Let u=(-1,3), v= (2,4) , and w = (2,-5) . Find the component forms of the following vectors. -3 v

Answers

Answer 1

Given u = (-1, 3), v = ( 2, 4) , and w = (2, -5), by applying scalar multiplication of vectors, -3v = -3.( 2, 4) = (-6, -12)

In the two-dimensional coordinate system, vectors can be split into x-component and y-component.

We can write, for example, a vector s = (4,–2), which means:

x-component = 4

y-component = –2

Some vector operations:

Addition / subtraction of vectors: Just add or subtract the corresponding components.
For example: q= (1,6) and s = (5,-3)
Then,
q + s = (1,6) +  (5,-3) = (1+5, 6-3) = (6, 3)Scalar multiplication: Multiply each component by the given scalar.
For example: t = (2,–1)
Then,
5t = 5. (2,–1) = (5 . 2, 5 . (–1)) = (10,–5)

In the given problem:

u = (-1, 3), v = ( 2, 4) , and w = (2, -5)

Then,

-3 v = -3 . (2, 4)

      = ( -3 . 2, -3 . 4)

      = (-6, -12)

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Related Questions

Six friends each use a $2-off coupons to buy themselves a movie tickets. They spend a total of $42. What is the price of one movie ticket without the coupon?

Answers

The price of one movie ticket without the coupon is  $9.

arithmetic operations

Arithmetic operators are used to perform mathematical operations like addition, subtraction, multiplication and division.

...

There are 7 arithmetic operators in Python :

Addition.

Subtraction.

Multiplication.

Division.

Modulus.

Exponentiation.

Floor division.

since they spend a total of  $42.

so the price of one movie ticket without the coupon is

⇒ (42+12)/6

⇒54/6

⇒ 9

so the price of one movie ticket will be  $9.

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On Earth with a gravitational acceleration \text{g} , the potential energy stored in an object varies directly with its mass m and its vertical height h .

a. What is an equation that models the potential energy of a 2 -kg skateboard that is sliding down a ramp?

Answers

Equation that models the potential energy of a 2 kg skateboard that is sliding down a ramp is :

U = 2gh

What is Gravitational acceleration ?

Gravitational acceleration can be defined as the acceleration of any object when the object is in free fall. or we can say that the gravitational acceleration is the quantity which describes the acceleration of free falling object within vacuum. It is denoted by g .

What is Potential Energy ?

Potential energy is the stored energy of the object which is generally based on the relative position of the various parts of the object. It is also known as gravitational energy.

Formula of potential energy :

U = mgh

where, U = gravitational energy

            m = mass of object

            g = gravitational acceleration

            h = vertical height  of object

In the question given,

mass = 2kg

as, U = mgh

therefore, U = 2gh

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The complete question is :

On Earth with a gravitational acceleration g , the potential energy stored in an object varies directly with its mass m and its vertical height h .

a. What is an equation that models the potential energy of a 2 -kg skateboard that is sliding down a ramp?

b. The acceleration due to gravity is g=-9.8m/s² . What is the height of the ramp if the skateboard has a potential energy of -39.2 kg m² /s² ?

Gil traveled 4. 5 miles and continues at a speed of 62. 5 miles per hour. Andy has traveled 29. 5 miles per hour and continues at a speed of 50 miles per hour. If the cars continue at the same speed, how many hours will it take for andy and gill to travel the same number of miles

Answers

If Gil traveled 4. 5 miles and continues at a speed of 62.5 miles per hour and Andy has traveled 29.5 miles and continues at a speed of 50 miles per hour, then the number of hours it will take for Andy and Gill to travel the same number of miles is equal to 2.

The number of hours it will take for Andy and Gill to travel the same number of miles can be determined by using an algebraic expression.

An algebraic expression to find the number of hours can be given as,

4.5 + 62.5(x) = 29.5 + 50(x)

Here, x is equal to the number of hours.

Solving to find the value of x,

62.5x - 50x = 29.5 - 4.5

12.5x = 25

x = 25 ÷ 12.5

x = 2

Hence, the number of hours it will take for Andy and Gill to travel the same number of miles is calculated to be 2.

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Which of the following is a rational number?


A. [tex]\sqrt{10}[/tex]

B.[tex]\sqrt{100}[/tex]

C.[tex]\sqrt{1000}[/tex]

D.[tex]\sqrt{100000}[/tex]

Can you please explain your answer I want to understand it

Answers

The rational numbers are √10, √1000 and √100000 . Options A, C and D

What is a rational number?

