Valentina purchased al- yards of nylon as shown on the sales slip. Including tax, how much change should she get back?
1 answer:
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This is a way to factoring trinomials (there exist different equivalent methods).
Multiply the trinomial but the term accompanying . This is the second line. Then, you could take the square of the
, ant try to create a factor () () that will correspond to the expression in the second line. That is, we want
In ? we put the corresponding numbers that, if we multiply them we will obtain 42, and if we add them we will obtain 13. This numbers are 6 and 7. Then, we have
The last step is divide by the number that we multipy in the first step.
Answer:
Step-by-step explanation:
The populational growth is exponential with a factor of 1.12 each year. An exponential function has the following general equation:
Where 'a' is the initial population (25,000 people), 'b' is the growth factor (1.12 per year), 'x' is the time elapsed, in years, and 'y(x)' is the population after 'x' years.
Therefore, the function P(t) that models the population in Madison t years from now is:
Answer:
10.5 feet
Step-by-step explanation:
In this problem, we have two similar triangles:
- One consists of the mailbox, its shadow and the hypothenuse
- The other one consists of the tree, its shadow and the hypothenuse
The two triangles are similar, so they have same proportions between their sides: therefore, we can apply the rule of three:
where
m = 36 in is the height of the mailbox
is the shadow of the mailbox
t is the height of the tree
is the length of the shadow of the tree
Solving for t, we find the height of the tree:
And since
1 feet = 12 inches
The height of the tree in feet is