Please answer the question CORRECTLY with a logical explanation. You will get brainliest guaranteed.

(a) f(x) =  \(log_2(x)\) is a logarithmic function

(b) g(x) = ∜x is a root function

(c) h(x) = \(2x^3/(1 - x^2)\) is a rational function

(d) u(t) = 1 - 1.1t + \(2.54t^2\) is a polynomial of degree 2

(e) v(t) = \(5^t\)is an exponential function

(f) w(θ) = sin θ \(cos^{2}\theta\) is a trigonometric function.

(a) f(x) = \(log_2(x)\) is a logarithmic function. Logarithmic functions have the logarithm of the independent variable as the output. Here, the logarithm base is 2.

(b) g(x) = ∜x is a root function. Root functions have the square root or higher roots of the independent variable as the output. Here, the root is a cube root.

(c) h(x) = \(2x^3/(1 - x^2)\) is a rational function. Rational functions are functions that are expressed as the quotient of two polynomials. Here, the numerator is a cubic polynomial and the denominator is a quadratic polynomial.

(d) u(t) = 1 - 1.1t + \(2.54t^2\) is a polynomial of degree 2. Polynomials are functions that are expressed as a sum of powers of the independent variable, with coefficients. The degree of a polynomial is the highest power of the independent variable.

(e) v(t) = \(5^t\) is an exponential function. Exponential functions have the independent variable as the exponent. Here, the base is 5.

(f) w(θ) = sin θ \(cos^{2}\theta\) is an algebraic function and a trigonometric function. Algebraic functions are functions that can be expressed using arithmetic operations and algebraic expressions. Trigonometric functions are functions that involve the ratios of the sides of a right triangle. Here, the function is a combination of sine and cosine functions.

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The complete question is -

Classify each function as a power function, root function, polynomial (state its degree), rational function, algebraic function, trigonometric function, exponential function, or logarithmic function.

(a) f(x) =  \(log_2(x)\)    

(b) g(x) = ∜x    

(c) h(x) = \(2x^3/(1 - x^2)\)    

(d) u(t) = 1 - 1.1t + \(2.54t^2\)                    

(e) v(t) = \(5^t\)    

(f) w(θ) = sin θ \(cos^{2}\theta\)

The ladder will reach a Height of approximately 43.46 meters on the building.

To find out how high on the building the ladder will reach, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the ladder forms a right triangle with the ground and the building. The base of the ladder is 7 meters, the height of the building is what we need to find, and the length of the ladder is given as 44 meters.

Using the Pythagorean theorem, we can set up the equation:

(Height of the building)^2 + 7^2 = 44^2

Simplifying the equation, we have:

(Height of the building)^2 + 49 = 1936

Subtracting 49 from both sides, we get:

(Height of the building)^2 = 1887

To find the height of the building, we take the square root of both sides:

Height of the building = √1887

Calculating the square root of 1887, we find that the height of the building is approximately 43.46 meters.

Therefore, the ladder will reach a height of approximately 43.46 meters on the building.

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The polynomial function of degree 3 f(x) = 1/7 x³ - 2/7 (x²) - 4/7 (x)  + 8/7

A polynomial is a mathematical equation that solely uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are sometimes known as indeterminates in mathematics.

Given:

Real roots: −2,2 (with multiplicity 1 and 2) and (3,f(3))=(3,35)

For root "a", the polynomial will have a factor (x -a).

The polynomial will be the product of the 2 factors can be shown as

p(x) = (x +2) (x - 2)²

Now, the value of p(3) = (5)(1)² = 5.

In order to make f(3) = 35, we need to multiply p(x) by 1/7.

