Mischa dives from a platform that is 10 meters above the water. Her dive takes her 2.3 meters below the surface of the water. How far does Mischa's dive take her?

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 two partial products of 513 x 46 are:

500 x 46 and 13 x 46.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division. 

We have,

513 x 46 = 23598

We need to find two partial products.

513 can be written as:

513 = 500 + 13

So,

= (500 + 13) x 46

= 500 x 46 + 13 x 46

= 23000 + 598

= 23598

The two partial products are 500 x 46 and 13 x 46.

Thus,

The two partial products of 513 x 46 are 500 x 46 and 13 x 46.

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Final answer:

To calculate 513 multiplied by 46, you should add the first partial product (3078) and the second partial product (20520) to get the total product of 23598.

Explanation:

To find the product of 513 multiplied by 46 using the partial products method, you'll need to break down the equation into parts based on place value and then add those parts together. The process is as follows:

Multiply the ones place of the second number by the entire first number. So, 6 (from the 46) times 513.

Multiply the tens place of the second number by the entire first number. That means 40 (from the 46, which is 4 tens) times 513.

To complete this calculation:

6 * 513 = 3078 (this is the first partial product).

40 * 513 = 20520 (this is the second partial product).

Now, we add both partial products together:

3078 + 20520 = 23598

So, 513 multiplied by 46 equals 23598.

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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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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To solve for 'x' in the equation 'abx-cdx=15m', rewrite the equation, factor out the 'x', and solve for 'x'. The solution is 'x = 15m / (ab - cd)', provided that 'ab' does not equal 'cd'.

To solve for x in the equation abx-cdx=15m, we need to firstly isolate the terms containing x. Let's start by rewriting the equation:

abx = cdx + 15m

Then, factoring out the x, we get:

x(ab - cd) = 15m

Finally, we can solve for x by dividing both sides of the equation by (ab - cd):

x = 15m / (ab - cd)

Note: this solution works provided that ab≠cd since division by zero is undefined in mathematics.

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Is the mapping, or movement, of all the points of a figure in a plane according to a common operation *

10 points

Reflection

Translation

Transformation

Rotation

is a transformation that "slides" each point of a figure the same distance and direction. *

10 points

Reflection

Translation

Transformation

Rotation

a transformation that flips a figure over a reflection line *

10 points

Reflection

Translation

Transformation

Rotation

is a transformation that turns a figure about a fixed point for a given angle *

10 points

Reflection

Translation

Transformation

Rotation

is generally used to generate more variable names for things which are similar *

10 points

Verticies

Prime

Congruent

Function

Plural of vertex meaning the corner where two lines meet *

10 points

Verticies

Prime

Congruent

Function

Same size same shape *

10 points

Clockwise

Counter Clockwise

Congruent

Prime

maps each input to one and only one output. *

10 points

Function

Clockwise

Congruent

Prime

in a curve corresponding in direction to the typical forward movement of the hands of a clock. *

10 points

Function

Clockwise

Counter Clockwise

Prime

in the opposite direction to the way in which the hands of a clock move around *

10 points

Function

Clockwise

Counter Clockwise

Prime

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.

The answer is stretch.

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.

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.