write an equation that models the sequence 400, 200, 100, 50,
a) y = 400(2x)
b) y = 50 (2x)
c) y =
1
2
x + 400
d) y = 400(
1
2
)x-1

D

Step-by-step explanation:

The terms of the sequence

400, 200, 100, 50, ...

These are the terms of a geometric sequence with n th term

= a

where a is the first term and r the common ratio

r = = =

The first term a = 400, hence

y = 400 → D

u = -(6/7)w

step-by-step explanation:

place all values with 'u' on one side of the equation.

4u + 8w = - 3u + 2w

4u + 3u = 2w - 8w

further simplify the equation by solving the addition and subtraction.

7u = - 6w

make 'u' the independent variable by placing its co-efficient on the right-hand side.

u = - (6/7)w

answer: solve 5\cdot 2^x=2405⋅2  

x

=2405, dot, 2, start superscript, x, end superscript, equals, 240.

solution

to solve for xxx, we must first isolate the exponential part. to do this, divide both sides by 555 as shown below. we do not multiply the 555 and the 222 as this goes against the order of operations!

\begin{aligned} 5\cdot 2^x& =240 2^x& =48 \\ \end{aligned}  

5⋅2  

x

2  

x

​    

=240

=48

​

step-by-step explanation: