When the value of the variable x is greater than or equal to -3, the result returned by the even function is 3.
x=-1x=−1x, equals, minus, 1, Then the correct option is C.
What is an even function?A true function f(x) is an even function if the yield value of the function f(-x) is the same as the value returned by the function f(x) for all values of x that fall within the domain of f.
It is recommended that the equation be saved in an even function:
f(-x) = f(x)
Therefore
f(x) = f(3) = 3
Let's assume that f(x) is a function that always returns even. Then there is also
f(-3) = f(3) = 3
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CQ
Select all input values for which f(x)=3f(x)=3f, left parenthesis, x, right parenthesis, equals, 3.
Choose all answers that apply:
(Choice A)
A
x=-5x=−5x, equals, minus, 5
(Choice B)
B
x=-3x=−3x, equals, minus, 3
(Choice C)
C
x=-1x=−1x, equals, minus, 1
(Choice D)
D
None of the above
Using substitution method, solve
3x-y=0
2x+y=5
Answer:
x=1 y=3
Step-by-step explanation:
Hello!
So, this says to use the substitution method. The substitution method is where you set one equation equal to one of the letters, and then put that whole equation in the other equation.
So->
3x-y=0
if we move the y to the other side we have:
3x=y
then we have our second equation:
2x+y=5
Now, we don't know what NUMBER y is yet, but we do know that it is equal to 3x. Thus, we can put it into the equation like this.
2x+(3x)=5
Then, we can add like terms and get:
5x=5
Dividing each term by five, we get
x=1
We could have also done this be solving for x in the equations and then substituting that in instead of y.
Now that we have x, we can easily put it into the equations and solve for y.
3x-y=0
3(1)-y=0
3=y
So now we know that x is equal to 1 and y is equal to 3.
When the Sun becomes a red giant it’s radius will become 100 times larger but it’s temperature will halve. By what factor would we expect the equilibrium temperature of Europa to change?
Answer:88888880.8
Step-by-step explanation:
0.9
Find the indicated angle measure.
The required measure of the alternate opposite angle is 25°
Given that,
The figure has been shown in which measure of the angle is to be dtermined.
The angle can be defined as the one line inclined over other line. the measure of an angle is measured in two units of degrees and in radiants.
Here,
2x - 1 = 5x - 40
5x - 2x = 40 - 1
3x = 39
x = 13
Now,
measures of the angle,
= 2x - 1 = 2 * 13 - 1
= 25°
and
5x - 40 = 5*13 - 40
= 65 - 40
= 25°
Thus, the required measure of the alternate opposite angle is 25°.
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PLEASE HELP QUICK
The equation of a line is y = 3/5x + 7.
(a) What is the slope of a line parallel to it?
(b) What is the slope of a line perpendicular to it?
a. The slope of a line that is parallel to y = 3/5x + 7 is: 3/5.
b. The slope of a line that is perpendicular to y = 3/5x + 7 is: -5/3.
How to Determine the Slope of Parallel Lines?Given a line is represented by the equation, y = 3/5x + 7, the slope (m) of the line is 3/5.
Any line that is parallel to y = 3/5x + 7 will have a slope (m) = 3/5 [same slope value].
On the other hand, any line that is perpendicular to y = 3/5x + 7 will have a slope of -5/3 [negative reciprocal].
Therefore:
a. The slope of a line that is parallel to y = 3/5x + 7 would be: 3/5.
b. The slope of a line that is perpendicular to y = 3/5x + 7 would be the negative reciprocal of 3/5, which is: -5/3.
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Please help, I'm super confused!!
You are solving a measurement problem where the numbers 5.2187 x 10^−3, 2.05 x 10^7, and 3.40 x 10^3 are multiplied. How many significant digits should the product have?
A. 5
B. 3
C. 2
D. 1
Using scientific notation, the number of significant digits that the product should have is:
B. 3.
What is scientific notation?A number in scientific notation is given by:
[tex]a \times 10^b[/tex]
With the base being [tex]a \in [1, 10)[/tex].
