1) ![y=-0.5x-2](https://tex.z-dn.net/?f=y%3D-0.5x-2)
The graph of the above equation is attached in the attachment below.
For all the values from negative infinity to -4, the function is positive.
X ∈ (-∞,-4]
2) ![y=-1.5x+3](https://tex.z-dn.net/?f=y%3D-1.5x%2B3)
To find the x- intercept, plug y =0
![0=-1.5x+3](https://tex.z-dn.net/?f=0%3D-1.5x%2B3)
![1.5x=3](https://tex.z-dn.net/?f=1.5x%3D3)
![x=2](https://tex.z-dn.net/?f=x%3D2)
x intercept = (2,0)
To find the y- intercept, plug x=0
![y=-1.5(0)+3](https://tex.z-dn.net/?f=y%3D-1.5%280%29%2B3)
![y=3](https://tex.z-dn.net/?f=y%3D3)
Y- intercept = ( 0,3)
3) ![y=13-x](https://tex.z-dn.net/?f=y%3D13-x)
Y- intercept = (0,13)
x- intercept = (13,0)
Area of triangle = ![\frac{bh}{2}](https://tex.z-dn.net/?f=%5Cfrac%7Bbh%7D%7B2%7D)
Area of triangle = ![\frac{13\times13}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B13%5Ctimes13%7D%7B2%7D)
Area =
sq unit.
4) The graphs of
and
is attached in the attachment below.
The intersection point is ( 5,-3)
5) A = (-3,0)
B = (4,5)
C = (0,-4)
Slope of AB = ![\frac{5-0)}{4-(-3)} =\frac{5}{7}](https://tex.z-dn.net/?f=%5Cfrac%7B5-0%29%7D%7B4-%28-3%29%7D%20%3D%5Cfrac%7B5%7D%7B7%7D)
Slope intercept of line ![y=mx+b](https://tex.z-dn.net/?f=y%3Dmx%2Bb)
Where, m is the slope and b is the y- intercept.
Plugging point A and the slope in the y- intercept to find the value of b.
![0=\frac{5(-3)}{7} +b](https://tex.z-dn.net/?f=0%3D%5Cfrac%7B5%28-3%29%7D%7B7%7D%20%2Bb)
![b=\frac{15}{7}](https://tex.z-dn.net/?f=b%3D%5Cfrac%7B15%7D%7B7%7D)
Equation of line AB: ![y=\frac{5x}{7} +\frac{15}{7}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B5x%7D%7B7%7D%20%2B%5Cfrac%7B15%7D%7B7%7D)
Slope of BC = ![\frac{-4-5}{0-4} =\frac{9}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B-4-5%7D%7B0-4%7D%20%3D%5Cfrac%7B9%7D%7B4%7D)
Plug C = (0,-4)
![-4=0+b](https://tex.z-dn.net/?f=-4%3D0%2Bb)
b=-4
equation of line BC= ![y=\frac{9x}{4} -4](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B9x%7D%7B4%7D%20-4)
Slope of line AC = ![\frac{-4-0}{0--3} =\frac{-4}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B-4-0%7D%7B0--3%7D%20%3D%5Cfrac%7B-4%7D%7B3%7D)
Equation of line AC = ![y=\frac{-4x}{3} -4](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B-4x%7D%7B3%7D%20-4)
Y intercept of AB = ![(0,\frac{15}{7} )](https://tex.z-dn.net/?f=%280%2C%5Cfrac%7B15%7D%7B7%7D%20%29)
9514 1404 393
Answer:
![\displaystyle\int^5_2 {(3x^3-7x)} \, dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cint%5E5_2%20%7B%283x%5E3-7x%29%7D%20%5C%2C%20dx)
Step-by-step explanation:
The interval of interest becomes the limits of integration. ∆x becomes dx, and the xi are replaced by the variable of integration, x.
Answer:
so ......when you write the equation for this question,
the original height (H) = current height + the decreased height
i.e.
H= 347m + 182m
H = 529 m
so the original height of the helicopter is 529 meters
Step-by-step explanation:
Answer:
11 = x
Step-by-step explanation:
The given angles are alternate interior angles so they have same measurement
66 = 6x divide both sides by 6
11 = x
The answer is 5.5 because 66/12= 5.5, hope this helps..