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USPshnik [31]
2 years ago
14

The base of the triangle is one and a half times it's height. what is height if area is 75

Mathematics
2 answers:
Setler [38]2 years ago
8 0
H=15cm
b=10cm 
i think, i asked my mom thats a teacher and she said it was correct.
Margarita [4]2 years ago
8 0
Answer:  The height is: 10.61 units. 
                       {or, write as:  "(7.5 √2)  units"}. 
_____________________________________________________
Explanation:
_____________________________________________________
Area of a triangle:  A = 1/2 * base * height = 1/2 * b * h ;

Given:  b = 1.5 * h ;
           A = 75 units²
______________________________
Solve for "h" ("height") ;  h = 1.5 b ;
_________________________________
So, we solve for "b" ; then we plug that value into the equation: 
  
        →   h = 1.5 b ;  to get the height, "h" ;
______________________________________________________
        →   75 = 1/2 * (b) (1.5 b) ;
______________________________________________________
         Multiply the ENTIRE equation by "2" ;
  to get rid of the fraction and decimals ; 
______________________________________________________
       →   2 * { 75 = 1/2 * (b) (1.5 b) } ;
______________________________________________________
       →  150  =  b * 3b ;
______________________________________________________
       →  150  =  3 b²  ;  
 
       ↔ 3 b²  =  150 ; 
______________________________________________________
 
            Now, divide EACH side of the equation by "3" ;
_________________________________________________
       →  3 b² / 3 = 150 / 3 ; 
_________________________________________________
       →     b²  =  50 ;
_________________________________________________
           Now, take the POSITIVE square root of each side of the equation;
to isolate "b" on one side of the equation; and to solve for "b" ;
_________________________________________________
        →   √(b²)  =  √50
<span>_________________________________________________
</span>        →      b  =  √50
_________________________________________________
        →     √50 = √25 *√2 = 5√2
_________________________________________________
        h = (1.5) b = (1.5) *(5) (
_____________________________________________________
Explanation:
_____________________________________________________
Area of a triangle:  A = 1/2 * base * height = 1/2 * b * h ;

Given:  b = 1.5 h ;
           A = 75 units²
______________________________
Solve for "h" ("height") ;  h = 1.5 b ;
_________________________________
So, we solve for "b" ; then we plug that value into the equation: 
  
        →   h = 1.5 b ;  to get the height, "h" ;
______________________________________________________
        →   75 = 1/2 * (b) (1.5 b) ;
______________________________________________________
         Multiply the ENTIRE equation by "2" ; 
  to get rid of the fraction and decimals ; 
______________________________________________________
       →   2 * { 75 = 1/2 * (b) (1.5 b) } ;
______________________________________________________
       →  150  =  b * 3b ;
______________________________________________________
       →  150  =  3 b²  ;  
 
       ↔ 3 b²  =  150 ; 
______________________________________________________
 
            Now, divide EACH side of the equation by "3" ;
_________________________________________________
       →  3 b² / 3 = 150 / 3 ; 
_________________________________________________
       →     b²  =  50 ;
_________________________________________________
           Now, take the POSITIVE square root of each side of the equation; 
to isolate "b" on one side of the equation; and to solve for "b" ;
_________________________________________________
        →   √(b²)  =  √50
_________________________________________________
        →      b  =  √50
_________________________________________________
        →      b  =  √50 = √25 *√2 = 5√2
_________________________________________________
        →      h = 1.5 * 5 * √2 ;
_________________________________________________
       →    h = (7.5 √2)  units ;
                           
                      or,  (7.5) * (√2) = 10.6066017177982129 units ;
_______________________________________________________
                                            → round to 10.61 units .
_______________________________________________________
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Let p_1 = <u><em>percentage of employed workers who have registered to vote.</em></u>

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So, Null Hypothesis, H_0 : p_1\leq p_2      {means that the percentage of employed workers who have registered to vote does not exceeds the percentage of unemployed workers who have registered to vote}

Alternate Hypothesis, H_A : p_1>p_2     {means that the percentage of employed workers who have registered to vote exceeds the percentage of unemployed workers who have registered to vote}

The test statistics that would be used here <u>Two-sample z test for proportions;</u>

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where, \hat p_1 = sample proportion of employed workers who have registered to vote = \frac{287}{513} = 0.56

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n_2 = sample of unemployed persons = 604

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                                       =  3.349

The value of z test statistics is 3.349.

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Since our test statistic is more than the critical value of z as 3.349 > 1.645, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which <u>we reject our null hypothesis</u>.

Therefore, we conclude that the percentage of employed workers who have registered to vote exceeds the percentage of unemployed workers who have registered to vote.

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