Using the Euler's formula, the number of segments in the pentagonal prism is: 15.
<h3>What is the Euler's Formula?</h3>
The Euler's formula is given as, F + V = E + 2, where:
- F = number of faces (number of regions)
- V = vertices
- E = number of edges (number of segments).
Given that the pentagonal prism has the following dimensions:
- F = 7
- V = 10
- E = number of segments = ?
Plug in the values into the Euler's formula, F + V = E + 2:
7 + 10 = E + 2
17 - 2 = E
E = 15
Therefore, using the Euler's formula, the number of segments in the pentagonal prism is: 15.
Learn more about the Euler's formula on:
brainly.com/question/1178790
Answer:
D. right 4, down 8
Step-by-step explanation:
The usual transformations applied to functions are ...
f(x) ⇒ f(x -h) . . . . translation right h units
f(x) ⇒ f(x) +k . . . . translation up k units
f(x) ⇒ k·f(x) . . . . . vertical scaling by a factor of k; reflection over x-axis when k < 0
f(x) ⇒ f(x/k) . . . . . horizontal scaling by a factor of k; reflection over y-axis when k < 0
In the above, "scaling" will be expansion when |k| > 1, compression when |k| < 1.
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Your transformation is ...
x^2 ⇒ (x -4)^2 -8
f(x) ⇒ f(x -4) -8
This is translation with h=4 and k=-8. That is, it is translation right 4 units and down 8 units.
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<em>Additional comment</em>
Like much of math, it is all about matching patterns.
Both the given lines in graph intersect at point (5 , -2), the point must satisfy both the equations.
and if we check the options, we will observe that D. option has both the equations that satisfy the given conditions.
that is ~
put y = - 2,we will get :
so, 1st equation satifys the condition. let's check out 2nd one.
put y = -2
Hence, we can conclude that the Correct choice is D
Answer:
The inequality is 
The greatest length of time Jeremy can rent the jet ski is 5 and Jeremy can rent maximum of 135 minutes.
Step-by-step explanation:
Given: Cost of first hour rent of jet ski is $55
Cost of each additional 15 minutes of jet ski is $10
Jeremy can spend no more than $105
Assuming the number of additional 15-minutes increment be "x"
Jeremy´s total spending would be first hour rental fees and additional charges for each 15-minutes of jet ski.
Lets put up an expression for total spending of Jeremy.
We also know that Jeremy can not spend more than $105
∴ Putting up the total spending of Jeremy in an inequality.
Now solving the inequality to find the greatest number of time Jeremy can rent the jet ski,
⇒ 
Subtracting both side by 55
⇒ 
Dividing both side by 10
⇒
∴ 
Therefore, Jeremy can rent for 
Jeremy can rent maximum of 135 minutes.
A. 16 is divisible by 2 but not divisible by 3
B. 23 is not divisible neither by 2 nor 3
C. 27 is not divisible by 2, however it's divisible by 3
D. 36 is divisible both by 2 and 3
So the only number we can focus on is 36:
36 ÷ 2 = 18
36 ÷ 3 = 12
36 ÷ 6 = 6
Answer: D, 36 supports the given conjecture.