When two numbers in scientific notation are multiplied, we have that:
The bases are multiplied.The power of 10 is kept.The exponents are added.For this problem, the product is given by:
[tex]5.2187 \times 10^{-3} \times 2.05 \times 10^7 \times 3.4 \times 10^3[/tex]
Multiplying the bases and adding the exponents, we have that:
[tex]5.2187 \times 2.05 \times 3.4 \times 10^{-3 + 7 + 3} = 42.8 \times 10^{7}[/tex]
42.8 has to be divided by 10 to assume for the base have only one digit, hence:
[tex]42.8 \times 10^{7} = 4.28 \times 10^6[/tex]
Hence, considering the rounding, the number has 3 significant digits(4, 2 and 8), and option B is correct.
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Mean: Use when there are no____
Ex: I, 3, 9, 5, 7, 8, 2, 3
data point that is very
______from the other data points.
Ex: 7, 10, 13, 6, 229, 9, 8
Median: Use when there are_____
Ex: 12, 108, 14, 15, 17, 13, 14,11
Mode: Use when your data can be put into_____
Ex: Students voting for their favorite flavor of Ice cream:
chocolate, vanilla, vanilla, strawberry, chocolate, chocolate
Answer:4
7
82
83
Step-by-step explanation:
REALLY EASY
what is the greatest common factor of 20x6y 40x4y2−10x5y5? 10x4y 10 x begin power 4 end power y 5x2y5 5 x squared y begin power 5 end power 5x4y 5 begin power 4 end power y 20x6y
The greatest common factor of [tex]20x^{6} y+40x^{4} y^{2} -10x^{5} y^{5}[/tex] is [tex]10x^{4} y[/tex] .
The greatest common factor of a set of numbers is defined as the largest number that divides all the numbers in that given set and leaves 0 as remainder in each case.
In the given expression
[tex]20x^{6} y+40x^{4} y^{2} -10x^{5} y^{5}[/tex]
Applying Prime Factorization and Writing all the terms in the above expression as
[tex]20x^{6} y=10x^{4}y *2x^{2}[/tex]
[tex]40x^{4} y^{2} =10x^{4} y*4y[/tex]
[tex]10x^{5} y^{5} =10x^{4}y*xy^{4}[/tex]
As we can see that [tex]10x^{4} y[/tex] is common and greatest in all the terms .
Hence [tex]10x^{4} y[/tex] is the Greatest common factor.
Therefore , the greatest common factor of [tex]20x^{6} y+40x^{4} y^{2} -10x^{5} y^{5}[/tex] is [tex]10x^{4} y[/tex] , the correct option is (a)[tex]10x^{4} y[/tex].
The given question is incomplete , the complete question is
What is the greatest common factor of [tex]20x^{6} y+40x^{4} y^{2} -10x^{5} y^{5}[/tex]
(a)[tex]10x^{4} y[/tex]
(b)[tex]5x^{2} y^{5}[/tex]
(c)[tex]5x^{4} y[/tex]
(d)[tex]20x^{6} y[/tex]
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At 6:00AM, the temperature was −16 degrees. By noon, the temperature had risen 28 degrees. What was the temperature at noon? Responses At 6:00AM, the temperature was −16 degrees. By noon, the temperature had risen 28 degrees. What was the temperature at noon?
1.Carla Sanborn, who was born on July 12, 1989, purchased $30,000 worth of ordinary whole-life insurance on August 25, 2020.
Her age for insurance purposes: ____years
Her annual premium: $____
2.Bruce Lovegren was born on September 27, 1950. On April 27, 1977, he purchased a $15,000 ten-year term life insurance policy.
His age for insurance purposes: ____ years
Annual premium he paid: $____
3. Edward Anderson has $30,000 of twenty-payment life. If he is twenty-six years old, what premiums will he pay?
semiannually: $___
quarterly: $___
monthly: $___
4. Tom Harris is twenty-four. He purchases $15,000 of ten-year term insurance. Calculate the following.
semiannually: $___
quarterly: $___
monthly: $___
5. Emily Webster purchased a twenty-year endowment policy at age 27 with a face value of $25,000. Calculate the following. (Use a thousands comma where applicable.)
