calculate the slope of the line given the points (-2, 6) and (0, 4)

The coordinate proof is a proof of a geometric theorem which uses "generalized" points on the Cartesian Plane to make an argument.The method usually involves assigning variables to the coordinates of one or more points, and then using these variables in the midpoint or distance formulas .For example, the following is a coordinate proof of the Triangle Midsegment Theorem , which states that the segment connecting the midpoints of two sides of a triangle is parallel to the third side and exactly half the length.Without loss of generality, we can assume that one side of the triangle lies on the xx -axis with one vertex at (0,0)(0,0) and the other vertex at(a,0)(a,0).Let the third vertex have the coordinates (b,c)(b,c) . We can assume without loss of generality that this third vertex lies in the first quadrant. (If it doesn't, you can just reflect the triangle over the xx - and/or yy -axis until it does.)

Example:

To Prove: XY¯¯¯¯¯¯XY¯ is parallel to PR¯¯¯¯¯PR¯ and

XY=12PRXY=12PR

Proof:

Using the midpoint formula , the coordinates of the midpoints XX and YY are

X(0+b2,0+c2)=X(b2,c2)Y(a+b2,0+c2)=Y(a+b2,c2)X(0+b2,0+c2)=X(b2,c2)Y(a+b2,0+c2)=Y(a+b2,c2)

First note that the slope is 00 , since

m=riserun     =(c2−c2)(b2−(a+b2))     =0(b2−(a+b2))     =0m=riserun     =(c2−c2)(b2−(a+b2))     =0(b2−(a+b2))     =0

So, XY¯¯¯¯¯¯XY¯ is parallel to PR¯¯¯¯¯PR¯ .

Now, compare the lengths of the two segments.

XY=a+b2−b2        =a2PR=a−0        =aXY=a+b2−b2        =a2PR=a−0        =a

So,

XY=12PRXY=12PR

Thanks to google for example

hope this helps

Answer:

triangle CDN ≅ triangle CBM

Statement | Reason

line DC ≅ __BC___ | The sides of a square are congruent.

line BM ≅ __DN___ | They are both half the length of a side of the square.

angle __D___ ≅ angle B | All the angles of a square are congruent.

triangle CDN ≅ CBM |  

by

SAS

Step-by-step explanation:

Answer:

  16.9 units

Step-by-step explanation:

Sometimes the easiest way to work these problems is to get a little help from technology. The GeoGebra program/app can tell you the length of a "polyline", but it takes an extra segment to complete the perimeter. It shows the perimeter to be ...

  14.87 + 2 = 16.87 ≈ 16.9 . . . units

_____

The distance formula can be used to find the lengths of individual segments. It tells you ...

  d = √((Δx)² +(Δy)²)

where Δx and Δy are the differences between x- and y-coordinates of the segment end points.

If the segments are labeled A, B, C, D, E in order, the distances are ...

  AB = √(5²+1²) = √26 ≈ 5.099

  BC = √(1²+3²) = √10 ≈ 3.162

  CD = Δx = 3

  DE = √(3²+2²) = √13 ≈ 3.606

  EA = Δy = 2

Then the perimeter is ...

  P = AB +BC +CD +DE +EA = 5.099 +3.162 +3 +3.606 +2 = 16.867

  P ≈ 16.9

Answer:

-12.00%

Step-by-step explanation:

;)

Answer:

12% decrease

Step-by-step explanation:

Answer:

The answer is: $ 30,593.09.

Step-by-step explanation:

To the gross income of $ 42,750 of Addison, the amounts of the payments made must be deducted, that is, $ 537.56, $ 918, $ 1,351.35, plus the exemption of $ 3,650, and also if they grant him the standard deduction of $ 5,700; Your taxable income would be: $ 42,750 - ($ 537.56 + $ 918 + $ 1,351.35 + $ 3,650 + $ 5,700) = $ 30,593.09

The answer is: $ 30,593.09.

The cross-section of a cube can be a non-rectangular parallelogram when the cutting plane is not perpendicular to the cube's base.

