Rename fractions and mixed numbers

Suppose M is the midpoint of Segment AB, P is the midpoint of Segment AM, and Q is the midpoint of segment PM.

DerKrebs [107]

The coordinates of M, P and Q in terms of a and b are $M = \frac{1}{2}\cdot a + \frac{1}{2}\cdot b$ , $P = \frac{3}{4}\cdot a + \frac{1}{4}\cdot b$ and $Q = \frac{1}{8}\cdot a - \frac{1}{8}\cdot b$ , respectively.

In this question we are going to use definitions of vectors and product of a vector by a scalar. Based on the information given on statement, we have the following vectorial formulas:

Location of M

$\overrightarrow{AM} = \frac{1}{2}\cdot \overrightarrow{AB}$

$\vec M - \vec A = \frac{1}{2}\cdot \vec B - \frac{1}{2}\cdot \vec A$

$\vec M = \frac{1}{2}\cdot \vec A +\frac{1}{2}\cdot \vec B$

$M = \frac{1}{2}\cdot a + \frac{1}{2}\cdot b$

Location of P

$\overrightarrow{AP} = \frac{1}{2}\cdot \overrightarrow{AM}$

$\vec P - \vec A = \frac{1}{2}\cdot \vec M - \frac{1}{2}\cdot \vec A$

$\vec P = \frac{1}{2}\cdot \vec A +\frac{1}{2}\cdot \vec M$

$\vec P = \frac{3}{4}\cdot \vec A + \frac{1}{4}\cdot \vec B$

$P = \frac{3}{4}\cdot a + \frac{1}{4}\cdot b$

Location of Q

$\overrightarrow{QM} = \frac{1}{2}\cdot \overrightarrow{PM}$

$\vec M - \vec Q = \frac{1}{2}\cdot \vec M - \frac{1}{2}\cdot \vec P$

$\vec Q = \frac{1}{2}\cdot \vec P - \frac{1}{2}\cdot \vec M$

$\vec Q = \frac{1}{2}\cdot \left(\frac{3}{4}\cdot \vec A + \frac{1}{4}\cdot \vec B\right) -\frac{1}{2}\cdot \left(\frac{1}{2}\cdot \vec A + \frac{1}{2}\cdot \vec B\right)$

$\vec Q = \frac{1}{8}\cdot \vec A -\frac{1}{8}\cdot \vec B$

$Q = \frac{1}{8}\cdot a - \frac{1}{8}\cdot b$

The coordinates of M, P and Q in terms of a and b are $M = \frac{1}{2}\cdot a + \frac{1}{2}\cdot b$ , $P = \frac{3}{4}\cdot a + \frac{1}{4}\cdot b$ and $Q = \frac{1}{8}\cdot a - \frac{1}{8}\cdot b$ , respectively.

We kindly invite to check this question on midpoints: brainly.com/question/4747771

4 0

2 years ago

Question 4 Given: g(x)=-3x2 + 5x and h(x) = 2x +1 Find: g(h(x+1)) Help

Nadusha1986 [10]

Answer:

9+10x

Step-by-step explanation:

Given: g(x)= -3x2 + 5x = -6+5x

and h(x) = 2x +1

Find: g(h(x+1))

1!

h(x+1)= 2(x+1) +1

=2x+3

2! substitute h(x+1)in function g(x)

g(h(x+1))= -6 + 5(2x+3)

= -6+10x+15

= 9+10x

ps. im not sure (-3x2 + 5x) is -6+5x (-3 multiply 2) or question is not clear

3 0

3 years ago

What’s the area in polynomial standard form

Trava [24]

Note that the Area of a rectangle is given by
Area = LB

Where L is the Length (the longer side) and B is the Breadth (or Width which is the shorter side).

From the image, L is (x+6).
Also from the image, B is (x+2)

This implies:
$Area = LB \\ \\ Area = (x + 6)( x + 2)$
Open up the bracket by multiplying both terms:
$Area = {x}^{2} + 2x + 6x + 12 \\ Area = {x}^{2} + 8x + 12$
Since the question says to leave it in polynomial form, that is your answer. Hope I helped? ☺️

3 0

3 years ago

Use distributive property to remove parenthesis. 2(w-8)

kupik [55]

It would be 2w-2(8)

i hope this helps!

3 0

4 years ago

Read 2 more answers

Helpppp meet please

fgiga [73]

Answer:

I think it’s 18