6-13x=24-10(2x+8)+62+7x

Angles <1 and <3 are proven to be congruent because they are both supplementary to the same angle <2, thus having the same measure as per the transitive property of equality.

When given that <1 and <2 are supplementary and that <2 and <3 are supplementary, we can prove that <1 is congruent to <3 through a series of logical steps. By definition, supplementary angles add up to 180 degrees. Therefore, if <1 and <2 are supplementary, we can write this as: m<1 + m<2 = 180 degrees (1). Similarly, if <2 and <3 are supplementary, that looks like: m<2 + m<3 = 180 degrees (2). By transposing m<2 from equation (1) to (2), we get m<1 = m<3, which implies that <1 is congruent to <3, as they have the same measure. This reflects the transitive property of equality where if a = b and b = c, then a = c. This conclusion demonstrates the Theorem 12, which states that if two angles are congruent to each other, their supplementary angles are also congruent.

The solution to the equation y^2 = 144/169 yielding two possible solutions for y which are 12/13 and -12/13.

Step 1: Take the square root of both sides of the equation to get y. Remember that taking the square root of a square will provide you with the original value. However, since every positive real number has two square roots, one positive and one negative, your answer will have two potential values.

Step 2: The square root of 144 is 12, and the square root of 169 is 13, thus the equation becomes:

y = ± (12/13)

Therefore, the two solutions to the equation are y = 12/13 and y = -12/13.

Answer:

The answer is n with the less than sign with it underlined and then 9 on the left side

Step-by-step explanation:

The reason why it is the less than sign with it underlined is because the problem says the greatest value and that sign mean at most which is also the greatest.

The answer is stretch.

The statement that best represents the information that should be in the box labeled 1 is; AB = BC. Hence, the correct option is A.

The reflexive property of congruence says that the considered geometric quantity, whether it be angle, line segment, or shape etc, is congruent to itself.

It is Given that A conjecture and a portion of the flowchart proof used to prove the conjecture are shown. AB is similar to BC.

Thus, By the segment congruence postulate, AB = BC

Therefore, the statement that best represents the information that should be in the box labeled 1 is; AB = BC.

Hence, the correct option is A.

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Multiplying 4762 by 33 through long multiplication involves multiplying 4762 by 3 and 30 separately, then adding the results to get the final answer of 157146.

To multiply 4762 by 33, you use long multiplication:

Step-by-step:

Thus, 4762 multiplied by 33 equals 157146.

The equation of the linear function will be y = (2/3)x + 4.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

A function with a rate of change of 2/3 and an initial value of 4. Then the equation of the linear function is given as,

y = (2/3)x + 4

The equation of the linear function will be y = (2/3)x + 4.

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Answer:

Given : George is driving at an average speed of 62 miles per hour.

To Find : Write an expression that would give his distance traveled for h hours.

Solution:

Speed = 62 miles/hour

Time = h hours

[tex]Distance = Speed \times Time[/tex]

[tex]Distance = 62h[/tex]

So, an expression that would give his distance traveled for h hours is [tex]Distance = 62h[/tex]

Now we are supposed to Make a table that records his distance for 3, 5.5, 7, and 8.5 hours.

So, At h = 3

[tex]Distance = 62(3)[/tex]

[tex]Distance = 186[/tex]

So, At h = 5.5

[tex]Distance = 62(5.5)[/tex]

[tex]Distance = 341[/tex]

So, At h = 7

[tex]Distance = 62(7)[/tex]

[tex]Distance =434[/tex]

So, At h = 8.5

[tex]Distance = 62(8.5)[/tex]

[tex]Distance =527[/tex]

So, Table :  

      Hours                  Distance (miles)

        3                             186

       5.5                           341

        7                             434

       8.5                          527

0.0001 can be represented as [tex]\(1 \times 10^{-4}\)[/tex] in scientific notation, showing its value with a coefficient of 1 and an exponent of -4. This notation simplifies large or small numbers, making them easier to work with in calculations and comparisons.

When converting a number to scientific notation, like 0.0001, we aim to express it as a coefficient multiplied by a power of 10. The coefficient is a number greater than or equal to 1 and less than 10, and the power of 10 indicates how many places the decimal point must be shifted to obtain the original number.

In the case of 0.0001, there are four decimal places. Each decimal place corresponds to a division by 10. So, to get from 0.0001 to 1, we need to multiply by 10 four times, which gives us [tex]\(10^{-4}\)[/tex]. This signifies that the decimal point needs to be moved four places to the right to reach 1.

So, 0.0001 can be written as [tex]\(1 \times 10^{-4}\)[/tex], where 1 is the coefficient (because it's between 1 and 10) and -4 is the exponent of 10.

Estimation helps to place the decimal point in a product correctly by counting the numbers of figures after the decimal points prior to finding the product, then shifting the decimal point from the back to the front in the order with which you've earlier counted it after the finding the product.

Estimation is used to approximate a large number of a particular number to its nearest whole number or significant figures.

The use of decimal points in estimation helps to separate the fractional part from the whole number.

For example, if we want to find the product of 4.23 and 2.1, we have three numbers altogether after the decimal point.

So;

       4.23

×         2.1

    4  2  3

8  4  6    

8  8  8  3  

So, starting from the back to the front, we will shift the decimal point in three places. Then the product of 4.23 and 2.1 is 8.883

Therefore, we can conclude that we've fully understood how estimation help you place the decimal Point in a product correctly.

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