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joja [24]
4 years ago
13

A number is decreased by 3 and then the result is doubled. if the new result is 6 more than half the original number, what is th

e value of the original number?
Mathematics
1 answer:
Blizzard [7]4 years ago
6 0
The answer is:  " 8 " .
________________________________
Explanation: 
________________________________
Let "x" represent the "original number".

2(x - 3) = 6 + (1/2)x ;  Solve for "x" ;
______________________________________
Multiple the ENTIRE EQUATION (both sides) by "2" ; to get rid of the fraction:

2*{2(x - 3) = 6 + (1/2)x} ; 

to get:

4(x - 3) = 12 + x ; 
___________________________
  Let us expand the "left-hand side" of the equation:
_____________________________________________
Note the "distributive property of multiplication" :
_____________________________________________
        a(b - c) = ab -  ac ; 
        
        a(b +c) = ab + ac ;
______________________________________________
So;  "4(x - 3)" = 4*x - 4*3 = 4x - 12 ; 
______________________________________________
Rewrite the equation:
_______________________________________________
  4x - 12 = 12 + x ;

Subtract "x" from EACH side of the equation; and Add "12" to EACH SIDE OF THE EQUATION; 
______________________________________________
  4x - 12 - x + 12 = 12 + x - x + 12 ;

to get:
______________________________________________
     3x = 24 ; 
_____________________________________________
Now, divide EACH side of the equation by "3" ; to isolate "x" on one side of the equation; and to solve for "x" ;
_____________________________________________
    3x/3 = 24/3 ; 
_____________________________________________
      x = 8 .
_____________________________________________
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dedylja [7]

The unit rate is another way of saying speed, so we divide the distance over the time. We can pick on any row

If we pick row 1, then, speed = distance/time = 90/2 = 45

Row 2 says the same thing: 135/3 = 45

So does row 3: 225/5 = 45

and so on

Because the speed is 45 mph, the unit rate is 45 miles in one hour. The term "unit" implies how much distance can be covered in one unit of time, in this case 1 hour.

You have the correct answer. Nice work.

6 0
3 years ago
AS one of her chores Staci must vacum 1/2 of the house. If she has already vacumed 1/3 of her share tonight whatp part of the li
Tatiana [17]

Answer:

1/6

Step-by-step explanation:

sim[le thought


3 0
3 years ago
What is the vertex form of Y = x2 - 6x + 6?
ahrayia [7]

Answer:

\large\boxed{y=(x-3)^2-3}

Step-by-step explanation:

The vertex form of a quadratic equation <em>y = ax² + bx + c:</em>

<em>y = a(x - h)² + k</em>

(h, k) - coordinates of a vertex

We have the equation <em>y = x² - 6x + 6</em>.

Convert to the vertex form:

y=x^2-2(x)(3)+6\\\\y=\underbrace{x^2-2(x)(3)+3^2}_{(*)}-3^2+6\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2\qquad(*)\\\\y=(x-3)^2-9+6\\\\y=(x-3)^2-3\to h=3,\ k=-3

7 0
3 years ago
Thx to all that helped me!!! here is my last question
Leviafan [203]

Answer:

cousin: m-3

uncle: 5m

together: 6m-3

Step-by-step explanation:

if her cousin is 3 years younger, they would be m-3. since their uncle is her age times 5, he would be 5m. add those and you get 5m+m-3. combine the m's (and get 6m), then add the -3 to get 6m-3

4 0
3 years ago
Read 2 more answers
or security​ reasons, a company will enclose a rectangular area of 11,200 m2 in the rear of its plant. One side will be bounded
pychu [463]

The dimensions of the rectangle are 150 m and 75 m respectively.

Let x be the length of the rectangular area and y be the width of the rectangular area.

Its area A = xy

Given that its area is 11,000 m², xy = 11000 m² (1)

Also, since the bounding side of the building is 150 m long and the fencing is 300 m, the perimeter of the rectangular area is P = 150 m + 300 m = 450 m.

Also, the perimeter of the rectangular area is P = 2(x + y)

Since P = 450 m

2(x + y) = 450 m

x + y = 225 m (2)

Since the bounding side of the building represents one dimension of the rectangle, x = 150 m.

Substituting x into (2), we get the other dimension

x + y = 225

150 + y = 225

y = 225 m - 150 m

y = 75 m

So, the dimensions of the rectangle are 150 m and 75 m respectively.

Learn more about dimensions of a rectangular area here:

brainly.com/question/16818606

4 0
3 years ago
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