The coordinates of M, P and Q in terms of a and b are [tex]M = \frac{1}{2}\cdot a + \frac{1}{2}\cdot b[/tex], [tex]P = \frac{3}{4}\cdot a + \frac{1}{4}\cdot b[/tex] and [tex]Q = \frac{1}{8}\cdot a - \frac{1}{8}\cdot b[/tex], 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
[tex]\overrightarrow{AM} = \frac{1}{2}\cdot \overrightarrow{AB}[/tex]
[tex]\vec M - \vec A = \frac{1}{2}\cdot \vec B - \frac{1}{2}\cdot \vec A[/tex]
[tex]\vec M = \frac{1}{2}\cdot \vec A +\frac{1}{2}\cdot \vec B[/tex]
[tex]M = \frac{1}{2}\cdot a + \frac{1}{2}\cdot b[/tex]
Location of P
[tex]\overrightarrow{AP} = \frac{1}{2}\cdot \overrightarrow{AM}[/tex]
[tex]\vec P - \vec A = \frac{1}{2}\cdot \vec M - \frac{1}{2}\cdot \vec A[/tex]
[tex]\vec P = \frac{1}{2}\cdot \vec A +\frac{1}{2}\cdot \vec M[/tex]
[tex]\vec P = \frac{3}{4}\cdot \vec A + \frac{1}{4}\cdot \vec B[/tex]
[tex]P = \frac{3}{4}\cdot a + \frac{1}{4}\cdot b[/tex]
Location of Q
[tex]\overrightarrow{QM} = \frac{1}{2}\cdot \overrightarrow{PM}[/tex]
[tex]\vec M - \vec Q = \frac{1}{2}\cdot \vec M - \frac{1}{2}\cdot \vec P[/tex]
[tex]\vec Q = \frac{1}{2}\cdot \vec P - \frac{1}{2}\cdot \vec M[/tex]
[tex]\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)[/tex]
[tex]\vec Q = \frac{1}{8}\cdot \vec A -\frac{1}{8}\cdot \vec B[/tex]
[tex]Q = \frac{1}{8}\cdot a - \frac{1}{8}\cdot b[/tex]
The coordinates of M, P and Q in terms of a and b are [tex]M = \frac{1}{2}\cdot a + \frac{1}{2}\cdot b[/tex], [tex]P = \frac{3}{4}\cdot a + \frac{1}{4}\cdot b[/tex] and [tex]Q = \frac{1}{8}\cdot a - \frac{1}{8}\cdot b[/tex], respectively.
We kindly invite to check this question on midpoints: https://brainly.com/question/4747771
Mclane is playing a game where you get 5 points for correct answers and lose 3 points for incorrect answers. If he gets 6 questions correct and 7 questions incorrect, what was his final score?
Answer:
9
Step-by-step explanation:
final score = total points for correct answer - total points for wrong answer
total points for correct answer = 5 x 6 = 30
total points for wrong answer = 7 x 3 = 21
30 - 21 = 9 points
plzz help if right i give brainliest
Answer:
b. (x+6)(x-6)
Step-by-step explanation:
x^2-36 So to get to this answer you can do two things
1. Guess and check
2. Factor it out (which is what I like to do)
In order to get x^2 you need 2xs that are positive which knocks out c and d
Then to get to -36, you need to multiply a positive 6 and a negative 6
(This was poorly explained but if you need anymore help just lmk)
Solve the linear inequality: x ≤ -x + 4
Answer:
x ≤ 2
Step-by-step explanation:
i hope this helps :)
Find the 50th term of the
sequence:
65536, 49152, 36864, 27648...
A) 0.0495
B) 0.066
C) 0.088
D) 0.117
Find the volume of the right circular cone that’s has the radius of 4 inches and height of 12 inches
Answer:
64 pi in3.
Step-by-step explanation:
What are the zeros of f(0) ** - 202
OAX-5 and x4
BN-10 and x = 2
OCX-2 and x = 10
DX-4 and 5
Answer:
b
Step-by-step explanation:
3/4 ft= blank inches
When given a word problem, what should you always do to better visualize the problem?
