Write the equation of the line in fully simplified slope-intercept form

Answer:

see explanation

Step-by-step explanation:

(1)

Using the sine ratio in the right triangle

sin x = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{4}{6}[/tex] , then

x = [tex]sin^{-1}[/tex] ([tex]\frac{4}{6}[/tex] ) ≈ 41.8° ( to the nearest tenth )

(2)

Using the tangent ratio in the right triangle

tan x = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{29}{14}[/tex] , then

x = [tex]tan^{-1}[/tex] ([tex]\frac{29}{14}[/tex] ) ≈ 64.2° ( to the nearest tenth )

(3)

Using the cosine ratio in the right triangle

cos x = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{25}{40}[/tex] , then

x = [tex]cos^{-1}[/tex] ([tex]\frac{25}{40}[/tex] ) ≈ 51.3° ( to the nearest tenth )

Applying derivative concepts, the y-intercept of the line tangent to the curve at (2√3, √3) is: [tex]y = \sqrt{3}[/tex]

The equation of the line is:

[tex]y - y_1 = m(x - x_1)[/tex]

In which:

In this problem, point [tex](2\sqrt{3}, \sqrt{3})[/tex], hence [tex]x_1 = 2\sqrt{3}, y_1 = \sqrt{3}[/tex]

To find the value of [tex]\theta[/tex], we have that:

[tex]3\tan{\theta} = \sqrt{3}[/tex]

[tex]\tan{\theta} = \frac{\sqrt{3}}{3}[/tex]

[tex]\theta = \frac{\pi}{6}[/tex]

Then, for the slope:

[tex]\frac{dy}{d\theta} = 3\sec^{2}{\theta}[/tex]

[tex]\frac{dx}{d\theta} = 3\sec{\theta}\tan{\theta}[/tex]

Considering [tex]\theta = \frac{\pi}{6}[/tex]:

[tex]\frac{dy}{d\theta} = 3\left(\frac{2}{\sqrt{3}}\right)^2 = 2[/tex]

[tex]\frac{dx}{d\theta} = 3\left(\frac{2}{\sqrt{3}} \times \frac{\sqrt{3}}{3}\right) = 2[/tex]

[tex]m = \frac{\frac{dy}{d\theta}}{\frac{dx}{d\theta}} = 1[/tex]

Then, the equation of the line is:

[tex]y - y_1 = m(x - x_1)[/tex]

[tex]y - \sqrt{3} = x - 2\sqrt{3}[/tex]

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

The y-intercept is the value of y when x = 0, hence:

[tex]y = \sqrt{3}[/tex]

A similar problem is given at https://brainly.com/question/22426360

Answer:

Step-by-step explanation:

Find the miles per gallon rate of each car

Blue car:

Red car:

According the rates, the blue car could travel the greater distance

Answer: Start with y2-y1/x2-x1

-4+7/-6+3

Answer=2.5 or 5/2

DONT TRUST ME THOUGH

Step-by-step explanation:

Answer:

B

if f(x-4) then we should put x-4 where the x is spouse to be so;

-2(x-4)-1 =

-2x + 8 - 1 =

-2x + 7

Presumably you mean 555 as a number in base 10.

We have

555 = 5 • (100 + 10 + 1)

… = 5 • (4 • 25 + 2 • 5 + 1)

… = 5 • (4 • 5² + 2 • 5¹ + 1 • 5⁰)

… = 4 • 5³ + 2 • 5² + 1 • 5¹

… = 4210₅

we have: [tex](3,23)^{2} \neq (1,9)^{2} +(2,7)^{2}[/tex]

so the triangle isn't a right triangle

ok done. Thank to me :>

Answer:

Step-by-step explanation:

[tex]\frac{\sqrt{36x^3y^4}}{2x^{2/3}y^{-4}}=\frac{6x^{3/2}y^2}{2x^{2/3}y^{-4}}=3x^{5/6}y^6[/tex]

a=3, b=5/6, c=6

3*(5/6)*6= 15

Answer:

The time in Auckland, New Zealand in the 12+ time zone: 21:00

The time in Athens, Greece in the +2 time zone:  22:00

The time in Trinidad in the -4 time zone:  05:00

The time and date in Chicago in the -6 time zone: 02:00 2016-10-19

The time and date Bangkok in the +7 time zone: 11:00 2016-10-20

The time and date in Greenwich: 06:00 2016-10-29

The time and date in Abu Dhabi in the +4 time zone: 30:00 2016-10-30

The time and date in a country in the +12 time zone: Uzbekistan 23:00 2016-11-02

The time and date in a country in the -12 time zone: Brazil 23:00 2016-11-01

The time and date in Honolulu located in the -10 time zone: 01:00 2016-11-02

When the time in Sri Lanka is 09:30 on 2017-05-02, find the time and date in Los Angeles located in the -8 time zone in the USA. 01:30 on 2017-05-02

(These are the answers i calculate i am not sure if they are fully correct)

Answer:

Follow these steps and you will find how to make a perpendicular line.

