Answer:
5th option
52° bc its alternating interior with 2.
added together they would equal 180°
Answer:
it's D
Step-by-step explanation:
it's d because if 74 would be the same as the left side next to x and if you turn that into a problem like 180-74 and I got 180 cause half of a circle is 180 and then my answer would be 106 I'm not good at explaining but it's d
D will form a triangle
good luck
Answer:
26
Step-by-step explanation:
The two angles shown are a linear pair. Their sum is 180°.
(4z -8)° +(3z +6)° = 180°
7z = 182 . . . . . . . . . divide by °, add 2
z = 26 . . . . . . . . . . divide by 7
Answer:
a) (i)
, (ii)
, (iii)
, (iv)
, (v)
, (vi)
, (vii)
, (viii)
; b)
; c) The equation of the tangent line to curve at P (7, -2) is
.
Step-by-step explanation:
a) The slope of the secant line PQ is represented by the following definition of slope:
![m = \frac{\Delta y}{\Delta x} = \frac{y_{Q}-y_{P}}{x_{Q}-x_{P}}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B%5CDelta%20y%7D%7B%5CDelta%20x%7D%20%3D%20%5Cfrac%7By_%7BQ%7D-y_%7BP%7D%7D%7Bx_%7BQ%7D-x_%7BP%7D%7D)
(i)
:
![y_{Q} =\frac{2}{6-6.9}](https://tex.z-dn.net/?f=y_%7BQ%7D%20%3D%5Cfrac%7B2%7D%7B6-6.9%7D)
![y_{Q} = -2.222](https://tex.z-dn.net/?f=y_%7BQ%7D%20%3D%20-2.222)
![m = \frac{-2.222 + 2}{6.9-7}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B-2.222%20%2B%202%7D%7B6.9-7%7D)
![m = 2.22](https://tex.z-dn.net/?f=m%20%3D%202.22)
(ii) ![x_{Q} = 6.99](https://tex.z-dn.net/?f=x_%7BQ%7D%20%3D%206.99)
![y_{Q} =\frac{2}{6-6.99}](https://tex.z-dn.net/?f=y_%7BQ%7D%20%3D%5Cfrac%7B2%7D%7B6-6.99%7D)
![y_{Q} = -2.020](https://tex.z-dn.net/?f=y_%7BQ%7D%20%3D%20-2.020)
![m = \frac{-2.020 + 2}{6.99-7}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B-2.020%20%2B%202%7D%7B6.99-7%7D)
![m = 2](https://tex.z-dn.net/?f=m%20%3D%202)
(iii) ![x_{Q} = 6.999](https://tex.z-dn.net/?f=x_%7BQ%7D%20%3D%206.999)
![y_{Q} =\frac{2}{6-6.999}](https://tex.z-dn.net/?f=y_%7BQ%7D%20%3D%5Cfrac%7B2%7D%7B6-6.999%7D)
![y_{Q} = -2.002](https://tex.z-dn.net/?f=y_%7BQ%7D%20%3D%20-2.002)
![m = \frac{-2.002 + 2}{6.999-7}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B-2.002%20%2B%202%7D%7B6.999-7%7D)
![m = 2](https://tex.z-dn.net/?f=m%20%3D%202)
(iv) ![x_{Q} = 6.9999](https://tex.z-dn.net/?f=x_%7BQ%7D%20%3D%206.9999)
![y_{Q} =\frac{2}{6-6.9999}](https://tex.z-dn.net/?f=y_%7BQ%7D%20%3D%5Cfrac%7B2%7D%7B6-6.9999%7D)
![y_{Q} = -2.0002](https://tex.z-dn.net/?f=y_%7BQ%7D%20%3D%20-2.0002)
![m = \frac{-2.0002 + 2}{6.9999-7}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B-2.0002%20%2B%202%7D%7B6.9999-7%7D)
![m = 2](https://tex.z-dn.net/?f=m%20%3D%202)
(v) ![x_{Q} = 7.1](https://tex.z-dn.net/?f=x_%7BQ%7D%20%3D%207.1)
