Two lines meet at a point that is also the endpoint of two rays. Set up and solve the
appropriate equations to solve for the values of angles x and y.
​

The length of the side AC for the right triangle is 12√3 and the measure of angle C is equal to 30°.

The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.

The basic trigonometric ratios includes;

sine, cosine and tangent.

Considering angle 60 for the right triangle with side AC opposite it we get;

tan 60 = AC/12 {opposite side/adjacent side}

√3 = AC/12

AC = 12 × √3 {cross multiplication}

AC = 12√3

angle C = 180 - (60 + 90) {sum of interior angles of a triangle}

angle C = 180 - 150

angle C = 30°.

Therefore, using the tangent of angles 60 we have the side length AC to be 12√3 and the measure of angle C is 30°.

Question:

In the right triangle shown below, angle B = 60° and side length AB = 12. How long is the side AC, and what is the size of angle C?

Answer exactly, using a radical if needed.

Answer:

$38.82

Step-by-step explanation:

just add up all the numbers :)

Answer:

0.29166666666

Step-by-step explanation:

You divide 7/24 in a calculator and u get this anwer.

[tex]b_n=b_1*q^{n-1}\\b_1=1, q=\frac{3}{1} =3\\b_n=1*3^{n-1}[/tex]

(b and t are the same)

P.S. Hello from Russia

The measure of AD = 120 degrees

The measure of arc BC is 40 degrees. If you want the length, it's (2pi/9)(radius)

Answer:

AD=120 degrees

BC=40

Step-by-step explanation:

Answer:

The population will reach 39,400 after 17 years.

Step-by-step explanation:

Given that, The population grows at a rate 4%. The population of the town is 20,000 at a certain time.

Exponential function:

[tex]y(t)=y_0(1+r)^t[/tex]

y(t) = The population after t years

[tex]y_0[/tex] = Initial population.

r = Rate of grow

t = Time.

y(t)= 39400, [tex]y_0[/tex] = 20,000, r= 4%=0.04, t=?

[tex]39400=20000(1+0.04)^t[/tex]

[tex]\Rightarrow \frac{39400}{20000}=(1.04)^t[/tex]

[tex]\Rightarrow \frac{197}{100}=(1.04)^t[/tex]

Taking ln both sides

[tex]\Rightarrow ln|\frac{197}{100}|=ln|(1.04)^t|[/tex]

[tex]\Rightarrow ln|\frac{197}{100}|=t\ ln|(1.04)|[/tex]

[tex]\Rightarrow t= \frac{ln|\frac{197}{100}|}{ln|(1.04)|}[/tex]

[tex]\Rightarrow t\approx 17[/tex]

The population will reach 39,400 after 17 years.

Final answer:

To find the time it takes for a town's population to grow from 20,000 to 39,400 at a 4% annual growth rate, the exponential growth formula is used. After rearranging the equation and taking natural logarithms, it's found that it will take approximately 18 years for the population to reach 39,400.

Explanation:

Population Growth Calculation

To calculate how long it will take for a town's population of 20,000 to grow to 39,400 with an annual growth rate of 4%, we can use the formula for exponential growth:

P(t) = P_0 × (1 + r)^t

where:

P(t) is the future population

P_0 is the initial population

r is the growth rate (expressed as a decimal)

t is the time period in years

Starting with 20,000 people and wanting to get to 39,400:

39400 = 20000 × (1 + 0.04)^t

To solve for t, we need to:

Rewrite the equation as: (1 + 0.04)^t = 39400 / 20000

Take the natural logarithm of both sides: ln((1 + 0.04)^t) = ln(39400 / 20000)

Simplify: t × ln(1 + 0.04) = ln(1.97)

Divide by ln(1 + 0.04) to isolate t: t = ln(1.97) / ln(1.04)

Use a calculator to find the numerical value for t.

When calculated, t is approximately 18 years. Therefore, it will take roughly 18 years for the town's population to grow from 20,000 to 39,400.

Answer:

Statement 3

Step-by-step explanation:

y = -2/3x-24

Make x the subject

y + 24 = -(⅔)x

x = -(3/2)(y + 24)

Intersection variables

f^-1(x) = -(3/2)(x + 24)

Slope: -3/2

No domain restrictions

y-intercept: x = 0

-(3/2)(0+24)

-36

(0,-36)

x-intercepts: y = 0

0 = -(3/2)(x + 24)

x = -24

(-24,0)

Linear function, range is all real values of y

Answer:

[tex]f^{-1}(x)\: \textsf{ has a y-intercept of }\:(0,-36)[/tex]

[tex]f^{-1}(x)\: \textsf{ has a range of all real numbers.}[/tex]

Step-by-step explanation:

[tex]f(x)=-\dfrac{2}{3}x-24[/tex]

The given function has an unrestricted domain and range.

