If I had 18 cubes how many ways can I use to make a model of a park

For ΔABC with A(–5, –4), B(3, –2), and C(–1, 6), M is the midpoint of

Zarrin [17]

Answer:

The proposition is true, as $\overrightarrow{MN} = (2,5)$ and $\overrightarrow {AC} = (4, 10)$ satisfies the given expression ( $\overrightarrow{MN} = \frac{1}{2}\cdot \overrightarrow{AC}$ ).

Step-by-step explanation:

Vertices of the triangle ABC are located in $A(x,y) = (-5,-4)$ , $B(x,y) = (3,-2)$ and $C(x,y) = (-1, 6)$ , respectively. By definition of midpoint, we get that M and N are located in the following coordinates:

$M(x,y) = \frac{1}{2}\cdot A(x,y) +\frac{1}{2}\cdot B(x,y)$ (Eq. 1)

$M(x,y) = \frac{1}{2}\cdot (-5,-4)+\frac{1}{2}\cdot (3,-2)$

$M(x,y) = \left(-\frac{5}{2},-2 \right)+\left(\frac{3}{2},-1\right)$

$M(x,y) = (-1,-3)$

$N(x,y) = \frac{1}{2}\cdot B(x,y) + \frac{1}{2}\cdot C(x,y)$ (Eq. 2)

$N(x,y) = \frac{1}{2}\cdot (3,-2)+\frac{1}{2}\cdot (-1,6)$

$N(x,y) = \left(\frac{3}{2},-1\right)+\left(-\frac{1}{2},3 \right)$

$N(x,y) = (1, 2)$

Then, the relative vectors between A and C, as well as M and N are, respectively:

$\overrightarrow{AC} = C(x,y)-A(x,y)$ (Eq. 3)

$\overrightarrow{AC} = (-1, 6) -(-5,-4)$

$\overrightarrow {AC} = (4, 10)$

$\overrightarrow {MN} = N(x,y)-M(x,y)$ (Eq. 4)

$\overrightarrow {MN} = (1,2)-(-1,-3)$

$\overrightarrow{MN} = (2,5)$

By getting back into (Eq. 3), we find the following the result after some algebraic handling:

$\overrightarrow {AC} = (4, 10)$

$\overrightarrow{AC} = 2\cdot (2,5)$

$\overrightarrow {AC} = 2\cdot \overrightarrow {MN}$

$\overrightarrow{MN} = \frac{1}{2}\cdot \overrightarrow{AC}$

Which proofs the given affirmation.

6 0

3 years ago

John had 2⁄3 of his homework complete, Sarah had 5⁄10, Alex 7⁄8, and Michelle 1⁄2. Who completed the most of the homework assign

yuradex [85]

Hey there!

So, when finding who completed more, we would want to find the lowest denominator, but also, we would have to compare it with the numerator.

John: He completed 2/3, which is basically almost done.

Sarah: She only completed (half) of her homework.

Alex: He only did 7/8

Michelle: He/she only did 1/2, which is only half.

So, from looking at these fractions above, Michelle and Sarah are out.

We would just have to determine, which is finished more, John or Alex.

John had 2/3 & Alex 7/8

So, by comparing them both, 7/8 would be greater because the smaller the denominator is, and the closer that the numerator is to the denominator, this would mean that the homework is almost finished.

Your correct answer is Alex, he has completed more.

Hope this helps you!

4 0

3 years ago

PLEASE HELP !! BRAINLIEST AND 10 POINTS

Bumek [7]

POINT A I had the same question in my math class !!!

8 0

3 years ago

Lena is asked to write an explicit formula for the graphed geometric sequence (3,6.25) (2,2.5) (1,1)

harkovskaia [24]

The correct answer for this question is this one: "2.5"
Lena is asked to write an explicit formula for the graphed geometric sequence. The value, written as a decimal, should Lena use as the common ratio that is 2.5There exists the same question from other source with the image is shown.
Hope this helps answer your question and have a nice day ahead.

3 0

3 years ago

Read 2 more answers

PLEASE HELP THX MARK BRAINLEST

mote1985 [20]

Answer:

Are you giving any exam?

5 0

3 years ago