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
b) 8 x + 3 = 35
C)_times5=80/2
Answer:
b. 8×+3=35
Step-by-step explanation:
is the answer
Find the equation of a line that passes through (5,-3) and is perpendicular to y = x.
a) y=x+2
b) y=x-8
c) y=-x+2
d) y=-x-8
Answer:
B
Step-by-step explanation:
X is 5 and y is -3, so y is x minus 8, which is y=x-8
Mark has a £5 note. A litre of milk costs 80p. Mark buys as many litre cartons of milk as he can. How much money will he have left over?
please help mè to this
Science
Answer:
Wooden popsicles, Tissues.,glassbottles, juice cans, paper cups
True or False: If one of the legs in a right triangle is half of the hypotenuse, then the angle opposite to that leg is 60 degrees.
We want to see if the given statement is true or false.
We will prove that the statement is false.
The statement is:
" If one of the legs in a right triangle is half of the hypotenuse, then the angle opposite to that leg is 60 degrees."
We can use the rule:
Sin(θ) = (opposite cathetus)/(hypotenuse).
Let's define:
hypotenuse = H
opposite cathetus = H/2
Let's see if the given angle is equal to 60°, we will have:
Sin(θ) = (H/2)/H = 1/2
θ = Asin(1/2) = 30°
So we can see that the statement is false.
If you want to learn more, you can read:
https://brainly.com/question/6322314
< 1 and < 2 are supplementary angles . the m <2 =142, what is the m<1
Simplify 6-sqr25/4=..............
[tex]6 - \sqrt{ \frac{25}{4} } \\ = 6 - \frac{5}{2} \\ = \frac{12 - 5}{2} \\ = \frac{7}{2} \\ = 3.5[/tex]
Please I’ll mark brainiest and I’ll give extra points !!
Answer:
B
Step-by-step explanation:
2.75 x 0.10x
x in this case is 0
so 2.75 x 0.10x0
= 2.75
Question is in the pic :)
Answer:
Since +P looks to be 7, -P would be -7
Hope this helps :)
Answer:
-7
Step-by-step explanation:
P is a variable, and P can only have 1 value. Thanks to the number line, we know what this value is. P is positive 7. If we know that the set value of P is positive 7, then we can just treat it like it is positive 7.
P - 5 = 2
P + 3 = 10
So putting a negative sign in front of P will mean it will be
- (7)
25 hours in 5 days; 8 hours in 2 days are the rates equivalent.
Answer:
NO
Step-by-step explanation:
25 hours is 5 days is the same as 5 hours per day. 25 ÷ 5 = 5
8 hours in 2 days is the same as 4 hours per day. 8 ÷ 2 = 4
Giải phương trình:
sin*2x+sinxx.cox=1/2
Answer:
x = 9.47 degrees ( in first quadrant.
Step-by-step explanation:
sin2x + sinx cos x = 1/2
Now sinx cos x = 1/2sin2x so:
3/2sin2x = 1/2
sin2x = 1/2 / 3/2
sin2x = 1/2 * 2/3 = 1/3
2x = arcsin 1/3 = 19.47 degrees
x = 9.74 degrees to nearest hundredth.
1.) Keisha's kitchen is shaped like a square. The room has an area of 256 feet squared. Which is the length of one side of Keisha's kitchen?
Also the attachment, and is it rational or irrational?
Answer:
1. 16 ft
[tex]\sf 2.\quad \dfrac{29}{99}[/tex]
Step-by-step explanation:
Question 1Formula
Area of a square = s² (where s is the side length)
Given:
Area = 256 ft²Substitute the given area into the formula and solve for s:
[tex]\sf \implies 256=s^2[/tex]
[tex]\sf \implies \sqrt{256}=\sqrt{s^2}[/tex]
[tex]\sf \implies s=\pm 16[/tex]
As distance is positive, the length of one side of Keisha's kitchen is 16 ft.
Question 2Converting a recurring decimal to a fraction
Let x equal the recurring decimal:
[tex]\implies \sf x=0.292929...[/tex]
Create another number with recurring 29s by multiplying the above by 100:
[tex]\implies \sf 100x=29.292929...[/tex]
To solve these two equations and write x as a fraction, subtract the first equation from the second to remove all the recurring digits after the decimal point:
[tex]\begin{array}{r r c l}& \sf 100x &= &\sf 29.292929...\\- & \sf x&=& \sf \phantom{..}0.292929...\\\cline{1-4} & \sf 99x&=& \sf29\\\cline{1-4}\end{array}[/tex]
Therefore:
[tex]\implies \sf 99x=29[/tex]
[tex]\implies \sf x=\dfrac{29}{99}[/tex]
Therefore:
[tex]\sf \implies 0.\overline{29}=\dfrac{29}{99}[/tex]
Learn more about converting recurring decimals to fractions here:
https://brainly.com/question/27788661
https://brainly.com/question/27643441
Math experts please provide the product in standard form thank you so much
Answer:
[tex]2x^{3} -11x^{2} +18x-9[/tex]
Step-by-step explanation:
use foil thn combine like terms
After their first two plays, a football team's position is –7 yards with respect to the original line of scrimmage. How many yards does the team need to gain on its next play to get back to the original line of scrimmage?
Answer:
I think its 17 yards if I read that correctly
Answer:
Step-by-step explanation:Its location is based on the spot where the ball is placed after the end of the most recent play and following the assessment of any penalty yards.
You have a $25 gift card for a donut shop. Each donut costs $1.25. Write an equation in
slope-intercept and standard form that gives the amount (in dollars) that remains on the card as a
function of the total numbers of donuts you have purchased so far.
The equation of the given situation is required.
