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Leokris [45]
3 years ago
11

The length of a rectangle is 6 units and its width is 4 units. What is the approximate length of the diagonal of the rectangle?

Mathematics
1 answer:
ss7ja [257]3 years ago
5 0
The correct answer is:  [D]:  " 7.2 units" .
_______________________________________________________
Explanation:
________________________________________________________
Use the Pythagorean theorem:

a² + b² = c² ;

in which:  "6 units" and "4 units" equal the lengths of the right angle (formed by the rectangle);  and "c" is the length of the diagonal of the rectangle, or the "hypotenuse", of the right triangle formed by the rectangle;  We wish to solve for "c" ;
_______________________________________________

6² + 4² = c² ;  Solve for "c" ;

↔ c² = 6² + 4² ; 

         = (6*6) + (4*4) ;
 
         = 36 + 16 ;

        =  52 ;

    c² = 52 ;

Take the "positive square root" of each side of the equation; to isolate "c" on one side of the equation; and to solve for "c" ; 

  √(c²)  =  √52 ; 

    c = √52 ;  

At this point, we know the 7² = 49 ;  8² = 64 ;  so, the answer is somewhere between "7" and "8" ; yet closer to "7" ;  so among the answer choices given; 

The correct answer is:  [D]:  " 7.2 units" .
_________________________________________
However, let use a calculator:

c = √52 = 7.2111025509279786 ; which rounds to "7.2" ;
   which corresponds to:  
___________________________________________
Answer choice:  [C]:  " 7.2 units" .
___________________________________________
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Select all pairs of numbers that have a least common multiple of 30.
ddd [48]

5 and 6  and 3 and 10, the pairs of numbers that have a least common multiple of 30.

<u>Step-by-step explanation:</u>

Case 1: LCM (3, 6)

Prime factorization of 3:  1 \times 3

Prime factorization of 6:  2 \times 3

Using all prime numbers found as often as each occurs most often we take

               2 \times 3=6

Therefore LCM (3, 6) = 6.

Case 2: LCM (5, 6)

Prime factorization of 5:  1 \times 5

Prime factorization of 6:  2 \times 3

Using all prime numbers found as often as each occurs most often we take

                     5 \times 2 \times 3=30

Therefore LCM (5, 6) = 30

Case 3: LCM (3, 10)

Prime factorization of 3:  1 \times 3

Prime factorization of 10:  2 \times 5

Using all prime numbers found as often as each occurs most often we take

                    5 \times 2 \times 3=30

Therefore LCM (3, 10) = 30

Case 4: LCM (5, 10)

Prime factorization of 5:  1 \times 5

Prime factorization of 10: 2 \times 5

Using all prime numbers found as often as each occurs most often we take

                       5 \times 2=10

Therefore LCM (5, 10) = 10

8 0
3 years ago
Help anyone?? need to get this done
erik [133]
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3) 21
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6 0
2 years ago
Angle D has what measurement according to the protractor?
Aliun [14]

Answer:

B. 90^o

Step-by-step explanation:

We have been given a protractor and we are asked to find the measure of angle D.

We can see from our given protractor that the measure of angle D is 90 degrees as the ray OD crosses our protractor at 90 degrees.

Therefore, the measure of angle D is 90 degrees and option B is the correct choice.

6 0
3 years ago
If A={2,3,5,7} and B={2,4,6,8} then what is AnB?​
gregori [183]

Answer:

  • A∩B = {2}

Step-by-step explanation:

It asks for the common set of A and B.

<u>There only one element common to both the given sets:</u>

  • A={2,3,5,7} and B={2,4,6,8} ⇒ A∩B = {2}
6 0
3 years ago
Read 2 more answers
A.B,and C are collinear. AB=5x-19,and BC= 3x+4. Find an expression for AC if B is between A and C.
uysha [10]
Find A <span>if B is between A and C.
</span><span>A.B,and C are collinear so A, B and C are line up in a line</span>

AC = AB + BC

AB=5x-19,and BC= 3x+4 given;

So

AC = 5x-19 + 3x+4

Simplify

AC = 8x -15

4 0
3 years ago
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