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3 years ago

If m+1/m= 3, then prove that m^5+1/m^5= 123

Mathematics

1 answer:

Lady_Fox [76]3 years ago

6 0

Step-by-step explanation:

$\qquad\sf {:}\longrightarrow m+\dfrac {1}{m}=3$

$\qquad\sf {:}\longrightarrow m^2+1/m=3$

$\qquad\sf {:}\longrightarrow m^2+1=3m$

$\qquad\sf {:}\longrightarrow m^2-3m+1=0$

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A movie theater has a seating capacity of 329. The theater charges $5.00 for children, $7.00 for students, and $12.00 of adults.

kipiarov [429]

Answer:

170 children

74 students

85 adults

Step-by-step explanation:

Given

Let:

$C = Children; S = Students; A = Adults$

For the capacity, we have:

$C + S + A = 329$

For the tickets sold, we have:

$5C + 7S + 12A = 2388$

Half as many as adults are children implies that:

$A = \frac{C}{2}$

Required

Solve for A, C and S

The equations to solve are:

$C + S + A = 329$ -- (1)

$5C + 7S + 12A = 2388$ -- (2)

$A = \frac{C}{2}$ -- (3)

Make C the subject in (3)

$C = 2A$

Substitute $C = 2A$ in (1) and (2)

$C + S + A = 329$ -- (1)

$2A + S + A = 329$

$3A + S = 329$

Make S the subject

$S = 329 - 3A$

$5C + 7S + 12A = 2388$ -- (2)

$5*2A + 7S + 12A = 2388$

$10A + 7S + 12A = 2388$

$7S + 22A = 2388$

Substitute $S = 329 - 3A$

$7(329 - 3A) + 22A = 2388$

$2303 - 21A + 22A = 2388$

$2303 +A = 2388$

Solve for A

$A = 2388 - 2303$

$A = 85$

Recall that: $C = 2A$

$C = 2 * 85$

$C = 170$

Recall that: $S = 329 - 3A$

$S = 329 - 3 * 85$

$S = 329 - 255$

$S = 74$

Hence, the result is:

$C = 170$

$S = 74$

$A = 85$

8 0

3 years ago

Find the value of x when lines w and v are parallel.

VladimirAG [237]

Answer: B. 17

Step-by-step explanation:

4x-3 = 65

Add 3 on both sides

4x = 68

Divide by 4 on both sides

x = 17

BOOM!

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3 years ago

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The volume of a box V is given by the formula V=lwh, where l is length, w Is width, and h is height.

Nana76 [90]

1)Original Equation: V=lwh
Divide by lw: V/w=lw/lw(h)
Answer: h= V/lw

2)Set up the equation as V=lwh
Substitute the variables for numbers: 50=10(2)h
Multiply 10*2: 50=20h
Divide 50each side by 20 to get rid of 20h: 50/20=20/20
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The height of the box is 2.5 meters tall.

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3 years ago

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Is 1/9 >, <, or = {Negative} -4?

kvasek [131]

<u>Answer:</u>

1/9 > -4

because -4 is a negative no less than 0. whereas 1/9 is a positive no greater than 0.

So negative no can't be greater than positive no.

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3 years ago

(c) Find the number of sets where all three cards are the same for exactly $0$ attributes. (d) Find the number of sets where all

Cloud [144]

C. For the first card, there are three ways to choose the number of card.

For the another, there two options, and likewise there's only 1 choice of card. So there are 3 × 2 × 1 = 6 ways that the calculation can be chosen.

Doing this for the other attributes, we get 6 × 6 × 24 × 6 ways. But the order of cards does not count in a set of card, so we divide by 3! 6 * 6 * 24 × 6 ÷ 3! = 864. It means there are 864 sets for part.

D. The cards may have the same number, color, shapess, orshading.

However, also there are 6 × 24 × 6 × 3! = 144 sets of cards, If all the colors are thesame. How ever, also there are 144 sets of cards.

If all the calculation are the same. We get the same number for shape and shadings, so there are 4 × 144 = 576 sets of cards.

what is Probability?

Probability is branches of mathematics concerning numerical descriptions of how to the likely an event is to occurs, or how to the likely it is that a proposition is true. The probability of an event is a numbers between 0 and 1, where, roughly speaking, 0 indicates the impossibility of the events and 1 indicates certain of cards.

Learn more about Probability here

brainly.com/question/13604758

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