Find the slope of the line passing through each of the following pairs of po
(-6,0), (4,0)

Answer:

0=0, Infinite solutions

Step-by-step explanation:

For an answer to have an infinite solution, the two equations when you solve will equal 0=0. Here is a problem that has an infinite number of solutions. If you solve this your answer would be 0=0 this means the problem has an infinite number of solutions.

If this was helpful please give brainliest, have a great day!

x=2

x=10

Woulld really appriciate brainliest here is the steps below

1.1     Factoring  x2-12x+20  

The first term is,  x2  its coefficient is  1 .

The middle term is,  -12x  its coefficient is  -12 .

The last term, "the constant", is  +20  

Step-1 : Multiply the coefficient of the first term by the constant   1 • 20 = 20  

Step-2 : Find two factors of  20  whose sum equals the coefficient of the middle term, which is   -12 .

     -20    +    -1    =    -21  

     -10    +    -2    =    -12    That's it

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

                    x2 - 10x - 2x - 20

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 :

                   2 • (x-10)

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

                   (x-2)  •  (x-10)

            Which is the desired factorization

Equation at the end of step

1

:

 (x - 2) • (x - 10)  = 0  

STEP

2

:

Theory - Roots of a product

2.1    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:

2.2      Solve  :    x-2 = 0  

Add  2  to both sides of the equation :  

                     x = 2

Solving a Single Variable Equation:

2.3      Solve  :    x-10 = 0  

Add  10  to both sides of the equation :  

                     x = 10

Supplement : Solving Quadratic Equation Directly

Solving    x2-12x+20  = 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:

3.1      Find the Vertex of   y = x2-12x+20

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   6.0000  

Plugging into the parabola formula   6.0000  for  x  we can calculate the  y -coordinate :  

 y = 1.0 * 6.00 * 6.00 - 12.0 * 6.00 + 20.0

or   y = -16.000

Parabola, Graphing Vertex and X-Intercepts :

Root plot for :  y = x2-12x+20

Axis of Symmetry (dashed)  {x}={ 6.00}  

Vertex at  {x,y} = { 6.00,-16.00}  

x -Intercepts (Roots) :

Root 1 at  {x,y} = { 2.00, 0.00}  

Root 2 at  {x,y} = {10.00, 0.00}  

Solve Quadratic Equation by Completing The Square

3.2     Solving   x2-12x+20 = 0 by Completing The Square .

Subtract  20  from both side of the equation :

  x2-12x = -20

Now the clever bit: Take the coefficient of  x , which is  12 , divide by two, giving  6 , and finally square it giving  36  

Add  36  to both sides of the equation :

 On the right hand side we have :

  -20  +  36    or,  (-20/1)+(36/1)  

 The common denominator of the two fractions is  1   Adding  (-20/1)+(36/1)  gives  16/1  

 So adding to both sides we finally get :

  x2-12x+36 = 16

Adding  36  has completed the left hand side into a perfect square :

  x2-12x+36  =

  (x-6) • (x-6)  =

 (x-6)2

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

  x2-12x+36 = 16 and

  x2-12x+36 = (x-6)2

then, according to the law of transitivity,

  (x-6)2 = 16

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-6)2   is

  (x-6)2/2 =

 (x-6)1 =

  x-6

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

  x-6 = √ 16

Add  6  to both sides to obtain:

  x = 6 + √ 16

Accordingly,  B2  -  4AC   =

                    144 - 80 =

                    64

Applying the quadratic formula :

              12 ± √ 64

  x  =    —————

                   2

Can  √ 64 be simplified ?

Yes!   The prime factorization of  64   is

  2•2•2•2•2•2  

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).

√ 64   =  √ 2•2•2•2•2•2   =2•2•2•√ 1   =

               ±  8 • √ 1   =

               ±  8

So now we are looking at:

          x  =  ( 12 ± 8) / 2

Two real solutions:

x =(12+√64)/2=6+4= 10.000

or:

x =(12-√64)/2=6-4= 2.000

x=10

x=2

Hope this helps Would also appriciate brainliest

Answer:

Not sure what you mean, but I'm assuming you're referring to the sum of all the interior angles of a polygon. In that case:

Total sum of interior angles of a polygon ->

                               [tex]{180(n-2)[/tex]

However, if you are looking for the degrees of each interior angle, you must divide the total interior angle degrees by the amount of sides on the polygon, n

Degree of each interior angle of a polygon ->

                               [tex]\frac{180(n-2)}{n}[/tex]

In both cases, n represents the amount of sides the polygon has.

Answer:

D. 200-2/3x=2/5

Step-by-step explanation:

You can tell that one side of the equation is going to have only 2/5 because the problem said there was 2/5 of a ton left. You can also figure out that the equation should say 200-2/3x because the problem said that the conveyor belt removes 2/3 of a ton per minute. So, the equation should be...

200-2/3x=2/5, which is D.

Hope this helps c:

Answer: D

Step-by-step explanation:

The 2/3 is the rate and there is 2/5 leftover from the original 200 tons.

Answer:

2.375 or 2 3/8

Step-by-step explanation:

You want to do total weight over total number of items.

14 1/4 / 6 books = 2.375

Answer:

14.25 / 6 = 2.375 or 2 3/8

Answer:

22 rides happened in the hour.

Step-by-step explanation:

The way to solve this if by first dividing the 650 by the 30 then since the answer will be 21.6 that is basically like having 21 full rides then having one more ride a little over half full.

Answer:

It's the subtraction property of equality because you have to subtract.

Step-by-step explanation:

Answer: the first one

Step-by-step explanation:

No constant rate of change

Answer:

Step-by-step explanation:

vertex form of an equation of the parabola:  

f(x) = a(x - p)² + q

vertex (0, 3)  ⇒  p = 0,  q = 3

so:

   f(x) = a(x - 0)² + 3

    f(x) = ax² + 3

the parabola goes through point (1, -4)  ⇒  x=1,  f(x)=-4

   -4 = a(1)² + 3

   -4 = a + 3

    a = 7

Therefore the equation of the parabola in vertex form:

f(x) = 7x² + 3

Answer:

56

Step-by-step explanation:

z + 12w when z = 8 and w = 4

~Substitute

8 + 12(4)

~Simplify

8 + 48

~Add

56

Best of Luck!

We are provided with the value of z and w:

We have to find the value of z + 12w.....?

Since we have to find the value of the polynomials for the given values of variables. Plug the given values of z and w in the above question:

➝ z + 12w

➝ 8 + 12(4)

➝ 8 + 48

➝ 56

So, the required value of the polynomial is 56.

Carry on Learning [tex]![/tex]

Answer:

A. You can replace ‘a number’ with a variable to represent an unknown value.

C. Product means the result of multiplying two numbers.

D. The coefficient is 15.

E. In algebraic notation, you can represent the product of a number and a variable by writing the number and variable next to each other.

Step-by-step explanation:

EDGE 2020

The algebraic expression to model that "the product of a number and fifteen" is 15x, where x represents the unknown number. The statements A, C, and D are true.

Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.

The algebraic expression to model the unknown number problem "the product of a number and fifteen" is 15x, where x represents the unknown number.

From the given options, the following statements are true:

A. You can replace ‘a number’ with a variable to represent an unknown value.

C. Product means the result of multiplying two numbers.

D. The coefficient is 15.

B. is false because the product means the result of multiplying two numbers, not adding them.

E. is not necessarily true for all cases. The product of a number and a variable can be represented in different ways depending on the context and convention, such as using a dot or parentheses.

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Answer:

97.27 kg

Step-by-step explanation:

1kg = 2.2 lb

214 lb = ?kg

Make it into an equation:

1 kg/ 2.2 lb = ?kg / 214 lb

? = 1kg x 214lb ÷ 2.2 lb

?= 214lb ÷ 2.2 lb

? ≈ 97.27 kg / 214 pounds

Verify :

97.27 x 2.2 ÷ 214 ≈ 0.99 ≈ 1 kg

When an answer to a question uses the greater than symbol, that means any number above the number used is a possible answer to the equation. However, when it's just a simple "x = 2", then 2 is the only possible answer to that equation. Think about it as if it were on a graph. In the attached file I have a graph that is displaying the equation "x > 4". The entire shaded area to the right of 4 could be a possible answer.

Hope this helps.

Answer:

u didnt put questions

Step-by-step explanation:

Put a finger up. You have 1. Add 1 another finger by putting another finger up. If you count how many there are you get 2.

So 1+1 = 2.

Seriously though... why ask this.

Answer:

your mom

Step-by-step explanation:

Answer:

x=2

Step-by-step explanation:

f(x)=2^x

Now the given value is used:

4=2^x

x=2, because 2 squared is 4

Answer:

185

Step-by-step explanation:

Answer:

It entirely depends upon an individual.