Her annual premium is $___
Her semi-annual premium is $___
The difference between these payment options is $___
6. Tom Hornet purchases $7,000 of ten year term life. He is 31 years old.
His annual premium is $___
His quarterly premium is $___
The difference between the two options is $___
1. Her age is 41 years and her annual premium is $732.
2. His age for insurance purposes is 27 years.
Her annual premium is $556.
3. His semiannually premiums = $577
And, His quarterly premiums = $288.5
And, His monthly premiums = $96
4. His semiannually premiums = $312.5
His quarterly premiums = $156.25
His monthly premiums = $52
5. His semiannually premiums = $463
The difference between these payment options = $463
6. His quarterly premium is = $56.5
The difference between the two options is = $170
What is Division method?
Division method is used to distributing a group of things into equal parts.
Given that;
1. Carla Sanborn was born on July 12, 1936.
On October 25, 1977, She bought $30,000 worth of ordinary life insurance on August 25, 2020.
Now, firstly we have to find her age for insurance purpose and secondly her annual premium.
Since, The age for her insurance purposes will be calculated by the nearest birthday year.
So,
July 12 ,1989 - October 25, 2020 = 31 years.
Hence, She is 31 years of age.
Now, For Her annual premium we divide what she purchased with her age as,
$30,000/31 = $ 967.74
Which is approximately be $968.
2. Bruce Lovegren was born on September 27, 1950.
On April 27, 1977, he purchased a $15,000 ten-year term life insurance policy.
Now, firstly we have to find her age for insurance purpose and secondly her annual premium.
Since, The age for her insurance purposes will be calculated by the nearest birthday year.
So, September 27, 1950 - April 27, 1977 = 27 years
Now, For Her annual premium we divide what she purchased with her age as,
$15,000/ 27 = $555.55
Which is approximately be $556.
3. Edward Anderson has $30,000 of twenty-payment life.
He is twenty-six years old.
For His annual premium we divide what he purchased with his age as,
$30,000/ 26 = 1,153.84
Which is approximately be $1,154
Hence, His semiannually premiums = $1,154/2 = $577
And, His quarterly premiums = $1,154/4 = $288.5
And, His monthly premiums = $1,154/12 = $96
4. Tom Harris is twenty-four.
He purchases $15,000 of ten-year term insurance.
For His annual premium we divide what he purchased with his age as,
$15,000/ 24 = $625
His semiannually premiums = $625/2 = $312.5
His quarterly premiums = $625/4 = $156.25
His monthly premiums = $625/12 = $52
5. Emily Webster purchased a twenty-year endowment policy at age 27 with a face value of $25,000.
For His annual premium we divide what he purchased with his age as,
$25,000/27 = $926
His semiannually premiums = $926/2 = $463
The difference between these payment options = $926 - $463 = $463
6. Tom Hornet purchases $7,000 of ten year term life. He is 31 years old.
For His annual premium we divide what he purchased with his age as,
$7,000/31 = $225.8
His quarterly premium is $226/4 = $56.5
The difference between the two options is $226 - $56.5 = $170
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AB is bisected by midpoint M. Given A( 3 , 7) and the midpoint M( -2 , 9), find the other endpoint B.
The coordinates of endpoint B are (-7, 11)
Midpoint of a lineFrom the question, we are to determine the coordinates of the endpoint B
If the coordinates of the endpoints of a line, AB, are A(x₁, y₁) and B(x₂, y₂), then the coordinates of the midpoint is given by
((x₁+x₂)/2, (y₁+y₂)/2)
From the given information,
The coordinates of A are (3, 7) and the coordinates of the midpoint are (-2, 9)
Let the coordinates of endpoint B be (x, y)
Then,
(3+x)/2 = -2
3 +x =-4
x = -4 -3
x = -7
and
(7 + y)/2 = 9
7 + y = 18
y = 18 - 7
y = 11
Hence, the coordinates are (-7, 11)
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Simplify each expression.
ln e²
ln(e²) = 2, by properties of logarithm.