A rational number can be defined as a  number that can be expressed as a fraction.

It also has the numerator and denominators as integers and expressed in decimal forms.

Given the values;

√10√100√1000√100000

√10 = 3. 162

√100 = 10

√1000 = 31. 6

√100000 = 316. 22

Thus, the rational numbers are √10, √1000 and √100000 . Options A, C and D

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Which function family does the graphed function belong to? !!!!!70 POINTS!!!!!!

Answers

Answer:

Y=x³ is the parent graph I don't know if that helps.

Answer:

Cubic

Step-by-step explanation:

If AABC = ADEF, AB = 8, BC = 19, AC=14, EF = 4x-1, and DE=y-6, find the values of
x and y.

Answers

When given triangles are given then the value of x and y is 5 and 14 respectively.

When BC is similar to EF.

19= 4x-1

19+1=4x

20=4x

x=5

When DE is similar to AB

y-6 =8

y=8+6

y=14

Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent.

A pair of triangles are said to be similar if two pairs of corresponding angles in those triangles are congruent. We can conclude that the third pair must also be equal if the first two angle pairs are. When all three pairs of angles are equal, the sides of the three triangles must also be proportionate.

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11. Harry ordered 9.0 pizzas. Each pizza costs $13.95. How much does he need to pay?

Answers

Question:

11. Harry ordered 9.0 pizzas. Each pizza costs $13.95. How much does he need to pay?

Answer:

This is pretty simple, just multiply 9.0 by $13.95, which will give you the answer of $125.55.

* I am not responsible if you get this question wrong, for you are the one who asked the question. *

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If this helped, your welcome! Please know that I might be wrong, and if I am, I am truly sorry for that. But If you would, please make me brainliest.

I hope you have a great rest of your day! If there is an issue with this question, be happy to comment. <3

-niaxfandoms

Harry needs to pay $ 125.55 in total for the 9.0 pizzas he ordered at $ 13.95 each.

To calculate how much Harry needs to pay, multiply the number of pizzas (9.0) by the cost of each pizza ($ 13.95).

Total cost = Number of pizzas × Cost per pizza

Total cost = 9.0 × $ 13.95

To find the product, we can treat 9.0 as a whole number and then multiply:

Total cost = 9 × $ 13.95

Now, calculate the product:

Total cost = $ 125.55

Harry needs to pay $ 125.55 in total for the 9.0 pizzas he ordered at $ 13.95 each.

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Find the indicated number of geometrical mens
[tex]-32 and i[/tex]

Answers

The geometric mean between -32 and i is given by:

[tex]\sqrt{-32i}[/tex]

What is the geometric mean?

The geometric mean between n values is given by the nth root of the multiplication of these values.

For this problem, we have that:

There are 2 values, -32 and i.The multiplication is -32i.

Due to the two values, we take the square root, hence, the geometric mean between -32 and i is given by:

[tex]\sqrt{-32i}[/tex]

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A certain missing number will result in the expression 20x +24 when using the distributive property. what number must be multiplied by (5x +6) to result in the expression 20x+24

Answers

If a certain missing number will result in the expression 20x +24 when using the distributive property, then the number that must be multiplied by (5x + 6 ) to result in the expression 20x + 24  is 4.

The distributive property is a property of multiplication, according to which if two or more values that are added together are multiplied by a number, then the result will be the same if each of these values is multiplied separately with that number and then the products are added together.

Considering y to be the number that must be multiplied by (5x + 6),

y (5x + 6) = y(5x) + y(6)

As the expression is,

20x + 24

y(5x) = 20x and y(6) = 24

6y = 24

y = 24 ÷ 6

y = 4

This can be confirmed as follows,

y(5x) = 20x

Putting y = 4 in this equation,

4(5x) = 20x

Hence the number that must be multiplied by (5x + 6) to result in the expression 20x + 24 is calculated to be 4.

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Mariana and her children went into a movie theater and she bought $51.25 worth of candies and pretzels. Each candy costs $4.75 and each pretzel costs $3.25. She bought a total of 13 candies and pretzels altogether. Write a system of equations that could be used to determine the number of candies and the number of pretzels that Mariana bought. Define the variables that you use to write the system.

