Answer:
Answer:
\{ {{20x+30y=280} \atop {y=4x}} .{
y=4x
20x+30y=280
.
Where xx is the number of small boxes sent and yy is the number of large boxes sent.
Step-by-step explanation:
Let be xx the number of small boxes sent and yy the number of large boxes sent.
Since each small box can hold 20 books (20x20x ), each large box can hold 30 books (30y30y )and altogether can hold a total of 280 books, we can write the following equation to represent this:
20x+30y=28020x+30y=280
According to the information provided in the exercise, there were 4 times as many large boxes sent as small boxes. This can be represented with this equation:
y=4xy=4x
Therefore, the system of equation that be used to determine the number of small boxes sent and the number of large boxes sent, is:
\{ {{20x+30y=280} \atop {y=4x}} .{
y=4x
20x+30y=280
.
Answer:
162
Step-by-step explanation:
The number with "1" digit starts with 101 then 110 and so on.
This is a quadratic equation, i.e. an equation involving a polynomial of degree 2. To solve them, you must rearrange them first, so that all terms are on the same side, so we get
i.e. now we're looking for the roots of the polynomial. To find them, we can use the following formula:
where 
is a compact way to indicate both solutions 
and 
, while 
are the coefficients of the quadratic equation, i.e. we consider the polynomial 
.
So, in your case, we have 
Plug those values into the formula to get
So, the two solutions are