![y_{Q} =\frac{2}{6-7.1}](https://tex.z-dn.net/?f=y_%7BQ%7D%20%3D%5Cfrac%7B2%7D%7B6-7.1%7D)
![y_{Q} = -1.818](https://tex.z-dn.net/?f=y_%7BQ%7D%20%3D%20-1.818)
![m = \frac{-1.818 + 2}{7.1-7}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B-1.818%20%2B%202%7D%7B7.1-7%7D)
![m = 1.82](https://tex.z-dn.net/?f=m%20%3D%201.82)
(vi) ![x_{Q} = 7.01](https://tex.z-dn.net/?f=x_%7BQ%7D%20%3D%207.01)
![y_{Q} =\frac{2}{6-7.01}](https://tex.z-dn.net/?f=y_%7BQ%7D%20%3D%5Cfrac%7B2%7D%7B6-7.01%7D)
![y_{Q} = -1.980](https://tex.z-dn.net/?f=y_%7BQ%7D%20%3D%20-1.980)
![m = \frac{-1.980 + 2}{7.01-7}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B-1.980%20%2B%202%7D%7B7.01-7%7D)
![m = 2](https://tex.z-dn.net/?f=m%20%3D%202)
(vii) ![x_{Q} = 7.001](https://tex.z-dn.net/?f=x_%7BQ%7D%20%3D%207.001)
![y_{Q} =\frac{2}{6-7.001}](https://tex.z-dn.net/?f=y_%7BQ%7D%20%3D%5Cfrac%7B2%7D%7B6-7.001%7D)
![y_{Q} = -1.998](https://tex.z-dn.net/?f=y_%7BQ%7D%20%3D%20-1.998)
![m = \frac{-1.998 + 2}{7.001-7}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B-1.998%20%2B%202%7D%7B7.001-7%7D)
![m = 2](https://tex.z-dn.net/?f=m%20%3D%202)
(viii) ![x_{Q} = 7.0001](https://tex.z-dn.net/?f=x_%7BQ%7D%20%3D%207.0001)
![y_{Q} =\frac{2}{6-7.0001}](https://tex.z-dn.net/?f=y_%7BQ%7D%20%3D%5Cfrac%7B2%7D%7B6-7.0001%7D)
![y_{Q} = -1.9998](https://tex.z-dn.net/?f=y_%7BQ%7D%20%3D%20-1.9998)
![m = \frac{-1.9998 + 2}{7.0001-7}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B-1.9998%20%2B%202%7D%7B7.0001-7%7D)
![m = 2](https://tex.z-dn.net/?f=m%20%3D%202)
b) The slope at P (7,-2) can be estimated by using the following average:
![m \approx \frac{f(6.9999)+f(7.0001)}{2}](https://tex.z-dn.net/?f=m%20%5Capprox%20%5Cfrac%7Bf%286.9999%29%2Bf%287.0001%29%7D%7B2%7D)
![m \approx \frac{2+2}{2}](https://tex.z-dn.net/?f=m%20%5Capprox%20%5Cfrac%7B2%2B2%7D%7B2%7D)
![m \approx 2](https://tex.z-dn.net/?f=m%20%5Capprox%202)
The slope of the tangent line to the curve at P(7, -2) is 2.
c) The equation of the tangent line is a first-order polynomial with the following characteristics:
![y = m\cdot x + b](https://tex.z-dn.net/?f=y%20%3D%20m%5Ccdot%20x%20%2B%20b)
Where:
- Independent variable.
- Depedent variable.
- Slope.
- x-Intercept.
The slope was found in point (b) (m = 2). Besides, the point of tangency (7,-2) is known and value of x-Intercept can be obtained after clearing the respective variable:
![-2 = 2 \cdot 7 + b](https://tex.z-dn.net/?f=-2%20%3D%202%20%5Ccdot%207%20%2B%20b)
![b = -2 + 14](https://tex.z-dn.net/?f=b%20%3D%20-2%20%2B%2014)
![b = 12](https://tex.z-dn.net/?f=b%20%3D%2012)
The equation of the tangent line to curve at P (7, -2) is
.