Answers

Answer:

Step-by-step explanation:

you could use multiplication or addition,

Answer:

Step-by-step explanation:

can someone help me with this

Answers

Answer:

this is a little much if you broke it down into single questions I would be happy to help

Step-by-step explanation:

Answer:

The answer is below!!

Step-by-step explanation:

I. Fill in each step of the problem-solving process to solve this problem.

Cadence went to the amusement park and paid $14.25 for a souvenir refill cup. Refills cost $1.25 each. If Cadence spent a total of $23, how many refills did she get? ~

Step 1: What is the unknown?

The number of refills is the unknown.

Step 2: What is the key information that can be used to solve the problem?

Let x be the number of refills.

Step 3: What is a strategy (equation) that can be used to solve the problem?

Equation: 14.25 + 1.25x = 23

Step 4: What is the solution to the problem?

          ↓

[tex]\sf 14.25+1.25x=23[/tex]

[tex]\sf 14.25\cdot \:100+1.25x\cdot \:100=23\cdot \:100[/tex]

[tex]\sf 1425+125x=2300[/tex]

[tex]\sf 1425+125x-1425=2300-1425[/tex]

[tex]\sf 125x=875[/tex]

[tex]\sf \cfrac{125x}{125}=\cfrac{875}{125}[/tex]

[tex]\boxed{\sf x=7}[/tex]

Step 5: Check your answer.

To check your answer, plug x = 7 in the given term

[tex]\sf 14.25+1.25(7)=23[/tex]

[tex]\sf 14.25+8.75=23[/tex]

[tex]\sf 23=23[/tex]

→ → → →

II. Solve each problem. Show your work.

Jordan’s bill for car repairs was $500. The cost for parts was $240 and the mechanic charged $65 per hour. How many hours did it take the mechanic to repair Jordan’s car?

Let the number of hours = x

[tex]\sf 65x+240=500[/tex]

[tex]\sf 65x=260[/tex]

[tex]\sf x=4[/tex]

Therefore, it took the mechanic 4 hours to repair Jordan’s car!

→ → → →

2. Marcus made 6 baskets in his first basketball game. In each of the next 4 games, he made the same number of baskets. If he made a total of 34 baskets , how many baskets did he make in each of the 4 games?

Let x = baskets Marcus made in each of the 4 games

[tex]\sf 4x+6=34[/tex]

[tex]\sf 4x=34-6[/tex]

[tex]\sf \cfrac{4x}{4}=\cfrac{28}{4}[/tex]

[tex]\sf x=7[/tex]

Therefore, Marcus made 7 baskets in each of the 4 games!

And we're done!

________________________

Hope this helps!

Have a great day!

R is between P and T. PR = 3x, RT = 2x + 24 and
PT = 54. Find RT.
P
R
O is the midpoint of EH. Find EH.
Line segments

Answers

Based on the information given, the value of line RT is 36

What is a line segment?  

A line segment can be defined as the part of a straight line bounded by two distinct end point

It also contains every point on the line between its endpoints.

From the information given, we have line PT is a line with segments PR and RT and R is the point between P and T

This can be represented as;

PR + RT = PT

Where;

PR = 3xRT = 2x + 24 PT = 54

Substitute into the equation;

3x + 2x + 24 = 54

collect like terms

5x = 54 - 24

5x = 30

Make 'x' the subject of formula

x = 30/ 5

x = 6

But;

RT = 2x + 24

RT = 2(6) + 24

RT = 36

Thus, the value of line RT is 36

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E and f are supplementary. If m e = (9x-38) and m f = (2x+42) find m f

Answers

Given that angle E and angle F are supplementary, the numerical measure of angle F is 74°.

What is the numerical measure of angle F?

Supplementary angles are angles that sum up to 180 degrees.

Given the data in the question;

E and f are supplementaryMeasure of angle E = ( 9x - 38 )°Measure of angle F = ( 2x + 42 )°Numerical measure of angle F = ?

Since E and F are supplementary, it means they sum up to 180 degrees.

Measure of angle E + Measure of angle F = 180°

Plug in the given values and solve for x

( 9x - 38 ) + ( 2x + 42 ) = 180

9x + 2x - 38 + 42 = 180

11x + 4 = 180

11x = 180 - 4

11x = 176

Divide both sides by 11

11x = 176

11x/11 = 176/11

x = 16

Now, the numerical measure of angle F will be;

Measure of angle F = ( 2x + 42 )

Measure of angle F = 2( 16 ) + 42

Measure of angle F = 32 + 42

Measure of angle F = 74°

Given that angle E and angle F are supplementary, the numerical measure of angle F is 74°.

