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Anna71 [15]
3 years ago
13

Calculate the slope of the line on the graph using the

Mathematics
1 answer:
polet [3.4K]3 years ago
4 0

Given:

The graph of a line which represents position (m) at time (s).

To find:

The slope of the line.

Solution:

Formula for slope:

m=\dfrac{y_2-y_1}{x_2-x_1}

From the given graph it is clear that the line passes through two points (0,0) and (1,4).

Using the above formula, we get

m=\dfrac{4-0}{1-0}

m=\dfrac{4}{1}

m=4

Therefore, the slope of the line is  4 m/s.

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What is 6 to the negative 1 times (-2) to the third power times (-4) to the negative 2
nasty-shy [4]
The answer is:  \frac{1}{12}  .
____________________________________________
Explanation:
____________________________________________
We have:   " 6⁻¹  *  (-2)³  * (-4)⁻² = ? " ;
_______________________________________
Note:  "6⁻¹ = \frac{1}{6^1} = \frac{1}{6} "  .
 
Note the following property of exponents:
____________________________________
           a⁻ˣ = \frac{1}{x^a} ;  {x ≠ 0}.
____________________________________________
Note:  (-2)³  = (-2)*(-2)*(-2) = 4*(-2) = -8 .
_______________________________________
Note:  (-4)⁻²  = \frac{1}{(-4)^2}  ;
 
                     = \frac{1}{(-4)*(-4)} ;

                     = \frac{1}{16} ;
____________________________________
So; we have:
_____________________________________
6⁻¹  *  (-2)³  * (-4)⁻²  ;

=  \frac{(1*8*1)}{(6*16)} ;

→ Cancel out the "8" in the "numerator" (to a "1") ; and the "16" in the number (and change to a "2"); since: {"16÷8 = 2" ; and since:  "{8÷8=1"} ;

→and we have:

\frac{(1*1*1)}{(6*2)} ;

 =  \frac{1}{12} .
_____________________________________
 → The answer is:  \frac{1}{12}  .
_____________________________________
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