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dimulka [17.4K]
2 years ago
12

What is the area of triangle DEF?

Mathematics
1 answer:
FrozenT [24]2 years ago
3 0

Answer:

A=2\sqrt{14}\ units^2

Step-by-step explanation:

we know that

Heron's Formula is a method for calculating the area of a triangle when you know the lengths of all three sides.  

so

A=\sqrt{s(s-a)(s-b)(s-c)}

where

a, b and c are the length sides of triangle

s is the semi-perimeter of triangle

we have

a=5\ units,b=6\ units,c=3\ units

<em>Find the semi-perimeter s </em>

s=\frac{5+6+3}{2}=7\ units

Find the area of triangle

A=\sqrt{7(7-5)(7-6)(7-3)}

A=\sqrt{7(2)(1)(4)}

A=\sqrt{56}\ units^2

simplify

A=2\sqrt{14}\ units^2

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NEED HELP ASAP, WILL GIVE BRAINLIEST
Svetlanka [38]
Domain: [-5, 5)
range:(-4,4]
hope this helps
5 0
2 years ago
1. You are given the 3rd and 5th term of an arithmetic sequence. Describe in words how to determine the general term.
kozerog [31]

Step-by-step explanation:

1. In an arithmetic sequence, the general term can be written as

xₙ = y + d(a-1), where xₐ represents the ath term, y is the first value, and d is the common difference.

Given the third term and the fifth term, and knowing that the difference between each term is d, we can say that the 4th term is x₃+d and the fifth term is the fourth term plus d, or (x₃+d)+d =

x₃+2d. =x₅ Given x₃ and x₅, we can subtract x₃ from both sides to get

x₅-x₃ = 2d

divide by 2 to isolate d

(x₅-x₃)/2 = d

This lets us solve for d. Given d, we can say that

x₃ = y+d(2)

subtract 2*d from both sides to isolate the y

x₃ -2*d = y

Therefore, because we know x₃ and d at this point, we can solve for y, letting us plug y and d into our original equation of

xₙ = y + d(a-1)

2.

Given the third and fifth term, with a common ratio of r, we can say that the fourth term is x₃ * r. Then, the fifth term is

x₃* r * r

= x₃*r² = x₅

divide both sides by x₃ to isolate the r²

x₅/x₃ = r²

square root both sides

√(x₅/x₃) = ±r

One thing that is important to note is that we don't know whether r is positive or negative. For example, if x₃ = 4 and x₅ = 16, regardless of whether r is equal to 2 or -2, 4*r² = 16. I will be assuming that r is positive for this question.

Given the common ratio, we can find x₆ as x₅ * r, x₇ as x₅*r², and all the way up to x₁₀ = x₅*r⁵. We don't know the general term, but can still find the tenth term of the sequence

8 0
3 years ago
A huge Ping-Pong tournament is held in Beijing with 65,536 participants at the start of the tournament. Each round of
lisabon 2012 [21]

Answer:

After 16 rounds the champion of Ping-Pong player can be determined.

Step-by-step explanation:

This is an example of geometric progression,

First term = 65,536

\texttt{Common ratio = }\frac{1}{2}

Now we need to find which term is 1 in this GP.

N th term of GP is given by

             t_n=ar^{n-1}

Substituting

               1=65536\times \left ( \frac{1}{2}\right )^{n-1}\\\\\frac{1}{65536}=\left ( \frac{1}{2}\right )^{n-1}\\\\2^{n-1}=65536\\\\2^{n-1}=2^{16}\\\\n=17

Seventeenth term of this GP is 1.

That is after 16 rounds the champion of Ping-Pong player can be determined.

3 0
3 years ago
Find the unit rate for miles per hour. Round to the nearest hundredth if necessary. A cyclist rides 65 miles in 3 hours.
Natasha2012 [34]

22 (rounded to the nearest one)

4 0
3 years ago
HELP ME PLEASE FAST NOW PLEASE!!! ASAP
Juliette [100K]
Range is greater for the 13-14 year olds.
6 0
2 years ago
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