The possible roots for the given equation are, -1,3, -1-2i, -1+2i.
What do you mean by the roots of an equation?
The values of the variable that fulfill the equation are known as the roots of a quadratic equation. In addition, they are referred to as the "solutions" or "zeroes" of the quadratic equation. For instance, x = 2 and x = 5 satisfy the quadratic equation x2 - 7x + 10 = 0 and are hence the roots of the equation.
F(x) = x4-2x2-16x-15 has a root (zero) that you should find.
Finding x values for which F(x)=0 is the goal of the Polynomial Roots Calculator method set.
A tool from the list above is the rational roots test. Only numbers x that can be represented as the quotient of two integers, or rational roots, would be found.
According to the Rational Root Theorem, P and Q are factors of the Leading Coefficient and the Trailing Constant, respectively, if a polynomial zeroes for a rational number P/Q.
The Leading Coefficient is 1 and the Trailing Constant is -15 in this instance.
The component(s) are:
1 is the Leading Coefficient, while 1 is the Trailing Constant.
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Please help me complete this flowchart proof. The correct answer gets brainiest
The flowchart that is used to prove GR ║ F_K is presented as follows;
∠RND and ∠FDP are supplementary ⇒ ∠RND + ∠FDP = 180°
Given [tex]{}[/tex] Definition of supplementary
∠KDN ≅ ∠FDP [tex]{}[/tex] ⇒ ∠KDN = ∠FDP
Vertical angles are congruent[tex]{}[/tex] Definition of congruent angles
∠RND and ∠KDN are same side interior angles [tex]{}[/tex] ⇒∠RND + ∠KDN = 180°
Definition of same side interior angles[tex]{}[/tex] Substitution property
[tex]{}[/tex] GR ║ F_K
Same side interior angles formed between parallel lines that have a common transversal are supplementaryWhat are the relationships between the angles formed between parallel lines that have a common transversal?The relationships between the angles formed by a transversal and two parallel lines are;
Corresponding angles are congruentSame side interior angles are supplementaryLinear pair angles are supplementaryVertical angles are congruentAlternate interior angles are congruentAlternate exterior angles are congruentDefinition of congruency;
Two lines, shape or figure are said to be congruent if they have the same size and shape.
Supplementary angles;
Supplementary angles are angles that have a sum of 180°
Substitution property of equality
The substitution property sates that if an expression a = b, then the expression b can replace a in any equation and the equation will remain valid.
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Instructions: Show that the conjecture is false by finding a counterexample. Change the value of n below in order to make it a counterexample. "Two supplementary angles are not congruent."
The counterexample for "Two supplementary angles are not congruent." is
angle 100° and angle 80° are supplementary angels
angle 90° and angle 90° are supplementary angels
The instances show supplementary angles that are not congruent
What is counter examples?A specific situation that demonstrates that a statement is untrue is referred to as a counterexample.
Counterexamples provides instances that opposes the statement
In this case the two supplementary angles 100-and-80 and 90-and-90 are not congruent and hence a counterexample to the statement
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Please help me I’ll mark your answer brainly
The measure of angle B is x, while the measure of angle A is 2·x. The 70° measure of angle C and the angle sum property of the interior angles of a triangle indicates that angle B is [tex]36.\overline 6^{\circ}[/tex] and angle A is [tex]73.\overline 3^{\circ}[/tex]
What are the interior angles of a triangle?The interior angles of a triangle are the angles formed by the sides sides of the triangle.
The question can be solved by making use of the known properties of a triangle.
The angle sum property of the interior angles in a triangle gives;
The sum of the interior angles of a triangle is 180°
Therefore; x + 2·x + 70 = 180
3·x = 180° - 70° = 110°
[tex]x = \dfrac{110^{\circ}}{3} = 36\frac{2}{3} ^{\circ}[/tex]
The measure of angle A is 2·x
Which gives;
[tex]A = 2 \times 36\frac{2}{3} ^{\circ} = 73\frac{1}{3} ^{\circ} = 73.\overline 3^{\circ}[/tex]
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A standard deck of playing cards has 4 different suits (hearts, spades, clubs and diamonds) and 13 different ranks for the cards (ace, 2-10, jack, queen, king). In a poker game you are dealt a hand of 5 cards.
