Determine the solutions of the equation:
|1/3x + 9| - 3 = 21​

Correct option are C,D, E. g(x) > h(x) for x = -1, For positive values of x, g(x) > h(x), For negative values of x, g(x) > h(x).

A function is a type of rule that produces one output for a single input. This is illustrated by the equation y=x2. Any input for x results in a single output for y. Considering that x is the input value, we would state that y is a function of x.

They have the same value if x=0.

The first and second choices are not viable

for x=-1

g(-1)=1

h(-1)=-1

3. is accurate

4th , false G(x)>H for all values other than zero (x)

the proper ones are

For x=-1, g(x) exceeds h(x).

G(x) > h for positive values of x. (x).

G(x) > h for negative values of x (x).

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The science of statistics focuses on creating and researching strategies for gathering, analyzing, interpreting, and presenting empirical data.

A data set's mean (average) is calculated by summing all of the numbers in the set, then dividing by the total number of values in the set. When a data collection is ranked from least to greatest, the median is the midpoint. The number that appears most frequently in a data set is called the mode.

Adding the numbers together and dividing the result by the total number of numbers in the list yields the arithmetic mean. An average is most frequently used to refer to this. The value that appears the most frequently on the list is the mode.

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The solution is Option A.

The value of the 13th number from the equation A = ( -2/3 ) ( n - 1 ) is A = -8

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

A = ( -2/3 ) ( n - 1 )   be equation (1)

On simplifying the equation , we get

The thirteenth number in the list is n = 13

So , when n = 13

A = ( -2/3 ) ( n - 1 )

A = ( -2/3 ) ( 13 - 1 )

On further simplification , we get

A = ( -2/3 ) ( 12 )

A = ( -2 ) x 4

So , the value of A = -8

Hence , the thirteenth number in the list is A = -8

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Answer:

ok wirrudi 123 alf8 434 21 3dis w

The most appropriate choice for velocity and accleration will be given by-  Deacceleration of a car of 15 [tex]m/s^2[/tex] is a real world situation for which the rate of change is -15

What is velocity and acceleration?

Velocity

The distance travelled by a body per unit interval of time where the direction of the motion of a body is taken into account is known as velocity.

Velocity is a vector quantity as direction of motion of body is taken into account.

If d is the displacement of body and t is the time,

Velocity = [tex]\frac{d}{t}[/tex]

Acceleration

The rate of change of velocity of a body is called acceleration.

Acceleration is a vector quantity as direction of motion of a body is taken into account.

If [tex]\Delta[/tex]v is the change of velocity and t is the time,

Acceleration = [tex]\frac{\Delta v}{t}[/tex]

If velocity decreases then it is called Deacceleration

Here

Deacceleration of a car is 15 [tex]m/s^2[/tex]

That means rate of change of velocity of a car is -15 [tex]m/s^2[/tex]

This is a real world situation for which the rate of change is -15

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Let p(x) be the required polynomial.

we are given that p(x) has a zero 1 with multiplicity 2

in other word, this means that (x-1) occurs twice as a factor of p(x).

Expressions with polynomial functions include variables with various degrees, non-zero coefficients, positive exponents (of variables), and constants. A polynomial in "b" of degree 2 is, for instance, f(b) = 4b2 - 6.

Likewise, (x-3) appears as a factor of p(x) once.

we are also given that the degree of p(x) is 3.

So, p(x) can not have more than 3 linear factors.

Altogether,

p(x) = k(x-1)^2  (x-3), where constant k ∈ R - {0}.

We may take k = 1 and get the desired polynomial,

p(x) = ( x-1)^2 ( x-3) = x^3 - 5x^2 +7x -3

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Answer:

(f ⋅ g)(x) = f(g(x)) = 5·√(9 - x^2)

The domain is: -3 ≤ x ≤ 3

(g ⋅ f)(x) = g(f(x)) = √(9 - (5·x)^2)

The domain is: -0.6 ≤ x ≤ 0.6

The statement that represents the given inequality is:

The product of 8 and n decreased by 5 is less than 25.

The inequality is defined as follows:

8(n - 5) < 25.

The meaning of the expression n - 5 is given as follows:

n decreased by 5. (n is an unknown number).

The meaning of the expression 8(n - 5) is given as follows:

The product of 8 and n decreased by 5. (multiplication of two numbers is also called product).

The symbol of the inequality is given as follows:

<

Which represents the expression less than.

Considering the 25 on the other side of the inequality, the complete sentence is given as follows:

The product of 8 and n decreased by 5 is less than 25.