Step-by-step explanation:
1.Read the Entire Word Problem.
2.Think About the Word Problem.
3.Write on the Word Problem.
4.Draw a Simple Picture and Label It.
5.Estimate the Answer Before Solving.
6.Check Your Work When Done.
7.Practice Word Problems Often.
5.
Write the inequality in words.
3n < 52
A. fifty-two less than three times n
B. Three times n is less than or equal to fifty-two.
C. Three times n is less than fifty-two.
D. Three times n is greater than fifty-two.
Answer:
C
Step-by-step explanation:
3n= 3 times n
And it is less than 52
Answer:
C. Three times n is less than fifty-two.
Step-by-step explanation:
Write the equation of the line, with the given properties, in slope-intercept form.
Slope = -7, through (-5,5)
What is the equation of the line?
Answer:
y=-7x-30
Step-by-step explanation:
y-y1=m(x-x1)
y-5=-7(x-(-5))
y-5=-7(x+5)
y=-7x-35+5
y=-7x-30
A line is perpendicular to y = 3x - 8 and
intersects the point (6, 1).
Write the equation in slope-intercept form.
Answer:
Step-by-step explanation:
a line perpendicular to the give formula has a reciprocal slope and it's sign is changed also.
then m = -1/3 for our perpendicular line
y - 1 = -1/3(x -6)
y -1 = -1/3x + 2
y = -1/3x +3
there you go :)
Volume? Correct answers please
Answer:
V = 1385.44
Step-by-step explanation:
The equation for volume is V = π r 2 h! Where V = volume, r = radius (half the diameter), and h = height. Now lets substitute what we know into this equation!
Since we are giving the diameter (14) we must divide by 2 to find the radius.
14 ÷ 2 = 7
Radius = 7
Height = 9
V = ?
Time to plug these values in!
V = π [tex]7^{2}[/tex] (9)
We have to distribute pi to 7 square that term and then multiply the value by 9.
V = 1385.44
Hope this Helps! :)
Have any questions? Ask below in the comments and I will try my best to answer.
-SGO
please help me with this
Answer:5,2,4,8
Step-by-step explanation:hope it helped
Find the value of the ratio.
Can someone help please???
Jada's teacher fills a travel bag with 5 copies of a textbook. The weight of the bag and books is 17 pounds. The empty travel bag weighs 3 pounds. How much does each book weigh?
Answer:
Correct
5x + 3 = 17
Step-by-step explanation:
So we need to find the book wieght only so take away the bag's weight from the total. 17-3=14. Now it says 5 books so divide 14 by 5 which is 2.8.
= 2.8 pounds
Last year, a lighting supplier called Bright Idea shipped a total of 37,220 lamps to its distributors. This year, the supplier shipped 29,776 lamps. What is the percent of decrease in the number of lamps shipped annually?
Answer:
25%
Step-by-step explanation:
Given data
Last years shipment= 37220 lamps
These years shipment= 29776 lamps
% Decrease= Initial-Final/Initial*100
% Decrease= 37220-29776/29776*100
% Decrease= 7444/29776*100
% Decrease= 0.25*100
% Decrease= 25%
Hence the decrease is 25%
Santiago gave out a survey to some students in his school about their favorite color. 429 of those surveyed said their favorite color was blue. If 55% of the students surveyed said their favorite color was blue, how many students were surveyed in total?
Answer:
780
Step-by-step explanation:
Abbie is 5 years older than twice her sister’s age. Abbie is 25 years old. Which
equation can be used to find her sister’s age?
How much larger is 6 x 10^5 compared to
2 x 10^3?Explain how you know.
Answer:
6 x 10^5 is 300 times greater than 2 x 10^3.
Step-by-step explanation:
Use division to compare.
(6 × 10^5)/(2 × 10^3) = 6/2 × 10^5/10^3 = 3 × 10^2 = 3 × 100 = 300
6 x 10^5 is 300 times greater than 2 x 10^3.
There is 6 × 10⁵ is 300 times greater than 2 × 10³.
What is the Scientific Notation?Scientific Notation is a way of writing down in the easy form of very large or very small numbers.