[tex]f^{-1}(x)[/tex] is the notation for the inverse of the function.  The inverse of a function is a reflection in the line y = x

Finding the inverse of the given function

Swap f(x) for y:

[tex]\implies y=-\dfrac{2}{3}x-24[/tex]

Rearrange the equation to make x the subject:

[tex]\implies -\dfrac{2}{3}x=y+24[/tex]

[tex]\implies -2x=3y+72[/tex]

[tex]\implies x=-\dfrac{3}{2}y-36[/tex]

Swap the x for [tex]f^{-1}(x)[/tex] and the y for x:

[tex]\implies f^{-1}(x)=-\dfrac{3}{2}x-36[/tex]

The inverse function has a slope of -3/2

The domain of the inverse function is the range of the function.

The range of the inverse function is the domain of the function.

Therefore, the domain and the range are unrestricted.

The y-intercept of the inverse function is when x = 0:

[tex]\implies f^{-1}(x)\: \textsf{ has a y-intercept of }\:(0,-36)[/tex]

The x-intercept of the inverse function is when y = 0:

[tex]\implies -\dfrac{3}{2}x-36=0[/tex]

[tex]\implies -\dfrac{3}{2}x=36[/tex]

[tex]\implies x=-24[/tex]

[tex]\implies f^{-1}(x)\: \textsf{ has a x-intercept of }\:(-24,0)[/tex]

[tex]f^{-1}(x)\: \textsf{ has a y-intercept of }\:(0,-36)[/tex]

[tex]f^{-1}(x)\: \textsf{ has a range of all real numbers.}[/tex]

Answer:

.

Step-by-step explanation:

Answer:

-2x^2-8x+4

Step-by-step explanation:

Answer:6cm

Step-by-step explanation:

the answer is

Step-by-step explanation:

18. mark brainliest!

Answer:

720

I think..i hope it helps

The number of ways that 6 friends can sit together in a row of six empty seats is 720.

Permutation is defined as the calculation of a set such that it defines the number of ways that something can be arranged.

Given that,

Six friends go to a movie theater.

They have to be arranged in 6 different positions.

6 friends can be arranged in 6 different positions as 8P₈ ways.

Number of ways = 8P₈

                           = 8! / (8 - 8)!

                           = 8! / 0!

                           = 8!

                           = 720

Hence the number of ways that 6 friends can be arranged is 720 ways.

Learn more about Permutation here :

https://brainly.com/question/1216161

#SPJ3

Answer:

[tex](5, 6)[/tex]

Step-by-step explanation:

Step 1:  Solve for x in the first equation

[tex]x - y + y = -1 + y[/tex]

[tex]x = y - 1[/tex]

Step 2:  Plug in x into the second equation

[tex](y - 1) - 3y = -13[/tex]

[tex]y - 1 - 3y + 1 = -13 + 1[/tex]

[tex]-2y / -2 = -12 / -2[/tex]

[tex]y = 6[/tex]

Step 3:  Plug in y into the first equation

[tex]x - (6) + 6 = -1 + 6[/tex]

[tex]x = 5[/tex]

Answer:  [tex](5, 6)[/tex]

Answer:

a

Step-by-step explanation:

i like tacos:) thats the answer lol

The inequality for width(w) is 12[tex]\leq[/tex]w [tex]\leq[/tex] 33

An inequality statement in algebra uses the inequality symbol to show the relationship between two expressions. On either side of an inequality sign, the expressions are not the same. It implies that the articulation on the left-hand side ought to be more noteworthy than or not exactly the articulation on the right-hand side or the other way around.

Given that a machine can roll a paper wide as 33feet and narrow as 12 feet

here we can say that 33 feet is the maximum limit of machine and 12 feet is minimum .

so the equation of width(w) should lie between 12 and 33 , so width can be greater or equal to 12 and less and equal to 33.

Hence the possible inequality is 12[tex]\leq[/tex]w [tex]\leq[/tex] 33

Learn more about  inequality

https://brainly.com/question/17675534

#SPJ5

Answer:

A

Step-by-step explanation:

A line of best fit needs to match the direction of the points and fit in-between the points as much as possible

C is not the right direction

D is not the right direction

B is to the left of the points

Answer:

H

Step-by-step explanation:

Answer:

G

Step-by-step explanation:

The "range" is a collection of the plotted y values

The diver's maximum height is 28ft, so the range must be less than that.

G is a better answer than F because the diver will eventually reach the water. He will not dive infinitely downward.

Answer:

the correct answer is 14% (plzzzz brainlist this answer!)

proof:

Answer:

26.309932 MN  if gravity was normal gravity force and on basis salt water was 1030 kg/m3

Step-by-step explanation:

The rule below is something I just found.

