Vector u has its initial point at (-7, 2) and its terminal point at (11, -5). Vector v has a direction opposite that of vector u, and its magnitude is three times the magnitude of u. What is the component form of vector v?

A. v = <-54, 63>
B. v = <-162, -63>
C. v = <-54, 21>
D. v = <-162, 21>

Answer:

y = 4/3x+2/3

Step-by-step explanation:

the 2 coordinates provided are: (4,6) and (-5,-6)

y=mx+c

m= (y1-y2)/(x1-x2) = (-6-6)/(-5-4) = 4/3

sub x = 4, y = 6

6 = 4/3 * 4 + c

c = 2/3

Answer:

y = 4/3x+2/3

Step-by-step explanation:

Pick two points on the line to find the slope

(-5,-6) and (4,6)

m = (y2-y1)/(x2-x1)

m = ( 6 - -6)/( 4 - -5)

   = ( 6+6)/(4+5)

   = 12/9

  = 4/3

The slope intercept form of a line is y =mx+b where m is the slope and b is the y intercept

y = 4/3x+b

Substitute a point into the equation

6 = 4/3(4)+b

6 = 16/3+b

Subtract 16/3 from each side

18/3 - 16/3 =b

2/3 = b

y = 4/3x+2/3  

Answer:

the decimal number 6.45 written in scientific notation is 6.45 × 100 and it has 3 significant figures.

Step-by-step explanation:

Answer:

30.7

Step-by-step explanation:

Recall: SOH CAH TOA

We are to solve for the missing side

First, label the sides:

Reference angle (θ) = 61°

x = Opposite (this is opposite to the reference angle)

17 = Adjacent

Hypotenuse = side opposite to right angle

Apply TOA, which is:

Tan θ = Opp/Adj

Plug in the values

Tan 61° = x/17

17*Tan 61° = x

30.6688118 = x

x ≈ 30.7 (approximated to nearest tenth)

Answer:

(3x + 1)(x + 6)

3x^2 + 19x + 6

3x^2 + 18x + x + 6

3x^2 + 18x + x + 6

3x(x + 6) + x + 6

3x(x + 6) + x + 6

(3x + 1)(x + 6)

Haven't done this in a pretty long time so I might be wrong

Answer: A. The number 23 is prime, but 36 is composite.

=====================================================

Explanation:

Let's go through the possible answer choices

23 is indeed prime, and 36 is indeed composite.

33 is composite, and 42 is indeed composite.

21 is composite, and 25 is composite as well

27 is not prime, and 39 is composite.

Primes have only 2 factors: 1 and themselves.

And 33, 21 and 27 definitely have more than 2 factors. Hope this helps!

~Just a joyful teen

[tex]GraceRosalia[/tex]

Step-by-step explanation:

first blank: 0 seconds

second blank: 9.8 seconds

third blank: 5 seconds

fourth blank: 120 meters

Answer:

24 people

Step-by-step explanation:

((The numbers are up there, so I am not going to define each variable.))

For starters, there is no overlap between the double facilities groups, except the triple facility users, so:

19 + 9 + 16 - 4 = 40 people

Since there is overlap between single and double groups, you will need to subtract, so:

Gym: 73 - 19 - 16 = 38

Pool: 59 - 19 - 9 = 31

Track: 31 - 9 - 16 = 6

Total for 1 facility: 38 + 31 + 6 - 4 = 71 people

((Minus 4 because the 4 triple facility users overlap the double facility users (problem is in layers: layer 1 minus layer 2, then minus layer 3).))

Next, add the totals:

71 + 40 = 111 people (using facilities)

135 - 111 = 24 people (who didn't use any)

(((I'm not 100% sure on this answer, so if someone could check my work, that would be much appreciated.)))

A square pyramid has 4 triangles and the square base.

Calculate the area of one triangle, multiply that by 4 then add the area of the base.

Area of triangle = 1/2 x base x height = 1/2 x 5 x 12 = 30 square yards.

30 x 4 = 120 square yards

Area of base = 5 x 5 = 25 square yards

Total = 120 + 25 = 145 square yards.

