Answer:
2
Step-by-step explanation:
<u>Given AP where:</u>
<u>To find</u>
<u>Since</u>
- a₄ = a₁ + 3d
- a₂ = a₁ + d
- a₆ = a₁ + 5d
<u>Initial equations will change as:</u>
- a₁ + 3d = 2(a₁ + d) - 1 ⇒ a₁ + 3d = 2a₁ + 2d - 1 ⇒ a₁ = d + 1
- a₁ + 5d = 7 ⇒ a₁ = 7 - 5d
<u>Comparing the above:</u>
- d + 1 = 7 - 5d
- 6d = 6
- d = 1
<u>Then:</u>
- a₁ = d + 1 = 1 + 1 = 2
- a₁ = 2
The first term is 2
Answer:
centre = (13,0)
radius = 8
Step-by-step explanation:
The standard equation of the circle is
(x-x0)^2 + (y-y0)^2 = r^2 ...............(1)
where
(x0,y0) is the centre,
r is the radius.
For
(x-13)^2 + y^2 = 64 ..............(2)
we rewrite (2)
(x-13)^2 + (y-0)^2 = 8^2 ...............(3)
and compare (3) with (1)
to identify
x0 = 13, y0 = 0, and r = 8
Therefore
centre = (13,0)
radius = 8
The answer is 0.019 i think
Answer:
It is three times as large
Step-by-step explanation:
If a ration is also a fraction, and your wording is correct than an enlargement of 1:3 where 1 is the original shape would suggest that the 3 would be that same original shape, be enlarged in terms of 3 compares to 1 so a 300% enlargement.
if the original rectangle has a 16 cm perimeter, than the new rectangle has a 48 cm perimeter.
We performed the following operations:
![f(x)=\sqrt[3]{x}\mapsto g(x)=2\sqrt[3]{x}=2f(x)](https://tex.z-dn.net/?f=f%28x%29%3D%5Csqrt%5B3%5D%7Bx%7D%5Cmapsto%20g%28x%29%3D2%5Csqrt%5B3%5D%7Bx%7D%3D2f%28x%29)
If you multiply the parent function by a constant, you get a vertical stretch if the constant is greater than 1, a vertical compression if the constant is between 0 and 1. In this case the constant is 2, so we have a vertical stretch.
![g(x)=2\sqrt[3]{x}\mapsto h(x)=-2\sqrt[3]{x}=-g(x)](https://tex.z-dn.net/?f=g%28x%29%3D2%5Csqrt%5B3%5D%7Bx%7D%5Cmapsto%20h%28x%29%3D-2%5Csqrt%5B3%5D%7Bx%7D%3D-g%28x%29)
If you change the sign of a function, you reflect its graph across the x axis.
![h(x)=-2\sqrt[3]{x}\mapsto m(x)=-2\sqrt[3]{x}-1=h(x)-1](https://tex.z-dn.net/?f=h%28x%29%3D-2%5Csqrt%5B3%5D%7Bx%7D%5Cmapsto%20m%28x%29%3D-2%5Csqrt%5B3%5D%7Bx%7D-1%3Dh%28x%29-1)
If you add a constant to a function, you translate its graph vertically. If the constant is positive, you translate upwards, otherwise you translate downwards. In this case, the constant is -1, so you translate 1 unit down.
