Answer:
Rhombus
Step-by-step explanation:
Rhombus: A quadrilateral with four congruent sides and two pairs of parallel sides.
<h3>Hope it is helpful...</h3>
Answer:
x = 21.013155617496
Step-by-step explanation:
we have a right triangle then ,
![\cos \left( 36\right) =\frac{17}{x}](https://tex.z-dn.net/?f=%5Ccos%20%5Cleft%28%2036%5Cright%29%20%20%3D%5Cfrac%7B17%7D%7Bx%7D)
Then
![x=\frac{17}{\cos \left( 36\right) } = 21.013155617496](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B17%7D%7B%5Ccos%20%5Cleft%28%2036%5Cright%29%20%20%7D%20%3D%2021.013155617496)
Then
x ≈ 21
Look for a common number in all the terms
6(2a+3b-c)
Answer:
![x=-\frac{-20+\sqrt{-20w+3600}}{10},\:x=-\frac{-20-\sqrt{-20w+3600}}{10}](https://tex.z-dn.net/?f=x%3D-%5Cfrac%7B-20%2B%5Csqrt%7B-20w%2B3600%7D%7D%7B10%7D%2C%5C%3Ax%3D-%5Cfrac%7B-20-%5Csqrt%7B-20w%2B3600%7D%7D%7B10%7D)
Step-by-step explanation:
![w=-5\left(x-8\right)\left(x+4\right)\\\mathrm{Expand\:}-5\left(x-8\right)\left(x+4\right):\quad -5x^2+20x+160\\w=-5x^2+20x+160\\Switch\:sides\\-5x^2+20x+160=w\\\mathrm{Subtract\:}w\mathrm{\:from\:both\:sides}\\-5x^2+20x+160-w=w-w\\Simplify\\-5x^2+20x+160-w=0\\Solve\:with\:the\:quadratic\:formula\\\mathrm{Quadratic\:Equation\:Formula:}\\\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}\\x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}](https://tex.z-dn.net/?f=w%3D-5%5Cleft%28x-8%5Cright%29%5Cleft%28x%2B4%5Cright%29%5C%5C%5Cmathrm%7BExpand%5C%3A%7D-5%5Cleft%28x-8%5Cright%29%5Cleft%28x%2B4%5Cright%29%3A%5Cquad%20-5x%5E2%2B20x%2B160%5C%5Cw%3D-5x%5E2%2B20x%2B160%5C%5CSwitch%5C%3Asides%5C%5C-5x%5E2%2B20x%2B160%3Dw%5C%5C%5Cmathrm%7BSubtract%5C%3A%7Dw%5Cmathrm%7B%5C%3Afrom%5C%3Aboth%5C%3Asides%7D%5C%5C-5x%5E2%2B20x%2B160-w%3Dw-w%5C%5CSimplify%5C%5C-5x%5E2%2B20x%2B160-w%3D0%5C%5CSolve%5C%3Awith%5C%3Athe%5C%3Aquadratic%5C%3Aformula%5C%5C%5Cmathrm%7BQuadratic%5C%3AEquation%5C%3AFormula%3A%7D%5C%5C%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%5Cx_%7B1%2C%5C%3A2%7D%3D%5Cfrac%7B-b%5Cpm%20%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D)
![\mathrm{For\:}\quad a=-5,\:b=20,\:c=160-w:\quad x_{1,\:2}=\frac{-20\pm \sqrt{20^2-4\left(-5\right)\left(160-w\right)}}{2\left(-5\right)}\\x=\frac{-20+\sqrt{20^2-4\left(-5\right)\left(160-w\right)}}{2\left(-5\right)}:\quad -\frac{-20+\sqrt{-20w+3600}}{10}\\x=\frac{-20-\sqrt{20^2-4\left(-5\right)\left(160-w\right)}}{2\left(-5\right)}:\quad -\frac{-20-\sqrt{-20w+3600}}{10}\\The\:solutions\:to\:the\:quadratic\:equation\:are\\x=-\frac{-20+\sqrt{-20w+3600}}{10},\:x=-\frac{-20-\sqrt{-20w+3600}}{10}](https://tex.z-dn.net/?f=%5Cmathrm%7BFor%5C%3A%7D%5Cquad%20a%3D-5%2C%5C%3Ab%3D20%2C%5C%3Ac%3D160-w%3A%5Cquad%20x_%7B1%2C%5C%3A2%7D%3D%5Cfrac%7B-20%5Cpm%20%5Csqrt%7B20%5E2-4%5Cleft%28-5%5Cright%29%5Cleft%28160-w%5Cright%29%7D%7D%7B2%5Cleft%28-5%5Cright%29%7D%5C%5Cx%3D%5Cfrac%7B-20%2B%5Csqrt%7B20%5E2-4%5Cleft%28-5%5Cright%29%5Cleft%28160-w%5Cright%29%7D%7D%7B2%5Cleft%28-5%5Cright%29%7D%3A%5Cquad%20-%5Cfrac%7B-20%2B%5Csqrt%7B-20w%2B3600%7D%7D%7B10%7D%5C%5Cx%3D%5Cfrac%7B-20-%5Csqrt%7B20%5E2-4%5Cleft%28-5%5Cright%29%5Cleft%28160-w%5Cright%29%7D%7D%7B2%5Cleft%28-5%5Cright%29%7D%3A%5Cquad%20-%5Cfrac%7B-20-%5Csqrt%7B-20w%2B3600%7D%7D%7B10%7D%5C%5CThe%5C%3Asolutions%5C%3Ato%5C%3Athe%5C%3Aquadratic%5C%3Aequation%5C%3Aare%5C%5Cx%3D-%5Cfrac%7B-20%2B%5Csqrt%7B-20w%2B3600%7D%7D%7B10%7D%2C%5C%3Ax%3D-%5Cfrac%7B-20-%5Csqrt%7B-20w%2B3600%7D%7D%7B10%7D)
X^2 - 8x + 13 = 0
subtract 13 from both sides
x^2 - 8x = -13
-8/2 = -4, (-4)^2 = 16, add 16 to both sides
x^2 - 8x + 16 = -13 + 16
factor the left side
(x - 4)^2 = 3