How many ways are there to get dealt exactly a single pair? A pair is a hand with two cards of the same rank. (so two pairs, three of a kind, four of a kind, full house etc. aren't included)
The number of ways that there are to get dealt exactly a single pair is; 6,589,440 ways
What is the probability of Selection?The combination in probability selection is defined as a method where we count the number of ways a certain number of objects can be arranged in "n" different ways. If the number of different objects are "n", then it means that the number of ways that we can select "r" number of different objects is expressed as:
nCr = n!/(r!(n - r)!)
The total number of cards that we have in a deck of cards = 52.
There total number of different cards are 13 in number and this tells us that we can possibly have a pair of any one of the 13 cards. There are also 4 cards of the same rank and this means that the number of ways of selecting two cards of the same rank is; 4C2 = 6 ways
After selecting a card for the pair, we have 48 different cards as an option for the third card. Thereafter, we will have a total of 44 cards as an option for the fourth card and then 40 cards will be an option for the fifth card (due to the fact that none of the cards can be of same rank except for the pair of cards).
Therefore, the total number of ways that we can deal with exactly a single pair can be expressed as:
Number of ways = number of ways for the pair × number of ways for the third card × number of ways for the fourth card × number of ways for the fifth card
Plugging in the relevant values gives;
Number of ways = (13 × 6) × 48 × 44 × 40
= 6,589,440 ways
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reduce 12/16 to simplest terms
Answer: 3/4
Step-by-step explanation:
Find the GCD (or HCF) of numerator and denominator
GCD of 12 and 16 is 4
Divide both the numerator and denominator by the GCD
12 ÷ 4
16 ÷ 4
Reduced fraction: 3/4
Therefore, 12/16 simplified to lowest terms is 3/4.
Answer:.
Step-by-step explanation:
m∠M = 6x – 6 and m∠P = 4x + 10, what is m∠M?
i bet u cant solve it
For the given pair of parallel lines AG and BH , CF is the transversal then ∠ADE and ∠BEF are corresponding angles.
As given in the question,
Given :
Pair of parallel lines are AG and BH.
CF is the transversal.
Transversal CF intersect line AG at point D and
Transversal CF intersect line BH at point E
Four pair of corresponding angles
Two pair of alternate interior angles
Corresponding pair of angles in the pair of parallel lines are congruent.
∠ADE ≅ ∠BEF
∠ADE and ∠BEF are corresponding angles.
Therefore, for the given pair of parallel lines AG and BH , CF is the transversal then ∠ADE and ∠BEF are corresponding angles.
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Please Help
Find (f+g)(x)if f(x)=4x2-5x+8 and g(x)=2x2+x-2
Answer: (f+g)(x) = 6x²- 4x + 6
Step-by-step explanation:
We add f(x) and g(x) together, (4x²-5x+8) + (2x²+x-2)
Add like terms together, (4x²+2x²) + (-5x+x) +(8-2)
We are left with (f+g)(x) = 6x²- 4x + 6
Ms. Jones washed
2
7
of her laundry. Her son washed
1
3
of it. Who washed most of the laundry? How much of the laundry still needs to be washed?
The lifetimes of batteries created by a company are normally distributed with a
mean of 105 hours and a standard deviation of 12 hours. What percentage of these batteries will last between 90.6 and 109.8 hours?
Answer:
84.6
Step-by-step explanation:
The statement 4 less than a number is given w
The equation representing the statement - "4 less than a number is given w" as -
[w] = x where x ∈ (- ∞, 4)
What is Equation Modelling?
Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
We have the following statement - "4 less than a number is given w".
