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3 years ago

Which pair of angles must be supplementary?

Mathematics

2 answers:

Alex_Xolod [135]3 years ago

6 0

∠3 and ∠4 are angles that must be supplementary.

Elina [12.6K]3 years ago

4 0

If something is supplementary, that means that together they must equal 180.
A line=180

<3 and <1 are supplementary because they are linear pairs, meaning that together they must equal 180

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Sammi has 2 1/3 feet of rope. If he cuts the rope into pieces that are each 1/2 foot long, there will be 1/3 foot of rope left o

Stells [14]

Answer:

Step-by-step explanation:

Sammi has 2 1/3 feet of rope.

To write this type of fraction = 2 + 1/3 - The integer 2 in the expression is the amount of feet of rope that was cut.

Thus to know the number of 1/2 foot pieces produced, let this number be x. Thus, we have 1/2 of x pieces = 2

x/2 = 2; x = 2x2 = 4.

Thus, Sanmi has 4 pieces of 1/2 foot long piece each of rope.

4 0

3 years ago

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

2 years ago

Mr. Abraham is 36 years old. His wife is 6 years younger than him and their son is 24 years old younger than his wife. What is t

sesenic [268]

Hi!
We know that Mr. Abraham’s wife is 6 years younger than him, which is 36-6, which means his wife is 30 years old.

We also know that Mr A’s son is 24 years younger than his wife, which is 30-24, which is 6.

As of right now, we now know that:
Mr. A is 36
Mr. A’s wife is 30
Mr. A’s son is 6

It’s asking for the ratio of Him:Wife:Son, so 36:30:6.

BUT, it’s asking for simplest form, so divide each of those numbers by 6.

Your answer is: 6:5:1

8 0

2 years ago

What is the lcm of 6 and 8

Dafna1 [17]

Answer:

Explanation:

Method 1

First, list the multiples of both numbers:

$undefined$

To find the lowest common multiple (LCM) of 6 and 8, first express the numbers as a product of its prime factors.

$\begin{gathered} 6=2\times3 \\ 8=2\times2\times2=2^3 \end{gathered}$

Next, pick the highest powers for each of the numbers:

$\begin{gathered} \text{LCM}=2^3\times3 \\ =8\times3 \\ =24 \end{gathered}$

5 0

1 year ago

Find the equation of the axis of symmetry.<br>equation of axis of symmetry:

sleet_krkn [62]

9514 1404 393

Answer:

x = -4

Step-by-step explanation:

The axis of symmetry is the vertical line through the vertex. The vertex is the turning point, or minimum, of the function. It is (x, y) = (-4, 0). The x-coordinate there is -4, so the equation of the axis of symmetry is ...

x = -4

5 0

2 years ago