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sashaice [31]
3 years ago
13

In △XYZ , XZ=11 , YZ=8 , and m∠Z=31∘ .

Mathematics
1 answer:
Natalija [7]3 years ago
8 0

Answer:

The area of the triangle is 22.7 units²

Step-by-step explanation:

The formula of the area of a triangle using trigonometry is A = \frac{1}{2} (a)(b) sin(C), where a , b are two sides in the triangle and C is the angle between these two sides

In Δ XYZ

∵ XZ = 11 units

∵ YZ = 8 units

∵ m∠Z = 31°

∵ ∠Z is between the two sides XZ and YZ

∴ We can use the formula above to find the area of Δ XYZ

∵ Area Δ XYZ = \frac{1}{2} (XZ)(YZ) sin(Z)

∴ Area Δ XYZ = \frac{1}{2} (11)(8) sin(31)

∴ Area Δ XYZ = 22.6616753 unit²

- Round it to the nearest tenth

∴ Area Δ XYZ = 22.7 units²

The area of the triangle is 22.7 units²

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Answer:

2nd car is running faster than the first car by 2.01 units.

Step-by-step explanation:

Let's assume that

  • the velocity of first car,

v_1\ =\ 20i\ +\ 25j

  • and the velocity of second car

v_2\ =\ 30i

=> speed of first car,

u_1\ =\ \sqrt{(20)^2+(25)^2}

      =\ \sqrt{400+625}

       =\ \sqrt{1025}

       = 32.01 units

and speed of second car,

u_2\ =\ \sqrt{(30)^2+(0)^2}

        = 30 units

u_2\ -\ u_1\ =\ 32.01\ -30

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Hence, 2nd car is running faster than the first car by 2.01 units.

8 0
3 years ago
Factor the following , it is not prime
MrMuchimi
So 1/9-16z^2 this is a diffirence of two perfect squares thing
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4 0
3 years ago
A geologist examines 14 geological samples for iron concentration. The mean iron concentration for the sample data is 0.181 cc/c
kykrilka [37]

Answer:

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Step-by-step explanation:

We have that to find our \alpha level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\alpha = \frac{1-0.9}{2} = 0.05

Now, we have to find z in the Ztable as such z has a pvalue of 1-\alpha.

So it is z with a pvalue of 1-0.05 = 0.95, so z = 1.645

Now, find M as such

M = z*\frac{\sigma}{\sqrt{n}}

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M = 1.645*\frac{0.0318}{\sqrt{14}} = 0.0140

The lower end of the interval is the sample mean subtracted by M. So it is 0.181 - 0.0140 = 0.167 cc/m³.

The upper end of the interval is the sample mean added to M. So it is 0.181 + 0.0140 = 0.195 cc/m³.

The 90% confidence interval for the population mean iron concentration is between 0.167 cc/m³ and 0.195 cc/m³.

3 0
3 years ago
PLEASEE<br> Solve<br> x=6<br> 4x +y =20
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Answer: y = -4

Step-by-step explanation:

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8 0
2 years ago
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Answer:

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