Mathematics, 01.10.2019 21:30 marie003

Find the side indicates by the variable. round to the nearest tenth.

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Answer from: kekoanabor19

QUESTION 1

The given triangle is right triangle with an acute angle measuring $53\degree$ .

The length of the given side which is opposite to the $53\degree$ angle is 8 units.

Recall that;

$\sin(53\degree)=\frac{Opposite}{Hypotenuse}$

$\Rightarrow \sin(53\degree)=\frac{8}{u}$

$\Rightarrow u=\frac{8}{\sin(53\degree)}$

$\Rightarrow u=10.017$

$\Rightarrow u=10.0$ to the nearest tenth

QUESTION 2

The given right angle triangle has an acute angle measuring $68\degree$ .

The hypotenuse has length 11 units.

is the length of the opposite side.

We use the sine ratio again to obtain;

$\sin(68\degree)=\frac{c}{11}$

$c=11\sin(68\degree)$

c=10.197

c=10.2 to the nearest tenth.

QUESTION 3

This time the right angle triangle has an acute angle of $59\degree$ and the side opposite this angle is 26 units,

We again use the sine ratio to obtain;

$\sin(59\degree)=\frac{26}{k}$

$\Rightarrow k=\frac{26}{\sin(59\degree)}$

$\Rightarrow k=30.335$

$\Rightarrow k=30.3$ to the nearest tenth,

QUESTION 4

The given right angle triangle has an acute angle measuring $22\degree$ .

The hypotenuse has length 5 units.

is the length of the opposite side.

We use the sine ratio again to obtain;

$\sin(22\degree)=\frac{a}{5}$

$a=5\sin(22\degree)$

a=1.875

a=1.9 to the nearest tenth.

QUESTION 5

This time the given right angle triangle has an acute angle of $47\degree$ and the side opposite this angle has length 51 units.

The side we want to find is adjacent to the given angle. We use the tangent ratio to obtain;

$\tan(47\degree)=\frac{51}{b}$

$b=\frac{51}{\tan(47\degree)}$

b=47.558

b=47.6 to the nearest tent.

QUESTION 6

The given right angle triangle has an acute angle measuring $49\degree$ .

The hypotenuse has length 6 units.

The side whose length we want to find is opposite to the given angle, we use the sine ratio to get;

$\sin(49\degree)=\frac{n}{6}$

$\Rightarrow n=6\sin(49\degree)$

$\Rightarrow n=4.528$

n=4.5 to the nearest tenth.

Answer from: Quest

(2 x^3 + 7 x^2 + 5 x + 2)/(x (x + 2))

step-by-step explanation:

simplify the following:

x/x^2 + 3 x + 2 - (x (x + 1))/(x + 2)

combine powers. x/x^2 = x^(1 - 2):

x^(1 - 2) + 3 x + 2 - (x (x + 1))/(x + 2)

1 - 2 = -1:

x^(-1) + 3 x + 2 - (x (x + 1))/(x + 2)

put each term in 1/x + 3 x + 2 - (x (x + 1))/(x + 2) over the common denominator x (x + 2): 1/x + 3 x + 2 - (x (x + 1))/(x + 2) = (x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2)):

(x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2))

(x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2)) = ((x + 2) + 3 x^2 (x + 2) + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2)):

(2 + x + 3 x^2 (x + 2) + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2))

3 x^2 (x + 2) = 3 x^3 + 6 x^2:

(2 + x + 3 x^3 + 6 x^2 + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2))

2 x (x + 2) = 2 x^2 + 4 x:

(2 + x + 6 x^2 + 3 x^3 + 2 x^2 + 4 x - x^2 (x + 1))/(x (x + 2))

-x^2 (x + 1) = -x^2 - x^3:

(-x^2 - x^3 + 3 x^3 + 6 x^2 + 2 x^2 + 4 x + x + 2)/(x (x + 2))

grouping like terms, 3 x^3 - x^3 + 6 x^2 + 2 x^2 - x^2 + 4 x + x + 2 = (3 x^3 - x^3) + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2:

((3 x^3 - x^3) + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2)/(x (x + 2))

3 x^3 - x^3 = 2 x^3:

(2 x^3 + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2)/(x (x + 2))

6 x^2 + 2 x^2 - x^2 = 7 x^2:

(2 x^3 + 7 x^2 + (x + 4 x) + 2)/(x (x + 2))

x + 4 x = 5 x:

answer: (2 x^3 + 7 x^2 + 5 x + 2)/(x (x + 2))

Answer from: Quest

If you make it a little more clear i can answer it

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Find the side indicates by the variable. round to the nearest tenth.
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