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barxatty [35]
2 years ago
9

The blueprints for a police station show that one of the lamp posts has a motion detector on it, and that the equation (x+14)2+(

y−6)2=9 describes the boundary within which motion can be sensed. What is the greatest distance, in feet, a person could be from the lamp and be detected?
3 ft

6 ft

9 ft

81 ft
Mathematics
2 answers:
Lana71 [14]2 years ago
7 0

Answer: The greatest distance, in feet is the first one 3ft.

Aleksandr-060686 [28]2 years ago
3 0

Answer: 3 feet

Step-by-step explanation:

Given: The blueprints for a police station show that one of the lamp posts has a motion detector on it, and that the equation describes the boundary within which motion can be sensed. :

(x+14)^2+(y-6)^2=9 → which is a equation of a CIRCLE.

When we compare it to the standard form of equation of circle i.e. (x-(-14))^2+(y-6)^2=3^2 , we get the radius of the circle = 3

Consider the lamp post as the center of the area covered by the detector.

Then the greatest distance a person could be from the lamp and be detected = Radius of the circular area

=3 feet.

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Sheldon harvest the strawberries and tomatoes in his garden. He picks 1 2/5 kg lesss strawberries in the morning tha in the afte
Tpy6a [65]

Answer:

3\frac{13}{20}=3.65 kg.

Step-by-step explanation:        

Let S be amount of strawberries picked in the afternoon.

We have been given that Sheldon harvest the strawberries and tomatoes in his garden. He picks 1 2/5 kg less strawberries in the morning than in the afternoon and the strawberries picked in morning are 2\frac{1}{4} kg.

To find the amount of strawberries picked by Sheldon in the afternoon we will add 2\frac{1}{4} and 1\frac{2}{5}  :

S= 2\frac{1}{4}+1\frac{2}{5}      

Upon converting our given mixed fractions into improper fraction we will get,

S= \frac{9}{4}+\frac{7}{5}

Now let us have a common denominator.

S=\frac{9*5}{4*5}+\frac{7*4}{5*4}

S=\frac{45}{20}+\frac{28}{20}

S=\frac{45+28}{20}

S=\frac{73}{20}  

S=3\frac{13}{20}  

S=3.65

Therefore, Sheldon picked 3\frac{13}{20}=3.65 kg of strawberries in the afternoon.  

3 0
3 years ago
One positive number is one-fifth of another number. the difference of the two numbers is 84. find the numbers.
seraphim [82]
Answer:  The numbers are:  " 21 " and " 105 " .
___________________________________________________
Explanation:
___________________________________________________
Let "x" be the "one positive number:

Let "y" be the "[an]othyer number".

x = 1/5 (y)
___________________________________________________
Given that the difference of the two number is "84" ;  and that "x" is (1/5) of  "y" ;  we determine that "x" is smaller than "y".

So, y − x = 84 .

Add "x" to each side of this equation; to solve for "y" in terms of "x" ;

y − x + x = 84 + x  ;

 y = 84 + x ;
___________________________________________________
So, we have: 

 x = (1/5) y ;

and:  y = 84 + x  ;

Substitute "(1/5)y" for "x" ;  in  "y = 84 + x " ;  to solve for "y" ;

 y = 84 + [ (1/5)y ]

Subtract  " [ (1/5)y ] " from EACH SIDE of the equation ;

y − [ (1/5)y ] = 84 + [ (1/5)y ] −  [ (1/5)y ]  ;

to get:

  [ (4/5)y ] = 84 ;


       ↔    (4y) / 5 = 84  ;
      
        →  4y = 5 * 84  ;

      Divide EACH SIDE of the equation by "4" ; 
to isolate "y" on one side of the equation; and to solve for "y" ;

           4y / 4 = (5 * 84) / 4 ;

                 y =  5 * (84/4) = 5 * 21 = 105 .

   y = 105 .
___________________________________________________
Now, plug "105" for "y" into:
___________________________________________________
Either:
___________________________________________________
 x = (1/5) y ;

OR:

  y = 84 + x  ;
___________________________________________________
to solve for "x" ;
___________________________________________________
Let us do so in BOTH equations; to see if we get the same value for "x" ; which is a method to "double check" our answer ;
___________________________________________________
Start with:

x = (1/5)y 

    →  (1/5)*(105) = 105 / 5 = 21 ;  x = 21 ; 

___________________________________________________
So, x = 21;  y = 105 .
___________________________________________________
Now, let us see if this values hold true in the other equation:
___________________________________________________
y = 84 + x ;

105 = ? 84 + 21 ?
 
105 = ? 105 ? Yes!
___________________________________________________
The numbers are:  " 21 " and  "105 " .
___________________________________________________

6 0
3 years ago
HELP !!! Evaluate f(-2) for the function f(x) = 3x2 + 2x - 5
Phoenix [80]

Answer:

3

Step-by-step explanation:

So we have the function:

f(x)=3x^2+2x-5

To evaluate the value of f(-2), substitute -2 for x. Thus:

f(-2)=3(-2)^2+2(-2)-5

Square first:

f(-2)=3(4)+2(-2)-5

Multiply:

f(-2)=12-4-5

Now, subtract:

f(-2)=8-5=3

So:

f(-2)=3

And we're done!

4 0
2 years ago
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zepelin [54]

Answer:

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Step-by-step explanation:

Hope this helps!

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8 0
2 years ago
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DedPeter [7]
The arc is called B) Circle
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3 years ago
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