Find f(12) for the given piecewise function:
-18x+20, x < 19
f(x).
-16x²,
x ≥ 19
0-6478
0-5776
O-2304
0-196

Answer: 3 gallons per hour

Step-by-step explanation: 14-(3x) =5 14-5=9 9/3=3

Answer is - 2 [tex]\sqrt{3}[/tex] / 13

Cosecant Given a point P(x, y) on the terminal side of an angle θ in standard position

cosθ = cos (π + d) (d is the inner angle of the tringle)

       = - cos 2

       = - 4 / - [tex]\sqrt{(- 6^{2} + (- 4^{2} )[/tex]

       = - 4 / - [tex]\sqrt{36 + 16 }[/tex]

      = - 4 / -[tex]\sqrt{52}[/tex]

      = - 4 / 2[tex]\sqrt{13}[/tex]

      = - 2 / [tex]\sqrt{13}[/tex]

multiply by [tex]\sqrt{13}[/tex]

we get,

      = -  [tex]\frac{2 \sqrt{13} }{13}[/tex]

Formulae :

Arc cosecant      y = arcs(x) = csc-1(x). Another way to write x = csc(y).

Arccosine      y = arcos(x) = cos-1(x). Another way to write x = cos(y).

Arc cotangent    y = arcos(x) = cot-1(x). Another way to write x = cot(y).

Arc secant       y = arcsec(x) = sec-1(x). Another way to write x = sec(y).

Arcsine       y = arcsine(x) = sin-1(x). Another way to write x = sin(y).

Arctangent   y = arctan(x) = tan-1(x). Another way to write x = tan(y).

Learn more about angle theta here : brainly.in/question/20913260

SPJ9

Solution:

B.) [tex](6-\sqrt{33}, 6+\sqrt{33})[/tex]

Hope this helps! If so, please lmk! Thanks and good luck!

(a) There are 665280 ways of selection if the order of the choices matters.

(b) There are 924 ways of selection if the order of the choices does not matters.

(a)  If the order of the choices matters, then we must use the permutation formula that is

[tex]^nP_r = \frac{n!}{(n - r)!}[/tex]

Here n is the total no. of objects and r is chosen objects

We have n = 12

               r = 6

After we substitute the value we get

[tex]^{12}P_6 = \frac{12!}{(12 - 6)!}[/tex]

[tex]^{12}P_6 = \frac{12!}{6!}[/tex]

[tex]^{12}P_6[/tex] = 665280

Thus, there are 665280 ways of selection if the order of the choices matters

(b)  If the order of the choices does not matter, then we must use the combination formula that is

[tex]^nC_r = \frac{n!}{r!(n - r)!}[/tex]

After we substitute the value we get

[tex]^{12}C_6 = \frac{12!}{6!(12 - 6)!}[/tex]

[tex]^{12}C_6 = \frac{12!}{6! 6!}[/tex]

[tex]^{12}C_6 =[/tex] 12×11×10×9×8×7×6! / 6!×6!

[tex]^{12}C_6 =[/tex] 12×11×10×9×8×7/ 6!

​[tex]^{12}C_6 =[/tex] 665280/ 720

​[tex]^{12}C_6 =[/tex] 924

Thus, there are 924 ways of selection if the order of the choices does not matters.

Learn more about permutation formula

https://brainly.com/question/1216161

#SPJ9

The measures of the triangle's unknown angles will be 50° and 100°.

A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.

A triangle has one 30° angle, an unknown angle, and an angle with a measure that is twice the measure of the unknown angle.

Let 'a' and 'b' be the unknown angles of the triangle. Then the equation will be

∠a = 2 ∠b

We know that the angle sum of the triangle is 180°. Then the equation will be

∠a + ∠b + 30° = 180°

2∠b + ∠b = 150°

3∠b = 150°

∠b = 50°

Then the measure of the angle 'a' will be

∠a = 2 ∠b

∠a = 2 x 50°

∠a = 100°

The measures of the triangle's unknown angles will be 50° and 100°.

