For two ratios to form a proportion they have to be equal.
To see if two ratios are equal we express them in their simplest form.
In this case we notice that in the first ratio both numbers are multiples of five, then:

In the second case we notice that both numbers are multiples of 2, then:

Since both ratios can be simplified to the same final ratio, they form a proportion.
Answer:
The lemonade costs 1.4.
Step-by-step explanation:
This question is solved using a system of equations.
I am going to say that:
x is the cost of a cookie.
y is the cost of a lemonade.
Total cost for cookie and lemonade is 1.80.
This means that
.
As we want y, we have that 
Lemonade costs 1.00 more than the cookie?
This means that:

So




The lemonade costs 1.4.
Answer:
<u>Question 3</u>
Given expression:

Both parentheses share a common term.
To factor out a common term: ab + ac = a(b + c)


-------------------------------------------------------------------------------------------------
<u>Question 4</u>
To calculate the amount of money Rajni had to begin with, sum the three amounts she spent:

As
, then:

Collect and sum the whole numbers:


As
, then



Answer:
3.9984i-3.0021j
Step-by-step explanation:
Due to the fact that we are only asked for the components on A, we will focus on that information.
The first thing we need to do is to dimension the magnitud of A as a hypotenuse of a right triangle. As the vector is ponting in south-east direction, we can asume that it´s (i) component will be positive and it´s (j) component will be negative.
Now, using trigonometric functions we can find the components of the vector A by multiplying the magnitude by -sin(x) for (j) and cos(x) for (i).
-5sin(36.9)=-3.0021
(this component is negative due to the fact that the vector is pointing down)
5cos(36.9)= 3.9984
Now we write in the correct notation x(i) + y(j)
3.9984i-3.0021j