Answer:
1a. 58/99
1b. 53/90
1c. 29/50
Step-by-step explanation:
let's start with the easiest one
1.(c)
0.58 = 58/100 = 29/50
that is the simplest possible form, as 29 is a prime number and not a factor of 50.
1.(a)
0.585858585858... = 58×0.0101010101010101...
now, we know that 1/"double digit" (like 1/22) mostly produces a repeating pattern with a period length of 2 after the decimal point.
and we find
1/99 = 0.01010101010101...
so, our solution is
58 × 1/99 = 58/99
that is the simplest possible form, as 58 and 99 do not share any factors.
1.(b)
0.5888888888888... = 0.5 + 0.0888888888888... =
= 0.5 + 8×0.01111111111111... = 0.5 + 8×1/10 × 0.1111111111...
we know how to create 0.11111111111... :
1/9 = 0.111111111111111...
so, our solution is
0.5 + 8 × 1/10 × 1/9 = 0.5 + 8/90 = 5/10 + 8/90 =
= 45/90 + 8/90 = 53/90
this is the simplest possible form, as 53 is already a prime number and not a factor of 90.
The y intercept (when x=0) is 40
the slope is 15 ( slope= rise/run= 15/1=15)
therefore, the equation of the line is y=15x+40
Step-by-step explanation:
area=length x width
91=(x+2)(2x+3)
91=x^2+5x+6
x^2+5x-85=0
x=14.2 orx=-24.1
Answer:
Option D. y=6x
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a direct variation if it can be expressed in the form 
or 
In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin
<em>Verify each case</em>
case a) y=(1/6)x+6
Is a linear equation, but is not a direct variation. The line not passes through the origin
case b) y=6/x
The equation represent an inverse variation
case c) y=6x-6
Is a linear equation, but is not a direct variation. The line not passes through the origin
case d) y=6x
The equation represent a direct variation
Answer:
reserves increase by $100 million and the money supply increases by more than $100 million.
Step-by-step explanation:
Consider the provided information.
It is given that central bank buys $100 million worth of bonds, that means an amount of $100 million in the deposits account of the account holders.
Therefore the reserves increase by $100 million.
It is also given that there are no excess reserves, it means banks can lend the reserves and that will increase the money supply by more than $100 million.
Hence, reserves increase by $100 million and the money supply increases by more than $100 million.
