Solve the following inequality: 20t + 9, 200 ≤ 16,000
Answer in interval notation.

The value of x is 13 units and the value of y is 13 units

The given triangle is right triangle

The ratio of the given triangle angles = 45-45-90 degrees

To find the length of the sides we have to use the trigonometric functions

sin θ = Opposite side / hypotenuse

cos θ = Adjacent side / hypotenuse

tan θ = Opposite side / adjacent side

Find the value of x

sin 45 = Opposite side / 13[tex]\sqrt{2}[/tex]

Opposite side = 13[tex]\sqrt{2}[/tex] × sin 45

= 13 units

Similarly

cos 45 = Adjacent side / 13[tex]\sqrt{2}[/tex]

Adjacent side =  13[tex]\sqrt{2}[/tex] × cos 45

= 13 units

Therefore, the length of the side x and y is 13 units

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The Horton family subscribes to 3 premium channels. The total monthly subscription fee for the excel cable company is 48 dollars. The Horton family will save 24 dollars in one year by using the less expensive company.

(A) To find the number of premium channels for which the total monthly subscription fee for the excel and best cable companies will be the same, we set these two expressions equal to each other and solve for x:

32 + 8x = 26 + 10x

8x - 10x = 26 - 32

-2x = -6

x = 3

Therefore, the Horton family subscribes to 3 premium channels.

(B) The total monthly subscription fee for the excel cable company is 32 + 8 × 2 = 48 dollars if the Horton family subscribes to 2 premium channels. The total monthly subscription fee for the best cable company is 26 + 10 × 2 = 46 dollars if the Horton family subscribes to 2 premium channels.

Since the total monthly subscription fee for the best cable company is less than the total monthly subscription fee for the excel cable company, the Horton family should subscribe to the best cable company in order to spend less money.

(C) If the Horton family subscribes to the best cable company for one year, they will save 48 - 46 = 2 dollars per month. Over the course of one year, they will save 2 × 12 = 24 dollars.

Therefore, the Horton family will save 24 dollars in one year by using the less expensive company.

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The number of people were 200 in the theater when it was full.

What is a theater?

In architecture, a theatre, usually spelled theatre, is a structure or area where a play can be conducted in front of spectators. The term comes from the Greek theatron, which means "a place of seeing." The actual performance usually takes place on a stage in a theatre.

Given that, the theater was full when the movie began.

76 people leave the theater before end the movie. At the end of the movie, there is 124 people left.

Apply algebraical operation that is addition to find the required answer.

Therefore, the number of people that was present at the beginning of the movie is (76 + 124) = 200.

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The net pay of Billy after 8% taxes and 10% retirement policy is $1600.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, From Billy's salary of $2000 8% of his paycheck goes to income taxes, and 10% automatically goes into retirement.

So, To obtain a net salary of Billy we'll subtract the percentage amount of 8% and 10% from the base of $2000.

Therefore, Net pay of Billy is {2000 - (8/100)×2000 - (10/100)×2000}.

= {2000 - 160 - 200}.

= (2000 - 360).

= $1640

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The composition function for the given situation is (c·r·b)(x) or (r·c·b)(x). Therefore, options B and F are the correct answers.

The given functions are c(x)=2x, b(x)=x+5 and r(x)=0.75x.

When the result of one function is used as the input for another, this is known as a composite function.

The most common kind of critical hit simply deals additional damage, most commonly dealing double the normal damage that would have been dealt, but many other formulas exist as well (such as ignoring defense of the target or always awarding the maximum possible damage).

A critical hit has the base damage x multiplied, next the damage reduction is applied to the critical hit. Bonus damage is not subject to damage reduction or critical hits, so this is applied last.

Here, Critical hit × Bonus × Damage reduction

That is, (c·r·b)(x) or (r·c·b)(x)

The composition function for the given situation is (c·r·b)(x) or (r·c·b)(x). Therefore, options B and F are the correct answers.

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use y = mx + b

this is slope and y intercept

m is slope       b is y intercept

y = 1/4x -2

In the exponent, the value of n when 5 is rounded to the nearest power of 10 will be 100000.

The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.

The value of n when 5 is rounded to the nearest power of 10 will be:

= 10^5

= 100000

The value is 10000.

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Answer:

look it up

Step-by-step explanation:

Answer:

18.6 miles

Step-by-step explanation:

Subtract Distance traveled from total distance

Total distance: 24 miles

Distance Traveled: 5.4 miles

24 - 5.4 = 18.6

Answer:

11

Step-by-step explanation:

Answer:

To solve the equation f(x) = 3, we can set the expression for f(x) equal to 3 and then solve for x. In other words, we want to find the values of x that make the equation 5 - \frac{x}{r^2} + 5 + 6 = 3 true.