More about the triangle link is given below.

https://brainly.com/question/25813512

#SPJ1

Answer: please=356

Step-by-step explanation:

219 +485 = 348 + please

704=348 + please

please=356

The required rate for ratio of the two different quantities i.e

Gabby worked 30/4 hours per day.

Option (c) is correct.

Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.

Given:

Gabby worked 30 hours in 4 days.

According to given question we have

The ratio of the two quantities of the different kind and in the different units is a fraction that shows how many times one quantity is of the other.

By the use of arithmetic we have,

Gabby worked 30 hours in 4 days means

4 days= 30 hours

1 days = 30/4 hours

Therefore, the required rate for ratio of the two different quantities i.e

Gabby worked 30/4 hours per day.

Learn more details about arithmetic here:

https://brainly.com/question/11559160

#SPJ1

Answer: 30/4 hours per day

Step-by-step explanation:

Answer:

easy

Step-by-step explanation:

How to solve a system of equations by elimination.

Write both equations in standard form.

Make the coefficients of one variable opposites.

Add the equations resulting from Step 2 to eliminate one variable.

Solve for the remaining variable.

Substitute the solution from Step 4 into one of the original equations.

Answer:

I think it's because of the down payment and the positive slope because you are going to pay in installments by months.

Answer:

B

Step-by-step explanation:

from seeing the steps listed the answer should be b would be helpful if u posted the diagram along

If two years ago, his account was worth $215,613. After losing 13 of its original value, it then gained 12 of its new value back. The current value of his Roth IRA is: $215,613.

First step is to calculate the value loss

Value loss=1/3× original  value

Value loss= 1/3× $215,613

Value loss= $71,871

Second step is to calculate the new value

New value=$215,613-$71,871

New value= $143,742

Third step is to calculate the value gained

Value gained= 1/2× new value

Valued gained=1/2× $143,742

Valued gained=$71,871

Fourth step is to calculate the current value

Current value= $143,742+$71,871

Current value=$$215,613

Therefore If two years ago, his account was worth $215,613. After losing 13 of its original value, it then gained 12 of its new value back. The current value of his Roth IRA is: $215,613.

Learn more about value here: https://brainly.com/question/8965865

#SPJ1

valid . some trees grow flowers i belive

The value of x is 11 units and the length of side RS = 11x-4 is 117 units.

with measurement BC = 60, CD = 50.

Triangle RST : RS = 11x-4, ST = 70

Two figures are said to be similar if they are the same shape. In more mathematical language, two figures are similar if their corresponding angles are congruent , and the ratios of the lengths of their corresponding sides are equal.

Given:

BC = 60 and CD = 50

RS = 11x - 4 and ST = 70

Now, considering

BC : CD = RS : ST

60 : 50 = 11x - 4 : 70

60/50 = (11x - 4)/70

50 * (11x - 4) = 70 * 60

11x - 4 = 84

11x = 88

x = 11

So, RS = 11x - 4

RS = 11 x 11 - 4

RS = 117

Hence, the value of x is 11 and the length of side RS is 117

Learn more about triangle here:

https://brainly.com/question/28567395

#SPJ1

The day of the month is nominal (option c).

Nominal data is data that can be labelled or classified into mutually exclusive categories within a variable.  A nominal variable is a categorical variable that is qualitative.

A ratio scale is quantitative. A ratio scale is a variable with a true zero. An example is weight. An interval variable is a variable where each value is measured along a scale. An example of an interval variable is credit score.

To learn more about nominal variable, please check: https://brainly.com/question/28432671

#SPJ1

Answer:

r = e or 2.718282

Step-by-step explanation:

a) simplify both sides of the equation

2.718282 = r

b) flip the equation

r = 2.718282

Answer:

B: 3x+(4x+2)=180

Step-by-step explanation:

Supplementary angles are those angles that sum up to 180 degrees. The question gives you the two angles that compose the 180 degree angle thus you get the equation:

Angle 1 + Angle 2 = Supplementary Angle

In this case we see that these two angles are Angles B and C and a supplementary angle is 180 degrees thus:

(4x+2)+3x = 180

Furthermore this also allows you to find x.

