The table shows three unique functions. (TABLE IN PIC) Which statements can be used to compare the characteristics of the functions? Select two options. f(x) has an all negative domain. g(x) has the greatest maximum value. All three functions share the same range. h(x) has a range of all negative numbers. All three functions share the same domain.
Answers
Answer:
Correct answers are:
g(x) has the maximum greatest value.
h(x) has a a range of all negative numbers.
Step-by-step explanation:
Let us learn about the domain and range of a function first.
Domain of a function is the input that we give to the function for which there is a valid output.
For example, let us consider a function:
[tex]y=F(x) = x^2[/tex]
So, the value of 'x' that we provide to the function is known as the domain of function.
Range of a function is the output value when any input is given to the function.
For example,
[tex]y=F(x) = x^2[/tex]
Let us put x = 4, which will be in the domain of function.
the output will be y = 16 which will be in the range of the function.
Now, let us consider the given functions f(x), g(x) and h(x).
Domain of f(x) i.e. the value of x for which the output is defined is:
{-2, -1, 1, 2}
Range of f(x) = [tex]\{4, 4\frac{1}2, 5\frac{1}2, 6\}[/tex]
Max value of f(x) = 6
Domain of g(x) i.e. the value of x for which the output is defined is:
{-2, -1, 1, 2}
Range of g(x) = [tex]\{6, 6\frac{1}2, 7\frac{1}2, 8\}[/tex]
Max value of g(x) = 8
Domain of h(x) i.e. the value of x for which the output is defined is:
{-2, -1, 1}
Range of h(x) = [tex]\{-3, -2\frac{1}2, -1\frac{1}2\}[/tex]
Max value of h(x) = [tex]-1\frac{1}2[/tex]
For x = 2, the value of h(x) is not given i.e. it is not defined at x = 2, so it is not in the domain. So, domain of all the three functions is not same.
So, the correct options are:
g(x) has the maximum greatest value.
h(x) has a a range of all negative numbers.
Answer:
B,D
Step-by-step explanation:
Edge 2020 100%
Related Questions
Simplfy the following expressions:
Answers
Answer:
1st one = d y^27
2nd one = b 2x^9
Step-by-step explanation:
1st one: since the power is being raised to the power of 3 you multiply the numbers
2nd one: the powers aren't being raised so you add the powers together.
12x^13y^10/6X^4y^10
then dividing for exponents is subtracting them so
2x^9 since y gets canceled out
Write the improper fraction as a mixed number 29/5
Answers
Answer:
5 4/5
Step-by-step explanation:
29 ÷ 5 = 5
29 - 25 = 4
Since 5x5 is 25 and we have 4 as a remainder we put it over the original denominator 5.
I really hope this helps.
29/5 as a mixed number is 5 and 4/5.
To convert the indecorous bit29/5 into a mixed number.
First, divide the numerator( 29) by the denominator( 5) and express the result as a whole number and a bit.
Now, 29 divided by 5 equals 5 with a remainder of 4.
The quotient( 5) becomes the whole number part of the mixed number, and the remainder( 4) becomes the numerator of the bit part, while the denominator remains the same.
Thus, 29/5 as a mixed number is 5 and 4/5.
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Brainliest to whoever gets this correct This word problem has too much information. Which fact is not needed to solve the problem? Tanisha tried to sell all her old CDs at a garage sale. She priced them at $2 each. She put 80 CDs in the garage sale, but she sold only 35 of them. How many did she have left? A. All of the information is needed. B. Tanisha sold the CDs for $2 each. C. Tanisha put 80 CDs in the sale. D. Tanisha sold 35 of the CDs.
Answers
Answer:
B. Tanisha sold the CDs for $2 each.
Step-by-step explanation:
In triangle ABC, the right angle is at vertex C, a = 714 cm and the measure of angle A is 78° . To the nearest cm, what is the length of side c?
Answers
Answer:
c = 730cm
Step-by-step explanation:
The first thing we would do is to draw the diagram using th given information.
