What are the domain and range of h(x) = 3|x|?

Answer:

[tex]\textsf{Vertex form}: \quad f(x)=(x-4)^2+2[/tex]

[tex]\textsf{Standard form}: \quad f(x)=x^2-8x+18[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{5.6 cm}\underline{Vertex form of a quadratic equation}\\\\$y=a(x-h)^2+k$\\\\where:\\ \phantom{ww}$\bullet$ $(h,k)$ is the vertex. \\ \phantom{ww}$\bullet$ $a$ is some constant.\\\end{minipage}}[/tex]

From inspection of the given graph:

Substitute the vertex and point (0, 18) into the vertex formula and solve for a:

[tex]\begin{aligned}y&=a(x-h)^2+k\\\implies 18&=a(0-4)^2+2\\18&=a(-4)^2+2\\18&=16a+2\\16a&=16\\a&=1\end{aligned}[/tex]

Substitute the found value of a and the vertex into the formula:

[tex]\implies y=1(x-4)^2+2[/tex]

[tex]\implies f(x)=(x-4)^2+2[/tex]

To write the equation in standard form, expand the brackets:

[tex]\implies f(x)=(x-4)^2+2[/tex]

[tex]\implies f(x)=(x-4)(x-4)+2[/tex]

[tex]\implies f(x)=x^2-8x+16+2[/tex]

[tex]\implies f(x)=x^2-8x+18[/tex]

The simple form of all the expressions are:

-3 + 4m + (-7) - 6m = -2m -10

6x + (-1) - 3x + 12 = 3x + 11

3xy +2z - 16 + 6xy = 9xy +2z - 16

-4x - 8 + 2x + (-3) - 5x = -7x - 11

3m² - m + 7 + 3m² + 1 = 6m² - m + 8.

What is the simple form of the polynomial?

f(x) = anxn + anxn+1 +... + a2x2 + a1x + a0 is the formula for a polynomial. The greatest power of x in an expression is the polynomial's degree. Polynomials of degree 0, 1, 2, 3, and 4 are constant (non-zero) polynomials, linear polynomials, quadratics, cubics, and quartics, respectively.

We have,

-3 + 4m + (-7) - 6m

6x + (-1) - 3x + 12

3xy +2z - 16 + 6xy

-4x - 8 + 2x + (-3) - 5x

3m² - m + 7 + 3m² + 1

The simple form of the expressions:

-3 + 4m + (-7) - 6m

= -2m -10

6x + (-1) - 3x + 12

= 3x + 11

3xy +2z - 16 + 6xy

= 9xy +2z - 16

-4x - 8 + 2x + (-3) - 5x

= -7x - 11

3m² - m + 7 + 3m² + 1

= 6m² - m + 8

Hence, the simple form of all the expressions are:

-3 + 4m + (-7) - 6m = -2m -10

6x + (-1) - 3x + 12 = 3x + 11

3xy +2z - 16 + 6xy = 9xy +2z - 16

-4x - 8 + 2x + (-3) - 5x = -7x - 11

3m² - m + 7 + 3m² + 1 = 6m² - m + 8

To learn more about the simple form of the polynomial visit,

https://brainly.com/question/24138077

#SPJ4

The rational function f(x) = (x - 3) / (x + 2) have a domain corresponding to any real number except x = - 2.

In this problem we find a defined rational functions whose numerator and denominator are both linear equation. The domain of a function is the set of all values of x such that f(x) exists.

By function theory, the domain of all linear equations is the set of all real numbers and the domain of rational equations is the domain of the numerator except the values of x such that the denominator becomes zero.

Then, we need to determine the values of x such that:

x + 2 = 0

x = - 2

The domain of the rational function f(x) = (x - 3) / (x + 2) is all the real numbers except x = - 2.

To learn more on rational equations: https://brainly.com/question/4356325

#SPJ1

Answer: 80

Step-by-step explanation:

⇒  −(8 − 12) + 60 + (−4)²

⇒ -(-4) + 60 + 16

⇒ 4 + 60 + 16

⇒ 80

Answer:

slope = 4

points on graph = (0,0), (1,4)

Step-by-step explanation:

line going through quadrants 1 and 3. Straight line.

Answer:

x = 3y/4 + 17/4 and

x = 5y/2 + 5/2

Step-by-step explanation:

hope this help

The equation of the line that is parallel to the line y = 1/2x + 2 is: y = 1/2x + 5/2.

Recall that if two lines are parallel, they will have the same slope (m).

Slope of a line (m) = change in y / change in x.

The slope (m) of the equation, y = 1/2x + 2, that represents a line is 1/2.

This means that the line that is parallel to it will also have a slope (m) that is equal to 1/2.

