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3 years ago

Write 0.45 as a fraction in simplest form.

Mathematics

2 answers:

marishachu [46]3 years ago

4 0

Answer:

$\frac{9}{20}$

Step-by-step explanation:

$\frac{0.45}{1} \times \frac{100}{100} = \frac{45}{100}$

find the gcf

gcfbof 45 and 100 is 5

$\frac{0.45}{45} \div \frac{5}{5} = \frac{9}{20}$

$0.45 = \frac{9}{20}$

Maurinko [17]3 years ago

3 0

Answer:

9/20

Step-by-step explanation:

0.45=45/100=9/20

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If a line includes the points (8,0) and (20,12). What is its equation in slope-intercept form?

aev [14]

The slope-intercept form:

$y=mx+b$

m - slope

b - y-intercept

The formula of a slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

substitute the coordinates of the points (8, 0) and (20, 12) to the formula:

$m=\dfrac{12-0}{20-8}=\dfrac{12}{12}=1$

y = 1x + b = x + b

Put the coordinates of the point (8, 0) to the equation of a line:

0 = 8 + b <em>subtract 8 from both sides</em>

-8 = b

<h3>Answer: y = x - 8</h3>

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3 years ago

Find the value of x.

kirza4 [7]

Hey there :)

Here we need to use Trigonometry!

The given angle is 61°
The opposite to the angle is 22
So x is the adjacent

The trigonometric ratio that uses opposite and adjacent is tan
( I have uploaded a picture to help you )

tan α = $\frac{opposite}{adjacent}$
tan 61 = $\frac{22}{adj}$
adj = $\frac{22}{tan(61)}$
adj ≈ 12.19 ≈ 12

x = 12

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3 years ago

Find the value of x to the nearest tenth

kenny6666 [7]

Step-by-step explanation:

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3 years ago

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3 years ago

Find , , and if and terminates in quadrant .

ioda

sin2x =12/13

cos2x = 5/13

tan2x = 12/5

STEP - BY - STEP EXPLANATION

What to find?

• sin2x

• cos2x

• tan2x

Given:

tanx = 2/3 = opposite / adjacent

We need to first make a sketch of the given problem.

Let h be the hypotenuse.

We need to find sinx and cos x, but to find sinx and cosx, first determine the value of h.

Using the Pythagoras theorem;

hypotenuse² = opposite² + adjacent²

h² = 2² + 3²

h² = 4 + 9

h² =13

Take the square root of both-side of the equation.

h =√13

This implies that hypotenuse = √13

We can now proceed to find the values of ainx and cosx.

Using the trigonometric ratio;

$\sin x=\frac{opposite}{\text{hypotenuse}}=\frac{2}{\sqrt[]{13}}$ $\cos x=\frac{adjacent}{\text{hypotenuse}}=\frac{3}{\sqrt[]{13}}$

And we know that tanx =2/3

From the trigonometric identity;

sin 2x = 2sinxcosx

Substitute the value of sinx , cosx and then simplify.

$\sin 2x=2(\frac{2}{\sqrt[]{13}})(\frac{3}{\sqrt[]{13}})$ $=\frac{12}{13}$

Hence, sin2x = 12/13

cos2x = cos²x - sin²x

Substitute the value of cosx, sinx and simplify.

$\begin{gathered} \cos 2x=(\frac{3}{\sqrt[]{13}})^2-(\frac{2}{\sqrt[]{13}})^2 \\ \\ =\frac{9}{13}-\frac{4}{13} \\ =\frac{5}{13} \end{gathered}$

Hence, cos2x = 5/13

tan2x = 2tanx / 1- tan²x

$\tan 2x=\frac{2\tan x}{1-\tan ^2x}$ $=\frac{2(\frac{2}{3})}{1-(\frac{2}{3})^2}$ $=\frac{\frac{4}{3}}{1-\frac{4}{9}}$ $=\frac{\frac{4}{3}}{\frac{9-4}{9}}$ $=\frac{\frac{4}{3}}{\frac{5}{9}}$ $=\frac{4}{3}\times\frac{9}{5}=\frac{4}{1}\times\frac{3}{5}=\frac{12}{5}$

$\tan 2x=\frac{\sin 2x}{\cos 2x}=\frac{\frac{12}{13}}{\frac{5}{13}}=\frac{12}{5}$

Hence, tan2x = 12/5

Therefore,

sin2x =12/13

cos2x = 5/13

tan2x = 12/5

3 0

1 year ago