Find the domain and range of the function y = f(x) = r2.=Domain:help (inequalities)Range:help (inequalities)

The absolute value function |x| always returns a non-negative number. It takes any number x and returns x if it's already non-negative, or -x if it is negative in order to make it positive.

\(|x|=\begin{cases}x&\text{for }x\ge0\\-x&\text{for }x<0\end{cases}\)

For the equation

-3 + 4 |2x - 5| = 14

rearrange terms to get

|2x - 5| = 17/4

Now,

• if 2x - 5 ≥ 0, then |2x - 5| = 2x - 5. Then

2x - 5 = 17/4

• and if instead 2x - 5 < 0, then |2x - 5| = -(2x - 5), so that

-(2x - 5) = 17/4, or

2x - 5 = -17/4

In the first case,

2x - 5 = 17/4

2x = 17/4 + 5 = 37/4

x = 37/8

In the second case,

2x - 5 = -17/4

2x = -17/4 + 5 = 3/4

x = 3/8

Explanation:

Let's draw a vertical line to split the figure into two rectangles.

The rectangle on the left is 42 by 9, so its area is 42*9 = 378.

The rectangle on the right is 7 by 20 giving an area of 7*20 = 140.

Overall, the entire area is 378+140 = 518 square yards

Solution:

Draw the rectangle:

Refer to image~

Finding the area of the rectangle:

Finding the area of the unshaded region:

Subtract the area of the unshaded region from the area of the rectangle.

The area of the figure is 518 yd².

Answer:

-1/5

Step-by-step explanation:

subtract -2/5with -3/5and you will get -1/5

Answer:

This is an example of correlation because there is an obvious relationship between the two scenarios

Step-by-step explanation:

This is not cause-and-effect therefore cannot be causation or "cause"

To simplify the expression (2x-3)(5x^2-2x+7), we can use the distributive property.

First, multiply 2x by each term inside the second parentheses:

2x * 5x^2 = 10x^3

2x * -2x = -4x^2

2x * 7 = 14x

Next, multiply -3 by each term inside the second parentheses:

-3 * 5x^2 = -15x^2

-3 * -2x = 6x

-3 * 7 = -21

Combine all the resulting terms:

10x^3 - 4x^2 + 14x - 15x^2 + 6x - 21

Now, combine like terms:

10x^3 - 19x^2 + 20x - 21

So, the simplified expression is 10x^3 - 19x^2 + 20x - 21.

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Answer:

D

Step-by-step explanation:

a quartic function is a polynomial of the 4th degree. that means that in the function expression the highest exponent of a term of x is 4.

y = ax⁴ + bx³ + cx² + dx + e

with a not 0.

the degree of a polynomial expression defines also how many zeroes (x values that create y = 0, that means points where the graph intersects the x-axis) there are.

a function has as many zeroes as the degree of the polynomial.

so, we are looking for potentially 4 zeroes.

the only graph that fulfills that is D.

the left "touch" of the graph on the x-axis counts for 2 (but equal) zeroes.

you can always test by virtually shifting the graph up or down and see, what are the max. x-axis intersections you can create.

if shifting D down a little bit you see, that this left "touch" turns into 2 intersections.

the same would apply for a "bend" or turn in the graph that does not even touch the x-axis.

if the original graph has not enough real x-axis intersections, it means that the remaining zeroes are then "imaginary" complex numbers (based on the sqrt(-1) = i).

a polynomial of the nth degree, must have n zeroes.

as a consequence it must have n-1 turns (even if the corresponding curve segments don't intersect with the x-axis in the real number space).

Answer:graph d

Step-by-step explanation:

just took the test

Answer:

Therefore, the earliest time to take the next pill is after 10.85 hours and the latest time is before 15.14 hours have passed.

Step-by-step explanation:

The concentration of the drug in your system after ingesting 100.0 mg can be calculated using the formula:

C = D / V

where C is the concentration, D is the dose, and V is the volume of distribution (assumed to be constant).

At the initial time, t = 0, the concentration is:

C(0) = 100.0 mg / V

After one half-life, t = 16 hours, the concentration is:

C(16) = C(0) / 2 = 50.0 mg / V

After two half-lives, t = 32 hours, the concentration is:

C(32) = C(16) / 2 = 25.0 mg / V

After three half-lives, t = 48 hours, the concentration is:

C(48) = C(32) / 2 = 12.5 mg / V

To find the earliest and latest times to take the next 100.0 mg pill, we need to calculate the concentration at those times and make sure it stays between 20.0 mg and 140.0 mg.

