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3 years ago

Please answer my question

Mathematics

1 answer:

katrin [286]3 years ago

4 0

Graph 1:

(-infinity, 2) U [3, infinity)

Graph 2:

{-8, -2} U (3, 8]

Graph 3:

(-infinity, 3) U (3, infinity)

Graph 4:

(-8, -2) or {3}

Graph 5:

(-8, -2) U (-2, infinity)

Hope this helps!

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Given $a \equiv 1 \pmod{7}$, $b \equiv 2 \pmod{7}$, and $c \equiv 6 \pmod{7}$, what is the remainder when $a^{81} b^{91} c^{27}$

Blizzard [7]

$\begin{cases}a\equiv1\pmod7\\b\equiv2\pmod7\\c\equiv6\pmod7\end{cases}$

$a^{81}\equiv1^{81}\equiv1\pmod7$

$b^{91}\equiv2^{91}\pmod7$

$2^{91}\equiv(2^3)^{30}\times2^1\equiv8^{30}\times2\pmod7$
$8\equiv1\pmod7$
$2\equiv2\pmod7$
$\implies2^{91}\equiv1^{30}\times2\equiv2\pmod7$

$c^{27}\equiv6^{27}\pmod7$

$6^{27}\equiv(-1)^{27}\equiv-1\equiv6\pmod7$

$\implies a^{81}b^{91}c^{27}\equiv1\times2\times6\equiv12\equiv5\pmod7$

6 0

3 years ago

HELPPPPPPPPP ASAPPPPPPPP PLSSSS

yanalaym [24]

-1/3(px-2) = 9

ok! so first we want to isolate x.

multiply both sides by -3/1 (this is the reciprocal of -1/3)

(px-2) = -27

px = -27 + 2

px = -25

x = -25/p

hope this helped!

8 0

3 years ago

What is x if 2-3x=x+2

ratelena [41]

Answer:

x=0

Step-by-step explanation:

it cancels

3 0

4 years ago

What is -12.41 - (-9.95)?

Marina CMI [18]

Answer:

-2.46

Step-by-step explanation:

-12.41+9.95=-2.46

5 0

3 years ago

Suppose an individual makes an initial investment of $3,000 in an account that earns 6.6%, compounded monthly, and makes additio

makkiz [27]

Answer:

b) $17,400

d) $33,517.20

Step-by-step explanation:

a) $28,482.19 . . . . future value of all deposits

b) The initial deposit was $3000, and there were 144 deposits of $100 each, for a total of ...

$3000 +144×100 = $17,400 . . . . total deposited

c) $558.62

d) 60 monthly withdrawals were made in the amount $558.62, for a total of ...

60×$558.62 = $33,517.20 . . . . total withdrawn

_____

<em>Additional information about (a) and (c)</em>

(a) The future value of the initial deposit is the deposit multiplied by the interest multiplier over the period.

A = P(1 +r/n)^(nt) = 3000(1 +.066/12)^(12·12) = 3000·1.0055^144 ≈ 6609.065

The future value of $100 deposits each month is the sum of the series of 144 terms with common ratio 1.0055 and initial value 100.

A = 100(1.055^144 -1)/0.0055 ≈ 21,873.123

So, the total future value is ...

$6609.065 +21873.123 ≈ $28482.188 ≈ $28,482.19

(c) The withdrawal amount can be found using the same formula used for loan payments:

A = P(r/n)/(1 -(1 +r/n)^(-nt)) = $28482.19(.0055)/(1 -1.0055^-60) ≈ $558.62

7 0

4 years ago