Hello! I can help you with this!
a. The function that would best represent Samantha's account is f(5) = 500(1 + 0.04)^5. This is because $500 is the principal, the interest rate is 4%, and we're looking for the amount in the savings account 5 years later.
b. Okay. 1 = 0.04 is 1.04. 1.04^5 is 1.216652902. It's a long decimal, but don't delete it. Multiply that decimal by 500 and you get 608.32645 and other numbers behind it or 608 when rounded to the nearest dollar. Samantha will have about $608 in her savings account in 5 years.
Note: The formula goes like this: f(x) = P(1 + r)^x. This means, you add 1 and the simple interest rate in decimal form together and raise that up by the exponent. There is no shortcuts for this, so you'll have to use the calculator. There will be a very long decimal, but don't clear it. Instead, multiply it by the principal to get the answer. It seems very complicating, but if you do this right, it gets easier overtime and you'll make less errors. There are more complex problems out there, so this formula is very important, but it was kept simple for this question.
1 hr 18 minutes and 27 seconds hmmm
there are 60 minutes in 1 hr, thus 18 minutes is 18/60 hrs or 0.3hr.
so 1hr 18min is 1.3 hrs
there are 60 seconds in 1 minute and 60 minutes in 1 hr, thus 60*60 seconds in 1hr, or 3600 seconds, so, 27 seconds is just 27/3600 hrs, or 0.0075 hrs.
so, 1.3 hr or 1.3000 hr for that matter plus 0.0075, is just
1.3075 hrs.
a)
so, they covered 26.2 miles in 1.3075 hrs, so the average speed is just 26.2/1.3075, or about 20.0382409177 miles/hr
b)
We known that the figures are similar if and only if the corresponding sides and and angles have the common scale factor. In this item, the scale factor is 0.6. The length of AB is determined by multiplying the length of FG with the scale factor. That is,
AB = FG x scale factor
AB = (12 cm) x 0.6
AB = 7.2 cm
Thus, the length of side AB is 7.2 cm.
How many facts does it take to make triangles congruent? Only 3 if they are the right three and the parts are located in the right place.
SAS where 2 sides make up one of the three angles of a triangle. The angle must between the 2 sides.
ASA where the S (side) is common to both the two given angles.
SSS where all three sides of one triangle are the same as all three sides of a second triangle. This one is my favorite. It has no exceptions.
In one very special case, you need only 2 facts, but that case is very special and it really is one of the cases above.
If you are working with a right angle triangle, you can get away with being given the hypotenuse and one of the sides. So you only need 2 facts. It is called the HL theorem. But that is a special case of SSS. The third side can be found from a^2 + b^2 = c^2.
You can also use the two sides making up the right angle but that is a special case of SAS.
Answer
There 6 parts to every triangle: 3 sides and 3 angles. If you show congruency, using any of the 3 facts above, you can conclude that the other 3 parts of the triangle are congruent as well as the three that you have.
Geometry is built on that wonderfully simple premise and it is your introduction to what makes a proof. So it's important that you understand how proving parts of congruent triangles work.
