Answer:
A
Step-by-step explanation:
The graph shows the graph existing for all values greater than x = -2 and the filled in circle at x = -2 shows that that point is also included, giving our answer
Answer:
Cosine Formula :
AC² = AB² + BC² - 2(AB)(BC)cosB
AC² = (40)² + (60)² - 2(40)(60)cos(115°)
AC² = 1600 + 3600 - (4800×(-0.42))
AC² = 5200 + 2016
AC² = 7216
AC = √(7216)
AC = 84.95 km
Hence, the distance of the straight line AC is <u>84.95 km</u>
- <u>84.95km</u> is the right answer.
Answer:
The possible measures of the midsegment are <u>32 units and 212 units</u>.
Step-by-step explanation:
Given:
A triangle PQR with the midsegment made by sides PQ and PR has length equal to
and the base length QR opposite to the midsegment is
.
From midsegment theorem, we know that, the midsegment is a line parallel to the base opposite to it and half the length of the base length.
Therefore, Midsegment =
Base length QR
![8x^2+12x+36=\frac{1}{2}(4x^2+60x+120)\\\\8x^2+12x+36=2x^2+30x+60\\\\(8x^2-2x^2)+(12x-30x)+(36-60)=0\\\\6x^2-18x-24=0\\\\6(x^2-3x-4)=0\\\\x^2-3x-4=0\\\\x^2+x-4x-4=0\\\\x(x+1)-4(x+1)=0\\\\(x+1)(x-4)=0\\\\x=-1\ or\ x=4](https://tex.z-dn.net/?f=8x%5E2%2B12x%2B36%3D%5Cfrac%7B1%7D%7B2%7D%284x%5E2%2B60x%2B120%29%5C%5C%5C%5C8x%5E2%2B12x%2B36%3D2x%5E2%2B30x%2B60%5C%5C%5C%5C%288x%5E2-2x%5E2%29%2B%2812x-30x%29%2B%2836-60%29%3D0%5C%5C%5C%5C6x%5E2-18x-24%3D0%5C%5C%5C%5C6%28x%5E2-3x-4%29%3D0%5C%5C%5C%5Cx%5E2-3x-4%3D0%5C%5C%5C%5Cx%5E2%2Bx-4x-4%3D0%5C%5C%5C%5Cx%28x%2B1%29-4%28x%2B1%29%3D0%5C%5C%5C%5C%28x%2B1%29%28x-4%29%3D0%5C%5C%5C%5Cx%3D-1%5C%20or%5C%20x%3D4)
Now, midsegment can be calculated using the values of 'x'.
First, plug in -1 for 'x'. This gives,
![Midsegment=8(-1)^2+12(-1)+36\\\\Midsegment=8\times 1-12+36\\\\Midsegment=8-12+36=32\ units](https://tex.z-dn.net/?f=Midsegment%3D8%28-1%29%5E2%2B12%28-1%29%2B36%5C%5C%5C%5CMidsegment%3D8%5Ctimes%201-12%2B36%5C%5C%5C%5CMidsegment%3D8-12%2B36%3D32%5C%20units)
Now, plug in 4 for 'x'. This gives,
![Midsegment=8(4)^2+12(4)+36\\\\Midsegment=8\times 16-48+36\\\\Midsegment=128+48+36=212\ units](https://tex.z-dn.net/?f=Midsegment%3D8%284%29%5E2%2B12%284%29%2B36%5C%5C%5C%5CMidsegment%3D8%5Ctimes%2016-48%2B36%5C%5C%5C%5CMidsegment%3D128%2B48%2B36%3D212%5C%20units)
Therefore, the possible measures of the midsegment are 32 units and 212 units
Answer:
X= 1, Y= 4, Z= -2
Step-by-step explanation:
(3(6x-2y-3z=4)) + (-2(9x-3y+3z=-9))
Z=-2
Substitute in Z
(6x-2y+6=4) + (3x+2y-4z=7)
X=1
Substitute in Z and X
3+2y-4=7
Y=4