The unknown sides are 60.81cm and 51.57cm while the unknown angle is 58degrees

4a) Given the following

Opposite side = 38cm (side facing the given angle)

Required

Adjacent and hypotenuse side

According to SOH CAH TOA

[tex]tan \theta = \frac{opp}{hyp}\\tan 32=\frac{38}{hyp}\\hyp=\frac{38}{tan 32}\\hyp=\frac{38}{0.6249}\\hyp= 60.81cm[/tex]

Next is to get the adjacent

[tex]Cos 32=\frac{adj}{60.81}\\adj=60.81cos32\\adj=60.81(0.8480)\\adj= 51.57cm[/tex]

Next is to get the missing angle

Since sum of angle in the triangle is 180degrees

32 + 90 + x = 180

122 + x = 180

x = 180 - 122

x = 58degrees

The unknown sides are 60.81cm and 51.57cm while the unknown angle is 58degrees.

Learn more about the properties of triangles here: https://brainly.com/question/16908652

Answer:

Step-by-step explanation:

a1=219

d=a2-a1=226-219=7

2018=219+7n-7

1806=7n

n=258

S258=[(219+2018)/2*258

S258=288573.

Answer:

I think the correct answer is F. y = 6x

We will see that the line equation is y = 6*x

A general linear equation is written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

If we know that the line passes through two points (x₁, y₁) and (x₂, y₂) then we can write the slope as:

[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

In this case, the line passes through the points: (0, 0) and (-1/2, -3)

Then the slope is:

[tex]a = \frac{0 - (-3)}{0 - (-1/2)} = 6[/tex]

Then the line is of the form y = 6*x + b

To find the value of b, we use the fact that the line passes through the point (0, 0), then we have:

0 = 6*0 + b

0 = b

We can conclude that the line is y = 6*x

If you want to learn more about linear equations, you can read:

https://brainly.com/question/4074386

Answer:

Step-by-step explanation:

[tex] \frac{1}{15} \times \frac{1}{3} [/tex]

[tex] = \frac{1}{15 \times 3} [/tex]

[tex] = \frac{1}{45} (ans)[/tex]

Answer:

For a point defined bt a radius R, and an angle θ measured from the positive x-axis (like the one in the image)

The transformation to rectangular coordinates is written as:

x = R*cos(θ)

y = R*sin(θ)

Here we are in the unit circle, so we have a radius equal to 1, so R = 1.

Then the exact coordinates of the point are:

(cos(θ), sin(θ))

2) We want to mark a point Q in the unit circle sch that the tangent has a value of 0.

Remember that:

tan(x) = sin(x)/cos(x)

So if sin(x) = 0, then:

tan(x) = sin(x)/cos(x) = 0/cos(x) = 0

So tan(x) is 0 in the points such that the sine function is zero.

These values are:

sin(0°) = 0

sin(180°) = 0

Then the two possible points where the tangent is zero are the ones drawn in the image below.

Answer: 12

Step-by-step explanation:

16 X 20c = 3.20

12 x 5c = 0.60

total is 3.80

Amy has 12 five c coins.

Trả lời:

86 và 91

Giải thích từng bước:

Cho hai số là x và y. Nếu tổng của chúng là 177, thì;

x + y = 177 ... 1

Nếu 17 bị trừ đi số đầu tiên, nó được biểu thị là x - 17

Nếu 25 được thêm vào số thứ hai l, nó được biểu thị bằng y + 25

Nếu số thứ nhất bây giờ bằng 2/3 số thứ hai, thì:

x-17 = 2/3 (y + 25) .... 2

Từ 1, x = 177-y ... 3

Thay thế 3 thành 2

177-y-17 = 2/3 (y + 25)

160-y = 2/3 (y + 25)

3 (160-y) = 2 (y + 25)

480-3y = 2y + 50

-3y-2y = 50-480

-5y = -430

y = 430/5

y = 86

Vì x = 177-y

x = 177-86

x = 91

Do đó hai số là 86 và 91

Answer:

15

Step-by-step explanation:

(3x-1+2x+1)(3) -> 3 is the plug-in for x

3x-1+2x+1=5x

5*3=15

15

Answer:

15

Step-by-step explanation:

f(x) = 3x -1

g(x) = 2x+1

(f+g)(3)

find g(3) = 2(3)+1 = 6+1 = 7

Then find f(3) = 3(3) -1 = 8

f(3) + g(3) = 7+8 = 15

Answer: 16x^2 + 24x + 9

Step-by-step explanation:

Simplified version: (4x+3)^2

Answer:the answer is 9

Step-by-step explanation:

Answer:

[tex]y= 3[/tex]

Step-by-step explanation:

Given

[tex]RT = 6[/tex]

[tex]k = 1.5[/tex] --- dilation ratio

See attachment

Required

Determine length, y

First, we calculate length R'T.