Let's first find the earliest time at which the concentration drops below 20.0 mg.

20.0 mg / V = C(16 + x) = 50.0 mg / V / (2^(x/16))

Solving for x:

2^(x/16) = 50.0 / 20.0 = 2.5

x/16 = log2(2.5)

x = 16*log2(2.5) = 16*0.678 = 10.85

So the earliest time to take the next pill is after 10.85 hours.

Now let's find the latest time at which the concentration goes above 140.0 mg.

140.0 mg / V = C(16 + x) = 50.0 mg / V / (2^(x/16))

Solving for x:

2^(x/16) = 50.0 / 140.0 = 0.3571

x/16 = log2(0.3571)

x = 16*log2(0.3571) = -15.14

So the latest time to take the next pill is before 15.14 hours have passed.

Answer:

the answer is A. 15 :))) hope i helped!!

Answer:

D 15x

Step-by-step explanation:

because you add 10+5 which is 15 and it still needs to be multiplied by x so the result is 15x and what ever x is is what it would be multiplied by

Travis' famous letter, addressed to "The People of Texas and All Americans in the World," in which he passionately appealed for reinforcements and vowed to "never surrender or retreat," has become a symbol of the fortitude and sacrifice displayed by the Texan defenders at the Alamo.

The commander of the Texan forces at the Alamo during the famous battle in 1836 was Colonel William B. Travis. Travis, a lawyer and soldier, was chosen as the leader of the Texan garrison at the Alamo, a former mission turned fortress in San Antonio, Texas. He assumed command of the Texan forces in early 1836 and played a crucial role in the defense of the Alamo against the Mexican army led by General Santa Anna.

Travis and his men, along with notable figures such as James Bowie and Davy Crockett, bravely defended the Alamo against overwhelming odds for thirteen days. Despite their courage and determination, the Texan defenders were ultimately overrun by the Mexican forces on March 6, 1836, and suffered heavy casualties, including the deaths of Travis, Bowie, and Crockett.

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The given fraction is -18/7

During the process of reciprocal, the numerator becomes denominator and vice versa

So, the reciprocal of -18/7 is 7/-18

Answer : - 7/18

Answer:

3/5

Step-by-step explanation:

15 and 25 go into 5 so you divide 15 by 5 that's 3 and 25 by 5 which is 5

The solution to the given inequality would be \(x > -4\) (a.k.a. Option B)

Hope this helps!

Answer:

1.) 10: 1, 2, 5, 10.

15: 1, 3, 5, 15,

Answer would be 5.

2.) 18: 1, 2, 3, 6, 9, 18

21: 1, 3, 7, 21

Answer would be 3.

3.) 12: 1, 2, 3, 4, 6, 12.

24: 1, 2, 3, 4, 6, 8, 12, 24.

Answer would be 12.

4.) 8: 1, 2, 4, 8.

20: 1, 2, 4, 5, 10, 20.

Answer would be 4.

5.) 14: 1, 2, 7, 14.

28: 1, 2, 4, 7, 14, 28.

Answer would be 14.

Step-by-step explanation:

Using the listing method, you would first list the common factors of each number, to which that number could be multiplied by. Then, you would search for the greatest common factor.

para la escuela necesito mucho para mi escuela

The converse of the statement will be : if x^2 = 100 then x = -10, which is not true.

In order to write a converse of a conditional statement "p then q",  will be "q then p" the hypothesis and conclusion interchanges.

Then the converse of the statement will be :

if x^2 = 100 then x = -10,

which is not true.

Since , x = +10, then x^2 = 100

Therefore, if x^2 = 100 then x = -10, which is not true.

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Answer:

ghhc

For Max, it takes 12 hours to clean the house, so in 1 hour he will complete 1/12 of the task.

For Maggie, it take 4 hours to clean the house, so in 1 hours she will complete 1/4 of the task.

Both of them working together means that in 1 hour they will complete 1/12 plus 1/4:

Thus, in 1 hours both working together will make 1/3 of the task. To make the full task, they will need a total of 3 hours, because:

That is, 3 hours times the fraction of the task per hours gives 1 total task.

So, they will need 3 hours to complete and the sister is correct.

The area of the square with a side length of 3.1 meters is 9.61 square meters.

