Find the measure of the arc or angle indicated by the question mark.

The domain of g(x)= 3x^2 is Real number and it's range is {y∈R / y≥0}

The domain of h(x)= -3x^2 is Real number and it's range is {y∈R / y ≤0}

The domain of a function f(x) is the set of all values for which the function is defined, and the domain of a function is the set of all values that f takes on. The domain and range are defined for a relation and are the sets of all x-coordinates and all y-coordinates of ordered pairs.

The graph of f(x)= x^2 is given

We need to find the domain and range of g(x)=3x^2 and h(x)= -3x^2

The Graph of 3x^2 is different from x^2 in terms of plotting

When ,

x= -2 g(x)=12

x=-1 g(x)=3

x=0 g(x)=0

x=1 g(x)=3

x=2 g(x)=12

The Graph of -3x^2 is different from x^2 in terms of plotting

When ,

x= -2 g(x)=-12

x=-1 g(x)= -3

x=0 g(x)=0

x=1 g(x)= -3

x=2 g(x)=-12

Domain of g(x) is R and it's range is {y∈R / y≥0}

Domain of h(x) is R and it's range is {y∈R / y ≤0}

Learn more about domain and range here:

https://brainly.com/question/28100489

#SPJ1

Answer:

120 ft cubed

Step-by-step explanation:

V=lwh

V=10(4)(3)

V=120 ft cubed

The domain of the graph is the set of all real values

The domain is the set of x values of the graph

From the graph, the x values extend in both directions without end

This means that the x values can accommodate all real values

Hence, the domain of the graph is the set of all real values

Read more about domain at:

https://brainly.com/question/13113489

#SPJ1

Answer: See the attached image below for the filled in table.

=========================================================

Explanation:

The domain is the set of all allowed x inputs of a function.

The term "radicand" refers to the stuff under the square root.

We cannot have a negative number under the square root. Therefore, the radicand must be 0 or larger.

The first function must have [tex]4x+6 \ge 0[/tex] which becomes [tex]4x \ge -6[/tex] and leads to [tex]x \ge -\frac{6}{4}[/tex] aka [tex]x \ge -\frac{3}{2}[/tex]

So x = -3/2 is the smallest input allowed. Which is where the interval notation of [tex]\left[-\frac{3}{2}, \infty)[/tex] comes from. It's the interval spanning from -3/2 (inclusive) to infinity. This represents the set of all possible x inputs of the first function.

--------

Follow this same idea for problem 2. The steps would be something like this:

[tex]-20x - 6 \ge 0\\\\-20x \ge 6\\\\x \le \frac{6}{-20}\\\\x \le -\frac{3}{10}\\\\[/tex]

The inequality sign flips because we divided both sides by a negative number. That then leads to the interval notation of [tex](-\infty, -\frac{3}{10}\big][/tex]

The interval spans from negative infinity (exclusive) to -3/10 (inclusive).

--------

Problem 3 would have these steps

[tex]5x-16 \ge 0\\\\5x\ge 16\\\\x\ge \frac{16}{5}\\\\\big[\frac{16}{5}, \infty)\\\\[/tex]

No sign flip happens since we divided both sides by a positive number.

--------

Lastly, here are the steps for problem 4

[tex]20+6x \ge 0\\\\6x \ge -20\\\\x \ge -\frac{20}{6}\\\\x \ge -\frac{10}{3}\\\\\big[-\frac{10}{3}, \infty)[/tex]

Don't forget to use the square bracket to include the endpoints mentioned. We always use curved parenthesis for either infinity because we can't ever reach infinity. In a sense, we "approach" infinity.

Once again, all of this is summarized in the filled out table shown below (attached image). Feel free to ask any questions if they come to mind.

Answer:  [tex]f^{-1}(\text{x}) = (\text{x}-9)^2+4[/tex] when [tex]\text{x} \ge 9[/tex]

=================================================

Work Shown:

[tex]f(\text{x}) = 9 + \sqrt{\text{x} - 4}\\\\\text{y} = 9 + \sqrt{\text{x} - 4}\\\\\text{x} = 9 + \sqrt{\text{y} - 4}\\\\\text{x}-9 = \sqrt{\text{y} - 4}\\\\(\text{x}-9)^2 = (\sqrt{\text{y} - 4})^2\\\\(\text{x}-9)^2 = \text{y}-4\\\\(\text{x}-9)^2+4 = \text{y}\\\\f^{-1}(x) = (\text{x} - 9)^2+4[/tex]

Explanation:

I replaced f(x) with y. After that I swapped x and y, then solved for y to get the inverse.

The smallest that [tex]\sqrt{\text{x}-4}[/tex] can get is 0, which means the smallest f(x) can get is 9+0 = 9. The range for f(x) is [tex]\text{y} \ge 9[/tex]

Since x and y swap to determine the inverse, the domain and range swap roles. Therefore, the domain of the inverse [tex]f^{-1}(\text{x})[/tex] is [tex]\text{x} \ge 9[/tex]

So we will only consider the right half portion of the parabola.

The graph is below. The red curve mirrors over the black dashed line to get the blue curve, and vice versa.

Answer:

[tex]f^-^1(x)=(x-9)^2+4[/tex]   OR [tex]x^2-18x+85[/tex] if you simplify it

Step-by-step explanation:

to find the inverse function you have to switch x and y with each other and solve for y.

[tex]y=9+\sqrt{x-4}\\x=9+\sqrt{y-4}[/tex]           step 1: switch x and y with each other

[tex]x-9=\sqrt{y-4}[/tex]           step 2: subtract 9 from both sides

[tex](x-9)^2=\sqrt{y-4}^2[/tex]     step 3: square both sides to get rid of the square root

[tex](x-9)^2=y-4\\(x-9)^2+4=y\\[/tex]         step 4: add 4 to both sides

you could leave the answer like this or you can simplify to get [tex]x^2-18x+85[/tex]

The linear inequality of the given graph is: D. y < -2x + 3.

First, using two points on the line, (0, 3) and (1.5, 0), find the slope (m).

Slope (m) = change in y / change in x = (3 - 0) / (0 - 1.5)

Slope (m) = 3/-1.5 = -2.

Next, substitute (x, y) = (0, 3) and m = -2 into y = mx + b to find the value of b.

3 = -2(0) + b

3 = 0 + b

b = 3

Substitute m = -2 and b = 3 into y < mx + b (the shaded part is at the left, so we use the "<" sign)

y < -2x + 3

Learn more about inequality graph on:

https://brainly.com/question/9774970

#SPJ1

It is important to be able to express a clear and coherent argument visually or in writing because without establishing coherence, your reader will not be able to know or understand the key points that you are trying to express or show.

Coherence is known to be a key quality for kind of good academic write up.

Note that in the area of academic writing, the ways that ideas flows is very important and as such, it need to be smooth and logical.

Therefore  without coherent argument , the reader cannot understand the key points that a person is trying to show and thus hinders the readability of your work.

Learn more about coherent argument from

https://brainly.com/question/1415305

#SPJ1

Answer:

y = -1.5x + 3.5

Step-by-step explanation:

Slope intercept form is y=mx+b.

3x + 2y = 7

2y = -3x + 7

y = -1.5x + 3.5

Answer:

-3/2x+7/2=y

Step-by-step explanation:

Answer:

First, use the distributive property and distribute 8 to the [tex](x,2)[/tex] in the first part of the equation to get [tex]8x + 16[/tex].

Next, also use the distributive property to distribute the 4 to the [tex](2x+9)[/tex] in the second part of the equation to get [tex]8x+36[/tex].

The simplified equation looks like this: [tex]8x+16=8x+36[/tex].

The answer is k = 7.

As the graph has been shifted down 7 units, the translation can be represented as :

g(x) = f(x) - 7

(0.5)x - k = (0.5)x - 7

k = 7

Deposit $625 into a money market account with a 5% rate for 1 year would result in more money.

To do this, we make use of 1.50% interest rate

Here, we have:

Initial, a= 625

Rate, r = 1.5%

The exponential growth equation is

A(t) = a * (1 + r)^t

So, we have:

A(t) = 625 * (1 + 1.5%)^t

Evaluate

A(t) = 625 * 1.015^t

Hence, the exponential growth equation is A(t) = 625 * 1.015^t

Here, t = 25.

So, we have:

A(25) = 625 * 1.015^25

Evaluate

A(25) = 906.84

Hence, the value in 25 years is $906.84

#Investment A

a = 625

r = 1.5%

t = 5

So, we have:

A(5) = 625 * 1.015^5

Evaluate

A(5) = 673.3

#Investment B

a = 625

r = 5%

t = 1

So, we have:

A(1) = 625 * 1.5^1

Evaluate

A(1) = 937.5

By comparison, 937.5 is greater than 673.3

Hence, deposit $625 into a money market account with a 5% rate for 1 year would result in more money.

Read more about exponential growth equation at:

https://brainly.com/question/23729449

#SPJ1

The option which makes more sense for Jake to choose is option (1) He can accept the tie, and the game is over.

The complete question is added as an attachment

From the complete question, the probability in part D is

Probability = 33.5%

The options to choose one from are:

The calculated probability is less than 0.5.

This means that Jake is more likely to lose than win

So, the best option for Jake is option (A) walk away

Hence, the option which makes more sense for Jake to choose is option (1) He can accept the tie, and the game is over.

Read more about probability at:

https://brainly.com/question/24756209

#SPJ1

The angle m∠ABC is 70 degrees.

The angle in a rhombus can be found as follows;

The opposite angle of a rhombus are congruent.

Therefore,

∠B = 140 degrees

Hence, the diagonal of a rhombus bisect an angle.

Therefore,

m∠ABC = 140 / 2

m∠ABC = 70 degrees.

learn more on rhombus here: https://brainly.com/question/11966028

#SPJ1

Answer:

#3

Step-by-step explanation:

To create a number line to represent x<= 0, draw a solid circle at 0 (because 0 is included), then draw an arrow extending to the left (because it's less than or equal to).