So, f(x) = (1/7) p(x)

f(x) = (1/7) (x +2) (x - 2)²

f(x) = 1/7 x³ - 2/7 (x²) - 4/7 (x)  + 8/7

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Answer:

\(r \geqslant - 16\)

Step-by-step explanation:

\( \frac{ - 10 + r}{2} \geqslant - 13\)

multiply both sides by 2:

\( - 10 + r \geqslant - 26\)

add 10 on both sides:

\(r \geqslant - 16\)

Answer:

\(r \ge -16\)

Step-by-step explanation:

To solve any equation/inequality:

1. get the variable to show up exactly once

2. isolate it

\(\frac{-10+r}{2} \ge -13\)

Multiply both sides by 2 and simplify (note that we're multiplying by a positive, not a negative, so the direction of the inequality stays the same, whereas multiplying or dividing by a negative would have changed the direction of the inequality)

\(\frac{-10+r}{2} *2 \ge -13 *2\)

\(-10+r \ge -26\)

Add 10 to both sides, and simplify

\((-10+r)+10 \ge (-26)+10\)

\(r \ge -16\)

There will be 12 slices of pizza left over, which can be expressed as 3/2 or 1 1/2 slices in fraction form.

To find out how much pizza will be left over, we need to calculate the total number of slices available and subtract the number of slices consumed by the players.

Given that there are six pizzas and each pizza has eight slices, the total number of slices available is 6 pizzas * 8 slices/pizza = 48 slices.

Since there are 36 players on the team, and each player has one slice, the total number of slices consumed is 36 slices.

To determine the remaining slices, we subtract the consumed slices from the total available slices: 48 slices - 36 slices = 12 slices.

Therefore, there will be 12 slices of pizza left over.

To express this as a fraction, we can write it as 12/1, which simplifies to 12. This means there will be 12 whole slices of pizza left over.

If you would like to express it as a fraction in its simplest form, you can write it as 12/8. By dividing both the numerator and denominator by their greatest common divisor, which is 4, we get 3/2. So, in fraction form, there will be 3/2 or 1 1/2 slices of pizza left over.

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Explanations:

The given expression is:

To know which fraction will go into the blank, we consider the options one by one, and which ever is true is the correct choice.

Find the LCM so that both fractions have a common denominator and see if what happens at the numerator is true

Option A is 1/8, therefore lets see if 2/3 is truly less that 1/8

Option B is 3/6. Let us see if 2/3 is truly less than 3/6

Option C is 3/5. Let us see if 2/3 is truly less than 3/5

Option C is 3/4. Let us see if 2/3 is truly less than 3/4

2/3 < 3/4 is the correct expression. Therefore, option D is the right choice

Answer:

 Job A pays pays better

Step-by-step explanation:

Job A pays more ($18,616) by $2,216 more

there are roughly 52 weeks in a year so multiply that by 40 to get the total hours worked in a year. = 2,080

2,080 hours worked per year multiplied by the hourly pay $8.95 = $18,616

Job A pays $18,616

Job B only pays $16,400

Answer:

Step-by-step explanation:

base area=41.57 in²

height=9 in

volume=41.57×9=374.13 in³

Answer:

x= 12/5

Step-by-step explanation:

Distribute the fraction and solve for x.

Answer: 4(5+2y)-3(3y+7)

Step-by-step explanation:

Use the distributive property for this ^^^

1 trillion to the tenth power is (10¹⁴)¹⁰ or  (10¹³)¹⁰.

So, 1 trillion to the tenth power:

Therefore, 1 trillion to the tenth power is (10¹⁴)¹⁰ or  (10¹³)¹⁰.

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Answer:

Step-by-step explanation:

The events are not independentd) The events are not mutually exclusiveStep-by-step explanation:Hi!Lets call: Gar = {homes with garage}Pool

Answer: 42

Step-by-step explanation: 15 -8=7 90/15=6 6*7=42

This distribution of snowfall amounts is skewed to the right

Data is said to be skewed to the right or positively skewed, when the tail of the distribution extends more towards the right side of the data. This means that there are a few larger values or outliers that pull the mean or median towards the higher end of the scale, resulting in a longer tail on the right side of the distribution.

