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https://web2.0calc.com/questions/geometry-question_69

TU = AM

Radius = sqrt[AB² + (CD/2)²] = 4√13

Five angles of a hexagon measure
\(119^\circ,~ 129^\circ,~ 140^\circ,~ 129^\circ,~\) and \(95^\circ\).
What is the measure of the sixth angle?

\(\begin{array}{|rcll|} \hline \small{119^\circ+129^\circ+140^\circ+129^\circ+95^\circ + x} &=& 4*180^\circ \\ x &=& \small{4*180^\circ -119^\circ+129^\circ+140^\circ+129^\circ+95^\circ} \\ x &=& 108^\circ \\ \hline \end{array} \)

Given 4*10^(2-x)=3*e^(2x+3) what would be the value of x?

\(\begin{array}{|rcll|} \hline 4*10^{2-x}&=&3*e^{2x+3} \\\\ && \boxed{ 10^{2-x}=e^{(2-x)\ln(10)}} \\\\ 4*e^{(2-x)\ln(10)}&=&3*e^{2x+3} \\\\ \dfrac{4}{3} &=& \dfrac{e^{2x+3}} {e^{(2-x)\ln(10)}} \\\\ \dfrac{4}{3} &=& e^{2x+3-(2-x)\ln(10)} \\\\ \dfrac{4}{3} &=& e^{2x+3-2\ln(10)+x\ln(10)} \\\\ \ln \left(\dfrac{4}{3} \right) &=& \ln\left( e^{2x+3-2\ln(10)+x\ln(10)} \right) \\\\ \ln \left(\dfrac{4}{3} \right) &=& 2x+3-2\ln(10)+x\ln(10) \\\\ 2x+x\ln(10) &=& \ln \left(\dfrac{4}{3} \right)+2\ln(10)-3 \\\\ x\Big(2+\ln(10)\Big) &=& \ln \left(\dfrac{4}{3} \right)+\ln(10^2)-3 \\\\ x\Big(2+\ln(10)\Big) &=& \ln \left(\dfrac{4*10^2}{3} \right)-3 \\\\ x\Big(2+\ln(10)\Big) &=& \ln \left(\dfrac{400}{3} \right)-3 \\\\ \mathbf{x} &=& \mathbf{ \dfrac{\ln \left(\dfrac{400}{3} \right)-3} {2+\ln(10)} } \\ \hline \end{array}\)

What is the numerical value of \(x\):
\(x = \dfrac{1}{3-\dfrac{1}{3-\dfrac{1}{3-\ldots}}}\)

\(\begin{array}{|rcll|} \hline x &=& \dfrac{1}{3-\dfrac{1}{3-\dfrac{1}{3-\ldots}}} \\\\ x &=& \dfrac{1}{3-x} \\\\ x(3-x) &=& 1 \\\\ 3x-x^2 &=& 1 \\\\ \mathbf{x^2-3x+1} &=& \mathbf{0} \\\\ x &=& \dfrac{3\pm \sqrt{9-4*1} }{2} \\\\ x &=& \dfrac{3\pm \sqrt{5} }{2} \\\\ \mathbf{x} &=& \mathbf{\dfrac{3-\sqrt{5} } {2} } \\ \hline \end{array}\)

(-3,0) and (-5,0)

means that    (x+3)(x+5) = y

                          y = x^2 + 8x+ 15

https://web2.0calc.com/questions/the-vertex-of-a-parabola-is-at-12-4-and-its-axis

he three letters can form  26 * 26 * 26 combos = 17576

  they have four positions in the six string plate they can be in

     17576 x 4

   then the remaining 3 numbers can form 1000 combos

      17576 * 4 * 1000 = ________ combos

x = 0rigianl amount

give away 1/3  and 4 more leaves     2/3 x - 4

give away 1/3 of remaining and 3 more     leaves     2/3 (2/3x-4) -3

 give 1/3 away of remaining and 3 more leaves         2/3 ( 2/3(2/3x-4)-3) - 3

                 and that = 3 left

   2/3 ( 2/3(2/3x-4)-3) - 3 = 3

   2/3 ( 4/9x - 8/3 -3) = 6

2/3 (4/9x - 17/3) = 6

8/27x - 34/9 = 6

x = 33 originally

Answer is 360 - 99 - 138...I'm sure you can do that yourself :)

They all sum to 360^o ...... need any more help than that?

https://web2.0calc.com/questions/let-a-b-c-be-points-on-circle-o-such-that-ab-is-a-diameter#r2

https://web2.0calc.com/questions/math_87917

x = origianl price

x - 6 * x/40  = 117

34/40 x = 117

x=117*40/34 = 137.65   dollars     Assuming prorated discounts  ( i.e.   6 discount for 40     3 discount for 20   etc)

If no prorated discount

x - 18 = 117

x = 135 dollars

TO :   579.24/2 = 289.62 km/hr

RETURN 579.24/5.6=103.43 km/hr

7.6 hours roundtrip  of 1158.48 km

Average = 152.43  km/ hr    = plane speed

152.43 - 103.43 = wind speed = 48.99=~~49 km/hr

Thadeus’s Thanksgiving feast was just too much! He started cooking the 70-pound turkey at 11:00 A.M.
At 11:30 A.M., he purchased 35 pounds of popcorn. He baked 700 pumpkin pies and half as many giblet-chip cookies. At 8:30 P.M., the turkey was finished cooking. His guests arrived at 6:00 P.M. They immediately ate 2/3 of the cookies! How long did it take Thadeus’s turkey to cook?

if the start time was 11:00 am and the end time was 8:30 PM, it took 1+8.5 = 9.5 -> 9 hrs and 30 minutes for the turkey to cook

hope this helps :)

it is in Quadrant III   so cos is negative     reference angle is   45⁰        Enough clues?

A quadrilateral has four points A(0,1), B(1,-3), C(5,-2) and D(4,0) as coordinates What is the area of quadrilateral ABCD?

Hello Guest!

\(A_{ABCD}=◻5\times 3+◿\ 4\times1/2- ◺\ 4\times1/2-◿\ 4\times1/2-◹\ 2\times 1/2\)

\(A_{ABCD}=15+2-2-2-1\)

\(A_{ABCD}=12\)

  !

x(x + 6) > 16 + x(x + 3)

x^2 + 6x > 16 + x^2 + 3x

3x>16

x > 16/3

Let's simplify first: 4x^2 + 10x + ____ is the square of a binomial

(a + b)^2 = a^2 + b^2 + 2ab

so (2x + 2.5)^2, so that means ____ = 25/4. 

4t^2 <= 9t - 2 - 13t + 2t^2

2t^2 +4t+2 <=0    

t^2 + 2t+2 <= 0

(t+1)^2 <= 0

t = -1     is the only answer

2t^2 <= -4t - 2

t^2 <= -2t - 1

t^2 + 2t + 1 <= 0

(t + 1)(t + 1) <= 0

t >= -1

x^2 + 8x + ____ + 3x^2 + 2x      condense

4x^2 + 10x + _____   

4 (x^2 + 2.5x) + ____

4 (x + 1.25)^2

4x^2 +10x  + 25/4            =  (2x +2.5)^2

Let f(x)=3x^2  - 4x - x^2 + 7x + 8. Find the constant k such that f(x)=f(k-x) for all real numbers x. 

Hello Guest!

\(f(x)=3x^2 - 4x - x^2 + 7x + 8=f(k-x) \)

\(k\in \mathbb R\ |\ 6\leq k<\infty\)

  !

hey,

this question has been answered before. check out this link: https://web2.0calc.com/questions/decimals_12

hope this helps :)