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guajiro [1.7K]
3 years ago
10

What is the area of the equilateral triangle with the length of each side equal to a?

Mathematics
2 answers:
Blizzard [7]3 years ago
6 0

Answer:

(C)

Step-by-step explanation:

From the given figure, it can be seen that the all the sides of the triangle are equal and are equal to a.

Now, area of the equilateral triangle is given as:

A=\frac{\sqrt{3}}{4}a^2

Now, we know that sin60^{\circ}=\frac{\sqrt{3}}{2}

then, (A) \frac{1}{2}asin60^{\circ}=\frac{\sqrt{3}}{4}a

which is not equal to the value of area of equilateral triangle, thus this option is not correct.

(B) 3asin60^{\circ}=\frac{3\sqrt{3}}{2}a

which is not equal to the value of area of equilateral triangle, thus this option is not correct.

(C) \frac{1}{2}a^2sin60^{\circ}=\frac{\sqrt{3}}{4}a^2

which is equal to the value of area of equilateral triangle, thus this option is correct.

(D) a^2sin60^{\circ}=\frac{\sqrt{3}}{2}a^2

which is not equal to the value of area of equilateral triangle, thus this option is not correct.

Stolb23 [73]3 years ago
3 0
Its the 3rd one !! 1/2a^2 sin 60
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Radda [10]

Answer:

c

Step-by-step explanation:

there are 8 parts and 4 of them are red= 4/8

which simplifies to 1/2

7 0
2 years ago
PLEASE THINS IS DUE BY 1 P.M TODAY. PLEASE HELP ME
zaharov [31]

6 {x}^{2}  {y}^{2} (y + 3xy + 6x)
6 0
3 years ago
Solve each equation. Show your work<br><br> 13a=-5<br> 12−b=12.5<br> -0.1=-10c
amid [387]
1) 13a=-5
Make a the subject of the formula by dividing both sides by 13(the coefficient of a)
13a/13=-5/13
Therefore a= -0.385

The second one). 12-b= 12.5
You take the 12 to the other side making b subject of the formula (-b in this case)
-b= 12.5-12
-b= 0.5
(You cannot leave b with a negative sign so you will divide both sides by -1 to cancel out the negative sign)

-b/-1= 0.5/-1
Therefore b=-0.5

The third one). -0.1= -10c
You will divide both sides by the coefficient of c(number next to c) which is -10
-0.1/-10= -10c/-10

Hence, c= 0.01
5 0
3 years ago
Seascapes rent small fishing boats for a day-long fishing trips. each boat can carry only 1200 lb of people and gear for safety
solmaris [256]

A. We are given that each person weighs 150 lb, each gear per person weighs 10 lb, and a total of 200 pounds of gear for the boat itself.

Since each person only carries one gear, therefore total weight per person in 160 lb (weight of person + weight of gear).

So let us say that x is the number of persons, the inequality equation is:

 

160 x + 200 ≤ 1200

 

 

B. There are three groups that wish to rent the boat.

> Solve the inequality equation when x = 4

160 (4) + 200 ≤ 1200

840 ≤ 1200           (TRUE)

 

> Solve the inequality equation when x = 5

160 (5) + 200 ≤ 1200

1000 ≤ 1200         (TRUE)

 

> Solve the inequality equation when x = 8

160 (8) + 200 ≤ 1200

1480 ≤ 1200         (FALSE)

 

So only the 4 people group and 5 people group can safely run the boat.

 

 

C. Find the maximum number of people that may safely use the boat, solve for x:

 

160 x + 200 ≤ 1200

160 x ≤ 1000

x ≤ 6.25

 

Therefore the maximum number of people that can safely use the boat is 6 people.

3 0
3 years ago
What is the range of the function graphed below?
PilotLPTM [1.2K]

Answer:

[-4,0) ∪ [2, ∞)

Step-by-step explanation:

For piecewise function domain and range, we need to understand the difference between "(" and "["  or  ")" and "]"

  • The parenthesis ( "(" and ")" ) are used for "open circles" in the graph.
  • The brackets ( "[" and "]" ) are use for "closed circles" in the graph.

Range is the set of y-values for which the function is defined.

Now,

The upper part of the function shows the graph going from y = 2 towards infinity (arrow). At y = 2 , there is closed circle, so this part range would be

[2, ∞)  (infinity is always with parenthesis)

Now, looking at bottom part, the function is defined from 0 (open circle) to -4 (closed). so we can write:

[-4,0)

This is the range, 2nd answer choice is correct.

[-4,0) ∪ [2, ∞)

3 0
3 years ago
Read 2 more answers
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