Find attached the diagram.
a = 714 cm
the measure of angle A = 78°
To determine c, we would apply sine rule. This is because we know the opposite and we are to determine the hypotenuse
sin78 = opposite/hypotenuse
sin 78 = 714/c
c = 714/sin 78 = 714/0.9781
c= 729.99
c≅ 730 cm ( nearest cm)
Find the critical value z Subscript alpha divided by 2 that corresponds to the given confidence level. 80%
Answers
Answer:
[tex] Conf= 0.80[/tex]
With the confidence level we can find the significance level:
[tex]\alpha =1-0.8=0.2[/tex]
And the value for [tex]\alpha/2=0.1[/tex]. Then we can use the normal standard distribution and we can find a quantile who accumulates 0.1 of the area on each tail and we got:
[tex] z_{\alpha/2}= \pm 1.28[/tex]
Step-by-step explanation:
For this problem we have the confidence level given
[tex] Conf= 0.80[/tex]
With the confidence level we can find the significance level:
[tex]\alpha =1-0.8=0.2[/tex]
And the value for [tex]\alpha/2=0.1[/tex]. Then we can use the normal standard distribution and we can find a quantile who accumulates 0.1 of the area on each tail and we got:
[tex] z_{\alpha/2}= \pm 1.28[/tex]
Anja is choosing her extracurricular activities for the year. She can choose one sport to play and one instrument to learn using the list below:
Sports: softball, basketball, tennis, or swimming
Instruments: guitar, piano, or clarinet. How many combinations are possible?
Answers
Answer:
The number of possible combinations of sports and instrument that Anja can select is 12.
Step-by-step explanation:
In mathematics, the procedure to select k items from n distinct items, without replacement, is known as combinations.
The formula to compute the combinations of k items from n is given by the formula:
[tex]{n\choose k}=\frac{n!}{k!\cdot(n-k)!}[/tex]
It is said that Anja can choose one sport to play and one instrument to learn using the list below:
Sports: softball, basketball, tennis, or swimming
Instruments: guitar, piano, or clarinet.
There 4 options for sports and 3 for an instrument.
Compute the number of ways to select one sport to play as follows:
[tex]n (S)={4\choose 1}=\frac{4!}{1!\cdot(4-1)!}=\frac{4!}{3!}=\frac{4\times3!}{3!}=4[/tex]
Compute the number of ways to select one instrument to learn as follows:
[tex]n(I)={3\choose 1}=\frac{3!}{1!\cdot(3-1)!}=\frac{3!}{2!}=\frac{3\times2!}{2!}=3[/tex]
Compute the number of possible combinations of sports and instrument that Anja can select as follows:
Total number of possible combinations = n (S) × n (I)
[tex]=4\times 3\\=12[/tex]
Thus, the number of possible combinations of sports and instrument that Anja can select is 12.
Answer:
12
Step-by-step explanation:
Simplify: |4-5| / 9 × 3³ - 2/5 a.61/10 b.13/5 c.11/10 d.-2/15
Answers
━━━━━━━☆☆━━━━━━━
▹ Answer
Answer = b. 13/5
▹ Step-by-Step Explanation
|4 - 5| ÷ 9 × 3³ - 2/5
|-1| ÷ 9 × 3³ - 2/5
1 ÷ 9 × 3³ - 2/5
1/9 × 3³ - 2/5
1/3² × 3³ - 2/5
3 - 2/5
Answer = 13/5
Hope this helps!
- CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
Answer:
[tex] \boxed{\sf b. \ \frac{13}{5}} [/tex]
Step-by-step explanation:
[tex] \sf Simplify \: the \: following: \\ \sf \implies \frac{ |4 - 5| }{9} \times {3}^{3} - \frac{2}{5} \\ \\ \sf 4 - 5 = - 1 : \\ \sf \implies \frac{ | - 1| }{9} \times {3}^{3} - \frac{2}{5} \\ \\ \sf Since \: - 1 \: is \: a \: negative \: constant, \: |-1| = 1: \\ \sf \implies \frac{1}{9} \times {3}^{3} - \frac{2}{5} \\ \\ \sf {3}^{3} = 3 \times {3}^{2} : \\ \sf \implies \frac{ \boxed{ \sf 3 \times {3}^{2}} }{9} - \frac{2}{5} \\ \\ \sf {3}^{2} = 9 : \\ \sf \implies \frac{3 \times 9}{9} - \frac{2}{5} \\ \\ \sf \frac{9}{9} = 1 : \\ \sf \implies 3 - \frac{2}{5} [/tex]
[tex] \sf Put \: 3 - \frac{2}{5} \: over \: the \: common \: denominator \: 5 : \\ \sf \implies 3 \times \frac{5}{5} - \frac{2}{5} \\ \\ \sf \implies \frac{3 \times 5}{5} - \frac{2}{5} \\ \\ \sf 3 \times 5 = 15 : \\ \sf \implies \frac{ \boxed{ \sf 15}}{5} - \frac{2}{5} \\ \\ \sf \implies \frac{15 - 2}{5} \\ \\ \sf 15 - 2 = 13 : \\ \sf \implies \frac{13}{5} [/tex]
If we express $2x^2 + 6x + 11$ in the form $a(x - h)^2 + k$, then what is $h$? (ignore the $)
Answers
Answer:
h = - [tex]\frac{3}{2}[/tex]
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Given
y = 2x² + 6x + 11 ( factor out 2 from the first 2 terms )
= 2(x² + 3x) + 11
Using the method of completing the square
add/subtract ( half the coefficient of the x- term )² to x² + 3x
y = 2(x² + 2([tex]\frac{3}{2}[/tex] )x + [tex]\frac{9}{4}[/tex] - [tex]\frac{9}{4}[/tex] ) + 11
= 2(x + [tex]\frac{3}{2}[/tex] )² - [tex]\frac{9}{2}[/tex] + 11
= 2(x + [tex]\frac{3}{2}[/tex] )² + [tex]\frac{13}{2}[/tex] ← in vertex form
with h = - [tex]\frac{3}{2}[/tex]
Erika has 3 pieces of ribbon. Each piece is 25 yards long. She needs to cut pieces that are 22 inches long. What is the greatest number of 22 inch pieces she can cut from the 3 pieces of ribbon
Answers
Answer:
She can cut 122 pieces.
Step-by-step explanation:
She has 3 pieces of ribbon that are 25 yds long. In total, she has 75 yds, which is equal to 2700 in. Erika needs 22 in. pieces, so just divide 2700 by 22 to get your number.
2700/22 ≈ 122.72
76% is between which of the following two numbers?
Answers
Hey there!
You haven't provided any answer options but here's how you would solve a problem like this.
To find the number in between two numbers, you add it up and divide it by two!
So, what's between 1 and 3? Well you do 1+3 is 4 then divide by 2 you get 2!
100 and 580? You add them to get 680 then divide by two you get 340!
In between 0.57 and 0.69? Adding gives you 1.26 and then divide by two and we have 0.63!
And with percents, let's do 45% and 67%. You add you get 112% and then divide by two you have 56%!
So, with your answer options just add them up and divide by two and see which one gives you 76%!
I hope that this helps!
g The sampling distribution of the sample means is the curve that describes how the sample means are distributed. True or False Explain
Answers
Answer:
This Statement is True.
Check Explanation for why it is true.
Step-by-step explanation:
The sampling distribution of sample means arises when random samples are drawn from the population distribution and their respective means are computed and put together to form a distribution. Hence, the curve of this sampling distribution of sample means will show how the sample means are distributed. Hence, this statement is true.
Hope this Helps!!!
A tablet contains 0.5 mg of medication. A patient receives 5 tablets a day. How many mg patient receive per day?
Answers
Answer:
2.5 mg
Step-by-step explanation:
.5 x 5 = 2.5
Which sentence in this excerpt from Common Sense by Thomas Paine supports the claim that the American colonies could thrive independently from Britain? I have heard it asserted by some, that as America hath flourished under her former connection with Great Britain that the same connection is necessary towards her future happiness, and will always have the same effect. Nothing can be more fallacious than this kind of argument. We may as well assert that because a child has thrived upon milk that it is never to have meat, or that the first twenty years of our lives is to become a precedent for the next twenty. But even this is admitting more than is true, for I answer roundly, that America would have flourished as much, and probably much more, had no European power had any thing to do with her. The commerce, by which she hath enriched herself, are the necessaries of life, and will always have a market while eating is the custom of Europe.
