the diagonal of a square is 50cm long. how long are the sides of the square?

Hope you could get an idea from here.

Doubt clarification - use comment section.

The equation [tex]p^3+q^3+r^3=(\frac{1}{p^3}+\frac{1}{q^3}+\frac{1}{r^3})p^2q^2r^2[/tex] has been proved to be true

The equation is given as:

[tex]\frac pq = \frac qr[/tex]

Cross multiply

[tex]pr = q^2[/tex]

Rewrite as:

[tex]q^2 = pr[/tex]

Also, we have:

[tex]p^3+q^3+r^3=(\frac{1}{p^3}+\frac{1}{q^3}+\frac{1}{r^3})p^2q^2r^2[/tex]

Substitute [tex]q^2 = pr[/tex]

[tex]p^3+q^3+r^3=(\frac{1}{p^3}+\frac{1}{q^3}+\frac{1}{r^3})p^3r^3[/tex]

Expand

[tex]p^3+q^3+r^3=\frac{1}{p^3} \times p^3r^3 +\frac{1}{q^3} \times p^3r^3 +\frac{1}{r^3} \times p^3r^3[/tex]

Simplify

[tex]p3+q3+r3=r^3 +\frac{1}{q^3} \times p^3r^3 + p^3[/tex]

Rewrite as:

[tex]p3+q3+r3=r^3 +\frac{1}{q^3} \times (pr)^3 + p^3[/tex]

Substitute [tex]pr = q^2[/tex]

[tex]p3+q3+r3=r^3 +\frac{1}{q^3} \times (q^2)^3 + p^3[/tex]

[tex]p3+q3+r3=r^3 +\frac{1}{q^3} \times q^6 + p^3[/tex]

Divide q^6 by q^3

[tex]p3+q3+r3=r^3 +q^3 + p^3[/tex]

Rewrite the equation as:

[tex]p3+q3+r3=p^3 +q^3 + r^3[/tex]

Hence, the equation has been proved

Read more about equations at:

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Answer:

it will be broken into 9*what ever x is

Hope This Helps!!!

Answer:

9×x

Step-by-step explanation:

18+9x+2

20+9×x

that means 9 and x

Answer:

y=-1/2x-8

Step-by-step explanation:

y-y1=m(x-x1)

y-(-5)=-1/2(x-(-6))

y+5=-1/2(x+6)

y=-1/2x-6/2-5

y=-1/2x-3-5

y=-1/2x-8

Answer:

a rectangle with 2 yards and 3 yards

Step-by-step explanation:

12 yards and 23 yards

x and 2x - 1

------------------------------------

2 and 3 = x and 2x - 1

2 and 2(2) - 1 = 2 and 3

I might be wrong.

Answer:

-8

Step-by-step explanation:

Answer:

6(3r + 2s)

Step-by-step explanation:

Find the gcf of 18 and 12, then divide both and put it inside the parentheses.

Answer:

Second Graph.

Explanation:

It's the only graph that is concave down and the slope is decreasing.

Answer:

125

Step-by-step explanation:

because 3125 divided 25 equals 125.

how do you want me to show you how i divided?

Answer:

125 is the answer, you can check this by simply multiplying 125 by 25, which will give you 3125.

Step-by-step explanation:

Answer:

2$ compatible numbers are 200 and 100

Step-by-step explanation:

Answer:

im pretty sure that the answer is -50.5 feet.

Step-by-step explanation:

Answer:

  y = -x +2

Step-by-step explanation:

The slope can be found from the slope formula:

  m = (y2 -y1)/(x2 -x1)

  m = (6 -5)/(-4 -(-3)) = 1/-1 = -1

The y-intercept can be found from ...

  b = y -mx

  b = 5 -(-1)(-3) = 2

The slope-intercept equation for the line is ...

  y = mx +b

  y = -x +2 . . . . use the values of m and b we found

Step-by-step explanation:

the distance between 2 points is the Hypotenuse of a right-angled triangle. its legs are the x and y coordinate differences.

and so, we can use Pythagoras

c² = a² + b²

with c being the Hypotenuse, and a, b being the legs.

so,

the x difference is 9-12 = -3

the y difference is 31-25 = 6

therefore,

distance² = (-3)² + 6² = 9 + 36 = 45

distance = sqrt(45) = 6.708203932...