It’s a known fact that humans need social interaction. Lack of which can affect their social behaviour and mindset. Whilst most would agree that e-learning is widely preferred by the younger generation, it is undeniably detaching them from social interactions.

When kids or students are engrossed in learning online, they’re missing out on social interactions that can open various doors of the mind, be it creative or observational skills. It’s understood that e-learning allows an individual to study far and beyond the subject and gives them an opportunity to explore multiple fields of their interest, one can’t ignore that it chains them to the system as well.

The deal-breaker in such a situation is an individual. If they demand social interaction, they would keep their digital device aside for once and would get indulge in social interaction. If they’re of another kind, they would prefer spending their days and nights just exploring and reading about new things online.

So, in my opinion, it’s quite subjective to narrow down the overall benefits and drawbacks of e-learning.

I hope I have answered your question.

To find m, we can use the formula y2 - y1 / x2 - x1

x1 = 2

y1 = 50

x2 = 4

y2 = 90

Let's plug these numbers into our formula.

m = 90 - 50 / 4 - 2 = 40/2 = 20

So far our equation looks like: y = 20x + b

Now, let's plug one of the points into our equation.

50 = 20(2) + b

Simplify

50 = 40 + b

Subtract 40 from both sides.

10 = b

The final equation is: y = 20x + 10

Answer:

ok. its  8/24. but if you got to simplify its 1/3

Step-by-step explanatin

you do 5*4 (the numerator) and 6*4(the denomerator).

this is the lcd(least comon )denominator.

repaet the steps for 2/4 but multiply by 6 on each number

once    

thats

done

its

your

answer

Answer:

5/6 – 2/4

= (10–6)/12

= 4/12

= 1/3

Answer:

y=x+4

y=6x-1

y=x+3

No picture of graph sorry cant describe how I would set these on a number line

Answer:

y=x+4

y=6x-1

y=x+3

Step-by-step explanation:

Answer:

x < -7 or x > -4

Step-by-step explanation:

Answer:

17 minutes

Step-by-step explanation:

To answer this question, all we have to do is subtract the original amount of money on the phone card by what is remaining after Keiko's call:

20 - 17.28 = 2.72

Now, we divide this number by 0.16:

2.72 / 0.16 = 17

So, Keiko's call lasted 17 minutes

Hope this helps :)

Step-by-step explanation:

Hey there!

The point shows the coordinates of (-2,1) and (4,6).

Now, When two points are given on a st.line, we use double point formula.

So, use formula;

[tex](y - y1) = \frac{y2 - y1}{x2 - x1} (x - x1)[/tex]

Put all values of x and y coordinates.

[tex](y - 1) = \frac{6 - 1}{4 + 2} (x + 2)[/tex]

Simplify it.

[tex](y - 1) = \frac{5}{6} (x + 2)[/tex]

[tex]y = \frac{5}{6} x + 2 \times \frac{5}{6} + 1[/tex]

[tex]y = \frac{5}{6} x + \frac{ 8}{3} [/tex]

Therefore, the equation of a line is y= 5/6x+8/3.

Hope it helps...

Answer:

84

Step-by-step explanation:

Answer:

50 cups of coffee

Step-by-step explanation:

So what you do is take 3.50 then subtract 1.50 to get the profit of one cup of coffee. ($2) Then you do the $100 and divide it by the $2 and find out how many cups of coffee he has to sell to get to the $100. (50)

Answer:

18cm

Step-by-step explanation:

Find the image to the question attached.

From the ruler, we are to find the distance between R and S i.e RS

From the ruler, R is on 8 and S is on 26.

Initial point R = 8

Final point S = 26

Length of RS = Final point S - initial point R

RS = 26 - 8

RS = 18

Hence the length of RS is 18cm

Answer:

a = undefined/no real solution

Step-by-step explanation:

Expand

24a - 22 = -4 + 24a

24a - 24a = -4 + 22

0a = 18

a = undefined/no real solution (when something is divided by 0 it becomes undefined)

The equation 24a - 22 = -4(1 - 6a) have no solution for the variable "a".

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

Given:

equation 24a - 22 = -4(1 - 6a)

1. Distribute the -4 to the terms inside the parentheses:

  24a - 22 = -4 + 24a

2. Simplify the equation by combining like terms:

  24a - 22 = 24a - 4

3. Rearrange the equation by moving all the terms involving "a" to one side and the constant terms to the other side:

  24a - 24a = -4 + 22

4. Simplify  24a - 24a = -4 + 22:

  0 = 18

The equation 0 = 18 is not true, which means there is no solution.

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