The complete problem is:

Sal wrote the statement below to represent the inequality 8(n - 5) < 25. Which words should Sal use to complete the verbal statement? The product of 8 and n decreased by 5 is ___________

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Answer:

Step-by-step explanation:

Answer:

C≈97.39in

Step-by-step explanation:

Answer:97.39

Step-by-step explanation:

Answer:

434

Step-by-step explanation:

Steps:

156.24 ÷ 36% = 156.24 ÷ 0.36 = 434

Both Laquita and Tori wrote a correct equation which is the correct answer would be an option (A).

Let the required line would be as

⇒ y - y₁ = [(y₂ - y₁)/(x₂ -x₁ )](x - x₁ )

Here x₁ = 0 and y₁ = 37

x₂ = 4 and y₂ = 99

The equation of the line is obtained by substituting these values into the above equation;

⇒ y - 37 = (62/4)x

⇒ y - 37 = 15.5x

⇒ y = 15.5x +37

This equation is written by Laquita.

Multiply by 2 both sides of the equation,

⇒ 2y = 31x + 74

⇒ 31x - 2y = 74

This equation is written by Tori.

Therefore, both Laquita and Tori wrote a correct equation.

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The function g(x) is a dilated form of f(x) and the dilation scale factor [K] in this case is (3/4). The graphs f(x) and g(x) are attached with the answer.

The general equation of a straight line is -

y = mx + c

Where -

[m] is the slope of the line.

[c] is the y - intercept.

Given is the following equation-

g(x) = 3/4 f(x)

Since, the functions are not given, we will assume them by ourselves. You can use the same procedure for any pair of functions of the form -g(x) = n f(x)

Assume that -

f(x) = 2x + 1

Now -

g(x) = (3/4) f(x)

g(x) = (3/4)(2x + 1)

g(x) = (3/2)x + 3/4

Now, both the graphs f(x) and g(x) are attached below. In general, g(x) is a dilated form of f(x) and the dilation scale factor [K] in this case is (3/4).

Therefore, the function g(x) is a dilated form of f(x) and the dilation scale factor [K] in this case is (3/4). The graphs f(x) and g(x) are attached with the answer.

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Okay, here we have this:

Considering that if the graph of the line rises from left to right, then it means that the slope is positive. On the other hand, if the graph of the line falls from left to right, the slope will be negative.

So, according with this finally we obtain that the correct answer is that the slope is negative.

Answer:

Negative

Step-by-step explanation:

Because MATH

Given that z₁= −7i and z₂ = 4+3i, the difference z₁ −  z₂ in rectangular form is; -4 - 10i

Addition of complex numbers is basically the same thing as adding two-dimensional vectors that are located on the x-y Cartesian plane.

Now, it is pertinent to note that when doing vector addition, we denote the x-component with i^ and y-component with j^.

We should also not that when adding complex numbers, the x-component is the real part and y-component is the imaginary part.

Geometrically, we can say that the addition of complex numbers can be equated to the addition of vectors in x-y plane.

Thus by the the parallelogram law of vector addition, we will be able to find the resultant vector.

In rectangular coordinates,

z₁ = -7i

z₂ = 4 + 3i

Then, z₁ - z₂ = -7i - (4 + 3i)

= -7i - 4 - 3i

= -4 - 10i

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Answer:

2880 seats

Step-by-step explanation:

r1 r2 r3 r36

20 + 20+4 + 20+4+4 + ···+20+4×35

total seats = ((20 + 20+4×35)÷2)×36= 2880

The approximate value of log₈1000 is 0.30.

                [tex]log_{10}x[/tex] [tex]= ln(x) / ln(10)[/tex]

The given values are:

In 8 ≈ 2.08 and In 1000 ≈ 6.91

To find the approximate value of log₈1000,

log₈1000 =  In 8/In 1000

              = 2.08/6.91

              ≅ 0.30

Therefore, the approximate value of log₈1000 is 0.30.

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the expression for the given situation is given as follows,

12.25x + 3.99 = 77.49 $

here, x = no. of shirt

so the correct answer is option D

The answer is A, because if one minute corresponds to 10 gallons of water, then the amount of gallons is the minutes times 10.

The relation given can be classified as a function as every single input corresponds to a single output value.

The difference between a relation and a function lies in the fact that a relation can have many outputs for a single input, but a function has a single input for a single output. The statement above is the distinctive property between a relation and a function.

The relation given in the task content is a function as every single input has a single output as evident in the function.

Hence, the domain of the function is; {x | x : 0, 2, 3} while the range is; {y | y : 0, 22, 33}.