We can start by simplifying the left side of the equation by combining like terms. This gives us

5 - \frac{x}{r^2} + 5 + 6 = 5 + 5 - \frac{x}{r^2} + 6 = 10 - \frac{x}{r^2} + 6

Next, we set this expression equal to 3 and solve for x:

10 - \frac{x}{r^2} + 6 = 3 \quad \Rightarrow \quad 10 - 6 = 3 - \frac{x}{r^2} \quad \Rightarrow \quad \frac{x}{r^2} = 7

To solve for x, we can multiply both sides of the equation by r^2:

x = 7r^2

Therefore, the solutions to the equation f(x) = 3 are $x = 7r^2$. Note that this is a general solution, and it may not give all the possible values of $x$ that make the equation true. It's also possible that there are no solutions, depending on the value of $r$.

Any fraction whose numerator is the same number as its denominator will equal 1, which is 100%. Hence, fraction [tex]\frac{5}{5}[/tex] is a fraction that equals 100%.

Answer:

[tex]\frac{5}{5}[/tex]

Step-by-step explanation:

To get a percentage out of a fraction, you divide the fraction and then move the decimal point two places to the right. [tex]\frac{5}{5} =1[/tex]  is also equal to 1.0

Move the decimal two places to the right and you get 100%

Two-column proof

See missing statements and reasons below.

    Statement                                      Reason                                          

The value of f(-3) if f(x) = 5x - 10 and g(x) = -x + 4 is -25.

Equation: A statement that two variable or integer expressions are equal. In essence, equations are questions, and the motivation for the development of mathematics has been the systematic search for the answers to these questions.

Given:

f(x) = 5x - 10 and g(x) = -x+4

Calculate the  f(-3) by putting the value of x = -3 as shown below,

f(x) = 5(-3) - 10

f(x) = - 15 - 10

f(x) = -25

Therefore, the value of f(-3) if f(x) = 5x-10 and g(x) = -x+4 is -25.

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Answer:

B

Step-by-step explanation:

This is the only pair of functions where [tex]f(g(x))=g(f(x))=x[/tex].

Answer:

The answer is p = -6/3. This is the value of p that makes the original equation true.

Step-by-step explanation:

To solve this equation, we must first isolate the variable p on one side of the equation. To do this, we can use the properties of equality to add or subtract the same value from both sides of the equation.

First, we can subtract 2p from both sides of the equation to get rid of the 2p term on the left side. This gives us 0 = -3p - 6/4.

Next, we can add 6/4 to both sides of the equation to get rid of the constant term on the right side. This gives us 6/4 = -3p.

Finally, we can multiply both sides of the equation by -4/3 to get rid of the coefficient -3 on the right side. This gives us -6/3 = p.

Therefore, the value of p that makes the equation true is p = -6/3.

Using a system of equations to solve the problem, the candy distributor must mix 190 Kilograms of the 20% chocolate and 10 Kilograms of the 60% chocolate to create 200 Kilograms of a 22% fat-content chocolate.

A system of equations means two or more equations solved simultaneously.

They are known as simultaneous equations and can be solved graphically, by elimination, by substitution, or matrix.

The fat-content of one of the chocolate blend = 20%

The fat-content of the second chocolate blend = 60%

The expected mixture will have a fat-content = 22%

The total kilograms of the end mixture = 200 kilograms

Let the 20% fat-content chocolate = x

Let the 60% fat-content chocolate = y

x + y = 200 ... Equation 1

Solving for x, x = 200 - y

0.2x + 0.6y = 0.22(200)  ... Equation 2

By substitution in Equation 2:

0.2(200 - y) + 0.6y = 44

40 - 0.2y + 0.6y = 44

40 + 0.4y = 44

0.4y = 4

y = 10

x = 200 - y

x = 190 (200 - 10)

Based on the system of equations, 190 kilograms of the 20%-fat-content chocolate must be mixed with 10 kilograms of the 60% fat-content chocolate.

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The ordered pair (1, 12) lies on the graph of the exponential function f(x) = 3(2)2x. which is the correct answer would be option (A).

The graph of an exponential function of the form f(x) = abˣ is a curve that passes through the point (0, a), where a is the initial value of the function.

In the given equation, the initial value is 3, so the graph of f(x) passes through the point (0, 3).

To find other points on the graph of f(x), we can plug different values of x into the equation and solve for the corresponding value of y.

For example, if we plug x = 3 into the equation, we get:

f(3) = 3(2)² × 3

= 3(16)

= 48

Therefore, point (3, 48) does not lie on the graph of f(x).

Similarly, if we plug x = 1 into the equation, we get:

f(1) = 3(2)² × 1

= 3(4)

= 12

Thus, point (1, 12) lies on the graph of f(x).

