Answer:
Step-by-step explanation:
Given:
To find:
- Summation notation of the given series
Summation Notation:
Where n is the number of terms and 
is general term.
First, determine what kind of series it is, there are two main series that everyone should know:
A series that has common difference.
A series that has common ratio.
If you notice and keep subtracting the next term with previous term:
Two common difference, we can in fact say that the series is arithmetic one. Since we know the type of series, we have to find the number of terms.
Now that brings us to arithmetic sequence, we know that first term is 5 and last term is 251, we’ll be finding both general term and number of term using arithmetic sequence:
<u>Arithmetic Sequence</u>
Where 
is the nth term, 
is the first term and 
is the common difference:
So for our general term:
And for number of terms, substitute = 251 and solve for n:
Now we can convert the series to summation notation as given the formula above, substitute as we get:
A sandwich store charges a delivery fee to bring lunch to an office.
Delivery cost - D
Meatball sandwich cost - M
One office pays $40.50 for 5 meatball sandwiches.
40.50 = 5M + D
Another office pays $66.50 for 9 meat ball sandwiches
66.50 = 9M + D
A. How much does each meatball sandwich add to the cost of delivery?
D = 40.50 - 5M = 66.50 - 9M
40.50 - 5M = 66.50 - 9M
9M - 5M = 66.50 - 40.50
4M = 26.00
M = 6.50
B. What is the delivery fee
D = 40.50 - 5M = 40.50 - 5(6.50) = 40.50 - 32.50 = 8.00
Check
66.50 = 9M + D = 9(6.50) + 8 = 58.50 + 8.00 = 66.50
Answer:
Complementary
Step-by-step explanation:
Answer:
The freezing point of the water with the added potassium is 24 degrees Fahrenheit.
Step-by-step explanation:
To find the freezing point of the water with the added potassium, you need to subtract 8 degrees from the initial freezing point of water, This is because you know that after adding potassium to water, the freezing point went down by 8 degrees Fahrenheit. So you need to subtract 8 degrees from the initial freezing point of water (32 degrees Fahrenheit). 32º F - 8º = 24º F. So the freezing point of the water with the added potassium is 24 degrees Fahrenheit.
If at least two sides and one angle of two triangles are similar, then the triangles are congruent.
What in mathematics is the congruent?
- It is claimed that two figures are "congruent" if they can be positioned exactly over one another.
- Both the shape and size of the bread slices are same if you lay one slice on top of the other.
- Congruent refers to having precisely the same form and size.
Use the Third Angles Theorem for two figures are congruent.
When two of a triangle's angles match up with two of another triangle's angles, the third angle must likewise match up.
If at least two sides and one angle of two triangles are similar, then the triangles are congruent.
Learn more about congruent
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