Answer: ![\large \boldsymbol {C) \ AB=\sqrt{41} }](https://tex.z-dn.net/?f=%5Clarge%20%5Cboldsymbol%20%7BC%29%20%5C%20AB%3D%5Csqrt%7B41%7D%20%7D)
Step-by-step explanation:
- The formula for the distance between points:
- Coordinates of point A (0;5 ); coordinates of point B(4;0)
![\bf AB= \sqrt{(0-4)^2+(5-0)^2} =\sqrt{16+25} =\sqrt{41}](https://tex.z-dn.net/?f=%5Cbf%20AB%3D%20%5Csqrt%7B%280-4%29%5E2%2B%285-0%29%5E2%7D%20%3D%5Csqrt%7B16%2B25%7D%20%3D%5Csqrt%7B41%7D)
Answer:
<h3>
![x = 5 + \sqrt{35} \: \: \:or \: \: \: x = 5 - \sqrt{35} \\](https://tex.z-dn.net/?f=x%20%3D%205%20%20%2B%20%20%5Csqrt%7B35%7D%20%20%5C%3A%20%20%5C%3A%20%20%5C%3Aor%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20x%20%3D%205%20-%20%20%5Csqrt%7B35%7D%20%20%5C%5C)
</h3>
Step-by-step explanation:
x² - 10x + 25 = 35
Move 35 to the left side of the equation
That's
x² - 10x + 25 - 35 = 0
x ² - 10x - 10 = 0
Using the quadratic formula solve the equation
That's
<h3>
![x = \frac{ - b\pm \sqrt{ {b}^{2} - 4ac } }{2a}](https://tex.z-dn.net/?f=x%20%3D%20%20%5Cfrac%7B%20-%20b%5Cpm%20%5Csqrt%7B%20%7Bb%7D%5E%7B2%7D%20-%204ac%20%7D%20%7D%7B2a%7D%20)
</h3>
From the question
a = 1 , b = - 10 , c = - 10
Substitute the values into the above formula and solve
That's
![x = \frac{ - - 10\pm \sqrt{( { - 10})^{2} - 4(1)( - 10) } }{2(1)} \\ = \frac{10\pm \sqrt{100 + 40} }{2} \\ = \frac{10\pm \sqrt{140} }{2} \\ = \frac{10\pm2 \sqrt{35} }{2} \\ = \frac{10}{2} \pm \frac{2 \sqrt{35} }{2} \\ = 5\pm \sqrt{35}](https://tex.z-dn.net/?f=x%20%3D%20%20%5Cfrac%7B%20-%20%20-%2010%5Cpm%20%5Csqrt%7B%28%20%7B%20-%2010%7D%29%5E%7B2%7D%20-%204%281%29%28%20-%2010%29%20%7D%20%7D%7B2%281%29%7D%20%20%5C%5C%20%20%3D%20%20%5Cfrac%7B10%5Cpm%20%5Csqrt%7B100%20%2B%2040%7D%20%7D%7B2%7D%20%20%5C%5C%20%20%3D%20%20%5Cfrac%7B10%5Cpm%20%5Csqrt%7B140%7D%20%7D%7B2%7D%20%20%5C%5C%20%20%3D%20%20%5Cfrac%7B10%5Cpm2%20%5Csqrt%7B35%7D%20%7D%7B2%7D%20%20%5C%5C%20%20%3D%20%20%5Cfrac%7B10%7D%7B2%7D%20%5Cpm%20%5Cfrac%7B2%20%5Csqrt%7B35%7D%20%7D%7B2%7D%20%20%5C%5C%20%20%3D%205%5Cpm%20%5Csqrt%7B35%7D%20)
We have the final answer as
<h3>
![x = 5 + \sqrt{35} \: \: \:or \: \: \: x = 5 - \sqrt{35} \\](https://tex.z-dn.net/?f=x%20%3D%205%20%20%2B%20%20%5Csqrt%7B35%7D%20%20%5C%3A%20%20%5C%3A%20%20%5C%3Aor%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20x%20%3D%205%20-%20%20%5Csqrt%7B35%7D%20%20%5C%5C%20)
</h3>
Hope this helps you
Answer:
C
Step-by-step explanation:
Work backwards. You are given -3 , -30 for C. If you add -3 + 3 and the divide it by 2 , you get 0. If you add 8 + -20 and divide by 2 you get -6 , so the answer is C.
Answer:
28 scrapbook pages is the answer
Ok lets do this like this:
<span>Let x = length
Let y = width
From this we know that area A=xy.
</span><span>Now, perimeter is P=2x+2y
cost would be 3(2x)+2(2y) or 6x +4y=$6,000.00.
From this cost equation we solve for x in terms of y
6x=6000-4y
x=1000-(4y)/6.
</span>now lets substitute this value in the area equation A=xy.
A=(1000-4y/6)y
<span>A=1000y−4<span>y2</span>/6=1000y−2<span>y2</span>/3</span>
differentiate and set to equal zero (0)
<span>1000−(−4y/3)=0</span><span>
Solve for y and obtain y=750ft</span>