What is Logarithm?The opposite of exponentiation is the logarithm.This indicates that the exponent to which a fixed number, base b, must be raised in order to obtain a specific number x, is represented by the logarithm of that number.A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.
Now, as we know by properties of logarithm, [tex]log_b(a)^m = m(log_b(a))[/tex],
ln (e²) = 2 ( ln(e))
Also, as ln (e) = 1, ln (e²) = 2 (1) = 2.
Hence, ln(e²) = 2, by properties of logarithm.
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Jim made $238 for 17 hours of work.
At the same rate, how many hours would he have to work to make 126 ?
The number of hours in which Jim will make $126 is equal to 9 hours.
What is the unit rate ?
An unit rate is a ratio that is used for comparing two different kinds of quantities which have different units.
It is given that Jim has made $238 after working for 17 hours.
If we try to find out the unit rate that how much he earn in 1 hour then it can be find out by dividing money earned by no. of hours he has worked.
So , the in 1 hour Jim will make money :
= 238 / 17
= $14
Now , we have to find out that how many hours he has to work to make 126. So , for this we need to divide it by 14 which is the unit rate.
The no. of hours in which Jim will make $126 will be :
= 126 / 14
= 9 hours
Therefore , the number of hours in which Jim will make $126 is equal to 9 hours.
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Solve by factoring. Check your answers. 2 x²+x=3
The factoring of the expression 2 x²+x=3 is (x-1) (2x+3)
By ordering the values, we get:
2x² + x - 3 = 0
To solve this exercise, we have to follow the rules of factoring:
1. Factor 1 from 1x:
2x² + x - 3 = 0
2x² + (-2 + 3) x -3 = 0
2. Apply the distributive property:
2x² - 2x + 3x - 3 = 0
3. Groups the first two terms and the last two terms:
(2x² - 2x) + 3x - 3 = 0
4. Factorize the greatest common denominator (GCM) of each group:
2x(x - 1) + 3(x - 1) = 0
5. Simplify the common term (x - 1) with the distributive property:
(x-1) (2x+3)
What is factoring?Is a technique that consist of decomposition of a factor into a product of another factor, which when multiplied together give the original number.
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A university's freshman class has 8600 students. 1634 of those students are majoring in Economics. What percentage of the freshman class are Economics majors?
Answer:
[tex]19\%[/tex]
PercentagesPercentages are evaluated values that say how much of a whole is occupied by that value. For example, if we were to say 75% of a strawberry pie remained, we could also see this as 3/4, or three-fourths.
To solve this particular problem, we will need to divide two values and convert a decimal to a percentage.
SolveFirst, set up the fraction of economics majors that are freshman students to the total number of freshman students.
[tex]\displaystyle \frac{1634}{8600}[/tex]
Then, divide the two using a calculator or long division.
[tex]\displaystyle \frac{19}{100}[/tex]
Finally, to convert this to a decimal, use a calculator.
[tex]0.19[/tex]
To convert a decimal to a percentage, multiply the decimal by 100.
[tex]0.19 \times 100 = 19\%[/tex]
The final answer is [tex]19\%[/tex].
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Answer:
19%
Key Points:
Freshman class size: 8,600 studentsEcon Major: 1,634 studentsIn order to find the percentage of freshman majoring in economics, we must divide the econ major students by the overall size of the freshman class.
[tex]\frac{1634}{8600}[/tex]
Our next step is to grab a calculator and input 1634 ÷ 8600. You can alternatively use the long division method but a calculator would work best. After calculating, your answer should come out to be 0.19
Now, you need to multiply it by 100 so that you can create a percentage.
0.19 × 100 = 19%
Therefore, 19% of the freshman class are economics majors.