Answers
Answer:
A
Step-by-step explanation:
Answer:
"But even this is admitting more than is true, for I answer roundly, that America would have flourished as much, and probably much more, had no European power had any thing to do with her."
Step-by-step explanation:
Checked 2021
Simplify. Remove all perfect squares from inside the square root. \sqrt{30b^5}= 30b 5
Answers
Answer:
The answer is b=0 or b=9.085603
The equation is solved and the perfect squares are removed from the square root and A = b²√( 30b )
What is an Equation?
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 = √( 30b⁵ )
On simplifying the equation , we get
We can simplify the given expression by breaking down the number inside the square root into its prime factors:
30b⁵ = 2 x 3 x 5 x b⁵
Since we are looking to remove all perfect squares, we can remove the factors of 2 and 3, which are the only perfect squares present in the prime factorization of 30. This leaves us with:
30b⁵ = 2 x 3 x 5 x b⁵
= 2 x 3 x 5 x b⁴ x b
= 30b⁴ x b
Therefore, we can simplify the original expression as:
√(30b⁵) = √(30b⁴ x b) = √(30b⁴) x √b
A = b²√30 x √b
Hence , the expression √(30b⁵) simplifies to A = b²√30 x √b
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Diane borrowed 8000 at a rate of 7%, compounded semiannually. Assuming she makes no payments, how much will she owe after 6 years?
Do not round any intermediate computations, and round your answer to the nearest cent.
Answers
Answer: $12088.55
Step-by-step explanation:
A = p(1+r/n)^nt
A = 8000(1+0.07/2)^2*6
A = 12088.54926
Given the figure below, find the values of x and Z.
Please explain step by step how to solve, this is a guide for a test.
Answers
Answer:
(x, z) = (7, 69)
Step-by-step explanation:
Easy first: 69° and z° are vertical angles, so congruent:
z = 69
__
The angle marked with an expression in x is supplementary to either of the other two:
(6x +69)° +69° = 180°
6x = 42 . . . . . . . . . . . . divide by °, subtract 138
x = 7 . . . . . . . . . . . . . . divide by 6
In this problem, y = c1ex + c2e−x is a two-parameter family of solutions of the second-order DE y'' − y = 0. Find a solution of the second-order IVP consisting of this differential equation and the given initial conditions. y(−1) = 9, y'(−1) = −9
Answers
Answer:
[tex]y(x)=\frac{9}{e^{1} } e^{-x} =3.310914971e^{-x}[/tex]
Step-by-step explanation:
This problem is very simple, since they give the solution for the differential equation from the start. So basically, you need to evaluate the initial conditions into the solution, and the derivative of the solution in order to find the value of the constants [tex]c_1[/tex] and [tex]c_2[/tex].
So, first of all, let's find the derivative of [tex]y(x)[/tex]:
[tex]y'(x)=c_1 e^{x} -c_2e^{-x}[/tex]
Now, let's evaluate the first initial condition:
[tex]y(-1)=c_1e^{-1} +c_2e^{-(-1)} =9\\\\c_1e^{-1} +c_2e^{1}=9\hspace{10}(1)[/tex]
Now, the second initial condition:
[tex]y'(-1)=c_1 e^{-1} -c_2e^{-(-1)}=-9\\\\c_1 e^{-1} -c_2e^{1}=-9\hspace{10}(2)[/tex]
Combining (1) and (2) we have a 2x2 System of Equations. Let's use elimination method in order to solve it:
[tex](1)+(2):\\\\c_1e^{-1} +c_2e^{1} +c_1e^{-1} -c_2e^{1}=9-9\\\\2c_1e^{-1} =0\\\\Hence\\\\c_1=0[/tex]
Replacing [tex]c_1[/tex] into (1)
[tex](0)e^{-1} +c_2e^{1}=9\\\\c_2e^{1}=9\\\\Hence\\\\c_2=\frac{9}{e^{1} } =3.310914971[/tex]
Therefore the solution of the second-order IVP is:
[tex]y(x)=\frac{9}{e^{1} } e^{-x} =3.310914971e^{-x}[/tex]
Which of the following cannot have a Discrete probability distribution? a. The number of customers arriving at a gas station in Christmas day b. The number of bacteria found in a cubic yard of soil. c. The number of telephone calls received by a switchboard in a specified time period. d. The length of a movie
Answers
Answer:
d. The length of a movie
Step-by-step explanation:
A discrete random variable is a variable which only takes on integer values.
