute:}\\\\5(6-1)\\\\5(6)-5(1)\\\\30-5\\\\\text{You would see that this is equal to answer choice C, therefore making}\\\text{C your answer}\\\\\boxed{\text{C). 30 - 5}}[/tex]

Answer:

they are equivalent

Step-by-step explanation:

8/6

Divide the top and bottom by 2

4/3

16/12

Divide the top and bottom by 4

4/3

They are  the same so they are equivalent

Step-by-step explanation:

31/2×5/23 (use reciprocal)

31×5=155

155÷46=3.369565217

155/46

3 and 17/46

Answer:

36 minutes past 1, or 1:36

Step-by-step explanation:

A watch normally has an hour hand that does one revolution in 12 hours.

It takes 1 hour to go from the 1 o'clock position to the 2 o'clock position.

Since 1 hour equals 60 minutes, it takes 60 minutes to go from the 1 o'clock position to the 2 o'clock position.

The hour hand is 3/5 of the way from 1 to 2, so the number of minutes past 1 o'clock is 3/5 of 60 minutes.

3/5 of 60 minutes =

= 3/5 * 60 minutes

= 3/5 * 60/1 minutes

= 180/5 minutes

= 36 minutes

The time is 36 minutes past 1, or 1:36

Answer:

A

Step-by-step explanation:

This is because vertical angles are always congruent, they cross diagonally which makes them equal to each other.

When two perpendiculars line intersect the angles formed must be a right angle. Hence option b is correct.

The angle can be defined as the one line inclined over other line.

Here, When perpendicular lines intersect each other the angle formed between them is 90 degree. So the angles are right angles.

Thus, when two perpendiculars line intersect the angles formed must be a right angle.

Learn more about angles here:
https://brainly.com/question/13954458

#SPJ2