Question 1 (3 points) study the Proof Given.

List the reasons for Items 2,3, & 4.

Right the number and then the answer.
Question 2 (3 points
)Study the Proof: Give the reasons for the missing reason. List the number and then state the reason.

The image of number 3/2 is shown in number line is shown in figure.

We have to given that,

Number on a number line,

⇒ 3/2

Now, We can simplify as,

⇒ 3/2

⇒ 1.5

Therefore, A number 1.5 shown in figure.

So, The image of number 3/2 is shown in number line is shown in figure.

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Answer:

Step-by-step explanation:

answer is 1

Answer:

Are these all of the options to pick from for this question? If so, then your answer would be A.) five heads.

Explanation:

PLATO

Answer:

Step-by-step explanation:

Answer:A repeating pattern of figures that completely covers a plane, without gaps or overlaps, is called a tessellation.

Step-by-step explanation:

Therefore, A repeating pattern of figures that completely covers a plane, without gaps or overlaps, is called a tessellation.

The GCF of 25 and 12 is 1, which means they are relatively prime. Another example of a pair of relatively prime numbers is 8 and 15, as their only common divisor is 1.

The greatest common factor (GCF) of 25 and 12 is 1. Numbers that have a GCF of 1 are called relatively prime. Another pair of numbers whose GCF is 1 could be 8 and 15. To verify, we look for any common divisors. The divisors of 8 are 1, 2, 4, and 8 while the divisors of 15 are 1, 3, 5, and 15. The only common divisor is 1, which confirms they are relatively prime.

Final answer:

You see lightning before hearing thunder due to the faster speed of light compared to sound. A simultaneous occurrence suggests the lightning is very close, while a delay indicates distance, with every five seconds equaling approximately one mile.

Explanation:

During a storm, you see the flash of lightning before you hear the roar of thunder because light travels much faster than sound. Lightning, a massive discharge of electricity, heats and expands the air rapidly, creating the sound of thunder. The difference in the travel speeds of light (3 × 10⁸ meters per second) and sound means that we perceive these events at different times.

If you saw the flash of lightning and heard the roar of thunder at the same time, it would mean that the lightning strike occurred very close to your location, practically overhead. Conversely, a noticeable delay between the flash of lightning and the sound of thunder indicates that the lightning strike is farther away. Each 5-second gap between seeing lightning and hearing thunder equates to approximately one mile distance from the lightning strike.

To estimate the distance of a storm, you only need to know the speed of sound, as the speed of light is so fast that the time it takes for light to reach you is negligible for this calculation. This method of estimating distance helps understanding the physical phenomena and ensuring safety during storms.

Answer: 5

Step-by-step explanation:

Given : Leslie needs to roll an 8 with 2 dice to win a game.

Number of outcomes , when we roll a die {1 ,2,3,4,5,6} =6

When we roll two dice the total number of outcomes are:

[tex]6\times6=36[/tex]

The possible outcomes when we roll two dice :-

(1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)

(2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)

(3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)

(4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)

(5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)

(6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6)

The favorable outcomes to get sum as 8 :-

{(2,6), (6,2), (3,5), (5,3), (4,4)}

Hence, the number of possible outcomes are there for her to win = 5

In relation to the surface, before swimming up, the diver was -5.875 feet under the water. The negative sign implies that the diver was beneath the surface of the water.

The diver's position in relation to the surface before swimming to the top is represented by a negative number because swimming upwards implies moving in a positive direction. In this case, the diver was -5.875 feet from the surface before they started swimming up. This negative sign indicates that the diver was beneath the surface of the water.

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The price of a single ticket is given by the expression [tex]\( \frac{70n - 1500}{n} \),[/tex] where n represents the number of tickets sold.

To find the price of a single ticket, we need to understand that the profit P(n) represents the income from ticket sales.

In the given equation [tex]\( P(n) = 70n - 1500 \)[/tex], n represents the number of tickets sold, and P(n) represents the profit from selling n tickets.

If we divide the total profit P(n) by the number of tickets n, we can find the price of a single ticket.

So, the price of a single ticket is given by:

[tex]\[ \text{Price of a single ticket} = \frac{P(n)}{n} \][/tex]

Substituting [tex]\( P(n) = 70n - 1500 \)[/tex], we get:

[tex]\[ \text{Price of a single ticket} = \frac{70n - 1500}{n} \][/tex]

Now, the price of a single ticket is dependent on the number of tickets sold, so we cannot determine a specific price without knowing the value of n. However, we can say that as the number of tickets sold increases, the price per ticket decreases due to the fixed costs (expressed by the constant term -1500) being spread out over a larger number of tickets.

Answer:

The values of [tex]x=30^{\circ}[/tex] and [tex]y=20^{\circ}[/tex].

Step-by-step explanation:

A Linear pair is a pair of adjacent angles formed when two lines intersect.

In the given figure, [tex]80^{\circ}[/tex] and  [tex]4x-y[/tex] , [tex]4x-y[/tex] and   [tex]x+2y+10^{\circ}[/tex] form a linear pair.

By linear pairs theorem, we have

[tex]80^{\circ}+4x-y=180^{\circ}[/tex]

[tex]4x-y+x+2y+10^{\circ}=180^{\circ}[/tex]

On solving we get,

[tex]4x-y=100^{\circ}[/tex]     ....(1)

[tex]5x+y=170^{\circ}[/tex]     .....(2)

Now, to solve equation (1) and (2) by simultaneously; we get [tex]x=30^{\circ}[/tex]

putting the value of x in equation 1 we get,

[tex]4x-y=100^{\circ}[/tex]

[tex]4\cdot 30^{\circ}-y=100^{\circ}[/tex]

[tex]120^{\circ}-y=100^{\circ}[/tex]

On simplify we have, [tex]y=20^{\circ}[/tex]

Therefore, the values of x and y are: [tex]30^{\circ}[/tex] and [tex]20^{\circ}[/tex]

The equation 3 x + 6 = 72 be used to find the first integer.

Option 4 is true.

Here,

The sum of three consecutive even integers is 72.

Let x represent the first integer, x + 2 represent the second integer, and x + 4 represent the third integer.

We have to find equation which can be used to find the first integer.

What is Integers?

An integer is a whole number (not a fractional number) that can be positive, negative, or zero.

Now,

The sum of three consecutive even integers is 72.

So,

x + ( x + 2 ) + ( x+ 4 ) = 72

x + x + 2 + x+ 4 = 72

3x + 6 = 72

Hence, The equation 3 x + 6 = 72 be used to find the first integer.

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