1. At the hotel where you are a clerk at the front desk, there are 260 rooms. 5 points

Find thhe remainder when 7^203 is divided by 4

Aleksandr [31]

Using the square-and-multiply approach, we have

$7^{203}=7\times(7^{101})^2$
$7^{101}=7\times(7^{50})^2$
$7^{50}=(7^{25})^2$
$7^{25}=7\times(7^{12})^2$
$7^{12}=(7^6)^2$
$7^6=(7^3)^2$
$7^3=7\times7^2$

and so, using the property that, if $a_1\equiv b_1\mod n$ and $a_2\equiv b_2\mod n$ , then $a_1a_2\equiv b_1b_2\mod n$ , we get

$7\equiv3\mod4$
$7^2\equiv9\equiv1\mod4$
$7^3\equiv7\times1\equiv7\equiv3\mod4$
$7^6\equiv9\equiv1\mod4$
$7^{12}\equiv1\mod4$
$7^{25}\equiv7\times1\equiv7\equiv3\mod4$
$7^{50}\equiv9\equiv1\mod4$
$7^{101}\equiv7\times1\equiv7\equiv3\mod4$
$7^{203}\equiv7\times9\equiv3\times1\equiv3\mod4$

4 0

3 years ago

A number r tripled plus t quadrupled please help !!

ludmilkaskok [199]

This In Expression Form Is:
3r + 4t.
The Reason Why Is Because:
When You Triple r, That Is 3r, And When You Quadruple t, It becomes 4t. And Plus Means to Add. So, This Becomes 3r + 4t
I Hope this Helps!

6 0

3 years ago

Read 2 more answers

Drag each tile to the correct box. Not all tiles will be used.

katrin [286]

Answer+Step-by-step explanation:

$f^{-1}\left( x\right) =\frac{1}{7} x^{2}+3 \ ,\text{where}\ x\geq 0$

7 0

2 years ago

WILL MAKE U BRAINLIEST! Which equation can be used to solve for m∠1?

zlopas [31]

The answer is B.

This is because any angle formed by two chords is equal to half the sum of intercepted arcs.

4 0

3 years ago

Read 2 more answers

What is the equation of the line that is parallel to the line x = -2 and passes through the point (5.4)?

Leno4ka [110]

Lines parallel to each others only occur when two slopes of equations are same. The definition of parallel lines is:

$\large \boxed{m_1 = m_2}$

We are given the equation of a line which is x = -2. For x = a, the equation forms a verical line and has an undefined slope. These below are basic that you may need to learn when learning about the line graph:

y = a —> horizontal line; slope is 0.
x = a —> vertical line; slope is undefined.
For y = a, any a-values would have same x-values. For example, if we are given y = 2 then any domains or x-values can have the range of 2.
For x = a, any a-values would have same y-values or range.

Back to the question. We want to find the equation of a line that is parallel to the line x = -2 and passes through (5,4) point. Recall the definition of parallel line that both slopes of equations must equal. Since x = a for any a-values would give an undefined slope. That means our parallel would be x = b.

Because the line passes through (5,4) - for any a-values from x = a would give out the set of all real numbers for range. Therefore the equation of a line is x = 5.

Answer

The equation of a line that is parallel to x = -2 and passes through (5,4) is x = 5.

I hope this helps! If you have any doubts or questions, don't hestitate to ask in comment! Good luck on your assignment and have a great day!

4 0

3 years ago