Answer:

the answer is 17y 3y+6y is 9y plus 8y is 17y

Step-by-step explanation:

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Equation:}[/tex]

[tex]\mathsf{3y + 6y + 8y}[/tex]

[tex]\huge\textbf{Simplifying it:}[/tex]

[tex]\mathsf{3y + 6y + 8y}[/tex]

[tex]\huge\textbf{Combine the like terms:}[/tex]

[tex]\mathsf{(3y + 6y + 8y)}[/tex]

[tex]\mathsf{\rightarrow 3y + 6y + 8y}[/tex]

[tex]\huge\textbf{Simplify it:}[/tex]

[tex]\mathsf{\rightarrow 3y + 6y + 8y}[/tex]

[tex]\mathsf{\rightarrow 9y + 8y}[/tex]

[tex]\mathsf{\rightarrow 17y}[/tex]

[tex]\huge\textbf{Therefore, your answer should be: }[/tex]

[tex]\huge\boxed{\mathsf{17}\mathsf{y}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

98.3, 94.1, 89.9, 85.7 (Arithmetic)

1, 0, -1, 0 (Neither)

1.75, 3.5, 7, 14 (Geometric)

-1, 1, -1, 1..... (Geometric)

An arithmetic sequence has a common difference

A geometric sequence has a common ratio

Considering the given sequences one after the other:

For 98.3, 94.1, 89.9, 85.7,..........

The common difference, d = 94.1 - 98.3 = -4.2

Therefore, 98.3, 94.1, 89.9, 85.7 is an arithmetic sequence

For 1, 0, -1, 0......

The sequence does not have a common difference or a common ratio. Therefore, it is neither an arithmetic nor geometric sequence

For 1.75, 3.5, 7, 14,.....

The common ratio = 3/1.75 = 2

Therefore, it is a geometric sequnec

For -1, 1, -1, 1.....

The common ratio = 1/-1 = -1

It is a geometric sequence

Learn more on arithmetic and geometric sequences here: https://brainly.com/question/13613396

#SPJ1

Laura's walking speed is 4.50 feet per second.

Speed is the total distance travelled per time. Speed can be determined by dividing the distance walked by Laura by the time.

Average speed = total distance / total time

54 / 12 = 4.50 feet per second

To learn more about speed, please check: https://brainly.com/question/21734785

#SPJ1

The different ratios are 2 : 7, 2 : 9 and 7 : 9

The statement is given as:

8 out of 36 squares unfilled

This means that:

The part-to-part ratio is represented as:

Ratio = Unfilled : Filled

This gives

Unfilled : Filled = 8 : 28

Simplify

Unfilled : Filled = 2 : 7

The part-to-whole ratios are represented as:

Ratio = Unfilled : Total

Ratio = Filled : Total

So, we have:

Unfilled : Total = 8 : 36

Filled : Total = 28 : 36

Simplify

Unfilled : Total = 2 : 9

Filled : Total = 7 : 9

Hence, the different ratios are 2 : 7, 2 : 9 and 7 : 9

Read more about ratio at:

https://brainly.com/question/2328454

#SPJ1

Answer:

26.

Step-by-step explanation:

(11+14+23+16+x) / 5 = 18   where x is the value to be added.

(64 + x) / 5 = 18

64 + x = 90

x = 90 - 64

  =  26.

Answer:The radius is √16.

Step-by-step explanation:

Answer:

x-intercept = 8

Step-by-step explanation:

Hello!

An x-intercept is when the y-value is 0, or when the graph intersects the x-axis.

We can replace p(x) with 0 and solve for x.

The x-intercept is 8.

Answer:

104 miles.

Step-by-step explanation:

5 inches is 2 * 2.5 inches so the distance required is 2*52 = 104 miles.

Answer:

That is a variable.

Step-by-step explanation:

- opposed to a constant which is known and does not change.

Answer:

28.26658805 (I included every digit in case your teacher needs you to round)

Step-by-step explanation:

In order to find x, we need to isolate x by subtracting 15^2 and taking the square root of both sides.

Thus, we have:

[tex]15^2+x^2=32^2\\x^2=32^2-15^2\\\sqrt{x^2} =\sqrt{(32^2-15^2)} \\\sqrt{x^2}=\sqrt{799} \\x=28.26658805[/tex]

Answer:

Undefined

Step-by-step explanation:

No multiplicative inverse exists for 0

Answer:

undefined

Step-by-step explanation:

a single value can't be assigned to a fraction where the denominator is 0 so the value remains undefined.

Answer:

Below in bold.

Step-by-step explanation:

P = 1.50(1.065)^t        where P = population in millions and t = no. of years.

So we have

2.31 = 1.50(1.065)^t

(1.065)^t = 2.31/1.50

Taking logs:

t log 1.065 = log (2.31/1/50)

t  =   log (2.31/1/50) / log 1.065

  =  6.856 years.

Answer:

a) is the correct answer

Answer:

14 3/8 ft^2

Step-by-step explanation:

Area = length * width

=   2 7/8 * 5

=  23/8 * 5

= 115/8

= 14 3/8 ft^2.

Answer:

x ^ (1/3)

Step-by-step explanation:

solution:

the answer is in the picture I have sent.

I hope this will help you