The graphs shows the number of gallons of white paint that were mixed with gallons of blue paint

Given: ΔABC Prove: The three medians of ΔABC intersect at a common point.

Marta_Voda [28]

Given: ΔABC

When written in the correct order, the two-column proof below describes the statements and justifications for proving the three medians of a triangle all intersect in one point are as follows:

Statements Justifications

Point F is a midpoint of Line segment AB by Construction
Point E is a midpoint of Line segment AC
Draw Line segment BE
Draw Line segment FC

Point G is the point of intersection between
Line segment BE and Line segment FC Intersecting Lines Postulate

Draw Line segment AG by Construction

Point D is the point of intersection between
Line segment AG and Line segment BC Intersecting Lines Postulate

Point H lies on Line segment AG such that
Line segment AG ≅ Line segment GH by Construction

Line segment FG is parallel to line segment
BH and Line segment GE is parallel to line
segment HC Midsegment Theorem

Line segment GC is parallel to line segment
BH and Line segment BG is parallel to
line segment HC Substitution

BGCH is a Properties of a Parallelogram parallelogram (opposite sides are parallel)

Line segment BD ≅ Line segment Properties of a Parallelogram DC (diagonals bisect each other)

Line segment AD is a median Definition of a Median

Thus the most logical order of statements and justifications is: II, III, IV, I

7 0

3 years ago

-8× + 40 >-16 please help

Vesnalui [34]

Answer:

hi

Step-by-step explanation:

$- 8x + 40 > - 16 \: \: \: \: \: add \: - 40 \: to \: both \: sides \\ \\ - 8x + 40 - 40 > - 16 - 40 \\ - 8x > - 56 \\ divide \: both \: sides \: on \: - 8 \: and \: change \: the \: sign \\ \\ x < \frac{ - 56}{ - 8 } \\ x < 7$

8 0

3 years ago

I need an emergency help plssssss! :(

aivan3 [116]

Please find attached photograph for your answer.

Hope it helps.

Do comment if you have any query.

4 0

2 years ago

Read 2 more answers

The focus of a parabola is (0, - 2) The directrix of the parabola is the line y = - 3 What is the equation of the parabola

777dan777 [17]

Answer:

Option B: $\textbf{y} \hspace{1mm} \textbf{=} \hspace{1mm} \frac{\textbf{-1}}{\textbf{2}} \textbf{x}^{\textbf{2}} \hspace{1mm} \textbf{-} \hspace{1mm} \frac{\textbf{5}}{\textbf{2}}$

Step-by-step explanation:

When the focus (h, k) of a parabola and the equation of the directrix y = c are given, the equation of the parabola is given by:

$\textbf{(x - h)}^{\textbf{2}} \hspace{1mm} \textbf{+} \hspace{1mm} \textbf{k}^{\textbf{2}} \hspace{1mm} \textbf{-} \hspace{1mm} \textbf{c}^{\textbf{2}} \hspace{1mm} \textbf{=} \hspace{1mm} \textbf{2(k - c)y}}$

Here, we are given the focus: (h, k) = (0, -2)

Directrix: y = c = -3.

We substitute in the formula to get the equation of the parabola.

$(x - 0)^2 + (-2)^2 - (-3)^2 = 2(-2 - (-3))y$

$\implies x^2 + 4 - 9 = 2(- 2 + 3)y$

$\implies x^2 - 5 = 2(1) y$

$\implies 2y = x^2 - 5$

Dividing by 2, throughout we get:

$\textbf{y} \hspace{1mm} \textbf{=} \hspace{1mm} \frac{\textbf{-1}}{\textbf{2}} \textbf{x}^{\textbf{2}} \hspace{1mm} \textbf{-} \hspace{1mm} \frac{\textbf{5}}{\textbf{2}}$ which is the required answer.

5 0

3 years ago

At the skating rink, 6 out 10 skaters were able to skate under the limbo bar. Which names the fraction of skaters who were not a

Tasya [4]

2/5 because 10/10 minus 6/10 equals 4/10 which reduces to 2/5

7 0

3 years ago