Answer:
-2 > k > -7
Step-by-step explanation:
what you do to one section, you have to do to all
-5 < -5k - 15 < 20
add 15 to each part
10 < -5k < 35
divide by -5 (when you divide by a negative, it flips the inequality signs!)
-2 > k > -7
Answer:
A line that is perpendicular to y=2/5x-5 must have a slope of -5/2, but a line parallel to line y=5/2x+6 must have a slope of 5/2, and these slopes do not match up.
Explanation:
In order for a line to be parallel to another line, they must have the same slope. In order for a line to be perpendicular to another line, their slopes must be opposite reciprocals (meaning that when they are multiplied, the product is -1). From here you can find what slope the line must have to perpendicular or parallel to another line, and then you can see that the answers to not match up to be the same line!
Hope this helped :)
For this case we must solve the following quadratic equation:
![x ^ 2 + 2x-6 = 0](https://tex.z-dn.net/?f=x%20%5E%202%20%2B%202x-6%20%3D%200)
Where:
![a = 1\\b = 2\\c = -6](https://tex.z-dn.net/?f=a%20%3D%201%5C%5Cb%20%3D%202%5C%5Cc%20%3D%20-6)
The solution is given by:
![x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2a}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%20%7B-b%20%5Cpm%20%5Csqrt%20%7Bb%20%5E%202-4%20%28a%29%20%28c%29%7D%7D%20%7B2a%7D)
Substituting:
![x = \frac {-2 \pm \sqrt {2 ^ 2-4 (1) (- 6)}} {2 (1)}\\x = \frac {-2 \pm \sqrt {4 + 24}} {2}\\x = \frac {-2 \pm \sqrt {28}} {2}\\x = \frac {-2 \pm \sqrt {2 ^ 2 * 7}} {2}\\x = \frac {-2 \pm2 \sqrt {7}} {2}\\x = -1 \pm \sqrt {7}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%20%7B-2%20%5Cpm%20%5Csqrt%20%7B2%20%5E%202-4%20%281%29%20%28-%206%29%7D%7D%20%7B2%20%281%29%7D%5C%5Cx%20%3D%20%5Cfrac%20%7B-2%20%5Cpm%20%5Csqrt%20%7B4%20%2B%2024%7D%7D%20%7B2%7D%5C%5Cx%20%3D%20%5Cfrac%20%7B-2%20%5Cpm%20%5Csqrt%20%7B28%7D%7D%20%7B2%7D%5C%5Cx%20%3D%20%5Cfrac%20%7B-2%20%5Cpm%20%5Csqrt%20%7B2%20%5E%202%20%2A%207%7D%7D%20%7B2%7D%5C%5Cx%20%3D%20%5Cfrac%20%7B-2%20%5Cpm2%20%5Csqrt%20%7B7%7D%7D%20%7B2%7D%5C%5Cx%20%3D%20-1%20%5Cpm%20%5Csqrt%20%7B7%7D)
Thus, we have two roots:
![x_ {1} = - 1+ \sqrt {7}\\x_ {2} = - 1- \sqrt {7}](https://tex.z-dn.net/?f=x_%20%7B1%7D%20%3D%20-%201%2B%20%5Csqrt%20%7B7%7D%5C%5Cx_%20%7B2%7D%20%3D%20-%201-%20%5Csqrt%20%7B7%7D)
ANswer:
![x_ {1} = - 1+ \sqrt {7}\\x_ {2} = - 1- \sqrt {7}](https://tex.z-dn.net/?f=x_%20%7B1%7D%20%3D%20-%201%2B%20%5Csqrt%20%7B7%7D%5C%5Cx_%20%7B2%7D%20%3D%20-%201-%20%5Csqrt%20%7B7%7D)
Answer:
Answer choice A) About 38.47 square units
Step-by-step explanation:
Since all four sides of a square have the same length, the perimeter of a square is just 4 times one of the side lengths. The perimeter of the square and therefore the circumference of the circle is 5.5*4=22. The circumference of a circle is 2 times the radius multiplied by pi. The radius of this circle is therefore:
![\dfrac{22}{2\pi}\approx 3.503](https://tex.z-dn.net/?f=%5Cdfrac%7B22%7D%7B2%5Cpi%7D%5Capprox%203.503)
Since the area of a circle is
, the area of this circle is:
![\pi \cdot 3.503^2= 3.14\cdot 12.271\approx 38.47](https://tex.z-dn.net/?f=%5Cpi%20%5Ccdot%203.503%5E2%3D%203.14%5Ccdot%2012.271%5Capprox%2038.47)
Hope this helps!
Answer:
C , 30 N
Step-by-step explanation: