What decimal is equivalent to each fraction?

The sum of the diagonals of a rhombus is 5√2.

Alex

Greetings!
Let ABCD be a rhombus
AC + BD = 5√2 cm

Area of ABCD = Ar△ABD + Ar △BCD
$= \frac{1}{2} \times BD \times AO + \frac{1}{2} \times BD \times OC$
$= \frac{1}{2} BD (AO + OC)$
$\frac{1}{2} BD \times AC$

$So, \frac{ BD \times AC}{2} = 4 \: cm {}^{2}$
$BD \times AC = 8$
$Now, AC + \: BD = 5 \sqrt{2}$

Squaring both sides, we get
$AC {}^{2} + BD {}^{2} + 2 AC.BD =50$
$AC {}^{2} + BD {}^{2} + 2 \times 8 = 50$
$AC {}^{2} + BD {}^{2} = 50 - 16$
$AC {}^{2} + BD {}^{2} = 34$

In △AOB, we have
$OA {}^{2} + OB {}^{2} =AB {}^{2}$
$( \frac{ AC }{2} ) {}^{2} + ( \frac{ BD}{2} ) {}^{2} = AB {}^{2}$
$\frac{ AC {}^{2} } {4} + \frac{ BD {}^{2} }{4} = AB {}^{2}$
$AC {}^{2} + BD {}^{2} = 4 AB {}^{2}$
$34 = 4 AB {}^{2}$

Square rooting both sides
$\sqrt{34} = 2 AB$
$Perimeter = 4 \: AB \\ = 2 \times 2 \: AB \\ = 2 \: \times \sqrt{34 } \\ = 2 \sqrt{34 \: } units$ .

Hope it helps!

7 0

3 years ago

The sum of three consecutive even numbers is 582. What is the 1st number?

Snezhnost [94]

Answer:

d

Step-by-step explanation:

y

4 0

3 years ago

The half-life of the isotope Osmium-183 is 12 hours. Choose the equation below that gives the remaining mass of Osmium-183 in gr

raketka [301]

The given equations are incomprehensible, I'm afraid...

You're given that osmium-183 has a half-life of 12 hours, so for some initial mass M₀, the mass after 12 hours is half that:

1/2 M₀ = M₀ exp(12k)

for some decay constant k. Solve for this k :

1/2 = exp(12k)

ln(1/2) = 12k

k = 1/12 ln(1/2) = - ln(2)/12

Now for some starting mass M₀, the mass M remaining after time t is given by

M = M₀ exp(kt )

So if M₀ = 590 g and t = 36 h, plugging these into the equation with the previously determined value of k gives

M = 590 exp(36k) = 73.75

so 73.75 ≈ 74 g of Os-183 are left.

Alternatively, notice that the given time period of 36 hours is simply 3 times the half-life of 12 hours, so 1/2³ = 1/8 of the starting amount of Os-183 is left:

590/8 = 73.75 ≈ 74

6 0

3 years ago

Calculat the length of the circumference of a circle with diameter of 8cm.

mr_godi [17]

Hello there!

The formula for finding the circumference of a circle is 2 $\pi$ r (or 2*3*r in your terms). Although we don't have the radius yet, we can certainly find it pretty easily. Keep in mind that the radius will always be half the diameter. So, let's find the radius.

8 / 2 = 4; now we have everything we need to solve for the circumference.

2*3*4 is our expression. Now let's simplify it.
2 * 3 = 6
6 * 4 = 24

Your circumference is 24cm.

I hope this helps!

7 0

3 years ago

A travel agency made the table below to represent the profits it make on a certain vacation package.

Alex17521 [72]

Answer:

D. A quadratic function since the points are symmetric about the line $x=30$ .

Step-by-step explanation:

Please consider the complete question.

A travel agency made the table below to represent the profits it make on a certain vacation package.

x Profit per Person (in dollars), f(x)

10 500

20 800

30 900

40 800

50 500

Which of the following explains the best model for the data in the table?

A) An absolute value function since the values increase and then decrease

B) An exponential function since the ratio of the y-values are about the same.

C) A linear function since the function changes at a rate of 30 dollars per person

D) A quadratic function since the points are symmetric about the line x = 30.

First of all, we will graph all the given points on coordinate plane and then join the points to see the graph.

We can see that point (10,500) is symmetric to point (50,500). Point (20,800) is symmetric to point (40,800).

Upon looking at attached image, we can see that the data forms the shape of a downward opening parabola, which is symmetric to line $x=30$ .

Therefore, a quadratic function best represents the given data because the points are symmetric about the line $x=30$ .

7 0

3 years ago

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