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AleksAgata [21]
1 year ago
7

if $168.00 is the profit on a job, and this represents 8%of the contract price,what is the contract price?

Mathematics
1 answer:
Galina-37 [17]1 year ago
6 0

We are told that $168.00 represents 8% of the contract price; therefore,we know that

original price *( 8/100) = $168.00

Now, writing out "original price" is a bit space-consuming; therefore, we will just rename it and say

original price = OP

Then, our equation above can be written as

OP\times\frac{8}{100}=168

We solve for OP (original price) by multiplying both sides by 100 and then dividing by 8. This gives us

OP=\frac{100}{8}\times168\textcolor{#FF7968}{\therefore OP=2100}\text{\textcolor{#FF7968}{.}}

Hence, the original contract price is $2100.

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A 1 km long train travelling at a speed of 60km/h enter a tunnel 1km long. What time will the train take to come out of the tunn
zysi [14]

Answer:

2 minutes

Step-by-step explanation:

The front of the train enters the tunnel and travels 1 km before the rear of the train enters the tunnel.  Thus, the total distance traveled by the front of the train is 2 km, and this is covered in a certain number of hours:

Since distance = rate times time, time = distance / rate.  In this particular case we have:

                                              2 km

time = distance / rate = ------------------- = (1/30) hr

                                           60 km/hr

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3 0
2 years ago
What is the solution set of (x-2)(x-3)=3
natali 33 [55]

Answer:

x =(5-√13)/2= 0.697

x =(5+√13)/2= 4.303

Step-by-step explanation:

Step  1  :

Equation at the end of step  1  :

 (x - 2) • (x - 3) -  3  = 0  

Step  2  :

Trying to factor by splitting the middle term

2.1     Factoring  x2-5x+3  

The first term is,  x2  its coefficient is  1 .

The middle term is,  -5x  its coefficient is  -5 .

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   -5 .

     -3    +    -1    =    -4  

     -1    +    -3    =    -4  

     1    +    3    =    4  

     3    +    1    =    4  

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Equation at the end of step  2  :

 x2 - 5x + 3  = 0  

Step  3  :

Parabola, Finding the Vertex :

3.1      Find the Vertex of   y = x2-5x+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   2.5000  

Plugging into the parabola formula   2.5000  for  x  we can calculate the  y -coordinate :  

 y = 1.0 * 2.50 * 2.50 - 5.0 * 2.50 + 3.0

or   y = -3.250

Parabola, Graphing Vertex and X-Intercepts :

Root plot for :  y = x2-5x+3

Axis of Symmetry (dashed)  {x}={ 2.50}  

Vertex at  {x,y} = { 2.50,-3.25}  

x -Intercepts (Roots) :

Root 1 at  {x,y} = { 0.70, 0.00}  

Root 2 at  {x,y} = { 4.30, 0.00}  

Solve Quadratic Equation by Completing The Square

3.2     Solving   x2-5x+3 = 0 by Completing The Square .

Subtract  3  from both side of the equation :

  x2-5x = -3

Now the clever bit: Take the coefficient of  x , which is  5 , divide by two, giving  5/2 , and finally square it giving  25/4  

Add  25/4  to both sides of the equation :

 On the right hand side we have :

  -3  +  25/4    or,  (-3/1)+(25/4)  

 The common denominator of the two fractions is  4   Adding  (-12/4)+(25/4)  gives  13/4  

 So adding to both sides we finally get :

  x2-5x+(25/4) = 13/4

Adding  25/4  has completed the left hand side into a perfect square :

  x2-5x+(25/4)  =

  (x-(5/2)) • (x-(5/2))  =

 (x-(5/2))2

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

  x2-5x+(25/4) = 13/4 and

  x2-5x+(25/4) = (x-(5/2))2

then, according to the law of transitivity,

  (x-(5/2))2 = 13/4

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-(5/2))2   is

  (x-(5/2))2/2 =

 (x-(5/2))1 =

  x-(5/2)

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

  x-(5/2) = √ 13/4

Add  5/2  to both sides to obtain:

  x = 5/2 + √ 13/4

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

  x2 - 5x + 3 = 0

  has two solutions:

 x = 5/2 + √ 13/4

  or

 x = 5/2 - √ 13/4

Note that  √ 13/4 can be written as

 √ 13  / √ 4   which is √ 13  / 2

Solve Quadratic Equation using the Quadratic Formula

3.3     Solving    x2-5x+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   =    -5

                     C   =   3

Accordingly,  B2  -  4AC   =

                    25 - 12 =

                    13

Applying the quadratic formula :

              5 ± √ 13

  x  =    —————

                   2

 √ 13   , rounded to 4 decimal digits, is   3.6056

So now we are looking at:

          x  =  ( 5 ±  3.606 ) / 2

Two real solutions:

x =(5+√13)/2= 4.303

or:

x =(5-√13)/2= 0.697

4 0
3 years ago
Read 2 more answers
A cone has a slant length of 10 and a diameter of 8. Height is unknown.
patriot [66]

Answer: 153.56

Step-by-step explanation:

Hi, to answer this question we have to apply the next formulas:

Volume of a cone: 1/3 π r² h

Where r is the radius and h is the height (unknown)

Diameter = r x 2

8 = 2r

8/2 =r

r = 4  

Before calculating the volume we have to apply the Pythagorean Theorem to find h. (where the slant is the hypotenuse and h and r are the sides of the triangle)

10 ² = h² + 4²

Solving for h

100 = h² + 16

100-16 = h²

84= h²  

√84 =h

9.16= h

Back on the volume formula:

V= 1/3 π r² h

V =1/3 π 4² (9.16) =153.56

6 0
3 years ago
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