Answer:

x=6

Step-by-step explanation:

hope this helps! :D

have a miraculous day!! <3

Answer:

Any number that can be written as a fraction with integers is called a rational number . For example, 17 and −34 are rational numbers. (Note that there is more than one way to write the same rational number as a ratio of integers. For example, 17 and 214 represent the same rational number.)

Answer:

[tex]\frac{\pi}{6}[/tex] radians

[tex]cos(\frac{7\pi}{6})=-\frac{\sqrt{3}}{2}[/tex]

Step-by-step explanation:

A reference angle is an acute angle between the terminal arm/terminal side and the x-axis. In this case, the reference angle is [tex]\frac{7\pi}{6}-\pi=\frac{\pi}{6}[/tex].

As for [tex]cos(\frac{7\pi}{6})[/tex], we can identify the value of it using the unit circle as attached below. Recall that points on the unit circle are defined as [tex](cos(\theta),sin(\theta))[/tex], so [tex]cos(\frac{7\pi}{6})=-\frac{\sqrt{3}}{2}[/tex].

Answer:

1665 hertz

Step-by-step explanation:

30 x 3.33 = 1 (1 meter) so 500 x 3.33 = 1665 (1 meter of movement)

She saved 20%.

The price of the table was 250 and she bought it for 200, meaning 1/5 of the original price was marked off. 1/5 = 20% which means it was 20% off the original price.

Answer:

7

Step-by-step explanation:

y=kx is the general formula for direct proportion where k is the constant. In your equation instead of k there is 7 so 7 is the constant.

Answer:

no

Step-by-step explanation:

Answer:

a: -1/2

b: 15

Step-by-step explanation:

A system that has infinite solutions is the same line on top of itself.

Hope that helps

The third member of the Pythagorean triple is 28 and this can be determined by using the Pythagorean theorem.

Given :

21 and 35 are two members of a Pythagorean triple.

The following steps can be used in order to determine the third member of the Pythagorean triple:

Step 1 - The Pythagorean theorem can be used in order to determine the third member of the Pythagorean triple.

[tex]H^2 = P^2+B^2[/tex]

where the hypotenuse is H, the perpendicular is P, and the base is B of the right-angle triangle.

Step 2 - Now, substitute the value of H and P in the above expression in order to determine the value of 'B'.

[tex]35^2 = 21^2+B^2[/tex]

Step 3 - Simplify the above expression.

[tex]B^2= 784[/tex]

[tex]B = 28[/tex]

So, the third member of the Pythagorean triple is 28.

For more information, refer to the link given below:

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Answer:

the image was not clear....hope the values are correct

Answer is in the attached file.

Answer:

See answer below.

Step-by-step explanation:

P(v) = -4v³ + 12v² - 9v

Point (-5, -845) is not a point on the graph

P(-5) = -4(-5)³ + 12(-5)² - 9(-5)

P(-5) = 500 + 300 + 45

P(-5) = 800 + 45

P(-5) = 845                     point (-5, 845) is a solution

Answer: D and B

Step-by-step explanation:

D: 10/10 can be simplified to 1/1, or 1. 1 times 13 is equal to 13.

B: 4 x 13 is simply 52.

Hope this helps!

A. 5/6 x 13 = 10.83

B. 4 x 13 = 52

C. 3/4 x 13 = 9.75

D. 10/10 (1) x 13 = 13

B. 4 x 13 & D. 10/10 (1) x 13 are your answers.

Answer:

1. Becky, 2. No one, 3. Brian and Carol, 4. Tom, 5. Jake

Step-by-step explanation:

The order has to be Brian, Tom, Jake, Becky, and Carol.

1. Becky

2. No one

3. Brian and Carol

4. Tom

5. Jake