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3 years ago

Find the missing value and round to the nearest hundredth.

Mathematics

1 answer:

yarga [219]3 years ago

8 0

You have to use Trigonometric ratios here. I'll help you with a question, and you try to do the other two.

a. You are given the hypotenuse, and told to figure out the opposite. The trigonometric function that deals with that is sin(x), which is opposite over hypotenuse. So:
$sin(51)= \frac{y}{12}$

Solve for y:
$y = 12sin(51)$

Simplify:
$y = 8.043$

For these problems, you have to remember the ratios Sine, Cosine, and Tangent. An easy way is to make a mnemonic device. A good one that a lot of people use is SohCahToa. Which is Sine (Opposite, Hypotenuse), Cosine (Adjacent, Hypotenuse) and Tangent (Opposite, Adjacent). Remember trigonometry is just a glorified field of ratios of sides to angles. There are many more trigonometric ratios including inverse trigonometric ratios, reciprocal trigonometric ratios, and hyperbolic trigonometric ratios (which show up during differential calculus). But for now, focus on this. Haha.

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Name the Property Shown: 16=16 Question 1 options: Symmetric Property Transitive Property Reflexive Property Distributive Proper

Lemur [1.5K]

Answer:

reflexive property

Step-by-step explanation:

reflexive property states that a number equals itself, a = a, so since 16 = 16, or 16 equals itself, it's reflexive.

3 0

3 years ago

MATH HELP!!! 100PTS!!!

Lostsunrise [7]

Answer:

$x =\dfrac{20 +\sqrt{454}}{18}, \quad \dfrac{20 -\sqrt{454}}{18}$

Step-by-step explanation:

Given functions:

$p(x)=2x-4$

$r(x)=\dfrac{6x-1}{9x+1}$

Solve for p(x) = r(x):

$\begin{aligned}p(x) & = r(x)\\\implies 2x-4 & = \dfrac{6x-1}{9x+1}\\(2x-4)(9x+1)&=6x-1\\18x^2+2x-36x-4&=6x-1\\18x^2-40x-3&=0\end{aligned}$

As the found quadratic equation cannot be factored, use the Quadratic Formula to solve for x:

Quadratic Formula

$x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0$

Therefore:

$a=18, \quad b=-40, \quad c=-3$

Substitute the values of a, b and c into the quadratic formula and solve for x:

$\begin{aligned}\implies x & =\dfrac{-(-40) \pm \sqrt{(-40)^2-4(18)(-3)} }{2(18)}\\\\& =\dfrac{40 \pm \sqrt{1816}}{36}\\\\& =\dfrac{40 \pm \sqrt{4 \cdot 454}}{36}\\\\& =\dfrac{40 \pm \sqrt{4}\sqrt{454}}{36}\\\\& =\dfrac{40 \pm2\sqrt{454}}{36}\\\\& =\dfrac{20 \pm\sqrt{454}}{18}\end{aligned}$

Therefore, the solutions are:

$x =\dfrac{20 +\sqrt{454}}{18}, \quad \dfrac{20 -\sqrt{454}}{18}$

Learn more about quadratic equations here:

brainly.com/question/27750885

brainly.com/question/27739892

6 0

2 years ago

How to do the monomials

Cerrena [4.2K]

Given:

The given monomial expression is $\frac{16 y^{8}}{4 y^{2}}$

We need to simplify the given monomial expression.

Simplification:

Let us simplify the given expression.

Dividing the numbers 16 and 4, we get;

$\frac{4 y^{8}}{y^{2}}$

Let us apply the exponent rule $\frac{x^{a}}{x^{b}}=x^{a-b}$ in the above expression.

Thus, we get;

$4 y^{8-2}$

Subtracting the numbers in the numerator of the above expression, we get;

$4 y^{6}$

Thus, the simplified expression is $4 y^{6}$

8 0

3 years ago

Use the definition of a derivative to find f’(x).

tatyana61 [14]

Answer:

f'(x) = $-\frac{9}{x^2}$

Step-by-step explanation:

i) f(x) = 9 / x

ii) f'(x) = $$\lim_{h\to 0} \frac{f(x+h) - f(x)}{h} $ \hspace{0.2cm}$

$= $\lim_{h\to 0} \frac{\frac{9}{x+h} - \frac{9}{x} }{h} = \hspace{0.1cm} $\lim_{h\to 0} \frac{9x - 9(x+h)}{hx(x+h)} $ \hspace{0.1cm} = \hspace{0.1cm}$\lim_{h\to 0} \frac{-9h}{hx(x+h)} = $\lim_{h\to 0} \frac{-h}{x(x+h)} = \frac{-9}{x^2}$$

7 0

3 years ago

4x-12y=-8 what is the answer

umka21 [38]

Answer:

You aren't asked which variable to solve for.

If we're solving for x then

4x = 12y -8

x = 3y - (8/4)

If we're solving for y

-12y = -4x -6

12y = 4x +6

y = (x/3) + (1/2)

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers