A square has an area of 100cm^2.What is the perimeter of the square?

dangina [55]

The given expression is $\frac{-4}{5} \times \frac{3}{7} \times \frac{15}{16} \times (\frac{-14}{9})$ .

We need to simplify the given expression.

<h3>What is a rational number?</h3>

In mathematics, a rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q.

Now group the rational numbers $(\frac{-4}{5}\times \frac{15}{16} ) \times (\frac{3}{7}\times (\frac{-14}{9}))$

$=(\frac{-4}{16}\times \frac{15}{5} ) \times (\frac{3}{9}\times (\frac{-14}{7}))$

$=(\frac{-1}{4}\times \frac{3}{1} ) \times (\frac{1}{3}\times (\frac{-2}{1}))$

$=(\frac{-3}{4} ) \times (\frac{-2}{3})=\frac{1}{2}$

Therefore, the simplified value of the given expression is $\frac{1}{2}$ .

To learn more about the rational numbers visit:

brainly.com/question/17450097.

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8 0

2 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

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

OR

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

Hence, tan2x = 12/5

Therefore,

sin2x =12/13

cos2x = 5/13

tan2x = 12/5

3 0

1 year ago

Evaluate the expression for x=5, y=3,and z=1/4. <br> 5x−6y+20z/4yz

Anna11 [10]

Just substitute each number into the expression:
5(5) - 6(3) + 20(1/4)/4(3)(1/4) = 25 - 18 + 5/3 = 7 + 5/3 = 26/3 or 8 and 2/3.

4 0

3 years ago

Read 2 more answers

PLEASE ANSWER THESE I RLLY NEED HELP I DONT UNDERSTAND I WILL MARK YOU AS BRAINLIEST IF YOU ANSWRR CORRECTLY PLS AND TY

faust18 [17]

Answer:

Step-by-step explanation:

5. You are asked to write an equation of the line in slope-intercept form, so you need to determine the slope of the line and the y-intercept.

You're lucky. One of the points, (0,1), has an x-coordinate of 0, so you know that the y-intercept is 1.

Use the coordinates of the points to determine the slope of the line.

slope = (difference in y-coordinates)/(difference in x-coordinates) = (10-1)/(3-0) = 9/3 = 3

The slope-intercept equation of the line is y = 3x+1

:::::

7. When x = 0, function A = 0 and function B = 3, so function B has a greater initial value.

7 0

3 years ago

Find the centroid of the region bounded by the given curves y=8sin(4x), y=8cos(4x)

Luba_88 [7]

A cosine is just a sine shifted to the left by π/2. A cosine of 4x is shifted to the left by only π/8 because of the factor 4. Sketch them.

The region we're looking for is this sausage-shaped part between the cos and the sin.

The x intercepts are at π/8 for the cosine and π/4 for the sine. The midpoint between them is at (π/8 + π/4)/2 = 3/16π.

The region is point symmetric around the x axis, so the y coordinate of the centroid is 0.

So the centroid is at (3/16π, 0)

5 0

3 years ago

A square has an area of 100cm^2.What is the perimeter of the square?​

A square has an area of 100cm^2.What is the perimeter of the square?