A garden hose was left on in a yard and spilled 78 gallon every 23 minute. Find the average number of gallons spilled per minute.

Answer:

Step-by-step explanation:

y=mx+b       b= y-intercept   y-intercept=where the line crosses the y-axis    m=slope         slope== rise/run or slope formula, m=y2-y1/x2-x1

For example, number 1's slope is 5/3.  On a graph, you would go up 5 (not in block, but in numerical value) and right 3.   The y-intercept is -2.  This is where your line starts on the graph.

sorry, cant help ya there buddy

Answer:

X=4 or X=-2

Step-by-step explanation:

Step-1 : Multiply the coefficient of the first term by the constant   1 • -8 = -8  

Step-2 : Find two factors of  -8  whose sum equals the coefficient of the middle term, which is   -2 .

     -8    +    1    =    -7  

     -4    +    2    =    -2    That's it

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

                    x2 - 4x + 2x - 8

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

                   x • (x-4)

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

                   2 • (x-4)

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

                   (x+2)  •  (x-4)

            Which is the desired factorization

Equation at the end of step

1

:

 (x + 2) • (x - 4)  = 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  

Subtract  2  from both sides of the equation :  

                     x = -2

Solving a Single Variable Equation:

2.3      Solve  :    x-4 = 0  

Add  4  to both sides of the equation :  

                     x = 4

Supplement : Solving Quadratic Equation Directly

Solving    x2-2x-8  = 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 = x2-2x-8

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   1.0000  

Plugging into the parabola formula   1.0000  for  x  we can calculate the  y -coordinate :  

 y = 1.0 * 1.00 * 1.00 - 2.0 * 1.00 - 8.0

or   y = -9.000

Parabola, Graphing Vertex and X-Intercepts :

Root plot for :  y = x2-2x-8

Axis of Symmetry (dashed)  {x}={ 1.00}  

Vertex at  {x,y} = { 1.00,-9.00}  

x -Intercepts (Roots) :

Root 1 at  {x,y} = {-2.00, 0.00}  

Root 2 at  {x,y} = { 4.00, 0.00}  

Solve Quadratic Equation by Completing The Square

3.2     Solving   x2-2x-8 = 0 by Completing The Square .

Add  8  to both side of the equation :

  x2-2x = 8

Now the clever bit: Take the coefficient of  x , which is  2 , divide by two, giving  1 , and finally square it giving  1  

Add  1  to both sides of the equation :

 On the right hand side we have :

  8  +  1    or,  (8/1)+(1/1)  

 The common denominator of the two fractions is  1   Adding  (8/1)+(1/1)  gives  9/1  

 So adding to both sides we finally get :

  x2-2x+1 = 9

Adding  1  has completed the left hand side into a perfect square :

  x2-2x+1  =

  (x-1) • (x-1)  =

 (x-1)2

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

  x2-2x+1 = 9 and

  x2-2x+1 = (x-1)2

then, according to the law of transitivity,

  (x-1)2 = 9

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-1)2   is

  (x-1)2/2 =

 (x-1)1 =

  x-1

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

  x-1 = √ 9

Add  1  to both sides to obtain:

  x = 1 + √ 9

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

  x2 - 2x - 8 = 0

  has two solutions:

 x = 1 + √ 9

  or

 x = 1 - √ 9

Solve Quadratic Equation using the Quadratic Formula

3.3     Solving    x2-2x-8 = 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   =    -2

                     C   =   -8

Accordingly,  B2  -  4AC   =

                    4 - (-32) =

                    36

Applying the quadratic formula :

              2 ± √ 36

  x  =    —————

                   2

Can  √ 36 be simplified ?

Yes!   The prime factorization of  36   is

  2•2•3•3  

√ 36   =  √ 2•2•3•3   =2•3•√ 1   =

               ±  6 • √ 1   =

               ±  6

So now we are looking at:

          x  =  ( 2 ± 6) / 2

Two real solutions:

x =(2+√36)/2=1+3= 4.000

or:

x =(2-√36)/2=1-3= -2.000

Answer:

trucks: 8, cars: 18

Step-by-step explanation:

Answer:

The correct option is C.

Step-by-step explanation:

It is given that line segment AB has a length of 3 units. It is translated 2 units to the right on a coordinate plane to obtain line segment A'B'.

