<em><u>The solution is (4, 4)</u></em>
<em><u>Solution:</u></em>
<em><u>Given system of equations are:</u></em>
![y = x^2 - 6x + 12 ------ eqn\ 1\\\\y = 2x - 4 ---------- eqn\ 2](https://tex.z-dn.net/?f=y%20%3D%20x%5E2%20-%206x%20%2B%2012%20------%20eqn%5C%201%5C%5C%5C%5Cy%20%3D%202x%20-%204%20----------%20eqn%5C%202)
<em><u>Substitute eqn 2 in eqn 1</u></em>
![x^2 - 6x + 12 = 2x - 4](https://tex.z-dn.net/?f=x%5E2%20-%206x%20%2B%2012%20%3D%202x%20-%204)
Make the right side of equation 0
![x^2 - 6x + 12 - 2x + 4 = 0\\\\x^2 -8x + 16 = 0](https://tex.z-dn.net/?f=x%5E2%20-%206x%20%2B%2012%20-%202x%20%2B%204%20%3D%200%5C%5C%5C%5Cx%5E2%20-8x%20%2B%2016%20%3D%200)
<em><u>Solve by quadratic equation</u></em>
![\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}\\\\x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\\mathrm{For\:}\quad a=1,\:b=-8,\:c=16:\\\\x=\frac{-\left(-8\right)\pm \sqrt{\left(-8\right)^2-4\cdot \:1\cdot \:16}}{2\cdot \:1}\\\\x=\frac{-\left(-8\right)\pm \sqrt{0}}{2\cdot \:1}\\\\x = \frac{8}{2}\\\\x = 4](https://tex.z-dn.net/?f=%5Cmathrm%7BFor%5C%3Aa%5C%3Aquadratic%5C%3Aequation%5C%3Aof%5C%3Athe%5C%3Aform%5C%3A%7Dax%5E2%2Bbx%2Bc%3D0%5Cmathrm%7B%5C%3Athe%5C%3Asolutions%5C%3Aare%5C%3A%7D%5C%5C%5C%5Cx%3D%5Cfrac%7B-b%5Cpm%20%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D%5C%5C%5C%5C%5Cmathrm%7BFor%5C%3A%7D%5Cquad%20a%3D1%2C%5C%3Ab%3D-8%2C%5C%3Ac%3D16%3A%5C%5C%5C%5Cx%3D%5Cfrac%7B-%5Cleft%28-8%5Cright%29%5Cpm%20%5Csqrt%7B%5Cleft%28-8%5Cright%29%5E2-4%5Ccdot%20%5C%3A1%5Ccdot%20%5C%3A16%7D%7D%7B2%5Ccdot%20%5C%3A1%7D%5C%5C%5C%5Cx%3D%5Cfrac%7B-%5Cleft%28-8%5Cright%29%5Cpm%20%5Csqrt%7B0%7D%7D%7B2%5Ccdot%20%5C%3A1%7D%5C%5C%5C%5Cx%20%3D%20%5Cfrac%7B8%7D%7B2%7D%5C%5C%5C%5Cx%20%3D%204)
<em><u>Substitute x = 4 in eqn 2</u></em>
y = 2(4) - 4
y = 8 - 4
y = 4
Thus solution is (4, 4)
Answer: He got to be elected president of the Republic of Texas.
6*6=36. he can line the jars pu 36 diff ways.
We have that
cos A=0.25
so
A=arc cos (0.25)-------> using a calculator----> A=75.5225°
Round to the nearest hundredth-----> A=75.52²
the answer is
the option <span>75.52°</span>
The trig functions that you need to deal with are
Sine
Cosine
Tangent
Cotangent
Cosecant
Secant
You need to write a single expression using all six trig functions such that the value of the expression equals 3.
To make this as simple as possible, the first thing I would do is look up the values of these functions and identify which ones are equal to either 1/2 or 1.0 or 2.0
sin(30º) = 1/2
sin(90º) = 1
cos(0º) = 1
cos(60º) = 1/2
tan(45º) = 1
csc(30º) = 2
csc(90º) = 1
sec(0º) = 1
sec(60º) = 2
cot(45º) = 1
If we only had to use three trig functions (sin, cos, tan), one possibility is
tan(45º) + cos(0º)/sin(30º) = 1 + 1/(1/2) = 1 + 2 = 3
noticed how I chose one each of the required functions and the operations so that the result = 3.
Now it is up to you to figure out how to combine all six trig functions so that they equal zero. There are many possibilities for you to choose from..