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nydimaria [60]
2 years ago
10

. A theater has 40 rows of seats, where the first row has 27 seats and each subsequent row has

Mathematics
1 answer:
MAXImum [283]2 years ago
6 0
<h3><em>Answer:</em></h3><h3><em></em></h3><h3><em>number of seats in theater = 1035</em></h3><h3><em></em></h3><h3><em>Step-by-step explanation:</em></h3><h3><em></em></h3><h3><em>Given in question as</em></h3><h3><em></em></h3><h3><em>Total number of rows of seat = 30</em></h3><h3><em></em></h3><h3><em>first row contain seat = 20</em></h3><h3><em></em></h3><h3><em>second row contain seat = 21 .. and so on</em></h3><h3><em></em></h3><h3><em>This is in arithmetic progression as 20 , 21 , 22 , 23 ...... so on</em></h3><h3><em></em></h3><h3><em>Then as number of terms N = 30 and first terms = a = 20</em></h3><h3><em></em></h3><h3><em>so we have to find Tn th terms</em></h3><h3><em></em></h3><h3><em>So, Tn th terms = first term + ( N -1 ) × d               d= common difference i.e 1</em></h3><h3><em></em></h3><h3><em>     Tn th terms = 20 + (30 - 1) × 1</em></h3><h3><em></em></h3><h3><em>Thus, Tn th terms = 49</em></h3><h3><em></em></h3><h3><em>i.e The number of seats in 30th row = 49</em></h3><h3><em></em></h3><h3><em>Now again Total number of seats in theater</em></h3><h3><em></em></h3><h3><em>sum of Nth terms = </em></h3><h3><em></em></h3><h3><em>so                         = </em></h3><h3><em></em></h3><h3><em>                            = 15 × 69 = 1035</em></h3><h3><em></em></h3><h3><em>Hence, Total number of seats in theater = 1035      Answer</em></h3>
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An orange triangular warning sign by the side of the road has an area of 266 square inches. The base of the sign is 9 inches lon
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Answer: the base is 28 inches. The altitude is 9 inches

Step-by-step explanation:

Let h represent the altitude of the sign.

Let b represent the length if the base of the sign.

The warning sign is triangular in shape.

The formula for determining the area of a triangle is expressed as

Area = 1/2bh

The base of the sign is 9 inches longer than the altitude. This means that

b = h + 9

If the area of the sign is 266 square inches, it means that

266 = 1/2 × h(h + 9)

266 × 2 = h(h + 9)

532 = h² + 9h

h² + 9h - 532 = 0

h² + 28h - 19h - 532 = 0

h(h + 28) - 19(h + 28) = 0

h(h + 28) - 19(h + 28) = 0

(h + 28)(h - 19) = 0

h = 19 or h = - 28

Since the height cannot be negative, then h = 19

b = h + 9 = 10 + 9

b = 28

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Answer:

(A) Always true

(B) Seldom true

Step-by-step explanation:

(A) Both sides of an equation can be multiplied by the same number without this action changing the solution of the equation.

Keyword here is "number".

Multiplying both sides of an equation by an equal quantity (same number) will result in same solution after solving for the unknown in the equation. This is because that numeric quantity can always be removed by dividing both sides of the equation by it or by a factor (or multiple) of it.

EXAMPLE:

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let's find the solution, in other words solve for the unknown value X.

4x - 15x = 6

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x = -6/11

Now multiply both sides of the equation by 3.

3(4x - 6) = 3(15x)

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Solve for X

12x - 45x = 18

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Reduce the fraction to its simplest form by looking for a number that can divide both numerator and denominator without remainder. In other words, think of a number that is a factor of 18 and a factor of 33.

That common factor or highest common factor (HCF) is 3.

Go ahead and reduce the fraction.

x will be reduced to -6/11

(B) Both sides of an inequality can seldom be multiplied by the same number, without such action changing the solution set of the equation.

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