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Flauer [41]
2 years ago
6

Determine whether a triangle can be formed with the given side lengths. If so, use Heron's formula to find the area of the trian

gle. (5 points) a = 240 b = 123 c = 207
Mathematics
1 answer:
AfilCa [17]2 years ago
4 0

Answer:

Triangle inequality rule states that the sum of eachpair of sides must be greater than the third sides.

240 + 123 > 207 true

240 + 207 > 123 true

123 + 207 > 240 true

A = √(s(s-a)(s-b)(s-c))

s is the semi-perimeter (a + b + c)/2

s = (240 + 123 + 207)/2

s = 285

A = √(285*(285-249)(285-123)(285-207))

A = 12,730 units^2

Step-by-step explanation:

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Find the length of side AB<br> Give answer to 3 significant figures
Rina8888 [55]

Answer:

AB = 8.857 cm

Step-by-step explanation:

Here, we are given a <em>right angle</em> \triangle ABC in which we have the following things:

\angle A = 90 ^\circ\\\angle C = 41 ^\circ\\\text{Side }BC = 13.5 cm

Side <em>BC </em>is the hypotenuse here.

We have to find the side <em>AB</em>.

Trigonometric functions can be helpful to find the value of Side AB here.

Calculating \angle B:

Sum of all the angles in \triangle ABC is 180^\circ.

\Rightarrow \angle A + \angle B + \angle C = 180^\circ\\\Rightarrow 90^\circ + \angle B + 41^\circ = 180^\circ\\\Rightarrow \angle B = 49^\circ

We know that <em>cosine </em>of an angle is:

cos \theta = \dfrac{\text{Base}}{\text{Hypotenuse}}\\\Rightarrow cos B = \dfrac{AB}{BC}\\\Rightarrow cos 49^\circ = \dfrac{AB}{13.5}\\\Rightarrow AB = 13.5 \times 0.656\\\Rightarrow AB = 8.857 cm

So, side AB = 8.857 cm .

6 0
1 year ago
A jar contains 4 white and 4 black marbles. We randomly choose 4 marbles. If 2 of them are white and 2 are black, we stop. If no
Airida [17]

Answer:

<em>Find the probability of success in a single trial and then think about the nature of the problem (when do we stop).  </em>

Step-by-step explanation:

Observe that in the single trial, we have (8 4) possibilities of choosing our set of balls. If we have chosen two white balls and two black balls, the probability of doing that is simply  

p=(4 2)*(4 2)/(8 4)

This is well know Hyper geometric distribution. Now, define random variable X that marks the number of trials that have been needed to obtain the right combination (two white and two black balls). From the nature of the problem, observe that X has Geometric distribution with parameter p that has been calculated above. Hence  

P(X = n) = (1— p)^n-1 *( p )

<em>Find the probability of success in a single trial and then think about the nature of the problem (when do we stop).  </em>

3 0
2 years ago
Round 645 to the nearest ten
Elena L [17]

645 rounded to the nearest 10 is 650, as 5 in the ones place rounds up.
6 0
2 years ago
Instructions:Select the correct answer from each drop-down menu. The sides of ∆ABC are 30 units, 40 units, and 60 units long. Th
andriy [413]

Answer:

The sides of ∆ABC are 30 units, 40 units, and 60 units long.

The perimeter will be = 30+40+60=130 units

Given is that ∆ABC and ∆XYZ are similar and the corresponding sides of ∆XYZ are 'r' times as long as the sides of ∆ABC.

So, perimeter of ∆XYZ will be : 130\times r=130r units.

----------------------------------------------------------------------------------------

The area of ∆ABC is n square units, so area of ∆XYZ will be :

\frac{1}{2}(r\times height)(r\times base)

= n\times r\times r

= nr^{2} square units.

8 0
2 years ago
An old rectangular tank with length 0.3 m could hold 154 L of water. A new similar tank has a length of 1.5 m. What is the capac
dimaraw [331]
The length of the new tank is 5 times bigger than the old one, so 154×5=770. As a result, the capacity of the new tank is 770L. Hope it help!
6 0
2 years ago
Read 2 more answers
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