Step-by-step explanation:

Open the compass to a radius less than half the segment.

Draw two arcs intersecting the line on both sides of the point.

Draw two arcs using the intersection points as the centers. ...

Construct a line between this point and the original point.

Hope this helped :) -ish

The percentage of the amount which should be expected to be paid from the insurance policy based on the part time work Helen has been doing is:

Based on the given question, we can see that partial disability benefit is the theme in play here as Helen has been sick and been working on a part time basis which helps her to be eligible for partial disability benefit.

Under this type of disability benefit, Helen is entitled to get about two-thirds of her average weekly wage because she is working part time because of her disability which is her sickness.

Read more about insurance policy here:

https://brainly.com/question/24441770

Answer:

2,160.00

Step-by-step explanation:

okay so first we have to find 4.5% of 12,000

which is 540, then multiply 540 by the four years and

540 x 4 = 2,160.00

The total loan amount would be equal to $14,310 in four years when Jay graduates.

Given the following data:

To determine how much (future value) the total loan amount would equal in four years when he graduates:

Mathematically, compound interest is given by the formula:

[tex]A = P(1 + r)^{t}[/tex]

Where;

Substituting the given parameters into the formula, we have;

[tex]A = 12000(1 + 0.045)^{4}\\\\A=12000(1.045)^{4}\\\\A=12000(1.1925)[/tex]

Future value, A = $14,310

Read more: https://brainly.com/question/16992474

Answer:

5.8

miles

Step-by-step explanation:

Since area is l×b or l×l since its a square(sides are equal) we can conclude that S×S=33.64

Another way to represent this is

[tex] {s}^{2} = 33.64[/tex]

to get S we can square root both sides

[tex]s = \sqrt{33.64} [/tex]

[tex] \sqrt{33.64} = 5.8[/tex]

Therefore S=5.8miles

Answer:

5⁵ is your answer bro mark me brainlist

Answer:

B im very sorry if im wrong <3

Step-by-step explanation:

Answer:48

Step-by-step explanation:Required equation is y - 36 = (24 - 36)/(2 - 1) (x - 1)

y - 36 = -12(x - 1)

y - 36 = -12x + 12

12x + y = 12 + 36

12x + y = 48

Answer:

Y=hx+25

Step-by-step explanation:

y=total price paid

h=hourly rate

x=number of hours

25=inital fee

Answer:

13

Step-by-step explanation:

Sorry no one answered in time, but you had it correct up to 26/2. 26/2 is correct (26 minutes for 2 people) but you need for 1 person so you divide by 2 to get 13 minutes per 1 person.

Answer:

  see attached

Step-by-step explanation:

The vector -u will be in the opposite direction of u. The magnitude is 7.81, but the angle is 129.81° -180° = -50.19°. A graph of it is attached.

_____

The (x, y) components are ...

  7.81(cos(-50.19°), sin(-50.19°)) ≈ (-5.00, -6.00)

Answer:

ñññ

Step-by-step explanation:

Answer:

I believe the inequality would be: p+2x3<40

Step-by-step explanation:

Not exactly sure if it is correct but p (number of pencils Sarahi has) added too the 2 more she finds, and then x3 (when she triples her amount). This is less then (<) what Damaris has (which is 40) so it would be p+2x3<40.

Again not sure if its completely correct, but i hope it helps :,)

[tex]\huge \bf༆ Answer ༄[/tex]

Here's the solution ~

Value of x is 64

Answer:

y=x

Step-by-step explanation:

y=mx+b

m is the slope

b is the y-intercept

Since the y-intercept is at the 0 axis, the y-intercept will be zero

So now the equation is looks like this:

y=mx (Since y=mx+0 doesn't make a difference)

Now find the slope

Which is 1

Thus y=x

Hope this helps!

Answer:

[tex]\displaystyle \frac{4(3x)^2}{(2x)^2} = 9 ,\ x \neq 0[/tex]

General Formulas and Concepts:

Pre-Algebra

Evaluations

Order of Operations: BPEMDAS

Algebra I

Distributive Property

Terms/Coefficients

Step-by-step explanation:

Step 1: Define

Identify.

[tex]\displaystyle \frac{4(3x)^2}{(2x)^2}[/tex]

Step 2: Simplify:

[tex]\\ \sf\longmapsto \dfrac{4(3x)^2}{(2x)^2}[/tex]

[tex]\\ \sf\longmapsto\dfrac{ 4(9x^2)}{4x^2}[/tex]

[tex]\\ \sf\longmapsto \dfrac{36x^2}{4x^2}[/tex]

[tex]\\ \sf\longmapsto \dfrac{x^2}{x^2}\left(\dfrac{36}{4}\right)[/tex]

[tex]\\ \sf\longmapsto \dfrac{36}{4}[/tex]

[tex]\\ \sf\longmapsto 9[/tex]