On a coordinate plane, 3 lines are shown. Line a has points (negative 3, 3) and (3, negative 3). Line b has points (negative 3, negative 2) and (2, 3). Line c is parallel to line b.

If line b is perpendicular to line a, and line c is perpendicular to line a, what is the slope of line c?

The magnitude and the direction of the resultant are approximately 57.871 and 198.676°.

Vectors are elements with two given characteristics: Magnitude and direction. A resultant is derived from the sum of vectors, the magnitude is the norm of a vector and the direction is the orientation of a vector. The resultant and its characteristics are described below:

[tex]\vec r = \left(\sum\limits_{i=1}^{n}x_{i}, \sum\limits_{i=1}^{n}y_{i}\right)[/tex]     (1)

[tex]\|\vec r\| = \sqrt{\left(\sum\limits_{i=1}^{n} x_{i}\right)^{2}+\left(\sum\limits_{i=1}^{n} y_{i}\right)^{2}}[/tex]   (2)

[tex]\theta = \tan^{-1}\frac{\sum\limits_{i=1}^{n}y_{i}}{\sum\limits_{i=1}^{n}x_{i}}[/tex]   (3)

Where [tex]\theta[/tex] is resultant angle, measured in degrees.

If we know that [tex]\|\vec u\| = 90[/tex], [tex]\theta_{u} = 40^{\circ}[/tex], [tex]\|\vec v\| = 60[/tex], [tex]\theta_{v} = 20^{\circ}[/tex], [tex]\|\vec w\| = 40[/tex] and [tex]\theta_{w} = 30^{\circ}[/tex], then the resultant, its magnitude and its direction:

[tex]\vec r = (-90\cdot \cos 40^{\circ}-60\cdot \sin 20^{\circ}+40\cdot \cos 30^{\circ}, 40\cdot \sin 30^{\circ}+60\cdot \cos 20^{\circ}-90\cdot \sin 40^{\circ})[/tex]

[tex]\vec r = (-54.824, 18.531)[/tex]

[tex]\|\vec r\| = \sqrt{(-54.824)^{2}+18.531^{2}}[/tex]

[tex]\|\vec r\| \approx 57.871[/tex]

[tex]\theta = \tan^{-1} \left(\frac{18.531}{-54.824}\right)[/tex]

[tex]\theta \approx 198.676^{\circ}[/tex]

The magnitude and the direction of the resultant are approximately 57.871 and 198.676°. [tex]\blacksquare[/tex]

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Answer:

135

Step-by-step explanation:

5/8=0.625

1-0.625=0.375

0.375 times 360=135

Answer:

87.407

Step-by-step explanation:

circumference = 2*pie*r

= 2*pie*17

=106.8/2

=53.4

53.4+(17*2)

=87.4

Answer:

Step-by-step explanation:

it 87.38

TRUST ME

Answer:

A

Step-by-step explanation:

i did this before and got it correct

The value of the difference of the functions is 3t^2/3

The difference in the growth of the specimen is 3t^2/3

Expoenential functions are written in the form y= ab^x

Given the following expoenential functions

A(t) = 5/6t^2/3

B(t) = 1/3t^2/3

a) Determine the function (A-B(t)

(A-B)(t) = A(t) - B(t)

Substitute

(A-B)(t) = 5/6t^2/3 - 1/3t^2/3
(A-B)(t) = (5/6-1/3)t^2/3
(A-B)(t) = 9/3t^2/3
(A-B)(t) = = 3t^2/3

b) This means that the difference in the growth of the specimen is 3t^2/3

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[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]

Let's solve ~

Perimeter of square is :

[tex]\qquad \sf  \dashrightarrow \:4 \times side \: length[/tex]

so, we can take side length as a, and solve for a ~

[tex]\qquad \sf  \dashrightarrow \:4a = 60[/tex]

[tex]\qquad \sf  \dashrightarrow \:a = 60 \div 4[/tex]

[tex]\qquad \sf  \dashrightarrow \:a = 15[/tex]

Now, since we know the side length. let's find Area of square :

[tex]\qquad \sf  \dashrightarrow \: {15}^{2} [/tex]

[tex]\qquad \sf  \dashrightarrow \:area = 225 \: m {}^{2} [/tex]

Answer:

The answer is 1

Step-by-step explanation:

5w² – 5w = 0

Add 5w both side

5w² – 5w + 5w = 5w – 5w

5w² = 5w

Now, Divide both side by 5w we get,

5w²/5w = 5w/5w

w = 1

Thus, The value of w is 1

Answer:

w = 1

Step-by-step explanation:

Given :

Bring 5w to the other side.

Answer:

1/8

Step-by-step explanation:

1/2 divided by 4 = 8 1/8ths

Answer:

  (3 +1.5π) ft ≈ 7.71 ft

Step-by-step explanation:

We see a semicircle, not a "composite figure." The perimeter of the semicircle is the sum of the length of the arc and the length of the straight edge:

  P = (1/2)πd +d . . . where d is the diameter and πd is the full circumference

  P = d(1 +π/2)

  P ≈ (3 ft)(1 +1.57) = 7.71 ft . . . . . using 3.14 for π

The perimeter of the figure is about 7.71 feet.

__

In terms of pi, the perimeter is ...

  P = (3 +1.5π) ft

Answer:

6

Step-by-step explanation:

[tex]8-6+4[/tex]

[tex]2+4\\6[/tex]

Answer: D

Step-by-step explanation:

Answer:

$399.75

Step-by-step explanation:

6.5% of $6,150 =

= 0.065 × $6,150

= $399.75

Answer: $399.75

He had to pay $399.75

formula:  Tax = Tax Rate * Purchase Price

Answer:

30 m is the original, and 60 m would be expanded

Step-by-step explanation:

perimeter=l+w+l+w so 12+3+12+3=30 and you could multiply that by 2 to make it 60m i believe

Answer:

He is incroredct because he should have multiplied the bases

Step-by-step explanation:

Answer:

A: He is incorrect because he multiplied the bases.

