Answer:
8428
Step-by-step explanation:
According to the Question,
- Given, A theater has 56 rows of seats. If there are 13 seats in the first row, 18 in the 2nd row, 23 in the 3rd row.
We have a number sequence 13, 18, 23, ...
- We can say that this is an arithmetic sequence because of the common difference 'd', is equal to 5, and the first term 'a1' is equal to 13.
- The formula for the sum of an arithmetic sequence with n terms is given is
![S_n= \frac{n}{2} [2a_1+(n-1)d]S](https://tex.z-dn.net/?f=S_n%3D%20%5Cfrac%7Bn%7D%7B2%7D%20%5B2a_1%2B%28n-1%29d%5DS)
.
Substitute the given values into the equation to solve for the sum of the 56 rows of seats.
![S_56= \frac{56}{2}[2(13)+(56-1)(5)]\\S_{56}=28\left[26+275\right]\\S_{56}=28\left[301\right]\\S_{56}=8428](https://tex.z-dn.net/?f=S_56%3D%20%5Cfrac%7B56%7D%7B2%7D%5B2%2813%29%2B%2856-1%29%285%29%5D%5C%5CS_%7B56%7D%3D28%5Cleft%5B26%2B275%5Cright%5D%5C%5CS_%7B56%7D%3D28%5Cleft%5B301%5Cright%5D%5C%5CS_%7B56%7D%3D8428)
Therefore, there are 8428 seats in all.
Step-by-step explanation:
Water is the universal solvent" with a grain of salt (pun intended). Of course it cannot dissolve everything, but it does dissolve more substances than any other liquid, so the term fits pretty well. Water's solvent properties affect all life on Earth, so water is universally important to all of us.
Answer:
A number line with an open circle on 2, a closed circle on 6, and shading in between
Step-by-step explanation:
Given:
3x+1 > 7 → inequality A
4x ≤ 24 → inequality B
Step 1
Solve inequality A
3x+1>7
3x>7-1
x>2
the solution is the interval------> (2,∞)
Step 2
Solve inequality B
4 x ≤ 24
4 ≤ 6
the solution is the interval------> (-∞,6]
Step 3
Find the solution of the compound inequality
Solution A ∩ Solution B
(2,∞) ∩ (-∞,6]=(2,6]
therefore
The answer is A number line with an open circle on 2, a closed circle on 6, and shading in between
Answer: i) 1 - 9x² - 12x
ii) 17 - 3x²
iii) - 20 + 10x² - x⁴
<u>Step-by-step explanation:</u>
g(x) = 3x + 2 h(x) = 5 - x²
i) h(g(x))
h(3x + 2) = 5 - (3x + 2)²
= 5 - (9x² + 12x + 4)
= 5 - 9x² - 12x - 4
= 1 - 9x² - 12x
ii) g(h(x))
g(5 - x²) = 3(5 - x²) + 2
= 15 - 3x² + 2
= 17 - 3x²
iii) h(h(x))
h(5 - x²) = 5 - (5 - x²)²
= 5 - (25 - 10x² + x⁴)
= 5 - 25 + 10x² - x⁴
= -20 + 10x² - x⁴
80%, 1000-200 = 800/1000 or 80%
