Find the value of x. give your answer in simplest radical form.

x = 5*sqrt(10)
"sqrt" stands for "square root"

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Refer to the attached image. The figure is not to scale. Notice how I've added in y and z (blue and red respectively)
The length y is the bottom horizontal leg for the triangle on the right.
The length z is the bottom horizontal leg for the triangle on the left.

To find x, we need to find y first, which will help us find z, and then we can finally get to x.

Let's find y first
To do this, we use the pythagorean theorem
a^2 + b^2 = c^2
y^2 + 9^2 = 15^2
y^2 + 81 = 225
y^2 + 81-81 = 225-81
y^2 = 144
sqrt(y^2) = sqrt(144)
y = 12 ... keep in mind that y is a length, so it needs to be positive

Notice how the y and z lengths combine to form a total length of 25 units
Therefore,
y+z = 25
12+z = 25
12+z-12 = 25-12
z = 13

Now that we know z = 13, we can find x. Again we use the pythagorean theorem one last time
a^2 + b^2 = c^2
z^2 + 9^2 = x^2
13^2 + 9^2 = x^2
169 + 81 = x^2
250 = x^2
x^2 = 250
sqrt(x^2) = sqrt(250)
x = sqrt(250)
x = sqrt(25*10)
x = sqrt(25)*sqrt(10)
x = 5*sqrt(10)
This is in simplest radical form as we can't factor 10 any further (there are no perfect square factors that go into 10). This is the exact length of side x

Note: using a calculator, 5*sqrt(10) = 15.8113883008419 approximately

Do the math. she originally had 50 dollars on her gift card and she had 12 dollars left on her gift card after she finished her shopping spree. if you subtract 50 minus 12 you get thirty eight dollars as your answer. so therefore, ciara spent 38 dollars total o

The mode of the numbers is 29.