Assume the number to be [x].
We can write the equation representing the statement -
"4 less than a number is given w" as a mathematical expression as -
[w] = x where x ∈ (- ∞, 4)
Therefore, the equation representing the statement - "4 less than a number is given w" as -
[w] = x where x ∈ (- ∞, 4)
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Jasenio is shooting target practice with a bow and arrow. His target is a paper rabbit that runs along a track. The track is 50 meters away from Jasenio and he estimates that by the time the arrow reaches it, the paper rabbit will be at a point about 10 meters to the right of what would be directly in front of him. At what true bearing should Jasenio aim his bow and arrow?
a) 3.49°
b) 11.31°
c) 78.46°
d) 78.69°
The true bearing at which Jasenio should aim his bow and arrow is; b) 11.31°
How to apply Trigonometric Ratios?
We have different trigonometric ratios such as;
sin θ = opposite/hypotenuse
cos θ = adjacent/hypotenuse
tan θ = opposite/adjacent
We are told the track is 50 meters away from Jasenio and that by the time the arrow reaches it, the paper rabbit will be at a point about 10 meters to the right of what would be directly in front of him.
This means that there will be a right angle triangle formed with the height as 50 m and the base length as 10m. Thus, by trigonometric ratios, we have;
tan θ = 10/50
where θ is the true bearing angle. Thus;
tan θ = 0.2
θ = tan⁻¹0.2
θ = 11.31°
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the table shows the number of pounds that 10 students in gary langs weight training class could bench press and squat. make a scatterplot to display the relationship between the bench press and squat weights for this sample. (use squat as the explanatory variable). describe the relationship shown in the scatterplot
The scatter plot that displays the relationship between the bench press and squat weights for this sample is given by the second image at the end of the answer.
From the scatter plot, it can be taken that the relationship is that the variables have a positive association, as when the bench press weight increases, so does the squat weight. The relationship, however, is not strong, as the scatter plot is not 100% increasing.
How to built the scatter plot?The scatter plot is built inserting all the points of the table in a graph, which are in the following input-output format:
(bench press weight, squat weight).
From the table given by the first image at the end of the answer, the points are listed as follows:
(95, 141), (111, 208), (113, 100), (125, 218), (135, 284), (145, 275), (165, 338), (180, 338), (140, 420), (196, 420), (95, 141), (111, 208).
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Simon uses 121 one-inch tiles to make his square mosaic. What is the length of one side of his mosaic?
Arianys runs a farm stand that sells grapes
and apples. Each pound of grapes sells for
$3.75 and each pound of apples sells for
$4. Arianys made $251.75 from selling a
total of 64 pounds of grapes and apples.
Determine the number of pounds of
grapes sold and the number of pounds of
apples sold.
The number of pounds of grapes sold is 17 pounds and the number of pounds of apples sold is 47 pounds.
According to the question,
We have the following information:
Cost of 1 pound of grapes = $3.75
Cost of 1 pound of apples = $4
Total cost made by selling = $251.75
And the weight of the apples and grapes sold = 64
Now, let's take the weight of grapes to be x pounds and the weight of apples to be y pounds.
So, we have:
x+y = 64
x = 64-y ....(1)
3.75x+4y = 251.75
Putting the value of x in this equation:
3.75(64-y)+4y = 251.75
3.75*64-3.75y+4y = 251.75
240+0.25y = 251.75
0.25y = 251.75-240
0.25y = 11.75
y = 11.75/0.25
y = 47 pounds
Now, putting this value of y in equation 1:
x = 64-y
x = 64-47
x = 17 pounds
Hence, the number of pounds of grapes sold is 17 pounds and the number of pounds of apples sold is 47 pounds.
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In a psychology class, 30 students have a mean score of 87.7 on a test. Then 21 more students take the test
and their mean score is 67.7.
What is the mean score of all of these students together? Round to one decimal place.
mean of the scores of all the students.