Slope intercept form [tex]y=-1.25x+25[/tex]
Standard form [tex]1.25x-y=25[/tex]
The total amount of money is $25.
Cost of one donut is $1.25
Let y be the amount of money left
x be the number of donuts bought.
So, the amount of money left after buying x donuts is
[tex]y=25-1.25x\\\Rightarrow y=-1.25x+25[/tex]
The standard form is [tex]1.25x-y=25[/tex]
Learn more:
https://brainly.com/question/11824567
https://brainly.com/question/12452575
Can anyone help me with this
Answer:
the answer is option D......
convert the unit
1.5kg to g
Answer:
The answer should be 1500g I think.
Frank multiplied 7 and 528 and got the product 3,696.
Which estimate shows that his answer is reasonable?
Step-by-step explanation:
I think because the last number in 528 is 8 therefore 7×8 is 56 and the product last number is 6 there you have it
When the data points on a graph shows a steady trend and it upward direction there is what?
Answer:
An upward trend
Step-by-step explanation:
When data points on a graph show a steady upward trend, it is typically referred to as a "positive correlation" or "positive trend."
We have,
A positive correlation means that as one variable increases, the other variable tends to increase as well.
In other words, there is a positive relationship between the two variables being plotted on the graph.
Positive correlation is often represented by a line that slopes upward from left to right on a scatter plot or graph.
Thus,
When data points on a graph show a steady upward trend, it is typically referred to as a "positive correlation" or "positive trend."
Learn more about positive correlations here:
https://brainly.com/question/27886995
#SPJ3
a sewing project requires material costing $44 plus tassels. If the material and tassels are to be purchased with four $20 dollar bills, how many tassels can be purchased if they cost $2.40 each
Answer:
i think the answer is 15
Step-by-step explanation:
four $20 bills would equal $80
$80- $44 because of materials gives you $36
$36 divided by 2.50 equals 15
i hope this makes sense :)
solved for x?
ax - b = x
-
Answer:
ax - b = x
+b +b
ax/a = c/a
d=x
Step-by-step explanation:
There are no numbers so I can't give a specific answer so I substituted numbers with letters :)
The length and width of a rectangle are two consecutive integers. The perimeter of the rectangle is 26. what is the length and the width? :)
Answer:
Width = 6
Length = 7
Step-by-step explanation:
Consecutive integers: x and x+1
2x + 2(x+1) = 26
2x +2x + 2 = 26
4x = 26 - 2
x = 24/4
x = 6
Can anyone help me with this question please ?
Answer:
-0.20412414523 there you go
HELP
15.4 = -2.1 + a/0.2
Answer:
a = 3.5
Step-by-step explanation:
15.4 = -2.1 + a/0.2
Combine like terms:
15.4 = 2.1 + 5a
Swap sides:
-2.1 + 5a = 15.4
what does it mean is x=5 a solution?
Answer:
it can mean that on a graph where y=0 and x=5 that the line goes through that point or I can just mean in an equation that if y is 0, then x is 5
So, I have a math problem, the problem is,16x^0+2x^2*y^-1,How do I solve if x = 2 and y = 4?
Answer:
Given x = 2 and y =4
so 16[tex]x^{0}[/tex]+2[tex]x^{2}[/tex][tex]y^{-1}[/tex]
= 16*[tex]2^{0}[/tex] + 2*[tex]2^{2}[/tex]*[tex]4^{-1}[/tex]
= 16 + (2*4)/4
=16 + 8/2
16 + 2
=18
Step-by-step explanation:
Determine the product of the binomial -5x-7 and the trinomial
3x2-4x-5. To earn full credit, show your work using a method explained in
the Orientation
Answer:
[tex]( - 5x - 7)(3 {x}^{2} - 4x - 5) \\ \\ - 15 {x}^{3} + 20 {x}^{2} + 25x - 21 {x}^{2} + 28x + 35 \\ \\ - 15 {x}^{3} + 20 {x}^{2} - 21 {x}^{2} + 25x + 28x + 35 \\ \\ = - 15 {x}^{3} - {x}^{2} + 53x + 35[/tex]
I hope I helped you^_^
I've been stuck on this for so long
y = 6/5x - 1
hope this helps :) !!
Answer:
[tex]y = \frac{6}{5}x - 1[/tex]
Step-by-step explanation:
use the formula
[tex]y = mx + b[/tex]
m is the slope and b is the y-intercept. Begin with b, where the line crosses the y-axis (vertical axis). It crosses at -1, so this is b.
Next move with m. Do rise/run. Start at the y-intercept and you are going to rise 6 and run 5 to the next point. So the slope is 6/5. Leave as an improper fraction. Plug-in for m. Since the line goes uphill from left to right it has a positive slope.
what is 4000ml to dm
Answer:
4
Step-by-step explanation:
Answer:
4 cubic decimeters.
....
suppose another line for a chair lift is placed at a constant distance c below the gondola line. what is the equation of the new line? is the new line also parallel to the hill? explain.
Answer:
Yes They are Parallel.
Step-by-step explanation:
The required equation of the line y = ax + c as of the old line and also the line is parallel to the hill.
Given that,
Suppose another line for a chair lift is placed at a constant distance c below the gondola line. the equation of the new line and is the line parallel to the hill is to be discussed.
A line is a straight curve connecting two points or more showing the shortest distance between the initial and final points.
Here,
The required new line is placed at a constant distance c below the gondola line,
If the line has a constant distance from the other line that implies that the line is parallel, and the equation of the line is given as,
y = ax + c
Thus, the required equation of the line y = ax + c as of the old line and also the line is parallel to the hill.
learn more about lines here:
brainly.com/question/2696693
#SPJ5