3 years ago

Which rules give a repeating pattern that has a 7 as the 15th number? Select all that apply.

Mathematics

1 answer:

Flura [38]3 years ago

3 0

The answer is c.1,9,7

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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

Help! How many different ways can you get a total of 100 by adding consecutive numbers?

Dafna11 [192]

Answer:

0 ways...

Step-by-step explanation:

First find one pair.

x and x + 1

2x + 1 = 100

2x = 99

x = 49.5

49.5 and 50.5

Since the only way is with decimals, there are 0 ways.

3 0

2 years ago

Read 2 more answers

Y=4 -2x<br> у = -5 + 4х<br> ||

kolezko [41]

Answer:

y=1

Step-by-step explanation:

y= 4 - 2x

y= -5 + 4x

4 - 2x = -5 + 4x

4 + 5 = 4x +2x

9 = 6x

9/6 = x

3/2 = x

y= 4 -2(3/2)

y = 4 - 3

y = 1

5 0

2 years ago

What is the area of a circle with a diameter of 21 centimeters?

sattari [20]

Area of a circle: πr²

Data:
diameter: 21 cm
radius=diameter/2=21 cm/2=10.5 cm

area of this circle: π(10.5 cm)²=110.25π cm² (≈346.36 cm²)

Answer: area=110.25π cm²

4 0

3 years ago

Read 2 more answers

Which expressions are equivalent to

Drupady [299]

Answer:

$\color{Blue}\huge\boxed{Answer}$

D. 16 + 3y +(-3.52)

4 0

3 years ago