The mean score of all the students is 79.5 and it is round off into one decimal place.
Mean
Mean refers the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.
Given,
In a psychology class, 30 students have a mean score of 87.7 on a test. Then 21 more students take the test and their mean score is 67.7.
Here we need to find the mean score of all students.
In order order to find the mean score, we have to calculate the total score of the students by multiplying the mean score by the number of students then we get,
=> 30 x 87.7 = 2631
Similarly, the total score for 21 students is,
=> 21 x 67.7 = 1421.7
So, the 51 students, cumulative score is
=> 2631 + 1421. 7 = 4052.7
Therefore, the mean score is calculated as,
=> 4052.7/51
=> 79.464
When we round off the value into one decimal place then we get
=> 79.5
Therefore, the mean value of all the students is 79.5.
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Find the focus and the directrix of the parabola with the equation y = - 1/12 (x - 4) 2. (A) Focus = (4, -1), directrix is y = -5 (B) Focus = (4,2), directrix is y = 5 (C) Focus = (4,1), directrix is y = -5 (D) Focus = (4, -1), directrix is y = 5
The focus of parabola is (4 , -1) and directrix is 5
The general equation of a parabola is: y = a(x-h)²+ k or x = a(y-k)² +h, where (h ,k) denotes the vertex. The standard equation of a regular parabola is y² = 4ax.
Focus: The point (a, 0) is the focus of the parabola
Directrix: The line drawn parallel to the y-axis and passing through the point (-a, 0) is the directrix of the parabola. The directrix is perpendicular to the axis of the parabola.
Given equation of parabola is :
y = - 1/12 (x - 4) - 2
Comparing it with standard equation,
h = 4
k = 2
a = -1/12
using Focus: (h, k+ (1/4a)) and Directrix: y = k - 1/4a)
=> focus = (4 , 2+(12/4×-1))
=> focus = (4 , 2-3)
=> focus = (4 , -1)
and directrix is : y = 2-(1/4×-1/12)
y = 2 + 12/4
y=2 + 3 => 5
So, the focus is (4,-1) and directrix is 5
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At 2 hours before sunset, the temperature is 0°F. At 2 hours after sunset, the temperature is −4°F. Identify the equation representing the temperature y, in degrees Fahrenheit, at x hours after sunset
The correct equation to representing the temperature y, in degrees Fahrenheit, at x hours after sunset will be;
⇒ y = - 4°x + 0°
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;
At 2 hours before sunset, the temperature is 0°F.
And, At 2 hours after sunset, the temperature is −4°F.
Now,
Let the temperature in degrees Fahrenheit = y
So, We can formulate;
⇒ y = - 4°x + 0°
Thus, The correct equation to representing the temperature y, in degrees Fahrenheit, at x hours after sunset will be;
⇒ y = - 4°x + 0°
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76 points and brainlist
The length of a bacterial cell is about 3 x 10−6 m, and the length of an amoeba cell is about 4.5 x 10−4 m. How many times smaller is the bacterial cell than the amoeba cell? Write the final answer in scientific notation with the correct number of significant digits.
2 x 102
2 x 103
0.7 x 101
6.67 x 102
Answer:
d the last one I think
Step-by-step explanation:
I am not really sure
Answer:
D.) 6.67 X 10^2
The graph below shows the daily low temperatures for one week in New Orleans, Louisiana. The shape of the temperature graph can be modeled by the quadratic function f (x) = 3x² 18x + 56, where 2 is the number of days starting Sunday, and f (2) is the temperature in Fahrenheit. Degrees Fahrenheit 60 50 40 30 20 10 0 - Sun. Mon. Tues Wed. Thu. Fri. Sat. a. Use the given quadratic function to approximate the temperature on Thursday. How does this approximation agree with the graph? b. Use the function and the quadratic formula to find when the temperature is 35 degrees Fahrenhait. (Hint: Set f (x) = 35 and solve.) Round the answer to one decimal place and interpret the decimal in terms of weekday and military time.
a. The numeric value at Thursday -> x = 4 is of 32 degrees, which agrees with the graph.
b. A numeric value of 35 degrees Fahrenheit is obtained on Monday and on Thursday, also agreeing with the graph.