Answer:

30

Step-by-step explanation:

Let the cat have a weight of x.

Then, the dog weighs 9x.

The hamster weighs x/20.

The mouse weighs 3x/10.

So, the dog is 9/(3/10) = 30 times as heavy.

The weight of the dog is 30 times the weight of the mouse.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Let the weight of the dog be x,
A dog is 9 times as heavy as a cat,
weight of the dog = 9x - - - - -(1)

A hamster is 20 times as light as a cat
Weight of the hamster = x /20

A mouse is 6 times as heavy as a hamster.

Weight of the mouse = 6(x /20)
m(20/6) = x

Now, put x = m(20/6) in equaiton 1,
weight of the dog = 9[m(20/6)]
weight of the dog = 30m

Thus, the weight of the dog is 30 times the weight of the mouse.

Learn more about simplification here:

https://brainly.com/question/12501526

#SPJ2

Answer:

[tex]a_{n}[/tex] = 96 [tex](\frac{1}{4}) ^{n-1}[/tex]

Step-by-step explanation:

there is a common ratio between consecutive terms, that is

[tex]\frac{24}{96}[/tex] = [tex]\frac{6}{24}[/tex] = [tex]\frac{1}{4}[/tex]

this indicates the sequence is geometric with explicit formula

[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]

where a₁ is the first term and r the common ratio

here a₁ = 96 and r = [tex]\frac{1}{4}[/tex] , then explicit formula is

[tex]a_{n}[/tex] = 96 [tex](\frac{1}{4}) ^{n-1}[/tex]

Step-by-step explanation:

Parallel Lines are lines that do not intercept with eachother. They have the same slope yet have different y-intercepts.

Draw two lines not touching.

Example

[tex]y = 5x + 1[/tex]

[tex]y = 5x + 2[/tex]

No examples

[tex]y = 5x + 2[/tex]

[tex]y = - \frac{1}{5} x + 2[/tex]

Hope this helps!

The population of a city after 5 years would be 261698.

We know the the formula for the exponential growth of the population is,

P(t) = a(1+r)^t

where, a is the initial population

t is the time period

r is the rate of growth

In this question, we have a = 210000, %R = 4.5

So, r = 0.045

We need to find the population after 5 years.

t = 5

Using above formula,

P = 210000 × ( 1 + 0.045)^5

P =  210,000 × (1.045)^5

P = 210,000 × 1.25

P = 261698.2

P ≈ 261698

Therefore, the population of a city after 5 years would be 261698.

Learn more about the exponential growth here:

https://brainly.com/question/11487261

#SPJ1

The number of coffee product he sells is 38.

He makes $11.50 per hour.

He earns $0.50 for each of these items he sells.

Last week he worked 30 hours and earned $364.

Therefore, the number of coffee product he sells last week can be calculated as follows:

let

x = number of coffee product he sells.

364 = 11.50(30) + 0.50(x)

364 = 345 + 0.50x

364 - 345 = 0.50x

19 = 0.5x

divide both sides by 0.5

x = 19 / 0.5

x = 38

Therefore, the number of coffee product he sells is 38.

learn more on sells here: https://brainly.com/question/17685612

#SPJ1

Step-by-step explanation:

3800 is the general amount, but before he can touch it, 800 and 200 are taken away from it for the described purposes.

so, what is left is

3800 - 800 - 200 = 2800

this is then the real amount he can do something with.

Answer:

It's coordinates are (1,-2)

Answer:

○ [tex]z(x - 1) = -x^2 + 17x - 13[/tex]

Step-by-step explanation:

We are told that:

[tex]z(x)= 15x - x^2 + 3[/tex],

and told to find an expression for [tex]z(x - 1)[/tex].