In a positively skewed distribution majority of the data is concentrated towards the lower values.

Considering the stemplot the majority of the data is in the lower values

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Answer:

to the second part

18.7 inches

Answer:

Five and four fifteenths

Step-by-step explanation:

Answer:

Can you show the whole question?

Answer:

The other endpoint is (-1, 1).

Step-by-step explanation:

What we know is one endpoint is at (5, -9). The midpoint is at (2, -4).

So, to find the slope, find (yB - yA)/(xB - xA)

(-4 -(-9))/(2 - 5)

(-4 + 9)/(2 - 5)

5/-3

The slope is -5/3.

Knowing this, subtract 3 from the midpoint's x, and add 5 to the midpoint's y.

((2 - 3), (-4 + 5))

The other endpoint is at (-1, 1).

Answer:

90

Step-by-step explanation:

for percentage

\(\frac{54}{60}\)×100

= 0.9×100

=90

Answer:

C

Step-by-step explanation:

Answer:

The answer is B if the octagon has side lengths of 8

Answer:

x=14.28

Step-by-step explanation:

24^2+x^2=28^2, Pythagorean theorem

x^2=28^2-24^2

x^2=(28+24)(28-24)

x^2=52*4

x^2=204

x is around 14.28

Answer:

AB = 10.398

Step-by-step explanation:

By cosine rule, we have:

AB² = AC² + BC² - 2(AC)(BC)cos(ACB)

⇒ AB² = 7² + 10² - 2(7)(10)cos(73)

⇒ AB² = 49 + 100 - 140cos(73)

⇒ AB² = 149 - 140cos(73)

⇒ AB² = 149 - 140cos(73)

⇒ AB² = 149 - 140(0.292)

⇒ AB² = 149 - 40.88

⇒ AB² = 108.12

⇒ AB = √(108.12)

⇒ AB = 10.398

Answer:

The price of a fruit bowl at the cafe is $3

Step-by-step explanation:

Answer: 3

Step-by-step explanation:

Got it right

Answer:

Step-by-step explanation:

6x+y = 4x+11y, isolate y terms on one side and x terms on another side by subtract 11y to both sides and subtract 6x to both sides

y -11y = 4x -6x, combine like terms

 -10y = -2x , divide both sides by -10

      y = (-2/-10)x, simplify the fraction

      y = (1/5) x

\(\tt 6x+y=4x+11y\\\\6x-4x=11y-y\\\\2x=10y\\\\y=0.2x\)

- - - - - - - - - - - - - - - -

There is some unnecessary information in the problem, first, it should be removed.

"The dosage of cough medicine for a child 4 to 6..."

"2 days"

Listing the age and days don't matter here, it's the rest of the problem that matters!

- - - - - - - - - - - - - - - -

"1/2(a teaspoon) every 4 hours,"  This is one dose. Multiply 1/2 by five to see how many teaspoons are consumed.

1/2 x 5 = 2 1/2 (teaspoons)

- - - - - - - - - - - - - - - -

Good luck! :)

~pinetree

Answer: short answer

Just checked it’s False

Hope this helps :))

Step-by-step explanation:

Answer:

B. False

Step-by-step explanation:

A P E X

To make the fractions equivalent, we need to find the missing numerators that would make them equal. Let's fill in the missing numerators:

1/2 and __/8

To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 4:

1/2 and 4/8

Now, the fractions are equivalent.

---

4/12 and __/60

To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 5:

4/12 and 20/60

Now, the fractions are equivalent.

---

2/3 and __/12

To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 4:

2/3 and 8/12

Now, the fractions are equivalent.

---

4/4 and __/8

To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 2:

4/4 and 8/8

Now, the fractions are equivalent.

Answer:

w=0,

w=-7

Step-by-step explanation:

Answer: See attached

Step-by-step explanation:

Answer:

4 5/32

Step-by-step explanation:

Hope this helps, if it does, can I have brainliest?