How to obtain the numeric value of a function or of an expression?To obtain the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.
In this problem, the function is defined as follows:
f(x) = 3x² - 18x + 56.
Giving the temperature in degrees Fahrenheit in x days after Sunday.
The day that represents Thursday is given by:
x = 4.
Hence the temperature is the numeric value of the function at x = 4, replacing both instances of x on the function by 4, hence:
f(4) = 3(4)² - 18(4) + 56 = 32 ºF.
Which agrees with the graph, as the Thursday's bar is a value slightly above 30, which can be interpreted as 32.
The numeric value is of 35 when:
3x² - 18x + 56 = 35
The solutions to the quadratic equation are:
x = 1.6, x = 4.4.
Hence the days are:
Monday and Thursday.
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Desmond is training for a bike race and is attempting to improve his average speed. With his old trainer, Desmond averaged a pace of 24 MPH. With his new trainer, he rode at an average speed of 30 MPH. By what percent did his average speed increase? %
The percent that Desmond average speed increase is 25%.
How to calculate the percentage?From the information, with his old trainer, Desmond averaged a pace of 24 MPH and with his new trainer, he rode at an average speed of 30 MPH.
It should be noted that the percentage increase in speed will be:
= Change in speed / Initial speed × 100
= (30 - 24) / 24 × 100
= 6/24 × 100
= 25%
The percentage is 25%.
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Natalie has a budget of $15,000 dollars to spend on tracking devices to study bison. A radio tracker costs $650 and a GPS tracker costs $1400. Natalie wants to buy at least 9 radio trackers and more than 3 GPS trackers. The following system of inequalities represents this situation, where x is the number of radio trackers and y is the number of GPS trackers. x ≥ 9 y > 3 650x + 1400y ≤ 15000
The inequality as per the question is x ≥ 9 and y > 3 and the diagram according to this is attached below.
What is an equality?Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare the two values. Less than (or less than and equal to), larger than (or greater or equal to), or not similar to signs are used in place of the equal sign in between.
As per the given information in the question.,
x ≥ 9 and,
y > 3
The equation is,
650 x + 1400 y ≤ 1
[tex]\frac{x/15000}{650}+\frac{y/15000}{1400} \leq 1[/tex]
x/23.07 + y/10.71 ≤ 1
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Need help with question 2b please
Answer:
20 mph
Step-by-step explanation:
If it took the car originally 12 minutes to travel the road with an average speed of 60 mph. Than you would just divide the average speed by three because it is taking 3 times the amount of time than it would originally.
36/12=3
60/3=20
20 mph
If P= (2, 7) and Q= (2, -3), which could be the coordinates of R if triangle PQR is isosceles?
If P= (2, 7) and Q= (2, -3), then for triangle to be isosceles coordinate of R must be 2
Let coordinates
P = (2, 7) and Q = (2, -3)
PR = QR
(X-2)^2 +(Y-7)^2 = (X-2)^2 + {Y-(-3)}^2
(Y-7) = {Y - (-3)}^2. or y - 7 = ±(Y
or Y^2 - 14Y + 49 = Y^2 + 6Y + 9
20Y = 40
Y=2
coordinates of R if triangle PQR is isosceles ;
Hence any point R on the line Y = 2 will make PQR a isosceles triangle
with PR = QR.
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Please help! Select the equation that represents the following linear graph:
Simplify quantity 15 x squared minus 18 end quantity over 6. 15x + 3 x + 3 quantity 5 x squared minus 18 end quantity over 2 quantity 5 x squared minus 6 end quantity over 2
The expressions are:
(5x² - 6)/ 2 5x² - 18/2 5x² -6 /2What is expression?A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:
An absolute numerical number is referred to as a constant.Variable: A symbol without a set value is referred to as a variable.Term: A term can be made up of a single constant, a single variable, or a mix of variables and constants multiplied or divided.Coefficient: In an expression, a coefficient is a number that is multiplied by a variable.Given:
15 x squared minus 18 end quantity over 6.
= 15x² - 18 / 6
= 3(5x² - 6)/ 6
= (5x² - 6)/ 2
and, 5 x squared minus 18 end quantity over 2
= 5x² - 18/2
and, 5 x squared minus 6 end quantity over 2
= 5x² -6 /2
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. You get an auto loan at 3.5% interest for 5 years; please answer the following.
A. You can afford a $250 per month car payment; how expensive a car can you afford?
B. You purchase a car for $8000 with a $2000 down payment, what are your monthly payments?
Using the monthly payment formula, it is found that:
A. You can afford a car at a price of $13,742.36.
B. The monthly payments are of $109.15.
What is the monthly payment formula?The monthly payments are given by the equation presented as follows:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
The variables involved in the equation are listed and explained as follows:
P is the initial amount.r is the interest rate.n is the number of payments.For item a, the parameters are given as follows:
A = 250, r/12 = 0.035/12 = 0.002917, n = 5 x 12 = 60
Hence the maximum value of the car is obtained as follows:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
[tex]250 = P\frac{0.002917(1.002917)^{60}}{(1.002917)^{60} - 1}[/tex]
0.0181919241P = 250
P = 250/0.0181919241
P = $13,742.36
For item b, the parameters are given as follows:
P = 6000, r/12 = 0.035/12 = 0.002917, n = 5 x 12 = 60
(P = 6000 as the 2000 of the down payment are already paid, hence not subjected to interest).
Hence the monthly payments are given as follows:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
[tex]A = 6000\frac{0.002917(1.002917)^{60}}{(1.002917)^{60} - 1}[/tex]
A = 6000 x 0.0181919241
A = $109.15.
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Simple random sampling uses a sample size of n from a population of size N to obtain data that can be sued to make inferences about the characteristics of a population. Suppose that, from a population of 50 bank accounts, we want to take a random sample of four accounts in order to learn about the population. How many different random samples of four accounts are possible?
If from a population of 50 bank accounts, we want to take a random sample of four accounts in order to learn about the population. The number of different random samples of four accounts that are possible is 230,300.
How to find the different random samples?Given data:
Number of population of bank account = 50
Random sample = 4 accounts
Now let find the different random samples of four account that are possible
Different random sample = 50! / (50 -4)! × 4!
Different random sample = 50! / 46! × 4!
Different random sample = 230,300
Therefore the different random samples is 230,300.
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I can determine if a function is linear or
nonlinear.
4. Determine if the table represents a
linear or nonlinear function.
Answer:
1st Table : Linear
2nd Table : Non-Linear
Step-by-step explanation:
To determine if the function is Linear or not , we find the change in y with a certain change in x
So for the 1st Table:
When x changes from x = 2 to x = 4 increased by 2
Then y changes from y = 3 to y = 0 decreases by 3
When x changes from x = 4 to x = 6 increased by 2
Then y changes from y = 0 to y = -3 decreases by 3
Since change in y is the same for the same change in x , Then the Function is Linear
So for the 2nd Table:
When x changes from x = 1 to x = 2 increased by 1
Then y changes from y = 1 to y = 4 increased by 3
When x changes from x = 2 to x = 3 increased by 1
Then y changes from y = 4 to y = 9 increased by 5
Since change in y is not the same for the same change in x , Then the Function is Non-Linear
Glad to Help
The production of a gold mine decreases by 5% per year.
What is the approximate half-life for the production decline?
Based on this approximate half-life and assuming that the
mine's current annual production is 5000 kilograms, about
what will its production be in 10 years?
Answer:d
Step-by-step explanation:d