A discrete distribution is used to describe the probability of the occurrence of each value of a discrete random variable.
From the given options, the length of a movie is not a discrete variable as it can have decimal values.
It therefore cannot have a Discrete probability distribution.
The correct option is D.
which term is the rate at which work is done
Answers
Answer:
The answer is power.Hope this helps you
Amit solved the equation StartFraction 5 over 12 EndFraction = Negative StartFraction x over 420 EndFraction for x using the steps shown below. What was Amit’s error?
Answers
Answer:
The product of 5/ 12 and –420 should have been the value of x.
Answer: D
Step-by-step explanation:
Took the test
Classify the following triangle. Check all that apply.
A. Isosceles
B. Right
C. Obtuse
D. Equilateral
E. Scalene
F. Acute
Answers
Answer:
Equilateral
Acute
Step-by-step explanation:
The sides are all equal as indicated by the lines on each side - Equilateral
The angles are all equal by the angle marks 180/3 = 60 which is less than 90 degrees. This makes the angles acute
Use the standard normal table to find P(z ≥ 1.06). Round to the nearest percent.
Answers
Answer:
14%
Step-by-step explanation:
On edge 2020
Question 3 of 10
2 Points
If h(x) =(fºg)(x) and h(x) = 3(x + 2), find one possibility for f (x) and g(x).
Answers
Answer:
[tex]\boxed{\sf \ \ \ \text{one possibility is } f(x)=3x \ and \ g(x)=x+2 \ \ \ }[/tex]
Step-by-step explanation:
hello
h(x)=f(g(x))=3(x+2)
if we have f(x)=3x and g(x)=x+2 then
f(g(x))=f(x+2)=3(x+2)
hope this helps
Lagrange's four-square theorem states that every positive integer can be written as the sum of four or
fewer square numbers. For instance, 23 - 32+32 +22+12 and 30 -5° +2° +1°. Write each
of the following integers as the sum of four or fewer square numbers.
a. 15
b. 24
0.33
d. any 3-digit, positive integer of your choosing
Answers
Answer:
15 = 3² +2² +1² +1²24 = 4² +2² +2²33 = 4² +4² +1²624 = 22² +10² +6² +2²Step-by-step explanation:
It doesn't always work to choose the largest possible square first.
a. 15 = 9 + 4 + 1 + 1 = 3² +2² +1² +1²
b. 24 = 16 + 4 + 4 = 4² +2² +2²
c. 33 = 25 + 4 + 4 = 5² +2² +2²
d. 624 = 484 +100 +36 +4 = 22² +10² +6² +2²
the length of a rectangular sheet of metal is 9.96m and it's breadth is 5.08m. Find the area of the metal.Correct the answer to 2 significant figures and then correct the answer to 0.1 meter square
Answers
Answer:
50.6 m²
Step-by-step explanation:
The area of a rectangle is length × breadth.
9.96 × 5.08
= 50.5968
Rounding.
⇒ 50.60
⇒ 50.6
The ratio of boys to girls in Jamal's class is 3:2. If four more girls join the class, there will be the same number of boys and girls. What is the number of boys in the class?
Answers
Answer:
12 boys
Step-by-step explanation:
From the above question:
Number of boys = 3
Number of girls = 2
Boys: Girls
3:2
Let :
a = boys
b = girls
Hence, a : b = 3 : 2
a/b = 3/2
Cross Multiply
2a = 3b .......... Equation 1
a = 3b/2
If four more girls join the class, there will be the same number of boys and girls
Hence,
a: b + 4 = 3 : 3
a/b + 4 = 3/3
Cross Multiply
3a = 3(b + 4)
3a = 3b + 12 ........ Equation (2)
From Equation 1: a = 3b/2
Substitute 3b/2 for a in Equation 2 we have:
3a = 3b + 12 .........Equation 2
3(3b/2) = 3b + 12
9b/2 = 3b + 12
Cross Multiply
9b = 2(3b + 12)
9b= 6b + 24
9b - 6b = 24
3b = 24
b = 8
Substitute 8 for b in Equation 1
a = 3b/2
a = 3 × 8/2
a = 24/2
a = 12
Therefore, the number of boys in the class is 12
if it takes four men to dig a land in 6 days.how many days will it take 6 men to build that same land.
