Need help with this one

Mathematics

1 answer:

steposvetlana [31]3 years ago

4 0

Answer:

∠TRS = 40°

Step-by-step explanation:

∠UTS is an exterior angle of the triangle

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles, that is

∠UTS = ∠TRS + ∠RST

9x - 15 = 3x + 16 + x + 9

9x - 15 = 4x + 25 ( subtract 4x from both sides )

5x - 15 = 25 ( add 15 to both sides )

5x = 40 ( divide both sides by 5 )

x = 8

∠TRS = 3x + 16 = (3 × 8) + 16 = 24 + 16 = 40°

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Rob is making a tent out of canvas in the shape of a square pyramid. Each side of the square base is 6 feet long, and the height

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The amount of balloons in the tent is 125.075 feet cube. From the given options, approximately, option D is correct

Solution:

Given, Rob is making a tent out of canvas in the shape of a square pyramid. Each side of the square base is 6 feet long, and the height is 6.3 feet.

Rob filled the tent with balloons,

We have to find which measurement BEST describes the amount of balloons in the tent?

As tent if filled with balloons the amount of balloons equals with volume of tent.

Volume of tent is given as:

$\text { volume of tent }=a^{2}+2 a \sqrt{\frac{a^{2}}{4}+h^{2}}$

where "a" is side length and "h" is height.

$\begin{array}{l}{\text { Then, Volume }=6.3^{2}+2(6.3) \sqrt{\frac{6.3^{2}}{4}+6^{2}}} \\\\ {=39.69+12.6 \sqrt{9.925+36}} \\\\ {=39.69+12.6 \times 6.7766=39.69+85.385} \\\\ {=125.075 \mathrm{ft}^{3}}\end{array}$