Identify the slope and y-intercept of each of the following lines. Then graph each line.
6x + 2y = 12
attached graph
I am confused...

The six trigonometric functions related to (x, y) = (20, 48): sin θ = 12/13, cos θ = 5/13, tan θ = 12/5, cot θ = 5/12, sec θ = 13/5, csc θ = 13/12.

Given the coordinates in rectangular form, that is, (x, y), where each component belongs to an orthogonal axis of reference. By trigonometry we have six functions to be calculated:

[tex]\sin \theta = \frac{y}{\sqrt{x^{2}+y^{2}}}[/tex]     (1)

[tex]\cos \theta = \frac{x}{\sqrt{x^{2}+y^{2}}}[/tex]     (2)

[tex]\tan \theta = \frac{\sin \theta}{\cos \theta}[/tex]     (3)

[tex]\cot \theta = \frac{1}{\tan \theta}[/tex]     (4)

[tex]\sec \theta = \frac{1}{\cos \theta}[/tex]     (5)

[tex]\csc \theta = \frac{1}{\sin \theta}[/tex]     (6)

If we know that x = 20 and y = 48, then the six trigonometric functions are, respectively:

[tex]\sin \theta = \frac{48}{\sqrt{20^{2}+48^{2}}}[/tex]

[tex]\sin \theta = \frac{12}{13}[/tex]

[tex]\cos \theta = \frac{20}{\sqrt{20^{2}+48^{2}}}[/tex]

[tex]\cos \theta = \frac{5}{13}[/tex]

[tex]\tan \theta = \frac{12}{5}[/tex]

[tex]\cot \theta = \frac{5}{12}[/tex]

[tex]\sec \theta = \frac{13}{5}[/tex]

[tex]\csc \theta = \frac{13}{12}[/tex]

The six trigonometric functions related to (x, y) = (20, 48): sin θ = 12/13, cos θ = 5/13, tan θ = 12/5, cot θ = 5/12, sec θ = 13/5, csc θ = 13/12. [tex]\blacksquare[/tex]

To learn more on trigonometric functions, we kindly invite to check this verified question: https://brainly.com/question/6904750

Volume of a tetrahedron with edge s

[tex]\\ \rm\Rrightarrow V=\dfrac{s^3}{6\sqrt{2}}[/tex]

According to question

[tex]\\ \rm\Rrightarrow V=\dfrac{4^3}{6\sqrt{2}}[/tex]

[tex]\\ \rm\Rrightarrow V=\dfrac{64}{6\sqrt{2}}[/tex]

[tex]\\ \rm\Rrightarrow V=\dfrac{32}{3\sqrt{2}}[/tex]

[tex]\\ \rm\Rrightarrow V=\dfrac{32}{4.2426406871192}[/tex]

[tex]\\ \rm\Rrightarrow V\approx 7.5425in^3[/tex]

Answer:

See below ~

Step-by-step explanation:

Volume of a tetrahedon

Solving for V

Graph

perimeter of paralleogram(p) = 2 ( a + b ) = 2 ( 44 + 66) = 2 × 110 = 220 cm = 220 × 10 = 2200 millimeter

a x a x c = 3.9 * 3.9 * 3 =45.6345.63 * 2 = 91.26a x b x c = 3.9 * 5.7 * 3 = 66.6966.69 + 91.26 = 157.95 cubic units

Answer:

d

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

find value at  12 =12

find value at 10 =    6

 so it changes   + 6    for a change from 10 to 12

6/2 = 3  

Answer:

[tex]y=\frac{1}{9}x+19/9[/tex]

Step-by-step explanation:

First get y by itself.

[tex]x-9y=-19\\-9y=-x-19\\[/tex]

Then variable y itself

[tex]y=(-x-19)*-1/9\\y=\frac{1}{9}x+19/9[/tex]

Answer:

a) growth b) decay

Step-by-step explanation:

In the function f (x) = b^x when b > 1, the function represents exponential growth.

In the function f (x) = b^x when 0 < b < 1, the function represents exponential decay.

a)b=2 > 1 this function growth

b)b=0.5 < 1 this function decay

0.765 (100) + .06 (.0765 x 100)

76.5  + .06 (76.5)  

76.5 + 4.59 = 81.09    Chris will pay $81.09

A better way ( if you don't care to know the tax just the bottom line of what it will cost) would be to do:

0.765x x 1.06 = 76.5 x 1.06 = $81.09 too.