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Answer:

80

Step-by-step explanation:

→ Work out how many rabbits after 60 days

20 rabbits

→ Work out how many rabbits after 90 days

40 rabbits

→ Work out how many rabbits after 120 days

80 rabbits

Answer:  D

Step-by-step explanation:

A. [tex]P=2(4)-3=5[/tex]

B. [tex]P=2(0)-3=-3[/tex]

C. [tex]P=2(0)-0=0[/tex]

D. [tex]P=2(4)-0=8[/tex]

Total pay be the at the end of the two weeks with rate of  $13.25 per hour and commission of $150 for selling each new car is $1319.75.

As given,

Rate of salesperson per hour pay = $13.25

Commission on selling each new car =$150

Amount of the pay earned by salesperson:

First week :

25 (13.25) + 3 (150)

= 331.25 + 450

= $781.25

Second week:

18 (13.25) + 2(150)

= 238.5 +300

= $538.50

Total pay of salesperson at the end of two weeks

=$(781.25 +538.5)

=$1319.75

Therefore, total pay be the at the end of the two weeks with rate of  $13.25 per hour and commission of $150 for selling each new car is  $1319.75.

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Answer:

Step-by-step explanation:

Given isosceles trapezoid MNFD with short base NF = 6 cm, diagonal ND perpendicular to leg MN, and triangle MND median NX = 5 cm, you want ...

MD is the hypotenuse of right triangle MND. The median from the right angle of a right triangle is half the length of the hypotenuse, so ...

  MD = 2·NX = 2·(5 cm)

  MD = 10 cm

In the attached diagram, we see that right triangle XYN has side XY = 3 (half of NF), and hypotenuse NX = 5 (given). These are two sides of a 3-4-5 right triangle, so the remaining side, altitude h, is 4.

  h = 4 cm

The attache diagram shows congruent side lengths MN and FD are the hypotenuse of a right triangle with sides YM = 2 and YN = 4. The Pythagorean theorem tells us the length of side MN is ...

  MN² = MY² +NY²

  MN² = 2² +4² = 4 +16 = 20

  MN = √20

  MN = FD = 2√5 ≈ 4.47

Triangle MND has a base length MD = 10 and a height h = 4. Triangle NFD has a base length NF = 6 and a height h = 4. The ratio of the areas of these two triangles is ...

  [tex]\dfrac{A_{MND}}{A_{NFD}}=\dfrac{\frac{1}{2}\cdot10\cdot4}{\frac{1}{2}\cdot6\cdot4}=\dfrac{10}{6}=\boxed{\dfrac{5}{3}}[/tex]

The ratio between the areas is 5 : 3.

__

Additional comment

We are also given the area of the trapezoid as 32 cm². That can be used to find the longer base and/or the altitude, or to check the answers we have for those values. It is redundant information.

The midpoint X of MD is the center of the circumscribing circle of the trapezoid and right triangles MND and MFD. The midpoint of the hypotenuse of a right triangle is always the circumcenter, so knowing the length NX tells us the radius of that circle, hence MX and XD.

Given:

Ratio of ounces of oil to gallons of gasoline = 9 : 11

Gallons of gasoline = 55 gallons

Let's find the ounces of oil.

To find the ounces of oil, we have the equation:

Thus, we have:

Let x represent the ounces of oil.

Cross multiply:

Therefore, there are 45 ounces of oil.

ANSWER:

45 ounces of oil

Let the smallest angle be represented as

Step 1: The largest angle of a triangle(let the largest angle =z) measures 9degrees less than 5 times the measure of the smallest angle, this statement is represented as

Step 2: let's calculate the middle angle (let the middle angle =y)

The middle angle measures three times that of the smallest angle, which means that

Recall that the total angles in a triangle give

Therefore,

Substituting we will have

Hence,

the smallest angle is = 21 degrees

Hence,

The largest angle = 96 degrees

Hence,

The middle angle = 63 degrees

The probability that the randomly selected sample is vulnerable or critically endangered is equal to 0.76

The probability can be determined using the following formula;

probability = number of desired events or outcomes ÷ total number of events or outcomes

The total is known to be 45, the favorable or desired outcomes can be calculated as follows;

number of desired outcomes = number of vulnerable species + number of critically endangered species

number of desired outcomes = 12 + 22

number of desired outcomes = 34

Now we calculate the probability by using the above formula;

probability = 34 ÷ 45

probability = 0.76

Therefore, 0.76 is the probability that the randomly selected species is vulnerable or critically endangered.

Although a part of your question is missing, you might be referring to this question:

In a random sample of 45 endangered species, 12 are categorized as vulnerable, 11 are categorized as endangered, and 22 are categorized as critically endangered. what is the probability that a randomly selected species from this sample is vulnerable or critically endangered? group of answer choices

11/45

0.24

0.83

0.76

12/45

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