Find the y-intercept by substituting m = 1/2 and (x, y) = (1, 3) into y = mx + b:

3 = 1/2(1) + b

3 = 1/2 + b

3 - 1/2 = b

5/2 = b

b = 5/2

To write the equation of the parallel line, substitute m = 1/2 and b = 5/2 into y = mx + b:

y = 1/2x + 5/2.

Learn more about the equation of parallel line on:

https://brainly.com/question/11345748

#SPJ1

Answer:

[tex]\frac{3}{8}[/tex]

Step-by-step explanation:

To find the y-intercept you need to put convert it into the equation:

y = mx + b where b = the y-intercept.

12x + 16y = 6. First rearrange the equation so y is on side of the equation.

16y = -12x + 6. Now divide by 16 so the equation has y as a stand alone value.

y = [tex]\frac{-3}{4}[/tex]x + [tex]\frac{3}{8}[/tex]

Therefore the y-intercept is [tex]\frac{3}{8}[/tex]

There are 300 students at Josefa Espinoza School.

reported viral illnesses very ... so the

in charge of the health of the Wisconsin area health department,

The study was in total in a sample of 60

According to the question. A journal article that involves a statistical study.

find:

a) The study descriptive or inferential

Yes, know the study is infrential according to the obtained from

Data

find :-) The Variable used in study. low,

과 a continuous variable. is size and weight

Know The sample is varied and representative

The value of c is 0 guaranteed by the Mean Value Theorem for Integrals for the function 2x+1 on the interval [3,6].

Mean value theorem states, roughly, that for a given planar arc between two endpoints, there is at least one point at which the tangent to the arc is parallel to the secant through its endpoints.

Given.

Function is 2x+1 on the interval [3,6]

f(x)=2x+1

f(x) continuous on [3, 6] and differentiable on (3, 6) so the MVT applies here.

f(3)=7

f(6)=13

Average rate of change of f on [3,6]

= (13-7) / (6-3) = 6/3=2

To find the c-value guaranteed by the MVT, such that the instantaneous rate of change when x = c is 2, we differentiate, set f'(x) = 2, and solve:

f'(x) = 2 and x = 1.

c = 0 is the only c-value in the interval at which the instantaneous rate of change = the average rate of change.

Hence, the value of c is 0 guaranteed by the Mean Value Theorem for Integrals for the function 2x+1 on the interval [3,6].

To learn more on mean value theorem click:

https://brainly.com/question/1581272

#SPJ1

Answer:

C) y - 2 = 2 ( x - 3 )

Step-by-step explanation:

This is point-slope form btw. Hope it helps!

Answer:

The table in the attached figure N 1

The graph in the attached figure n 2

Step-by-step explanation:

we have

x+2=y

we know that

To graph a linear equation the best way is plot the intercepts

Find the y-intercept

The y-intercept is the value of y when the value of x is equal to zero

For x=0

0+2=y

y=2

The y-intercept is the point (0,2)

Find the x-intercept

The x-intercept is the value of x when the value of y is equal to zero

For y=0

x+2=0

x=-2

The x-intercept is the point (-2,0)

Find additional points to create a table (is not necessary for plot the line)

For x=1

1+2=y

y=3

For x=2

2+2=y

y=4

The table in the attached figure N 1

Graph the linear equation ------> plot the intercepts a joined the points

see the attached figure N 2

If ratio of a to b is constant, and a = 9 when b = 6 then value of b is 4/3 when a is 2.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Given,

The ratio of a to b is constant,

a = 9 when b = 6.

We need to find value of b when a=2.

Let us consider the value be x.

Let us form an equation

9/6=2/x

Apply cross multiplication

9x=12

Divide both sides by 9

x=12/9=4/3

Hence, if ratio of a to b is constant, and a = 9 when b = 6 then value of b is 4/3 when a is 2.

To learn more on Ratios click:

https://brainly.com/question/13419413

#SPJ1

Answer:

#1. -6/7

#2. -3.2

Step-by-step explanation:

#1. (-2/7) + (-4/7)

You are adding two negative numbers.

When you add two positive numbers or two negative numbers, just ignore the signs and add the numbers as positive numbers. Then the answer has the same sign as the original numbers.

Step 1. Ignore the signs and make both numbers positive.

Add 2/7 and 4/7.

2/7 + 4/7 = 6/7

Step 2. Since the two numbers are originally negative, the answer is negative.

(-2/7) + (-4/7) = -6/7

#2. 5.4 + (-8.6)

When you add a positive number and a negative number, first make both numbers positive. Then, subtract the smaller positive number from the larger positive number. Finally, the answer has the same sign as the original number that corresponds to the larger positive number.

Here we do it step by step.

5.4 + (-8.6)

Step 1. Make both numbers positive. The numbers now are:

5.4 and 8.6

Step 2. Subtract the smaller positive number from the larger positive number.

8.6 - 5.4 = 3.2

Now look at the two positive numbers. 5.4 and 8.6. The larger number is 8.6. The original number that 8.6 came from is -8.6, a negative number, so the answer is negative.

5.4 + (-8.6) = -3.2

Answer:

Step-by-step explanation:

y - y₁ = m (x - x₁) would be your formula, since it's parallel you already have your slope, -x (which also equals 1 so technically -1). You have a point (8,9) and a slope -1, all you need to do is plug it in the formula.

Hope this helped!!

Answer: False

Step-by-step explanation:

This is because when u simplify 32x = 3(5x−8), it is 32x = 15x - 24

When u simplify 3(2x) = 3(5x − 8), you will get 6x = 15x - 24

Answer:

check the attached file

Step-by-step explanation:

Midpoint of the line segment from (1,-3) to(-5,2) is (-2,-1/2).

A straight line is just a line with no curves. So, a line that extends to both sides to infinity and has no curves is called a straight line.

The midpoint of a line segment is a point that lies exactly halfway between two points

The formula for midpoint (x,y)=(x₁+x₂/2,y₁+y₂/2)

We need to find midpoint of the line segment from (1,-3) to(-5,2)

Midpoint=(1-5/2,-3+2/2)

=(-4/2, -1/2)

=(-2,-1/2)

Hence, midpoint of the line segment from (1,-3) to(-5,2) is (-2,-1/2).

To learn more on Straight lines click:

https://brainly.com/question/29223887

#SPJ1

The values of the composite functions are

(r * q)(5) = 96

(q * r)(5) = 96

From the question, we have the following functions that can be used in our computation:

q(x) = x² + 7

r(x) = √(x + 4)

The composite functions are given as

(r * q)(5) and (q * r)(5)

The base functions of the above composite functions are

(r * q)(x) and (q * r)(x)

And they are calculated using

(r * q)(x) = r(x) * q(x)

(q * r)(x) = q(x) * r(x)

Substitute the known values in the above equations

So, we have the following equations

(r * q)(x) = (x² + 7) * (√(x + 4))

(q * r)(x) = (√(x + 4)) * (x² + 7)

Substitute 5 for x

(r * q)(5) = (5² + 7) * (√(5 + 4))

(q * r)(5) = (√(5 + 4)) * (5² + 7)

Evaluate the equations

(r * q)(5) = 96

(q * r)(5) = 96

Hence, the solution of the composite functions is 96

Read more about composite functions at

https://brainly.com/question/28949175

#SPJ1

Answer:

67.38

Step-by-step explanation:

134.76/2 = 67.38

May I please have brainliest for this? Thank you!

Answer:

120

Step-by-step explanation:

MNT is equal to RQT.

That means R equal to M, T equal to T, equal to N.

Q also equals 180-(T+R)

Q=180-(35+25)

Q=180-60

Q=120

Using the formula of simple interest, the total interest paid on a $20000 loan at rate of 2% over 4 years is $1600

Simple interest is calculated with the following formula: S.I. = P × R × T, where P = Principal, R = Rate of Interest in % per annum, and T = Time, usually calculated as the number of years. The rate of interest is in percentage r% and is to be written as r/100.

The formula is given S.I = P(1 + RT)

Data;

S.I = 20000(1 + 0.02 * 4)

S.I = 21600

The total interest paid is 21600 - 20000 = 1600

Learn more on simple interest here;

https://brainly.com/question/3575751

#SPJ1

The Range and Domain for the apples as per the given information is (1, 20) and (1, 20).

The difference between the greatest and lowest values of a set of integers is defined as its range. To find it, subtract the distribution's lowest number from its highest.

Because the term "range" can have multiple meanings, it is recommended that it be defined the first time it is used in a textbook or article. When older books use the term "range," they usually indicate what is currently known as the codomain. More recent works, if they use the phrase "range," usually use it to refer to what is now known as the picture. A number of current books avoid using the word "range" entirely to avoid confusion.

Given,

We need to spend $20 for each apple

And also given that,

The cost of each apple is $1

Here the independent variables are apples

Range=(1, 20)

Domain=(1, 20)

To know more about range, visit:

https://brainly.com/question/28135761

#SPJ1

The required property justifies the step is an addition property of equality.

What is mathematical property?

The rules governing how numbers relate to and interact with one another are known as mathematical properties. There are four fundamental properties. i.e. distributive, addition, commutative and subtraction.

Given, 2x +3 = -5x -1

Applying addition property of equality,

Adding 5x to both sides, we get

7x + 3 = -1

Hence, the required property justifies the step is an addition property of equality.

To learn more about mathematical property

https://brainly.com/question/6780033

#SPJ1

Answer:

Interval for constant cost = [0, 10,000] same as 0 <= x <= 10,000

Interval for increasing cost = (10,000, ∞) same as 10,000 < x < ∞

Be careful! note the use of different types of parentheses for each answer part as explained below

Step-by-step explanation:

We are only being asked for the two intervals, not the function definition itself which would have made it a little bit more work. A function has inputs and outputs. Here the input is gallons of water and output is $ cost.

Normally when asked for intervals we use a variable. Let's call it x which represents the gallons of water used

Since there is a base rate of $11.70 whether or not any water is consumed as long as it is less than or equal to 10,000 gallons we can state that over the interval 0 to 10000 (inclusive), the cost is constant

We can represent this interval in two ways
0 ≤ x ≤ 10,000

Another way of representing this interval is what we call interval notation. In interval notation the same thing  can be expressed as:

[0, 10000]    

Here 0 is referred to as the lower limit or bound(minimum) and the 10,000 is referred to as the upper limit or upper bound

Note the use of square brackets. This means that both upper and lower limits are included in the function. Such an interval is also called a closed interval.

After 10,000 gallons, the cost keeps increasing. There is no upper limit on the usage of water. So the lower limit is 10,000  (but does not include that number) and upper limit is infinity

We represent this interval as
10000 < x < ∞

Note that both upper and lower limits are excluded since ∞ is not realistic.

In interval notation this is represented as
(10000, ∞)

Here we are using regular brackets(parentheses) because this interval does not include lower and upper limits

This kind of interval is known as an open interval

Looks like the purpose of this question is to make sure what you understand in terms of interval notation and possibly open and closed intervals. The only relevant number there is the 10,000 gallons which represents the upper bound on the first interval. All the other numbers can be junked

Hope that is of help even if it was wordy

The value of n (FUGUR) will be;

⇒ n (FUGUR) = 112

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The data of mathematics students is,

60 study French, 30 study French and German

55 study German, 25 study French and Russian

75 study Russian, 35 study German and Russian

12 students study all the three languages.

Now,

Let F, G, R denote the set of students studying French, German and Russian respectively.

And, The data of mathematics students is,

n (F) = 60, n (F ∩ G) = 30

n (G) = 55, n (F ∩ R) = 25

n (R) = 75 , n (G ∩ R) = 35

n (F ∩ G ∩ R) = 12

Since, We know that;

⇒ n (FUGUR) = n (F) + n (G) + n (R) - n (F ∩ G) - n (F ∩ R) - n (G ∩ R)

                        + n (F ∩ G ∩ R)

Substitute all the values, we get;

⇒ n (FUGUR) = n (F) + n (G) + n (R) - n (F ∩ G) - n (F ∩ R) - n (G ∩ R)

                        + n (F ∩ G ∩ R)

⇒ n (FUGUR) = 60 + 55 + 75 - 30 - 25 - 35 + 12

⇒ n (FUGUR) = 112

Thus, The value of n (FUGUR) will be;

⇒ n (FUGUR) = 112

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ1

Answer:

9x + 6

Step-by-step explanation:

SOLUTION GIVEN: a number is divided by 9 and the remainder is 6,

TO DETERMINE: The remainder when six times the number is divided by 9

EVALUATION: Here it is given that the number is divided by 9 & the remainder is 6

We know that Dividend = Divisor × Quotient + Remainder 

By the given Divisor = 9

Remainder = 6

Let quotient = x

Then the number = Dividend = 9x + 6

Hence, the fractuon of the animals at the zoo are elephants is [tex]\frac{7}{12}[/tex].

What is the fraction?

A fraction defined as the part of the whole thing.

Fractions help to distribute and judge the numbers easily and make the calculation faster.

Here given that,

At the zoo [tex]\frac{1}{3}[/tex] of the animals are mammals [tex]\frac{1}4}[/tex] of the mammals are elephants.

So, the fraction of the animals at the zoo are elephants is

[tex]\frac{1}3}+\frac{1}{4}=\frac{4+3}{12}\\\\=\frac{7}{12}[/tex]

Hence, the fractuon of the animals at the zoo are elephants is [tex]\frac{7}{12}[/tex].

To know more about the fraction

https://brainly.com/question/8473591

#SPJ1

Taking into account the definition of a system of linear equations, the solution of the linear equation is (12,5).

A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.

Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied.

In this case, the system of equations to be solved is

y = 3/4x-4

y= -1/2x+11​

There are several methods to solve a system of equations, it is decided to solve it using the graphical method. This method consists of representing the graphs associated with the equations of the system to deduce its solution. The solution of the system is the point of intersection between the graphs since the coordinates of said point satisfy both equations.

In this case, graphing both equations, it is obtained that the point of intersection, and therefore the solution, is (12,5).

The graph of the system of equations is attached.

Learn more about system of equations:

brainly.com/question/19803308

#SPJ1