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A=7x
2
−3x+10
B=−4x
2
+6x−4


A-B=A−B=

Answers

Answer:

3/4

Step-by-step explanation:

7x +4x = - 3x+10+6x-4

11x=-3x+6x+10-4

11x=3x+6

11x-3x=6

8x=6

X=3/4


Describe and correct the error made in solving the equation.

Answers

The error is due to different bases of logarithmic value on both sides.

What is logarithmic equation ?

In, mathematics a logarithmic equation is inverse of exponential equation. That means, we can easily convert the logarithmic equation into exponential equation and vice versa. The basic form of the logarithm function can be written as [tex]log_{a}x[/tex] .

where, a is the base of function or equation

           x = expression

Mathematically, if [tex]a^x = N[/tex] is an exponential function then, this can be converted to logarithmic function as  [tex]log_aN = x[/tex].

There are many formulas that are given to us for solving several simple and complex problems based on logarithmic functions and logarithmic equations.

Some important formulas of logarithms :

[tex]log a + log b = log a.b[/tex][tex]log a - log b = log \frac{a}{b}[/tex][tex]log a^x = x loga[/tex][tex]log_aa=1[/tex][tex]log_a1=0[/tex]

In the question,

the error is due to different bases on both the sides.

correct solution is:

[tex]log_2x = 2log_39\\log _2x=log_39^ 2\\log_2x=log_33^4\\log_2x=4log_33\\log_2x=4\\x=16[/tex]

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The complete question is :

Describe and correct the error made in solving the equation.

[tex]log_2x = 2log_39\\log _2x=log_39^ 2\\x=9^2\\x=81[/tex]

please help please im giving so much

Answers

Answer:

D

Step-by-step explanation:

The highest number that divides exactly into two or more numbers. 3 and 9 cannot be divided by anything greater than 3.

Answer: i think its D.

Step-by-step explanation:

What are the coordinates of the point P that lies along the directed
segment from L(-6, 5) to M (4, -6) and partitions the segment in
the ratio of 1 to 3?

Answers

The coordinates of point P are ( -3.5, 2.25).

Given points L( -6, 5) and M( 4, - 6). We are to determine the coordinate of point P that lies along the directed line segment which partitions the segment in the ratio of 1 to 3.

The coordinates of the point that divides a line segment internally in the ratio m:n are given as follows:

[ (mx₂ + nx₁ ) / (m + n) , (my₂ + ny₁ ) / (m + n) ]

Now, m : n = 1 : 3

( x₁, y₁ ) = L( - 6 , 5 )

( x₂, y₂ ) = M( 4, - 6 )

Therefore,

P( x, y) =  [ ( 1 × 4 + 3 × -6 ) / 4 , ( 1 × - 6 + 3 × 5) / 4 ]

P( x, y) = [ ( 4 - 18 ) / 4 , ( - 6 + 15) / 4 ]

P( x, y ) = [ -14/4 , 9/4 ]

P( x, y) = ( - 7/2 , 9/4 )

P( x, y) = ( - 3.5, 2.25 )

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Determine the slope. (0, -6) & (-2, 8) Responses

Answers

The slope would be -7.

We are given the two points (0,-6) and (-2,8). We can use the formula of y-y/x-x to find the slope.

Our two y-values are -6 and 8. We can subtract those in the order of right to left:

8 - (-6) = 14

We can do the same for our x-values, -2 and 0:

-2 - 0 = -2

Our new fraction would be 14/-2. This is not arranged properly, and it can be divided. 14 / (-2) = -7. Therefore, our slope is -7.

angle a and angle B are supplementary angles. if M angle a equals 2X +27 and M angle B equals 5X -1 then find the measure of angle a 

Answers

The value of the angle A is; ∠A = 74°.

What is meant by the supplementary angles?The term "supplementary angles" refers to a pair of angles which always add up to 180°. These two angles are termed supplements of one another. In other words, because unless Angle 1 + Angle 2 = 180°, angles 1 and 2 are supplementary. Angles 1 and 2 are referred to as "supplements" in this case.Supplementary angles are classified into two types.supplementary angles adjacentNon-adjacent supplementary angles

From the stated question;

∠A =  2X +27 and ∠B = 5X -1.