Step-by-step explanation:

The correct answer would have been: [tex]6^{9}[/tex]

[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]

Let's use Unitary method ~

[tex]\qquad \sf  \dashrightarrow \:10 \:hr = 320 \: bagels[/tex]

[tex]\qquad \sf  \dashrightarrow \: 1\: hr = (320 \div 10) \: bagels[/tex]

[tex]\qquad \sf  \dashrightarrow \:1 \: hr = 32 \: bagels[/tex]

So, the rate per hour is 32 bagels ~

[tex]\qquad \sf  \dashrightarrow \:15 \: hr = (15 \times 32) \: bagels[/tex]

[tex]\qquad \sf  \dashrightarrow \:15 \: hr = 480\: bagels[/tex]

So, they can prepare 480 bagels in 15 hours

Answer:

480 bagels

Step-by-step explanation:

320 bagels in 10 hours.

⇒ 320 bagels = 10 hours

Divide 10 both sides to find the rate per hour:

⇒ 320/10 bagels = 10/10 hours

⇒ 32 bagels = 1 hours

Multiply 15 both sides to find the number of bagels in 15 hours

⇒ 32 bagels = 1 hours

⇒ 32 x 15 bagels = 1 x 15 hours

⇒ 480 bagels = 15 hours

Answer:

See below ~

Step-by-step explanation:

The function can be written as :

Answer:

39

Step-by-step explanation:

You find the area by multiplying the length times the height which is what I did 13 x 3 = 39

Answer:

34

Step-by-step explanation:

2 x 16 + 2

_________

2 x 16 = 32

_________

32 + 2 = 34

Answer:

30 or 64

Step-by-step explanation:

30 Because... 2 corns for every one till they rech 15..

that's mean (2 x 15)

64 Because... 2 corns plus 2 extra if they rech 16....

that's mean (4x16)

Answer:

2y² + 12y + 18

Step-by-step explanation:

2(y + 3)²

First use formula (a + b)² = a² + 2ab + b² to expand (y + 3)²:

(a + b)²

(y + 3)²

y² + 2*y*3 + 3²

y² + 6y + 9

Dont forget the 2:

2(y² + 6y + 9) <== distribute and multiply

2y² + 12y + 18

Hope this helps!

Answer:

i think is would be D

hope that helps if not i can change it

Step-by-step explanation:

The Neptune's time period of orbit is 164.3 earth years.

We have given that the mass of the sun is 2 × 1030 kg.

The distance between neptune and the sun is 30 au

[tex]T^2 = 4\pi ^2a^3/GM[/tex]

Where T is in earth years, a is astronomical units and

M = solar masses.

4π²/GM = 1,

Therefore we get

[tex]T^2 = a^3[/tex]

[tex]T = \sqrt(a^3)[/tex]

[tex]T = \sqrt(30^3)[/tex]

[tex]T = 164.3[/tex]

Therefore, the Neptune's time period of orbit is 164.3 earth years.

To learn more about the time period visit:

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Answer:

b. 164 earth years

Step-by-step explanation:

just took the quiz 2022

The expression f(x) = (x ^ 2 - 4)(x ^ 2 + 4x + 3 is a polynomial function

The factored form of f(x) = (x ^ 2 - 4)(x ^ 2 + 4x + 3) is f(x) = (x - 2)(x + 2)(x + 3)(x + 1)

The expression is given as:

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

Express as difference of two squares

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

Expand

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

Factorize the expression

f(x) = (x - 2)(x + 2)(x(x + 1) + 3(x + 1))

Factor out x + 1

f(x) = (x - 2)(x + 2)(x + 3)(x + 1)

Hence, the factored form of f(x) = (x ^ 2 - 4)(x ^ 2 + 4x + 3) is f(x) = (x - 2)(x + 2)(x + 3)(x + 1)

Read more about factored expressions at:

https://brainly.com/question/723406

Answer:

$703.04

Step-by-step explanation:

The equation for this is 625 x [tex]1.04^{years\\}[/tex].

So using the formula 625 x [tex]1.04^{3}[/tex] = $703.04

Answer:

$703.04

Step-by-step explanation:

Compound interest formula

[tex]\sf A=P(1+\frac{r}{n})^{nt}[/tex]

where:

Given:

Substituting given values into the formula:

[tex]\implies \sf A=625(1+\frac{0.04}{1})^{3}[/tex]

[tex]\implies \sf A=625(1.04)^{3}[/tex]

[tex]\implies \sf A=703.04[/tex]

Answer:

0.0138

Step-by-step explanation:

the division gives a value which is almost recurring hence we round off to get 0.0138

Answer:

72.5 (I did the math)

6/35

hope it helps...!!!

Answer:

(2/7) x (3/5)=  fraction form: 6/35   decimal form: 0.1714285

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

The circumference of a circle is [tex]2\pi r[/tex], while the diameter of a circle is 2r. [tex]\frac{2\pi r}{2r} = \pi[/tex]

Answer:

G

Step-by-step explanation:

Volume of a triangular prism = area of the base x height

(where the "bases" are the triangles)

Area of a triangle = 1/2 x base x height

Given:

⇒ area of base of prism = 1/2 x 3.1 cm x 4.8 cm = 7.44 cm²

Given:

⇒ Volume of the prism = 7.44 cm² x 2.6 cm = 19.344 cm³

Answer:

D.

Step-by-step explanation: