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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.

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3x° + 36° = 156°        (since alternate interior angles are equal)

        3x°  = 120 °

           x  = 40

Answer:

we gotta find compound amount here..

CA=compound amount

P=principal

R=rate of interest

T=time

Answer:

R=30 degrees Lm=6(square root of 3)

Step-by-step explanation:

R=L

LM=SR

Answer:

250 people

Step-by-step explanation:

let's first look for the missing 20%,

one way you can solve this is by cross multiplication:

since 80% is 200 then 80% = 200

and we know 20% is x then 20% = x (we use x because we don't know the amount of people)

so then we set it up:

[tex]\frac{x}{20}[/tex] × [tex]\frac{200}{80}[/tex]

now we cross multiply:

80x = 4000

= x = 50

now we need to find how many people were surveyed so we do:

200 + 50 = 250

250 people were surveyed

Answer:

They are difficult to diagnose through route medical tests. A careful analysis of signs and symptoms is far more productive in eliciting the diagnoses verses blood tests. At least through suck signs and symptoms the presumptive diagnosis of parasitic infestations can be made. It all just depends though.

Pls mark brainliest I would really appreciate it

Answer: They are difficult to diagnose through route medical tests. A careful analysis of signs and symptoms is far more productive in eliciting the diagnoses verses blood tests

3

[tex] \sf \sqrt{x + 3 = 12} [/tex]

[tex] \sf = \sqrt{x = 12 - 3} [/tex]

[tex] \sf = \sqrt{x = 9} [/tex]

[tex] \sf = \sqrt{9} [/tex]

[tex] \sf = \sqrt{3 \times 3} [/tex]

= 3

The solution of the linear equation [tex]\sqrt{x+3} = 12[/tex]  for the variable, x is 141.

Two algebraic expressions separated by an equal symbol in between them and with the same value of the expression are called equations.

Example = 2x +4 = 12

here, 4 and 12 are constants and x is variable

The solution of the equation can be calculated as:

[tex]\sqrt{x+3} = 12[/tex]

Squaring both side,

[tex]x+3 = (12)^2[/tex]

x+3 = 144

Subtract 3 from both the sides,

x = 141

The solution of the linear equation for the variable x is 141.

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Answer:

24

Step-by-step explanation:

12 per half hour means 24 per hour

Answer:

3x = 5

Step-by-step explanation:

9x = 4x + 5

-4x -4x

3x = 5

Answer:

h(x) = 4x + 5       h(x) = 9

9 = 4x + 5        9 - 5 = 4  and 5 - 5 = 0

4 = 4x          4 divided by 4 equals 1

Answer is x = 1.

--------------------------------------------------------

Check your answer:

9 = 4x + 5

Input the 1 into the variable x's place in the equation.

9 = 4 X 1 + 5

And now solve.

4 X 1 + 5 = 9

So, now we know that our answer is fully correct.

Step-by-step explanation:

Hope this helps. If there are any questions please ask them below in the comments. If there are no questions please have a great rest of your day/night!

Answer:

-3 < x < -1/2

Step-by-step explanation:

4<-2x+3<9

1<-2x<6

-1/2 > x > -3

so

-3 < x < -1/2

Step-by-step explanation:

2x + y = 5 (times 3)

6x + 3y = 25

↓↓↓↓↓↓↓↓↓↓↓↓

6x + 3y = 15

6x + 3y = 25

→ No solution ←

2x+y=5

6x+3y=25

As slopes are equal lines are parallel

So no solutions

Option D

Answer:

Hey, so it's actually pretty simple I'll try my best to explain it properly!

Step-by-step explanation:

So for the first blue circle the line that goes to the middle that's the radius. And to solve the area you need to know the radius. The formula to solve the area is A = [tex]\pi[/tex] [tex]r^{2}[/tex] so what we would do its 3.14 times 6 times 6 or 3.14 times 36 which would give us the area! Now for circumference, the equation for that is C = 2[tex]\pi r^{2}[/tex] which would look like 2 times 3.14 times 6 times 6 or 2 times 3.14 times 36 and that would give you the circumference.

Answer:

55

Step-by-step explanation:

15+10d

15+10(4)

15+40

55 minutes

It will take 55 minutes for Mark to bake 48 cookies.

15+10d

15+10(4)

15+40

55 minutes

Simply put, you can expect to bake cookies at 350 degrees Fahrenheit for 8-12 minutes. However, there are some things to consider when baking biscuits. The type of biscuit, the size of the biscuit, and the content of the fabric.

Preheat the oven to 350 ° F (or 325 ° F for a non-stick baking sheet). Place the cookie dough base about 2 inches apart on a non-oiled sheet pan. BRAKE for 10-14 minutes or until light brown. Cool 2 minutes; Remove from the top plate.

