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2 years ago

15

What is the value of (g o f)(-3)

2 answers:

Assoli18 [71]2 years ago

5 0

The answer is: gof = 1, 1, and 2

Rama09 [41]2 years ago

4 0

f(x) = 4x + 10

f(-3) = 4(-3) + 10 = -12 + 10 = -2

g(x) = 2x - 5

g(f(-3)) = 2(-2) - 5 = -4 - 5 = -9

Answer: -9

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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

2 years ago

Raul uses a credit card to take out a 3-year loan of $4500 at a rate of 15% to purchase

mars1129 [50]

Answer:

Amount of loan pay = $6.840 (Approx.)

Step-by-step explanation:

Given:

Amount of loan borrow = $4,500

Rate of interest = 15% = 0.15

Number of year = 3 year

Find:

Amount of loan pay

Computation:

Future value = Present value[1+r]ⁿ

Amount of loan pay = Amount of loan borrow[1+r]ⁿ

Amount of loan pay = 4,500[1+0.15]³

Amount of loan pay = 4,500[1.15]³

Amount of loan pay = 4,500[1.52]

Amount of loan pay = $6.840 (Approx.)

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2 years ago

Solve -2x + 6 = -20.<br><br> (A) -13<br> (B) 13<br> (C) -7<br> (D) 7

kow [346]

Answer: x=13

explanation:
-2x+6=-20
subtract 6 from both sides
-2x=-26
divide -2 by both sides
two negatives equals a positive
x=13

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3 years ago

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NemiM [27]

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