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Savatey [412]
3 years ago
5

Danielle is x years old. Her sister is five years older and her brother is half Danielle’s age. Write an expression in simplest

form for the sum of their ages
Mathematics
1 answer:
Alborosie3 years ago
7 0
Let x = Danielle, x + 5 = her sister, and .5x = her brother.

x + x + 5 + .5x = the sum of their ages.

Then we simplify to get 2.5x + 5 = the sum of their ages.
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Prove the divisibility of the following numbers:
Brut [27]

Answer:

Step-by-step explanation:

To prove divisibility, we need to factor the divident such that one of its factors matches the divisor.

(I use the notation x|y to denote that x divides y)

(A)

75^{30}|45^{45}\cdot15^{15}\\45^{45}\cdot15^{15}=3^{45}\cdot 15^{45}\cdot 15^{15}=\\=3^{45}\cdot 15^{60}=3^{45}\cdot 15^{30}\cdot 15^{30}=3^{45}\cdot (3\cdot5)^{30}\cdot 15^{30}=\\=3^{45}\cdot 3^{30}\cdot(5\cdot 15)^{30}=3^{45}\cdot 3^{30}\cdot(75)^{30}\\\implies\\75^{30}|3^{45}\cdot 3^{30}\cdot75^{30}

(B)

72^{63}|24^{54}\cdot 54^{24}\cdot2^{10}\\24^{54}\cdot 54^{24}\cdot2^{10}=(2^{162}\cdot 3^{54})\cdot(2^{24}\cdot 3^{72}) \cdot 2^{10}\\=2^{196}\cdot 3^{126}

In this case, it is easier to also factor the divisor to primes:

72^{63}=2^{189}\cdot 3^{126}

Both of these factor must be matched in the dividend in order to prove divisibility, and that indeed turns out to be true:

2^{189}\cdot 3^{126}|2^{196}\cdot 3^{126}\implies\\2^{189}|2^{196}\,\,\mbox{and}\,\,3^{126}|3^{126}

6 0
3 years ago
Grant pays 10 cents per minute plus $5 per month for telephone long distance. Write an algebraic expression for m minutes of lon
dolphi86 [110]
The question is asking for the amount of minutes Grant can possibly use in a month. So to <span>algebraically express this, the equation, </span>0.10 m+5=$ sums it up.
5 0
3 years ago
i was supposed to be on a bus, but there was a lady with a chicken on there. what is this, like, guatemala? what the hell? leave
dsp73

lol thats interesting.

4 0
3 years ago
PLEASE HELP ME ASAP!!!! A circle fits in a square with sides of 12 inches. What is the approximate area of the shaded region bet
den301095 [7]

Answer:

Depending on the shaded area, it will be less than 113 in², so not the last option

Step-by-step explanation:

Area of a circle is A= πr²

if it fits in 12 inch sides, 12 i the diameter and 6 is the radius

A= 3.14(6)²

A= 113 in²

Then, find what the shaded area is

4 0
3 years ago
At the season finale, you present the winner of Canadian Superstar with a recording-and-tour contract. The contract states that
Zina [86]

Answer:

Kindly check explanation

Step-by-step explanation:

Given that:

Winner is paid :

Monthly pay while on tour = $5000

Pay per CD sold =. $2

A) Equation which relates total earning in terms of number of months 'm' while on tour and the number 'n' of CD's sold.

(Monthly pay * number of months) + (pay per CD * number of CD's)

Earning = 5000m + 2n

B) How much will the winner earn after the first month if 500 CDs are sold?

m = 1, n = 500

5000(1) + 2(500) = $6000

C) Suppose after the third month on tour the new recording artist has earned a total of $74 000. How many GDs were sold?

m = 3

74000 = 5000(3) + 2n

74000 = 15000 + 2n

74000 - 15000 = 2n

59000 = 2n

n = 59000 / 2

n = 29500 CD's

D) In Canada, a record album or CD achieves gold status once it seLls 50 000 units. How much will the artist make if the CD goes gold after 6 months of touring?

n = Gold = 50000 ; m = 6

5000(6) + 2(50000)

30000 + 100000 = 130,000

3 0
3 years ago
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