In order to find [tex]z(x - 1)[/tex], we have to replace [tex]x[/tex] in the definition of [tex]z(x)[/tex] with [tex](x-1)[/tex]:

[tex]z(x - 1) = 15(x -1) - (x - 1)^2 + 3[/tex]

Now we can simplify:

⇒ [tex]z(x-1) = 15x - 15 - (x - 1)^2 + 3[/tex]      [Distributing 15 into the first brakets]

⇒ [tex]z(x-1) = 15x - 15 - (x^2 - 2x + 1) + 3[/tex]

⇒ [tex]z(x-1) = 15x - 15 - x^2 + 2x - 1 + 3[/tex]     [Distributing the minus sign]

⇒ [tex]z(x - 1) = 17x - x^2 -13[/tex]          [Combining like terms]

⇒ [tex]z(x - 1) = -x^2 + 17x - 13[/tex]

Therefore, the first option is the correct one.

Answer: e² - 4

Step-by-step explanation:

Differentiate of e²x - 3e-4x is e² - 4

Answer:

[tex]\dfrac{\text{d}y}{\text{d}x} = 2e^{2x}+12e^{-4x}[/tex]

Step-by-step explanation:

Given function:

[tex]y=e^{2x}-3e^{-4x}[/tex]

[tex]\boxed{\begin{minipage}{3.7cm}\underline{Differentiating $ax$}\\\\If $y=ax$, then $\dfrac{\text{d}y}{\text{d}x}=a$\\\end{minipage}}[/tex]

[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Differentiating $e^{f(x)}$}\\\\If $y=e^{f(x)}$, then $\dfrac{\text{d}y}{\text{d}x}=f\:'(x)e^{f(x)}$\\\end{minipage}}[/tex]

Therefore:

[tex]\begin{aligned}\implies \dfrac{\text{d}y}{\text{d}x} & = \dfrac{\text{d}}{\text{d}x} e^{2x}-\dfrac{\text{d}}{\text{d}x}3e^{-4x}\\\\& =2 \cdot e^{2x}-(-4)\cdot 3 e^{-4x} \\\\ &= 2e^{2x}+12e^{-4x}\end{aligned}[/tex]

The x and y nickels and a dime. She has up to 18 coins totaling a minimum of $1.10 in value. In the graphically representation we can see the line intersect each other at point (12,6).

Given that,

The x and y nickels and a dime. She has up to 18 coins totaling a minimum of $1.10 in value.

We have to create a graphic representation of this inequality system and choose a potential resolution.

x + y ≤18----->equation(1)

Amount in pennies: 5x+10y≥110------>equation(2)

solves by eq2 - 5×eq(1)

5x+10y - 5(x+y) = 120 - 5×18

5x + 10y -5x-5y  = 120 - 90

5y = 30

y=6

Then x=12

Therefore, x=12, y=6 is the point where two lines converge.

In the graphically representation we can see the equation (1) line and equation (2) line intersect each other at point (12,6).

To learn more about graphic visit: https://brainly.com/question/11764057

#SPJ1

Answer:

$5.90

Step-by-step explanation:

(7.19)(.82)  Put these numbers in your calculator and multiply them together.

5.8958 Round to the nearest cent

$5.90

The solution of the given trigonometric form equation as required in the complete task content is; x = nπ where n is any real number integer value.

It follows from the task content that the solution to the given trigonometric equation is to be determined.

Given;

Cos(x) - 1 = 0

Add 1 to both sides of the equation;

Cos (x) = 1

Therefore, the value of x can be determined by evaluating the cos inverse of (-1).

Hence,

x = Cos-¹(1)

x = nπ (where n is any integer real number value).

Ultimately, the solution of the given trigonometric form equation as required in the complete task content is; x = nπ where n is any real number integer value.

Read more on trigonometric equations;

https://brainly.com/question/2088730

#SPJ1