The scenario where a cube's cross-section can be a non-rectangular parallelogram occurs when the cutting plane is at an angle other than a right angle to the cube's base. This results in a parallelogram that is not a rectangle, as the cutting plane affects the shape of the cross-section.

When the cutting plane deviates from being perpendicular to the base of the cube, it creates a cross-section that is not a rectangle but can be a parallelogram with unequal angles and sides.

Understanding the geometric implications of the cutting plane's orientation is crucial in visualizing how the cube's cross-section can vary from a rectangular shape to a non-rectangular parallelogram.

Answer:Its C

Step-by-step explanation:

The mean age of the family members (46, 48, 21, 12, 15, and 8) is calculated by adding all the ages to get a sum of 150, and then dividing by the number of family members, which is 6, resulting in a mean age of 25 years old.

To calculate the mean age of the family members, you add up all of the ages and then divide by the number of family members. The ages given are 46, 48, 21, 12, 15, and 8. Let's find their sum:

Add the ages together: 46 + 48 + 21 + 12 + 15 + 8 = 150.

Count the number of family members, which is 6.

Divide the total sum of ages by the number of family members: 150 \/ 6 = 25.

Therefore, the mean age of the family members is 25 years old.

The problem involves trigonometry to determine the width of the sandpile. The angles of depression equate to angles of elevation from ground up. Using the tangent function and the provided angles of depression, the distances to the rocks are calculated and added together to get approximately 52 feet as the pile's width.

This problem involves the application of trigonometry, specifically the tangent function (tan) in relation to angle of depression. To start with, we need to note that the angle of depression is equivalent to the angle of elevation as observed from the ground upwards. Hence, if the angles of depression are 28° and 19° respectively, it would mean that the angles of elevation at the rocks would be 28° and 19° respectively.

We can use the formula for tangent, which is tan(θ)=Opposite/Adjacent. In this context, 'Opposite' is the height of the pile (11 feet), and 'Adjacent' is the distance from the base of the pile to the rock. We get two equations:

We rearrange to find D1 and D2. Finally, the total distance (width of the pile) is simply D1 + D2. Using a calculator, D1 is approximately 21 feet and D2 is approximately 31 feet. Hence, the width of the sandpile is approximately 52 feet when rounded to the nearest foot.

https://brainly.com/question/11016599

#SPJ3

Final answer:

To estimate the total cost, each item's price is rounded to the nearest half dollar: $1.85 to $2.00, $0.98 to $1.00, $3.49 to $3.50, $9.78 to $10.00, $6.18 to $6.00. Summing the rounded figures, the estimated total is $22.50.

Explanation:

To mentally estimate the total cost of the items, we round each item's price to the nearest half dollar and then add them up.

Adding up the rounded figures gives us: $2.00 + $1.00 + $3.50 + $10.00 + $6.00, which equals $22.50. Thus, the estimated total cost of the items is $22.50, rounded to the nearest half dollar.

The correct answer is:

11 containers.

Explanation:

We want 96 boxes total. Each container can hold either 10 small boxes or 8 large boxes. To solve this, we want to subtract multiples of 10 from 96 until we have a number that is divisible by 8. This is because we cannot have a fraction of a container full of either big or small boxes.

96-10(1) = 96 - 10 = 86; this is not divisible by 8.

96-10(2) = 96 - 20 = 76; not divisible by 8.

96-10(3) = 96 - 30 = 66; not divisible by 8.

96-10(4) = 96 - 40 = 56; this is divisible by 8.

This means there are 4 containers of small boxes, for 4(10) = 40 boxes, and 56/8 = 7 containers of large boxes, for 56 boxes. This is a total of 4+7 = 11 boxes for our 40+56 = 96 boxes.

Answer:

Then they'll pay $27.32

Step-by-step explanation:

In order to determine this, start by multiplying the cost of the meal by the tax amount.

25.30 * 8% = 2.02

Now add the tax to the meal cost

25.30 + 2.02 = 27.32