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Answer:

9 • sqrt(15)

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Answer: B) 19

Step-by-step explanation:

To solve this problem, simply plug in -4 for x:

[tex]f(x)=x^{2} +3\\f(x)=(-4)^{2} +3\\f(x)=16+3\\f(x)=19[/tex]

Hope it helps :) and let me know if you want me to elaborate/explain further

Answer:

D. -13

Step-by-step explanation:

If you substitute -4 in for x you get -4^2+3, so when you simplify you get -16+3 which equals -13.

f(x)=x^2+3

f(-4)= -4^2+3

f(-4)= -16+3

f(-4)= -13

Answer:

20 hours

Step-by-step explanation:

hope this helps

Answer:

[tex]170 \div 8.50 = 20[/tex]

She has worked 20 hours at that restaurant

Answer:

38

Step-by-step explanation:

-(5×-7-3)

-(-35-3)

-(-38)

38

(1st picture): y=2x+3 and y=x+5

(2nd picture): y=4x+2 and y =3x+2

(3rd picture): y=2x+1 and y =x+2

(4th picture): 3x and x+3

The solutions to the system of equations are (5,2), no solutions, (7,3), (2,7), no solutions and (3,5) respectively.

In mathematics, a set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.

(1) Systems of equations

2x + y = 12

x = 9 − 2y

See the graph given below the solution is the point (5,2).

(2) Systems of equations

x + 2y = 9

2x + 4y = 20

See the graph given below the solution is the point has no solution the two lines are parallel.

(3) Systems of equations

x + 3y = 16

2x − y = 11

See the graph given below the solution is the point (7,3).

(4) Systems of equations

y = 11 − 2x

4x − 3y = -13

See the graph given below the solution is the point (2,7).

(5) Systems of equations

y = 10 + x

-3x + 3y = 30

See the graph given below the system has no solutions.

(6) systems of equations

2x + y = 11

x − 2y = -7

See the graph given below the solution is the point (3,5).

Therefore, the solutions to the system of equations are given below in the figure.

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What did you partner think? i will answer in comments

Answer:

QS = 30

Step-by-step explanation:

Since R is the mid point QR = RS

Given QR = 6x – 51 and RS = 2x – 7 then

6x – 51 =  2x – 7, isolate like terms

  6x -2x = 51 -7 , combine like terms

        4x = 44, divide both sides by 4

         x = 11

QS = QR + RS

QS = 6x -51 +2x -7 , combine like terms

QS = 8x - 58, substitute x= 11 in the equation

QS = 8*11 -58, multiply 8 and 11

QS = 88 -58

QS = 30

Answer:

Harriet's Hair Styles

Step-by-step explanation:

Frank's Furters $6.24 /hr

Harriet's Hair Styles $80 for 12 hours weekly

$80 / 12 hr = $6.66/hr

Babysitting $250 a month for 10 hours after school a week. (Assume 4 weeks is a month.)

$250 / (4 wk * 10 hr/wk) = $250/ 40 hr = $6.25/hr

Answer: Harriet's Hair Styles

Harriet's Hair Styles has the highest hourly pay at $6.67 per hour.

To determine which job has the highest hourly pay, we need to calculate the hourly wage for each job based on the information provided.

Frank's Furters: $6.24 per hour.

Harriet's Hair Styles: $80 for 12 hours weekly.

Babysitting: $250 a month for 10 hours after school a week.

Let's calculate the hourly wage for each job:

Frank's Furters: $6.24 per hour.

Harriet's Hair Styles: $80 for 12 hours weekly

= $80 / 12 hours

= $6.67 per hour.

Babysitting: $250 a month for 10 hours after school a week

= $250 / (4 weeks x 10 hours)

= $6.25 per hour.

Hence, Harriet's Hair Styles has the highest hourly pay at $6.67 per hour.

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If M is the midpoint of PQ. MQ = 5x + 8 and PQ = 6x + 56, then PM = 58

Since M is the midpoint of PQ

PM  +   MQ   =   PQ................(*)

Given:

PQ  =  6x + 56

MQ  = 5x + 8

Substitute PQ and MQ into equation (*)

PM   +  (5x + 8)  =  6x  +  56

Collect like terms

PM   =  6x  +  56  -   (5x  +  8)

Expand the equation using the distributive rule

PM  =  6x  +  56  -  5x  -  8

PM  =  6x  -  5x  +  56  -  8

PM  =  x  +  48.........(**)

Equate MQ and PM

MQ   =   PM

5x  +  8    =   x  +  48

Collect like terms

5x  -  x  =  48  -  8

4x   =   40

Divide both sides by 4

4x / 4   =  40/4

x   =   10

Substitute x = 10 into equation (**)

PM  =  x  +  48

PM  =  10  +  48

PM   =  58

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Answer:

Maddie got 810 votes

Step-by-step explanation:

We'll call Maddie's votes x, and her opponent's votes y.

x + y = 1485

x = y + 0.20y (because she got the same number of votes as her opponent, PLUS another 20% of that number. Divide 20% by 100 to get the decimal equivalent) This can also be written as x = 1.2y

So our system is

x + y = 1485   and

x = 1.2y

Substitute the second equation's value for x into the first equation:

1.2y + y = 1485 then solve for y

2.2y = 1485

divide both sides by 2.2

y = 675

substitute that in and solve for x

x + y =1485

x + 675 = 1485

subtract 675 from both sides

x = 810

Please let me know if you have questions on this answer. Hope it helps.

Answer:

a=19

Step-by-step explanation:

8=1/3(a+5)            by dividing both sides by 1/3

24 = a+5              get 5 to other side with oposite sign

24-5 = a

a = 19

Answer:

a = 19

Step-by-step explanation:

8 = [tex]\frac{1}{3}[/tex] ( a + 5) ← multiply both sides by 3 to clear the fraction

24 = a + 5 ( subtract 5 from both sides )

19 = a

2.4 9 x10^7

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