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prisoha [69]
3 years ago
15

If r> 0 and r^t = 6.25r^t+2, then r =

Mathematics
1 answer:
Firdavs [7]3 years ago
4 0
I'm going to use n instead of t

rⁿ=6.25rⁿ+2
minus rⁿ both sides
0=5.25rⁿ+2
minus 2 both sides
-2=5.25rⁿ
divide both sides by 5.25
-2/5.25=rⁿ
take the nth root of both sides
\sqrt[n]{\frac{-2}{5.25}}= \sqrt[n]{r^n}
\sqrt[n]{\frac{-2}{5.25}}= r
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A movie theater has a seating capacity of 197. The theater charges $5.00 for children, $7.00 for students, and $12.00 of adults.
yarga [219]

Answer: 74 children attended

86 students attended

37 adults attended

Step-by-step explanation:

Let x represent the number of children that attended.

Let y represent the number of students that attended.

Let z represent the number of adults that attended.

The movie theater has a seating capacity of 197. It means that

x + y + z = 197- - - - - - - - - - - - -1

The theater charges $5.00 for children, $7.00 for students, and $12.00 of adults. If the total ticket sales was $ 1416, It means that

5x + 7y + 12z = 1416- - - - - - - - - - 2

There are half as many adults as there are children. It means that

It means that

z = x/2

x = 2z

Substituting x = 2z into equation 1 and equation 2, it becomes

2z + y + z = 197

y + 3z = 197- - - - - - - - - - - - -3

5 × 2z + 7y + 12z = 1416

10z + 7y + 12z = 1416

7y + 22z = 1416- - - - - - - - - - - 4

Multiplying equation 3 by 7 and equation 4 by 1, it becomes

7y + 21z = 1379

7y + 22z = 1416

Subtracting, it becomes

- z = - 37

z = 37

x = 2z = 2 × 37

x = 74

Substituting x = 74 and z = 37 into equation 1, it becomes

74 + y + 37 = 197

y = 197 - 74 - 37

y = 86

5 0
3 years ago
what is the radius of a circle with a circumference of 125 cm? round your answer to the nearest whole number .use 3.14
Lerok [7]

Answer:

19.9 i think

Step-by-step explanation:

125/3.14=39.8

39.8/2=19.9

hope i helped

5 0
3 years ago
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Solve for x. 9≤17−4x Enter your answer, as an inequality, in the box.
Stella [2.4K]
9 ≤ 17 - 4x

9 - 17 ≤ 17 - 17 - 4x

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hope this helps
4 0
3 years ago
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What is the value of the expression 3^−4 ?
ikadub [295]
3^-4 = 1/3^4 = 1/81

hope it helps!
4 0
3 years ago
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The length of a rectangle is five times its width. If the area of the rectangle is 320 cm^2, find its perimeter.
olchik [2.2K]
A = LW
A = 320
L = 5W

320 = W(5W)
320 = 5W^2
320/5 = W^2
64 = W^2
sqrt 64 = W
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L = 5W
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so the length (L) = 40 cm and the width (W) = 8 cm

P = 2(L + W)
P = 2(40 + 8)
P = 2(48)
P = 96  <=====
4 0
3 years ago
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