Answer: 45
Step-by-step explanation: 21 x 3 = 63, because 3x3 is 9. 9 tickets with a $2 discount would mean you take off $18, so I believe the answer would be 63-18=45.
1/3 of 45 is 15, meaning 15 students gave their speech on day 1
Today 2/5 of the remaining students gave their speech. That’s 12 more
So a total of 27 students gave their speeches. That means 18 students remain. The answer is 18
Answer:
16
Step-by-step explanation:
From the question given above, the following data were obtained:
Sum of N term (Sₙ) = 292
2nd term (T₂) = 8.5
5th term (T₅) = 13
Number of terms (N) =?
Next, we shall determine the first term (a) and the common difference (d) of the series. This can be obtained as follow:
T₂ = a + d
8.5 = a + d ........ 1
T₅ = a + 4d
13 = a + 4d ........ 2
Subtract equation 1 from equation 2 i.e
(2) – (1)
.. 13 = a + 4d
– 8.5 = a + d
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
4.5 = 3d
Divide both side by 3
d = 4.5 / 3
d = 1.5
Substitute the value of d into any of the equation to obtain the value of a. Here, we shall use equation 1.
8.5 = a + d
d = 1.5
8.5 = a + 1.5
Collect like terms
8.5 – 1.5 = a
a = 7
Finally, we shall determine the number of terms as follow:
Sum of N term (Sₙ) = 292
Common difference (d) = 1.5
First term (a) = 7
Number of terms (N) =?
Sₙ = n/2[2a + (n – 1)d]
292 × 2 = n[(2 × 7) + (n – 1)1.5]
584 = n[14 + 1.5n – 1.5]
584 = n[12.5 + 1.5n]
584 = 12.5n + 1.5n²
Rearrange
1.5n² + 12.5n – 584 = 0
Using formula method, the value of n can be obtained as follow:
a = 1.5
b = 12.5
c = –584
n = –b ± √(b² – 4ac) / 2a
n = –12.5 ± √(12.5² – 4 × 1.5 × –584) / 2 × 1.5
n = –12.5 ± √(156.25 + 3504) / 3
n = –12.5 ± √(3660.25) / 3
n = –12.5 ± 60.5 / 3
n = –12.5 + 60.5 / 3 or –12.5 – 60.5 / 3
n = 4 /3 or –73 / 3
n = 16 or –73 / 3
Since the number of terms can not be negative, therefore, the number of term is 16
Answer:
Option 1 is correct.
Step-by-step explanation:
We have to select the option which is not the condition of a Tessellation.
A tessellation is a regular pattern made up of shapes that perfectly fit together or we can say it is an arrangement of shapes closely fitted together, especially of polygons in repeated pattern with no overlaps and no gaps.
A tessellation use repeated shapes to completely cover a plane with no overlaps or gaps.
Daily life examples of tessellation are honey combs, to man-made objects, like architecture and quilts.
A tessellation can use one or more geometric shapes. Hence, from the given options only the first option is not a condition for tessellation.
I believe its already in standard form so you would just add it