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im really desperate can someone help
Answer: (Looking back, I may have gotten this question wrong, but if I haven't then nice.)
a) 13 degrees
b) acute angle
Step-by-step explanation:
Given that we know a triangle is 180 degrees. Lets recall what an obtuse, acute, right and reflex angle are.
Obtuse: An angle greater than 90 degrees
Acute: An angle less than 90 degrees
Right: An angle that is 90 degrees
Reflex: An angle in between 180-360 degrees
Since we know that two of the three angles are 54 and 113 degrees, we can say that 54+113+x=180. That means that the missing angle, x, is 13 degrees.
Knowing that 13 is less than 90, we can also say that the third angle is an acute angle.
need help i tried to do it on my own but ended up getting the wrong answer(attempting to try again to get a better score on it).
Answer:
25
Step-by-step explanation:
If youre going by 5's youd get 30 but then you gotta take away -5 so it comes out to 25
Answer:
25
Step-by-step explanation:
Find two decimals that are equivalent to (4 x 10) (7 x 1 over 100) write the decimals in the box
The given expression (4 × 10) + (7 × 1/100) expressed in decimal form is written as; 40.07
How to interpret Decimals?
We want to find the decimal that is equivalent to;
(4 × 10) + (7 × 1/100)
Now expanding the brackets contents, we have;
40 + 7/100
Now, 7/100 when written in decimal form gives;
7/100 = 0.07
Thus, the given expression (4 × 10) + (7 × 1/100) expressed in decimal form is written as;
(4 × 10) + (7 × 1/100)
40 + 0.07 = 40.07
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WILL GIVE YOU EXTRA BRAINLIEST POINTS IF YOU ANSWER THANKS
Based on the formulas given for PR and QR, the length of PR is 19.8 units.
What is the length of PR?The shape that is given is an equilateral triangle. This allows us to know that all the sides of the shape are equal.
This means that PR and QR are the same:
PR = QR
Equate both formulas as:
2n + 9 = 7n - 18
You can then solve for the value of n:
7n - 2n = 18 + 9
5n = 27
n = 5.4
The length of PR can then be solved by using substitution:
= 2n + 9
= 2 (5.4) + 9
= 19.8 units
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i really dont know this
Answer:
y=x+6
Step-by-step explanation:
The gradient of the line is change in y/ change in x
Thus meaning the gradient is 1. (defined as x)
The line crosses through the y-axis on the point (0,6)
So your euqation will be y = (1 - the gradient) x + (interception of y-axis) 6
Answer:
y = x + 6
Step-by-step explanation:
The general form of an equation of a line is
y= mx+b
y = slope ·x + y-intercept
Find the slope of the line, m:
-Pick any 2 points on the line, for example lets pick the points (0, 6) and (3, 10)
-Start at any of the points and go towards the other while note the path
start at (0, 6) and to go to (4, 10) we have to
go up (rise) 4 units from 6 to 10 and
go to the right (run) 4 from 0 to 4.
Slope = m = rise/run = 4/4 = 1
m = 1
Find the y-intercept, b:
The y-intercept is where the line intersects the y-axis. By looking at the given graph we can see y-intercept is 6.
b = 6
The equation of our line is
y = x + 6
A Store-It-All storage facility requires users to enter a four digit code, using numbers 0-9, to get through the gate. You need to get a box of winter clothes from your storage container, but you forgot the code.
How many possible codes are there if the digits cannot be repeated?
There are 5040 possible codes.
What is the probability that you will guess the correct code on your first try?
P(correct code) = Answer
1/5040
If the digits can be repeated, how many possible codes are there?
There are_______ different codes. ( Need this one answered)
There are 10000 different possible codes to guess the correct code on the first try..
A percentage, or a figure between 0 and 100 percent, can also be used to express probability. The likelihood of an event occurring increases with its probability value or percentage. How many potential outcomes an event has will determine how likely it is to occur.
1)There are 5040 possible codes if the digits are not repeated.
2)Probability of guessing correct code on first try p = 1/5040.
3)There are 10000 different codes, if the digits are repeated.