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Answer:

54% are females

Step-by-step explanation:

In total there would be 225 participants -

104 + 121 = 225

Next, Divide 121 and 225. After, multiply by 100.

225/121(100)=53.78

53.78 rounded to the nearest percent is 54.

I hope this helped your question!

In the broadest sense, inverse functions are those that "reverse" one another.

Any function can be solved for by substituting one variable for another to discover the inverse of that function.

Below is an example to help you understand.

Find the inverse of h (x) = (4x + 3)/(2x + 5)

Solution

H (x) should be changed to Y.

h (x) = (4x+3)/(2x+5) y = (4x + 3)/(2x + 5)

Change the order of x and y.

⟹ x = (4y + 3)/ (2y + 5).

The following formula should be used to solve for y in the equation above:

⟹ x = (4y + 3)/ (2y + 5)

Divide both sides by (2y + 5)

⟹ x (2y + 5) = 4y + 3

Distribute the x evenly.

⟹ 2xy + 5x = 4y + 3

isolate y.

⟹ 2xy – 4y = 3 – 5x

⟹ y (2x – 4) = 3 – 5x

Divide through by 2x - 4 to obtain;

⟹ y = (3 – 5x)/ (2x – 4) (2x – 4)

Finally, swap out y for h - 1. (x).

⟹ h – 1 (x) = (3 – 5x)/ (2x – 4) (2x – 4).

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The speed that the train travels is given as follows:

45 miles per hour.

The train travels at a constant speed, hence the distance traveled by the train over time is modeled by the proportional relationship defined as follows:

d = vt.

In which the variables of the equation are defined as follows:

Since the velocity is constant, it's equation is defined as follows:

v = d/t.

One point on the table is given as follows:

(1,45).

Hence the constant velocity of the train is calculated as follows:

v = 45/1 = 45 miles per hour.

The problem is given by the image shown at the end of the answer.

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Answer:

36.9 degrees

Step-by-step explanation:

distance that the plane travels (hypotenuse) = 1000m

horizontal distance (adjacent) = 800m

cos(angle) = adjacent/hypotenuse

cos(angle) = 800/1000

angle = cos-1(800/1000)

angle = 36.9 degrees

Answer:

Step-by-step explanation:

You want the solutions to the rational equation ...

  [tex]\dfrac{2}{2x-6}-\dfrac{x}{x^2-9}=\dfrac{3}{x-3}[/tex]

We choose to rewrite the equation in the form f(x) = 0. We can start by subtracting the term on the right side (from both sides).

  [tex]\dfrac{2}{2x-6}-\dfrac{x}{x^2-9}-\dfrac{3}{x-3}=0\\\\\dfrac{2}{2(x-3)}-\dfrac{x}{(x-3)(x+3)}-\dfrac{3}{x-3}=0\\\\\\\dfrac{(x+3)-x-3(x+3)}{(x-3)(x+3)}=0\qquad\text{cancel 2 in first term; common denominator}\\\\\\\dfrac{-3x-6}{(x-3)(x+3)}=0\qquad\text{collect terms}[/tex]

The "not-possible values" will be values of x that make the denominator zero: x = ±3. The solution is ...

  [tex]-3(x+2)=0\qquad\text{numerator must be zero}\\\\\boxed{x=-2}\qquad\text{divide by -3, subtract 2}[/tex]

In the original equation, we have ...

  [tex]\dfrac{2}{2(-2)-6}-\dfrac{-2}{(-2)^2-9}=\dfrac{3}{(-2)-3}\\\\\dfrac{2}{-10}-\dfrac{-2}{-5}=\dfrac{3}{-5}\\\\-\dfrac{1}{5}-\dfrac{2}{5}=-\dfrac{3}{5}\qquad\text{TRUE}[/tex]

__

Additional comment

We like to write the equation as a single fraction compared to zero so that any common factors can be cancelled from numerator and denominator. This helps prevent extraneous solutions. Here, there are none.

The inequality to use to find the number of pounds for Earthen red clay and Porcelain white clay is:

0.75r + 1.1w ≥ 100

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

A ceramic artist orders two types of clay.

Earthen red clay

Porcelain white clay

Amount to spend = $100 or more

Earthen red clay costs = $0.75 per pound

Porcelain white clay costs = $1.10 per pound.

The inequality to use to find the number of pounds for Earthen red clay and Porcelain white clay.

= 0.75r + 1.1w ≥ 100

where r is the number of pounds of earthen red clay, and w is the number of pounds of porcelain white clay.

Thus,

The number of pounds for Earthen red clay and Porcelain white clay can be found using the inequality:

0.75r + 1.1w ≥ 100

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