Factor completely, then place the answer in the proper location on the grid. 21a^2- 57a+30

Does anyone knows how to do this?

dedylja [7]

Answer:

(a) i) Vector BC = 3/2 a + 5b

ii) Vector AM = 15/4 a + 5/2 b

(b) Vector QP = -15/4 b where k = -15/4

Step-by-step explanation:

* Lets explain how to solve this problem

∵ ABCD is a trapezium

∵ AB // DC

∵ The vector AB = 3a

∵ Vector DC = 3/2 vector AB

∴ Vector DC = 3/2 × 3a = 9/2 a

∵ Vector AD = 5b

(a)

i) ∵ Vector BC = vector BA + vector AD + vector DC

∵ Vector AB = 3a , then vector BA = -3a

∵ Vector AD = 5b , vector DC = 9/2 a

∴ Vector BC = -3a + 5b + 9/2 a = (-3a + 9/2 a) + 5b

∴ Vector BC = 3/2 a + 5b

ii) ∵ Vector AM = vector AB + vector BM

∵ M is the mid-point of BC

∴ Vector BM = 1/2 vector BC

∵ Vector BC = 3/2 a + 5b

∴ Vector BM = 1/2(3/2 a + 5b) = (1/2 × 3/2) a + (1/2 × 5) b

∴ Vector BM = 3/4 a + 5/2 b

∴ Vector AB = 3a

∴ Vector AM = 3a + 3/4 a + 5/2 b = (3a + 3/4 a ) + 5/2 b

∴ Vector AM = 15/4 a + 5/2 b

(2)

∵ 7 DQ = 5 QC ⇒ divide both sides by 7

∴ DQ = 5/7 DC

∴ The line DC = 7 + 5 = 12 parts ⇒ DQ 5 parts and QC 7 parts

∵ DQ = 5/12 DC

∵ Vector DC = 9/2 a

∴ Vector DQ = 5/12 (9/2 a) = 45/24 a ⇒ divide up and down by 3

∴ Vector DQ = 15/8 a

∵ P is the mid point of AM

∴ Vector AP = 1/2(15/4 a + 5/2 b) = (1/2 × 15/4) a + (1/2 × 5/2) b

∴ Vector AP = 15/8 a + 5/4 b

∵ Vector QP = QD + DA + AP

∵ Vector DQ = 15/8 , then vector QD = -15/8 a

∵ Vector AD = 5b , then vector DA = -5b

∴ Vector QP = -15/8 a + -5b + 15/8 a + 5/4 b

∴ Vector QP = (-15/8 a + 15/8 a) + (-5b + 5/4 b)

∴ Vector QP = -15/4 b

∵ -15/4 is constant

∴ Vector QP = k b ⇒ proved

8 0

3 years ago

What is 1/9 (2m - 16) = 1/3 (2m +4)

Serjik [45]

Answer:

-7

Step-by-step explanation:

Hope it helped!

3 0

3 years ago

What is the probability of getting at least one 6 in four rolls of a single fair die?

Alik [6]

Every time you roll you have a 1/6 chance so rolling 4 times you have a 6x4= 24 and 1x4=4 so you have a 4/24 chance of getting a 6

4 0

3 years ago

Read 2 more answers

Mariah is completing a language arts review sheet she estimates that it takes her one minute to complete each multiple-choice qu

WARRIOR [948]

Answer:

The answer is below

Step-by-step explanation:

Given the time taken to answer each multiple choice question as one minute, the time taken to x multiple choice question = 1 minute/question × x questions = x minutes

Given the time taken to answer each essay question as six minute, the time taken to y essay question = 6 minute/question × y questions = 6y minutes

Therefore the total time taken to complete X multiple choice question and y essay questions = the time taken to x multiple choice question + the time taken to y essay question = x + 6y

6 0

3 years ago

Please help me on my geometry question, DUE SOON!

zavuch27 [327]

Answer:

70

Step-by-step explanation:

Basic Concept: Geometry

Formula:

Area of a polygon = $\frac{pa}{2}$

where p = perimeter and a = apothem

In this problem we are given the area and the apothem and we need to find the perimeter

To do so we want to plug what we are given into the formula and solve for the missing piece.

We are given the area (350) and the apothem (10)

So in the formula we would plug in 350 for the area and 10 for "a"

We would then have

$350 = \frac{10p}{2}$

Basic Concept: Algebra

Now we use basic algebra to solve for p (perimeter)

step 1 multiply each side by 2

$350*2=700\\\frac{10p}{2}*2=10p$

now we have 700 = 10p

Step 2 divide each side by 10

700/10=70

10p/10=p

we're left with p = 70

So we can conclude that the perimeter is equal to 70

5 0

3 years ago