The exponents are given in the question, as follows:
6 × 10⁵ and 2 × 10³
The exponents in scientific notation as a shorthand for the number of zeroes in the number.
We use division to compare.
( 6 × 10⁵)/(2 × 10³)
= 6/2 × 10⁵/10³
= 3 × 10²
= 3 × 100
= 300
This means 6 × 10⁵ is 300 times greater than 2 × 10³
Learn more about the Scientific Notation here :
https://brainly.com/question/20533245
#SPJ2
What should be done to x^2-10x in order to create a perfect square?
A)subtract 25
B)subtract 5
C)add 5
D)add 25
Answer: B)subtract 5
(x-5)^2-25
Step-by-step explanation:
2a=-10
Divide both sides by 2
2a/2=-10/2
Simplify
a=-5
Add and subtract
x^2-10x+(-5)^2-(-5)^2
Complete the square
(x-5)^2-(-5)^2
Simplify;
(x-5)^2-25
Answered by one other than the ONE & Only #QUEEN herself aka #DRIPPQUEENMO!!
HOPE THIS HELPED!!
property . Simplify the expression 2(5+r) using the distributive property.
Answer:
2x5 = 10
1xr = 2r
Ans : 10+2r
Step-by-step explanation:
[tex]\huge\boxed{Hi\:there!}[/tex]
We are asked to simplify the given expression using the Distributive Property.
All we have to do is multiply 2 times 5 and r:
2(5+r)
10+2r
[tex]\huge\boxed{Hope\:it\:helps!}[/tex]
[tex]\huge\bold{Good\:luck!}[/tex]
[tex]\huge\mathfrak{LoveLastsAllEternity}[/tex]
What percent of 2.5 is 0.2. Please helllllp. My whole family is trying to figure out this darn problem!
Answer: 8
Step-by-step explanation: hope this helps
Find the volume of the rectangular prisim 6cm 4cm 12cm
Answer:
288cm²
Step-by-step explanation:
The volume of a rectangular prism can be easily calculated by multiplying the height by the width by the length
Assuming that the lengths given ( 6cm, 4cm and 12cm ) are the width, height and length
If so then the volume is equal to 6 * 4 * 12
6 * 4 = 24
24 * 12 = 288
volume = 288cm²
Answer:
The answer is 288
Step-by-step explanation:
I don't want to go into detail because the first guy already did., but check your formulas and what you are given and find the answers
help plss need help with this
9514 1404 393
Answer:
2y
Step-by-step explanation:
Eliminating parentheses, we have ...
30x +30y -30x -28y
Grouping like terms gives ...
(30x -30x) +(30y -28y)
Simplifying leaves ...
0x +2y
2y
What is the answer to 8x<6? Please help
Answer:
x<3/4
Step-by-step explanation:
8x<6
x<6/8
x<3/4
I hope this helps
Answer:
x = 3/4
Step-by-step explanation:
x^2+18x+c I have to solve for c
Answer: 81
Step-by-step explanation:
Find the key features for m [x]=3x^2+13x-30
Answer:
x1= -6 and x2= 5/3
Step-by-step explanation:
good luck
The equation of the function is Y=4x+5.Find the value of y when
x=3
x=-2
The equation of the function is y = 4x + 5. Find the value of y when
x = 3
x = -2
Answer:-Given:-y = 4x + 5 [Equation]
To Find:-The value of y when x = 3 , x = -2
Solution:-y = 4x + 5 [Given equation]
[tex] \therefore [/tex] When x = 3 ,
y = 4 × 3 + 5 [Value of x is 3]
y = 12 + 5
y = 17 [Answer]Again, when x = -2 ,
y = 4 × (-2) + 5 [Value of x is -2]
y = -8 + 5
y = -3 [Answer]PLSS HELP ME ASAP!!!
What is the area of the triangle?
Answer:
45cm^2 is your answer :)
Step-by-step explanation:
how do i get only 50 point questions
Answer:
what?
Step-by-step explanation:
if your asking to filter out all questions for only those that give you 50 points, its not possible at this moment