235/4 equals 58.75
Hope this helps!
<span>sqrt(3x+7)=x-1 </span>One solution was found : <span> x = 6
</span>Radical Equation entered :
<span> √3x+7 = x-1
</span>
Step by step solution :<span>Step 1 :</span>Isolate the square root on the left hand side :
Radical already isolated
<span> √3x+7 = x-1
</span>
<span>Step 2 :</span>Eliminate the radical on the left hand side :
Raise both sides to the second power
<span> (√3x+7)2 = (x-1)2
</span> After squaring
<span> 3x+7 = x2-2x+1
</span>
<span>Step 3 :</span>Solve the quadratic equation :
Rearranged equation
<span> x2 - 5x -6 = 0
</span>
This equation has two rational roots:
<span> {x1, x2}={6, -1}
</span>
<span>Step 4 :</span>Check that the first solution is correct :
Original equation
<span> √3x+7 = x-1
</span> Plug in 6 for x
<span> √3•(6)+7 = (6)-1
</span> Simplify
<span> √25 = 5
</span> Solution checks !!
Solution is:
<span> x = 6
</span>
<span>Step 5 :</span>Check that the second solution is correct :
Original equation
<span> √3x+7 = x-1
</span> Plug in -1 for x
<span> √3•(-1)+7 = (-1)-1
</span> Simplify
<span> √4 = -2
</span> Solution does not check
2 ≠ -2
One solution was found : <span> x = 6</span>
Answer:
- a) AB = 10 units
- b) Midpoint is (2, 6)
===================
<h3 /><h3>Given</h3>
- Points A( - 1, 10) and B(5, 2)
<h3>To find</h3>
- a) The length of AB
- b) The midpoint of AB
<h3>Solution</h3>
a) Use the distance formula:
![d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}](https://tex.z-dn.net/?f=d%20%3D%20%5Csqrt%7B%28x_2-x_1%29%5E2%2B%28y_2-y_1%29%5E2%7D)
Substitute the coordinates and calculate:
![d=\sqrt{(5-(-1))^2+(2-10)^2} =\sqrt{6^2+(-8)^2} =\sqrt{36+64} =\sqrt{100} =10](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%285-%28-1%29%29%5E2%2B%282-10%29%5E2%7D%20%3D%5Csqrt%7B6%5E2%2B%28-8%29%5E2%7D%20%3D%5Csqrt%7B36%2B64%7D%20%3D%5Csqrt%7B100%7D%20%3D10)
The distance is AB = 10 units
b) Use midpoint formula and find x and y- coordinates of this point:
and ![y= \cfrac{y_1+y_2}{2}](https://tex.z-dn.net/?f=y%3D%20%5Ccfrac%7By_1%2By_2%7D%7B2%7D)
Substitute coordinates and find the midpoint:
and ![y= \cfrac{10+2}{2}=6](https://tex.z-dn.net/?f=y%3D%20%5Ccfrac%7B10%2B2%7D%7B2%7D%3D6)
The midpoint is (2, 6)
Answer:
1/2
Step-by-step explanation:
Please kindly check the attached file for explanation
Use TrianCal to draw a triangle with phi as Great Piramid (minimum perimeter given 2 equal heights) = maximun stability.
NOTE: Phi=(1+√5)/2≈1.62 and acos(1/Phi)≈51.83º