Translation is a rigid transformation. It means the shape and size of preimage and image are same. In other words we can say that the preimage and image are congruent.

Corresponding sides of congruent figures are congruent.

The length of A'B' is 3 units. Therefore the correct option is C.

Answer:

ok so i think it is 5/9

Step-by-step explanation:

both equal 0.5 in decimal point

Answer:

The last option is correct

Step-by-step explanation:

Eg: i take  -4/9

If your answer id 4/-9 , the negative sign will always go on the top so answer will be -4/9

Thus its similar

Hope you understood

if not I will explain again !

Your welcome !

Answer:

35111723

Step-by-step explanation:

17, 3, 23, 5, 11

3, 5, 11, 17, 23

35111723

Answer:

2+2=4

Step-by-step explanation:

Answer:

y + 7 = (-14/17)(x - 8)

Step-by-step explanation:

We want the equation of this line in the point-slope form y - k = m(x - h).

We are given two points (8, -7) and (-9, 7), and may arbitrarily choose one of them to serve as the point (h, k) in the point-slope form shown above.  Then the other point is represented by (x, y) in the point slope form shown above:

Let (h, k) be 8, -7) and let (x, y) be (-9, 7).  Then,  y - k = m(x - h) becomes:

7 - (-7) = m(-9 - 8), so that 14 = m(-17), and the slope is thus m = -14/17

The desired equation is then y + 7 = (-14/17)(x - 8) (which is in point-slope form).  

Another way to get this result would be to find m in the usual way:

          rise           14

m = ------------- = --------- = -14/17 (same as before).

           run           -17

Answer

21

Step-by-step explanation:

Answer:

b = 1/2m

Step-by-step explanation:

Let:

The prompt tells us that Beth is half as old as Meg. Therefore, mathematically, b = 1/2m.

a  y=x-4 if x>4

b INCOMPLETE

c 3r-15 is r<5

Answer:

Step-by-step explanation:

Answer:

this doesn't even make any sense

Step-by-step explanation:

both -5.4 and 5.4 go off the m.f grid

Answer:

a car accelerating down a hill

Step-by-step explanation:

because if an object is moving at a speed, then it has kinetic energy because its moving, not potential energy. potential energy is strored energy meaning that it has the potential to move.

Answer:

112.5 seconds

Step-by-step explanation:

Stephanie ran four laps around the school track in 7 minutes and 30 seconds. How many seconds per lap is that?

You need to do convert 7 minutes in to seconds because you cannot do anything to this unless you convert it.

Remember

1 minute = 60 seconds.

So do 7 times 60.

7 × 60

Which is 420 seconds.

Now add the 30 seconds to that.

420 + 30.

Which is 450 seconds.

Now divided 450 by 4.

450 ÷ 4.

Which is 112.5 seconds per lap.

Answer:

-5 x -2 = 10

Step-by-step explanation:

- x - = +

5 x 2 = 10

Answer:   1. 447

                2. 572

                3. 257

Step-by-step explanation:

Answer:

Your answer is $52.2 :)

Step-by-step explanation:

First, we need to find the sale, which is 40% of $70, we can do that by doing this equation: (40% x $70) / 100 = 28.  Now we minus 28 from 70 in this equation: 70 - 28 = 42.  Now we do tax, which is 10.1% of $42.  We can do the same equation, but with the new information, so the new equation is ($42 x %10.1) / 100 which is 4.2042, and since we are talking money, we can make 4.2042, 4.2 (Rounded 0.042 down). Lastly, we add $4.2 (Tax) and $48 (Discounted price) to get $52.2. You're welcome :D

Answer:

Function 1 has a greater Y intercept than that of function 2

Step-by-step explanation:

Y intercept can be found by replacing x by 0 or

x = 0 0f the given function.

in this case Function 1 has a Y intercept of 5 when x =0

on the other hand, function 2 crosses the y axis once at -1 which is the y intercept.

you can now clearly see that

y = 5 > y = -1

---> 5>-1

so that's why we conclude that 1 has a greater Y intercept.

Answer:

c

Step-by-step explanation:

I took the test

Answer:

There's not really a question to answer there, you've only stated the information that we know. From what I can see the only conclusion I can make is that Sterling plants a tree that is 4 3/4 feet tall, but that's already written and with all the information provided that's really all I can say.

Sorry if that's not exactly what you were looking for, maybe if there's more to the question re-post it with the entire question?