Answers
Answer:
4 daysSolution,
____________________________
Men ------------------------------ Days
4 ------------------------> 66 ------------------------> X (suppose)_____________________________
In case of indirect proportion,
4/6= 6/X
or, 6*X= 6*4 ( cross multiplication)
or, 6x= 24
or, 6x/6= 24/6 ( dividing both sides by 6)
x= 4 days
Hope this helps...
Good luck on your assignment..
Answer:
[tex]\boxed{4 days}[/tex]
Step-by-step explanation:
M1 = 4
D1 = 6
M2 = 6
D2 = x (we've to find this)
Since, it is an inverse proportion (more man takes less days for the work to complete and vice versa), so we'll write it in the form of
M1 : M2 = D2 : D1
4 : 6 = x : 6
Product of Means = Product of Extremes
=> 6x = 4*6
=> 6x = 24
Dividing both sides by 6
=> x = 4 days
A production facility employs 20 workers on the day shift, 15 workers on the swing shift, and 10 workers on the graveyard shift. A quality control consultant is to select 7 of these workers for in-depth interviews. Suppose the selection is made in such a way that any particular group of 7 workers has the same chance of being selected as does any other group (drawing 7 slips without replacement from among 45).
1. How many selections result in all 7 workers coming from the day shift?
2. What is the probability that all 7 selected workers will be from the day shift?
3. What is the probability that all 7 selected workers will be from the same shift?
4. What is the probability that at least two different shifts will be represented among the selected workers?
5. What is the probability that at least one of the shifts will be un-represented in that sample of workers?
Answers
Answer:
1. 77520
2. [tex]P_1[/tex] = 0.0017
3. [tex]P_2[/tex] = 0.0019
4. [tex]P_3[/tex] = 0.9981
5. [tex]P_4[/tex] = 0.2036
Step-by-step explanation:
The number of ways or combinations in which we can select x elements from a group of n can be calculated as:
[tex]nCx = \frac{n!}{x!(n-x)!}[/tex]
So, there are 77520 selections that result in all 7 workers coming from the day shift. It is calculated as:
[tex]20C7 = \frac{20!}{7!(20-7)!}=77520[/tex]
At the same way, the total number of selections of 7 workers from the 45 is 45C7, so the probability that all 7 selected workers will be from the day shift is:
[tex]P_1=\frac{20C7}{45C7} =0.0017[/tex]
The probability that all 7 selected workers will be from the same shift is calculated as:
[tex]P_2=\frac{20C7+15C7+10C7}{45C7} =0.0019[/tex]
Because the consultant can select all workers from the day shift (20C7) or can select all workers from the swing shift (15C7) or can select all workers from the graveyard shift (10C7).
On the other hand, the probability that at least two different shifts will be represented among the selected workers is the complement of the probability that all 7 selected workers will be from the same shift. So it is calculated as:
[tex]P_3 = 1- P_2=1 - 0.0019 = 0.9981[/tex]
Finally, the probability that at least one of the shifts will be un-represented in that sample of workers is:
[tex]P_4=\frac{25C7+30C7+35C7}{45C7} =0.2036[/tex]
Where 25C7 is the number of ways to select all 7 workers from swing or graveyard shift, 30C7 is the number of ways to select all 7 workers from day or graveyard shift and 35C7 is the number of ways to selects all 7 workers from day shift and swing shift.
A rectangle measures 18 cm x 3 cm what is its area
Answers
Answer:
Six
Step-by-step explanation:
The answer could be shown in multiple forms, but if I'm correct, the answer to this problem would be six.
find the average rate of change if the function f(x)=x^2+4x from x1=2 to x2=3
Answers
Replace x with 2 and solve:
2^2 + 4(2) = 4 + 8 = 12
Replace x with 3 and solve:
3^2 + 4(3) = 9 + 12 = 21
The difference between the two answers is : 21 -12 = 9
The difference between the two inputs is 3-2 = 1
The rate of change is the change in the answers I’ve the change in the inputs:
Rate of change = 9/1 = 9