Since point T is the center of dilation, then:

[tex]R'T = k * RT[/tex]

Substitute known values

[tex]R'T = 1.5 * 6[/tex]

[tex]R'T = 9[/tex]

y is between R'T and RT;

So:

[tex]y = R'T - RT\\[/tex]

[tex]y = 9 -6[/tex]

[tex]y= 3[/tex]

Answer:

either 4 or 9

Step-by-step explanation:

Answer:

m BC = 100

Step-by-step explanation:

Since the angle is at the center, the arc has the same measurement as the angle

m BC = 100

Answer:

363

Step-by-step explanation:

Formula for area of a circle

A = πr^2

Where r = radius

The circle has a given radius of 11

To find the area of the circle we simply substitute r in the formula with the value of the radius (11)

( Also note that the question says to use 3 for π )

A = πr^2

π = 3

r = 11

Substitute values in formula

A = (3)(11)^2

11^2 = 121

A = 121(3)

121(3) = 363

A = 363

Answer:

(√366 - 3)/24

Step-by-step explanation:

Given the following:

cos∝ = √3/8 and sinβ = √3/3

Sin(∝-β) = sin∝cosβ - cos∝sinβ

Get sin∝

Since cos∝ = √3/8

adj = √3

hyp = 8

opp = √8² - (√3)²

opp = √64 - 3

opp = √61

Recall that sin∝ = opp/hyp  

sin∝ = √61/8

Get cosβ

Since sinβ =  √3/3

opp = √3

hyp = 3

adj =√3² - (√3)²

adj = √9-3

adj = √6

Recall that cosβ = adj/hyp

cosβ = √6/3

Substitute the gotten values into the formula

Sin(∝-β) = sin∝cosβ - cos∝sinβ

Sin(∝-β) = ( √61/8)(√6/3)- (√3/8)(√3/3)

Sin(∝-β) = √366/24 - √9/24

Sin(∝-β) = (√366 - 3)/24

Answer:

6

Step-by-step explanation:

[tex]3x - 15 \geqslant 3[/tex]

[tex]3x \geqslant 3 + 15[/tex]

[tex]x \geqslant \frac{18}{3} [/tex]

[tex]x \geqslant 6[/tex]

Answer:

A

Step-by-step explanation:

[tex] \sf \: c = 3 \\ \sf \: d = 4 \\ \\ \sf \: 5cd \: = \: ?\\ \\ \sf \:5 cd \hookrightarrow \\ \sf = 5 \times (3) \times (4) \\ \sf = 5 \times 12 \\ = \underline{ \bf \: 60}[/tex]

-> Just substitute the values given for variables c & d in the equation 5cd & you'll get the answer.

Answer:

multiply each term in the bracket by the expression outside the bracket

:)

Step-by-step explanation:

Answer:

Here we have:

g(x) = 2*√x

And we know that it is related to a parent function, where the parent functions are:

Linear Function: f(x)=x.

Quadratic Function: ݂f(x)=x^2.

Square Root function: f(x)= √x.

Absolute Value function: f(x)=|x|

Cubic function: f(x)=x^3.

Cube Root function: f(x) = ∛x

Logarithmic function: f(x)=log x or f(x)=In x.

Exponential function: f(x) = a^x.

a) Because g(x) = 2*√x

We can see that it is related to the square root function, then the parent function is:

f(x) = √x

b) now we want to write g(x) in terms of f(x)

we have:

g(x) = 2*√x

we can replace √x by f(x)

then we get:

g(x) = 2*f(x)

Now we have g(x) in terms of f(x)