To find the area of a square, we need to multiply the length of one side by itself. In this case, the square has a side length of 3.1 m.

Area of a square = side length × side length

Substituting the given side length into the formula:

Area = 3.1 m × 3.1 m

To perform the calculation:

Area = 9.61 m²

It's worth noting that when calculating the area, we are working with squared units. In this case, the side length is in meters, so the area is expressed in square meters (m²). The area represents the amount of space enclosed within the square.

Remember, to find the area of any square, you simply need to multiply the length of one side by itself.

The area of the square with a side length of 3.1 meters is 9.61 square meters.

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The value of the expression is -3.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

2x + 3y - 4w  _____(1)

Now,

Substitute x = 2, y = 3, and w = 4 in (1).

So,

2x + 3y - 4w

= 2 x 2 + 3 x 3 - 4 x 4

= 4 + 9 - 16

= 13 - 16

= -3

Thus,

The value is -3.

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The value of 57.17 as a mixed number is - 57 17/100.

A mixed number is said to be in its simplest form if its fractional part's highest common factor, or HCF, is 1. When mixed numbers are simplified, the fraction value remains constant. We can say that the simplified mixed number and the actual mixed number are fractions that are equivalent.

A mixed number is made up of three components: a whole number, a numerator, and a denominator. The numerator and denominator are both components of the proper fraction that results in the mixed number.

In this case, -57.17 will be:

= -57 + (17/100)

= -57 17/100.

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Answer:

x = 84

Step-by-step explanation:

-12(x+12) + 1177 = 10 + 15

-12x - 144 + 1177 = 25

1033 = 25 + 12x

1008 = 12x

x = 84

The total area from the graph is 2.737.

Area is the amount of space occupied by a two-dimensional figure. In other words, it is the quantity that measures the number of unit squares that cover the surface of a closed figure. The standard unit of area is square units which is generally represented as square inches, square feet, etc.

First of all, lets calculate the points of intersection (P, Q, R)

x²+3=(x+2) +5

x²-2=√(x+2)

x⁴+4-4x²=x+2

x⁴-4x²-x+2=0

(x-2)(x³+2x²-1)=0

(x-2)(x+1)(x²+x-1)=0

x=2, -1, -1±√(1+4)/2

Clearly, the x-coordinate of Q is -1, P is -1-√5/2, R is -1+√5/2, S is 2

So the limit of integration will be

P( (-1-√5)/2, (-1-√5/2)² +3)=P((-1-√5)/2, (3+√5/2))

Q(-1, (-1)²+3)=Q(-1, 4)

Area A:

\(\int\limits^\frac{3+\sqrt{5} }{2} _4 {-\sqrt{-y-3}-((y-5)^2 -2)} \, dx\)

= \([\frac{-(y-3)^\frac{3}{2} }{\frac{3}{2} }-\frac{(y-5)^3}{3}+3y]^{\frac{3+\sqrt{5} }{2} }_4\)

= 2.07

Area B:

\(\int\limits^\frac{-1+\sqrt{5} }{2} _4 {-\sqrt{x+2}+5-(x^2+3)} \, dx\)

= \([\frac{-(x+2)^\frac{3}{2} }{\frac{3}{2} }+5x-\frac{x^3}{3}-3x]^{\frac{-1+\sqrt{5} }{2} }_{-1}\)

= 0.667

Total area = 2.07+0.667

= 2.737

Therefore, the total area from the graph is 2.737.

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Answer:

I may be wrong but I think it's D.

Step-by-step explanation:

I made an educated guess.

Answer:

10 x 17.1 = 171

Step-by-step explanation:

10 x 17.1 = 17.1

Answer:

4 L 600 mL

Step-by-step explanation:

1 L = 1000 mL

so 27 L 600 mL = 27000 + 600 = 27600 mL

27600/6 = 4600 mL

4 L 600 mL.

Answer:

suerte espero q te ayude

Answer:

\(\frac{dy}{dx} = 24 x + 21\)

Step-by-step explanation:

Explanation:-

Given that the function

      y = f(x) = 3 x ( 4 x + 7)

     y  = 3 x ( 4 x + 7)  

    y = 12 x² + 21 x ..(i)

Differentiating equation (i) with respective to 'x' , we get

\(\frac{dy}{dx} = 12 (2x) +21 (1)\)

\(\frac{dy}{dx} = 24 x + 21\)