From the property of supplementary angles;

∠A + ∠B = 180

Put the values;

2X +27 + 5X -1 = 180

On simplification;

7X = 154

X = 22

Put the value of X in ∠A =  2X +27.

∠A =  2 x 22 + 27

∠A = 74°.

Therefore, the measure of the angle A is ∠A = 74°.

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Hello , this is a question on Geometry and I don’t understand how to do this can someone pls help me ?.

Answers

Answer:

m∠COD = 83°(I assumed it was somewhere right in-between 80-89 degrees, so I picked 83 as the most logical in between those integers.)

∠COD is an acute angle since it's less than 90°.

I hope this helps you, let me know if you have concerns related to this question and I will help with that.

Evaluate: 50% of 3,000= ?

Answers

Answer:

1500

Step-by-step explanation:

imagine 30 / 5 = 15 then add the two zero's after  

Answer:

50% of 3,000 is 1500

Step-by-step explanation:

hope this helps!

What value of x makes this equation true?
x -3 = x +3
3 9

Answers

The value of x from the given linear equation x/3-3=x/9+3 is 27.

What is linear equation?

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included.

Given equation

x/3-3=x/9+3

=> x/3-x/9=3+3

=>(3x-x)/9=6

=>2x/9=6

=> x=9*6/2

x=27.

Therefore, the value of x from the given linear equation is 27.

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James has 23 cans, but the people gets 15 cans, What cans left?
A 13
B 8
C 10
D 7

Answers

Answer:

B

Step-by-step explanation:

23-15=8

Answer B
Because I just subtracted makes the most sense


Tanya bought 8.05 yards of fleece fabric to make costumes for a school play. She needs 1.25 yards of
fabric for each costume. How many costumes can Tanya make with the fabric she bought ( long division )

Answers

Answer: 6 costumes

Step-by-step explanation: 8.05 divided by 1.25 would be 6.44, but how can you make 6.44 costumes? The most costumes Tanya can make are 6 costumes for the school play.

a diver starts at 5 m and changes -16 m?

Answers

The depth that the driver is will be -11 meters

How to illustrate the information?

From the information, it was stated that diver starts at 5 m and changes -16 m.

Therefore, it should be noted that the depth that he is will be:

= Starting position + Change

= 5 + -16

= -11

Therefore. the depth that he is will be -11 meters.

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A diver starts at 5 m and changes -16 m. What depth is he now?

What is the least common denominator of 3/4 3/8 and 1/4

Answers

The least common denominator is 24!!!!!!!!!!!!

g = x - c solve for x

Answers

X=g+c
Is the correct answer

ABCD is a rectangle that represents a park
The lines show all the paths in the park
The circular path is in the center of the rectangle and has a diameter of 15m
calculate the shortest distance from A to C across the park using only the lines shown
image is attached below

Answers

Answer:

Hence,required shortest distance =102.89m

The shortest distance from A to C is 102.89 m.

What is Perimeter?

Perimeter refers to the total distance around the boundary of a two-dimensional shape. It is the sum of the lengths of all the sides of the shape.

Using Pythagoras theorem

AC² = 50²+80²

AC² =8900

AC =√8900

AC = 94.33

So, the distance removing the diameter

= 94.33-15

= 79.33

Now, Circumference of semicircle = πr

= 23.56 m

So, the possible distances

A - B - C = 50 +80= 130

A-C = 23.56 + 79.33= 102.89

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MN¯has an endpoint at M(–2, –2) and an endpoint at N(7, –5).

What is the length of MN to the nearest tenth?

Answers

The length of the segment MN is 9.5 units

How to determine the length of the segment MN?

The endpoints of the line segment MN are given as

M = (-2, -2)

N = (7, -5)

The length of the segment MN is calculated as:

MN = √(x2 - x1)^2 + (y2 - y1)^2

Substitute the known values in the above equation

So, we have

MN = √(-2 - 7)^2 + (-2 + 5)^2

Evaluate the sum and the difference

So, we have

MN = √-9^2 + 3^2

Evaluate the exponents

So, we have

MN = √81 + 9

Evaluate the sum

So, we have

MN = √90

Evaluate the exponents

So, we have

MN = 9.5

Hence, the length of the segment MN is 9.5 units

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what is the common denominator of 3/20 and 9/40 ?

Answers

Answer:

The answer is 40.

Step-by-step explanation:


Find the least common multiple (LCM) of the denominators in order to find the least common denominator (LCD).

Other Questions
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