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uranmaximum [27]
3 years ago
13

Find the indicated side of the triangle.

Mathematics
1 answer:
Damm [24]3 years ago
3 0

Answer:

\huge \orange{b = \boxed{ 6}  \sqrt{ \boxed{3}} }

Step-by-step explanation:

a = 12 \sin 30 \degree \\  \\  \implies \: a = 12 \times  \frac{1}{2} \\  \\  \implies \: \huge \red{ a = 6} \\  \\ b = 12 \cos 30 \degree \\  \\  \implies \: b = 12 \times  \frac{ \sqrt{3} }{2} \\  \\  \implies \: b = 6 \times   \sqrt{3}  \\  \\  \implies \:  \huge \orange{b = \boxed{ 6}  \sqrt{ \boxed{3}} }

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the sum of two.numbers is 25. one number is twice the second number plus seven. what are the the numbers? can I get a step by st
lana66690 [7]

Let x = the smaller number

Let 2x + 7 = the larger number

x + 2x + 7 = 25

3x = 18

x = 6

2x + 7 = 2(6) + 7 = 19

6 0
3 years ago
carrie missed 12% of problems on coach Blanes Texas History test The test had a total of 125 problems did Carrie get correct on
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Answer:

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3 years ago
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7 0
3 years ago
Determine how many points the parabola has in common with the x-axis and whether it's vertex lies above, on, or below the x-axis
Kipish [7]

Points "in common with the x-axis" are also known as the roots of the quadratic equation x^2-12x+12=0. You can apply the quadratic root formula to determine the roots, and also to determine how many such roots there are. With a quadratic (whose graph is a parabola), there can be maximum of 2 roots. But under certain circumstances, there may be only one or no such root.

The root formula for a generic quadratic ax^2+bx+c is as follows:

x_{1,2}=\frac{-b\pm\sqrt{b^2-4ac}}{2a}

The expression b^2-4ac under the square root is called the determinant. It is called so because it determines the number of real roots. If the determinant value is > 0, there will be 2 roots (and so the parabola will cross the x-axis in 2 points), if its value is =0, there will be only a single root (the the parabola will touch the x-axis in exactly one point), and, finally, if its value is < 0, the quadratic has no real root (andthe parabola will not have any x-intercepts).

So, let's take a look:

b^2-4ac= (-12)^2-4\cdot 1\cdot12=96

This means the parabola will intercept the x-axis at 2 points, two real roots.

Since the coefficient of the quadratic term is positive (a=1), the parabola is oriented "open-up." But since we already know the parabola intercepts in two points, the fact that it is open-up implies now that the vertex must lie below the x-axis (otherwise it could not intercept it).

8 0
4 years ago
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