Why the 1 in front of the .06?  The one includes the price of the coat so you don't have to add the tax on after.

Think about it like this. When you buy something you pay (even with an employee

discount) for all of it (100%) + the tax (in this case, it's 6%)  So you pay 106% of the cost of the item.  106% = 1.06

Answer:

The answer is 96

Step-by-step explanation:

Just write (16 x 6) x 1 = v and solve it by doing 16 x 6 and the answer would be 96 cm for the volume.

Answer:

  about 520,000

Step-by-step explanation:

Following directions, we evaluate the equation by putting the value where the variable is and doing the arithmetic.

__

The value of x will be the number of days between May 26 and May 12. That value is ...

  x = 26 -12 = 14

Then the number of mosquitos is estimated to be ...

  y = 230,000(1.06^14) ≈  520,008

About 520,000 mosquitos will inhabit the city on May 26.

_____

Additional comment

Typically, an "estimate" is one or two significant figures. So, 520,000 is a reasonable estimate. 520,008 has more precsision than can be justified.

The equations will be re-written such that the expression on one side can be graphed and the x-intercepts of the graph would indicate the solution.

A) 3X² = 81

Rewritten, we have  3X² - 81 = 0

This is also = 3(X² - 27) = 0

B) (X - 1)(X + 1) - 9 = 5X

Open the brackets and we have X² - 1 - 9 - 5x = 0

Simplified, we have X² - 5X - 10 = 0

C) X² - 9x + 10 = 32

Collect like terms and we have:
X² - 9X - 22 = 0

D) 6x(x - 8) = 29

Expand the bracket and collect like terms such that the equation is equal to zero and we have

6X² - 48x - 29 = 0

Using Desmos Graphing, the following results can be obtained showing that x intercepts at:

(a) (-5.196, 0) & (5.196, 0)

(b) (-1.531, 0) & (6.531, 0)

(c) (-2, 0) & (11, 0)

(d) (-0.564, 0) & (8.564, 0)

Learn more about graphed equations at:
https://brainly.com/question/14323743

Answer:

- 5/2

Step-by-step explanation:

Arrange this line equation into y = mx + b form   m = slope

 y = 2/5x + 12/5    

  then perpindicular line = - 1/m   = - 1/ (2/5) = - 5/2

Answer:

g(x)

Step-by-step explanation:

y-intersect for h(x) is -11 as shown in the table, where the x value is 0

y-intersect for f(x) you find out by subbing 0 in the place of x and get the y intersect value of 2.99

y-intersect of g(x) is 3 as shown in the drawing

as seen across the three y-intersects, the value of g(x) y-intesect is the greatest

Answer:

120

Step-by-step explanation:

[tex] \frac{1}{7} \div 3[/tex]

[tex] \frac{1}{7} \div \frac{3}{1} [/tex]

[tex] \frac{1 \times 1}{7 \times 3} [/tex]

[tex] = \frac{1}{21} [/tex]

The inequality that can be used to find the greatest number of plants you can buy is p ≤$20 / 1.50.

Here are inequality signs and what they mean:

> means greater than

< means less than

≥ means greater than or equal to

≤ less than or equal to

The inequality sign that would be used in this question is ≤.

(cost of plant x number of plants) ≤ total spending money

$1.50p ≤ $20

p ≤ $20 / 1.50

To learn more about inequality, please check: https://brainly.com/question/5031619

Answer:

The side lengths will form a triangle because 6+4 > 7

Step-by-step explanation:

For side lengths, the two smallest sides (ex. 6 and 4) must have a greater sum than then highest side length. Since 6+4 is greater than 7, it creates a triange. If it would have been 5+2 it would not have worked because it needs to be greater than, not less than or equal to.

