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CaHeK987 [17]
3 years ago
13

Evaluate f(x) when x=-10

Mathematics
1 answer:
adell [148]3 years ago
6 0

Answer:

f(x) = 10(10)+3 = 103 when x = 10

Step-by-step explanation:

Given a function piecewise as

f(x) = 2x-4 if -3<x<10

      = x^2+3, if 10<=x<13

We see from the definition of f(x) that the function has domain as (-3,13) and two sets defined from (-3,10) and [10,13).

Since 10 less than or equal to sign is there in the second function interval, we find that 10 is included in that.

Hence for finding f(10) we use the function defined for interval including 10 i.e. x^2+3

Substitute 10 for x in x^2+3

f(10) = 10^2+3

=103

Hence answer is 103

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The area of a rectangle is 980 in squared. the ratio of the length to the width is 5 : 4. find the length and the width.
ella [17]
Answer:   The length of the rectangle is 35 in.

                 The width of the rectangle is 28 in.
_________________________________________________________
Explanation:
_________________________________________________________
The formula for the area, "A", of a rectangle:

Area (A) = length (L) * width (w) ; 
 
  that is:   "  A  =  L  *  w  "  ;

A = 980 in²  (given);

ratio of the length to the width is:  " 5 : 4 " (given); 

→   Find the length (L) and the width (w).
_________________________________________________________

→  980 in²  =  (5x) * (4x) ; 

in which:  " 980 in² " is the area of the triangle; 

                 " 5x" = the length (L) of the rectangle, for which we shall solve; 

                 " 4x" = the width (w) of the rectangle, for which we shall solve.
_______________________________________________________
If we find solve for "x" ; we can solve for  "5x" and "4x" (the "length" and the "width", respectively);  by plugging in the solved value for "x" ; 
_______________________________________________________

   →  980 in²  =  (5x) * (4x) ; 

   ↔   (5x) * (4x) = 980 in²  ; 

   →   (5x) * (4x) = (5) * (4) * (x) * (x)  = 20 * x² = 20x² ;

   →  20x²  =  980 ;

Divide each side by "10" ; by canceling out a "0" on each side of the equation:

   →  2x² = 98 ; 

Now, divide each side of the equation by "2" ;

   → 2x² / 2  =  98 / 2 ; 

to get:  

→  x² = 49 ; 

Now, take the "positive square root" of each side of the equation;  (since a "length or width" cannot be a "negative value") ; 
    to isolate "x" on one side of the equation; & to solve for "x" ; 

→  ⁺√(x²) = √49 ; 

to get:

→  x = 7 ;
______________________________________________________
Now, we can solve for the "length" and the "width" ; 

→  The length is:  "5x" ;   

     5x = 5(7) =  " 35 in " ; 
______________________________________________________
→  The width is:  "4x" ; 

     4x =  4(7) =  "28 in."
______________________________________________________
Let us check our answer:

    →  A = L * w ; 

    →  980 in² = ?  35 in. * 28 in. ?? ; 

   Using a calculator:  "35 * 28 = 980" .  Yes!   ;
____________________________________________________
 { Also note:  " in * in = in² " ?  Yes! } .
____________________________________________________
3 0
3 years ago
How do you solve 372 divided by 12?
Anna007 [38]
12/372= 31 is the answer.
8 0
3 years ago
1/8 + 5/8?
Ronch [10]

Answer:

6/8

4/10

9/12

9/20

9/20

Step-by-step explanation:

8 0
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Which inequality best models the situation if variable h is the number of hours Miguel could practice the piano each week? Migue
Irina18 [472]
H is the number of hours Miguel could practice the piano each week.

Miguel goal is to practice the piano more than x hours per week.

h >= x

hence depending on the amount ot hours needed to practice each week, you have to set them to be the minimum, and any other larger quantity satisfies the proposition as well.
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4 years ago
Find the first term and the explicit formula a12=1/32 and r=1/2
Alexxx [7]

Answer:

see explanation

Step-by-step explanation:

The n th term of a geometric sequence is

a_{n} = a(r)^{n-1}

where a is the first term and r the common ratio

Given a_{12} = \frac{1}{32} and r = \frac{1}{2}, then

a (\frac{1}{2}) ^{11} = \frac{1}{32}, that is

\frac{a}{2^{11} } = \frac{1}{32}

\frac{a}{2048} = \frac{1}{32} ( cross- multiply )

32a = 2048 ( divide both sides by 32 )

a = 64 ← first term

Thus the explicit formula is

a_{n} = 64 (\frac{1}{2}) ^{n-1}

5 0
3 years ago
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