To calculate the force of gravity of an object, use the formula: force of gravity = mg, where m is the mass of the object and g is the acceleration of the object due to gravity. Since g is always 9.8 m/s^2, just multiply the object's mass by 9.8 and you'll get its force of gravity

Answer: on edg it’s the first answer ; Skewed

Answer:

Skewed

Step-by-step explanation:

On edge 2020

Answer:

453 of them

Step-by-step explanation:

if you do 482 times .94, it is 453.

Answer:

25 + 10x

Step-by-step explanation:

First, add the base $25 from the start.  

Next, add $10 per week.  The number of weeks is the unknown, and is represented by x, giving 10x.  

Put them together, you get 25 + 10x.  

Answer:

10x+25

Step-by-step explanation:

The answer is 10x+25 because 25 is the initial value, which is the y intercept. Then, since she saves 10$ per week, it is 10*x, x representing the number of weeks.

Answer:

The test contains 10 three-point questions and 14 five-point questions.

Step-by-step explanation:

x + y = 24

3x + 5y = 100

Try elimination.

-3x - 3y = - 72

2y = 28

y = 14

Then x = 10

So, we have 10  3-point problems  and 14 5-point problems.

Answer:

y = -7/3 x -5/3

Step-by-step explanation:

We first need to find the slope

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

   =(-4-3)/(1--2)

   = (-4-3)/(1+2)

   =-7/3

Slope intercept form of a line is

y=mx+b

y = -7/3x +b

Using the point (-2,3)

3 = -7/3(-2)+b

3 = 14/3 +b

Subtract 14/3 from each side

9/3 -14/3 =b

-5/3

y = -7/3 x -5/3

Answer:

[tex]\frac{-7}{3}[/tex]

Step-by-step explanation:

[tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

plug in the factors given,

[tex]\frac{-4-3}{1--2}[/tex]

then simplify

[tex]\frac{-7}{3}[/tex]

For this case we must solve the following equation:

[tex]\frac {4} {3} y-5 = -6[/tex]

Adding 5 to both sides of the equation we have:

[tex]\frac {4} {3} y = -6 + 5[/tex]

Different signs are subtracted and the major sign is placed.

[tex]\frac {4} {3} y = -1[/tex]

We multiply by 3 both sides of the equation:

[tex]4y = -3[/tex]

We divide by 4 on both sides of the equation:

[tex]y = - \frac {3} {4}\\y = -0.75[/tex]

Thus, the solution of the equation is [tex]y = -0.75[/tex]

Answer:

[tex]y = -0.75[/tex]

Answer:

An expression containing only numbers is called figures

Step-by-step explanation:

Answer:

B is the awnswer

Step-by-step explanation:

because it is right the spinner has five sections so 1 out of five but then 4 out of 15 times it was spun it landed on q

Answer:

72°

Step-by-step explanation:

Since c||d, ∠3 would be the same as ∠1

Since those two are supplementary angles, subtract 180 with 108 to get the measure of ∠1 which is 72°.

Since ∠1 and ∠3 are corresponding angles, they'll be congruent meaning ∠3 is also 72°.

Answer:

[tex](f.g)(x) = 3x^3-3x^2-24x+36[/tex]

Domain of (f.g)(x) = All real numbers  

[tex](\frac{f}{g})(x) = \frac{x+3}{3}[/tex]

Domain of (f/g)(x) = All Real Numbers

Step-by-step explanation:

Given functions are:

[tex]f(x) = x^2+x-6\\g(x) = 3x-6[/tex]

We have to calculate f.g and f/g

In order to find f.g we have to multiply both functions

[tex](f.g)(x) = (x^2+x-6)(3x-6)\\= 3x(x^2+x-6) - 6(x^2+x-6)\\= 3x^3+3x^2-18x-6x^2-6x+36\\= 3x^3+3x^2-6x^2-18x-6x+36\\=3x^3-3x^2-24x+36[/tex]

The domain of (f.g)(x) is all real numbers

Now

[tex](\frac{f}{g})(x) = \frac{f(x)}{g(x)}\\= \frac{x^2+x-6}{3x-6}\\=\frac{x^2+3x-2x-6}{3x-6}\\=\frac{x(x+3)-2(x+3)}{3(x-2)}\\=\frac{(x+3)(x-2)}{3(x-2)}\\=\frac{x+3}{3}[/tex]

The domain of (f/g)(x) is all real numbers.

Hence,

[tex](f.g)(x) = 3x^3-3x^2-24x+36[/tex]

Domain of (f.g)(x) = All real numbers  

[tex](\frac{f}{g})(x) = \frac{x+3}{3}[/tex]

Domain of (f/g)(x) = All Real Numbers

Answer:Do you have a word bank???