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

[tex] \textsf{Let's calculate the surface area of given right prism} [/tex]

[tex] \textbf{Area of Triangles :} [/tex]

[tex] \textsf{Since there are two triangles, } [/tex]

[tex] \textsf{Area of Triangles = 96 × 2 = 192 cm²} [/tex]

[tex] \textbf{Now, calculate the Areas of rectangles :} [/tex]

[tex] \textsf{Now add them all :} [/tex]

Answer:

Step-by-step explanation:

(16+12+20)*10+16*12= 48*10+192+480+192=672 c.m. squared

Answer:

It's the 2nd one 3y2-43y over 12y2

Step-by-step explanation:

First u do a common denominator u multiply on the first side by 6y on the second side by 4 then u solve it till u get 6y2-86y over 24y2 then simplify by dividing by 2

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

a)

First I will calculate the equation of the line that goes trough the points

C (0, 0) and (-4, 3).

y= mx + b

y = [(3-0)/ (-4 -0) ] x + 0

y = (-3/4)x  →the slope of tis line is (-3/4)

The slope of line l is the negative reciprocal of (-3/4) the slop of line that goes trough points C (0, 0) and (-4, 3) because the lines are ⊥.  

Slope of line l is 4/3

b)

The equation of l is

y= (4/3)x + b

for point (x= -4, y = 3) that belongs to the line l, we have

3 = (4/3) (-4) + b

3 = (-16/3) + b

3 + (16/3) = b

(9+16)/3 = b

25/3 = b

The equation of the line l in slope intercept form is :

y = (4/3)x + (25/3)

c)

The radius of circle C is the distance between C (0, 0) and (-4, 3).

d² = (x2-x1)² +(y2-y2)²

d = √(-4-0)² +(3-0)²

d = √16+ 9

d = 5 → the radius of the circle C is 5

d)

Line l intersects the y-axis at (25/3) as we previously found out.

The radius is 5.

...therefore the distance between the line l's y-intercept and the circumference of the circle is

(25/3 ) - 5  = (25 - 5·3)/3 = 10/3

The dot plots is an illustration of charts and graphs

The average score of period 7 is greater than the average score of period 1

From the dot plots in the complete question, we have the following frequency tables

Period 1                                                          Period 7

Score     Students                                          Score     Students

55           1                                                         65           1

70           1                                                         75           3

75           6                                                         80         5

80           6                                                         85         6

85           2                                                         90         3

90           3                                                         95        2

95           1                                                                

The average is calculated using:

[tex]\bar x = \frac{\sum fx}{\sum f}[/tex]

For period 1, we have:

[tex]\bar x_1 = \frac{55 * 1 + 70 * 1 + 75 * 6 + 80 * 6 + 85 * 2 + 90 * 3 + 95 * 1}{1 + 1 + 6 + 6 + 2 + 3 + 1}[/tex]

Evaluate the sum

[tex]\bar x_1 = \frac{1590}{20}[/tex]

Evaluate the quotient

[tex]\bar x_1 = 79.5[/tex]

For period 7, we have:

[tex]\bar x_7 = \frac{65 * 1 + 75 * 3 + 80 * 5 + 85 * 6 + 90 * 3 + 95 * 2}{1 + 3 + 5 + 6 + 3 + 2}[/tex]

Evaluate the sum

[tex]\bar x_7 = \frac{1660}{20}[/tex]

Evaluate the quotient

[tex]\bar x_7 = 83[/tex]

By comparison, 83 is greater than 79.5

Hence, the average score of period 7 is greater than the average score of period 1

Read more about dot plots at:

https://brainly.com/question/12276901

Answer:

The value of x = -1/2

Step-by-step explanation:

=> 10(2x-4)=100x

=> 20x - 40 = 100x

=> -40 = 100x - 20x

=> -40 = 80x

=> -40/80 = x

=> -1/2 = x

Answer:

A. [tex](x,y)[/tex] ⇒ [tex](kx, ky)[/tex]

Step-by-step explanation:

Because that's the dilation equation or formula

The total weight of the 14 packages that Melissa weighed is gotten as; Total weight = 42 pounds

We are given;

Mean weight = 3

Now,formula for mean is;

Mean = total/sample size

We are given;

Sample size = 14

Thus;

3 = total/14

Total = 3 * 14

Total weight = 42 pounds

Read more about Mean average at; https://brainly.com/question/20118982

#SPJ1

Answer:

i think it's c

Step-by-step explanation:

sorry if I'm wrong

Answer:

x+10

Step-by-step explanation:

Answer:

y = 3x - 6

Step-by-step explanation:

The line here is parallel

Equation of line