Given,
Total digits = 10.
{0,1,2,3,4,5,6,7,8,9}
4 digit code must be formed.
1. Code without repeating digits
→ 4 digit code
Therefore possible ways = 10×9×8×7
= 5040
2. Probability of guessing correct code on first try.
n(A)→ event which has correct code=1
n(S)→total possible ways=5040.
P(A) = n(A)/n(S) = 1/5040
3. If the digits are repeated
→ 4 digit repeated
Therefore possible ways = 10×10×10×10
= 104
= 10000 ways
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look at the pic and help need it done helppppppp
Answer:
A
Step-by-step explanation:
The opposite of cubing is cube root
cube rooting both sides would leave you with h = Sqr^3 of 343
If log x=5 , what is the value of 1/x ?
If the equation is log x=5 then the value of 1/x is equal to 0.00001.
Given that the equation is log x=5.
We are required to find the value of 1/x.
Equation is basically the relationship between two or more variables that are represented in equal to form. It may be linear equation,quadratic equation and cubic equation and many more depending on the power of variables present in the equation. The given equation contains logarithm.
The equation is log x=5.
Take the base of the log and raise it to both the sides of the equation:
[tex]10^{log x}[/tex]=[tex]10^{5}[/tex]
x=100000 (log 100000=5)
1/x=1/100000
1/x=0.00001
Hence if the equation is log x=5 then the value of 1/x is 0.00001.
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*Depressed 15 year old need helps* Brainliset to whoever responds i dont even care anymore if its right or wrong I wont judge ------decent points.....
[tex]y = \begin{cases}- 2x + 1& x > 1 \\- x + 2&x\leqslant1\end{cases}[/tex]
Step-by-step explanation:from the figure
(2,-3) (1,-1) => y = -2x + 1 (x > 1)(0,2) (1,1) => y = -x + 2 (x ≤ 1)[tex](x_1,y_1) \: (x_2,y_2) = >y = \frac{y_2 - y_1}{x_2 - x_1} \: x + a \\ a = y_1 - \frac{y_2 - y_1}{x_2 - x_1} \: x_1[/tex]
help would be appreciated <3
The coordinates of K' are (-2, 3) and the coordinates of M' are (-4, 1)
How to determine the coordinates of K' and M'?What are the coordinates of K'?
The graph represents the given parameter
On the graph, we have the following coordinates for point K
K = (4, 1)
The transformation vector is given as
[-6]
[2]
The transformation vector implies that
(x, y) = (x - 6, y + 2)
So, we have
K' = (4 - 6, 1 + 2)
Evaluate
K' = (-2, 3)
Hence, the coordinates of K' are (-2, 3)
What are the coordinates of M'?
The graph represents the given parameter
On the graph, we have the following coordinates for point M
M = (2, -1)
The transformation vector is given as
[-6]
[2]
The transformation vector implies that
(x, y) = (x - 6, y + 2)
So, we have
M' = (2 - 6, -1 + 2)
Evaluate
M' = (-4, 1)
Hence, the coordinates of M' are (-4, 1)
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0.25 (5 is recurring) decimal to fraction
Since the digit "5" is a recurring (repeating) in the given decimal, its fraction is equal to 23/90.
What is a fraction?A fraction can be defined as a numerical quantity which isn't expressed as a whole number. This ultimately implies that, a fraction is simply a part of a whole number.
The parts of a fraction.In Mathematics, a fraction comprises two (2) main parts and these include the following:
NumeratorDenominatorSince the digit "5" is a recurring (repeating) in the given decimal, its fraction can be written as follows:
0.25555556 = (25 - 2)/90
0.25555556 = 23/90
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AB formed by A(2, -7) and B(2, 3);CD formed by C(-4, 0) and D(-4, -5)
The length of the line AB is 10
The length of the line CD is 5
What is a line segment?A line segment is bounded by two distinct points on a line.
We have,
AB formed by A(2, -7) and B(2, 3)
CD formed by C(-4, 0) and D(-4, -5)
The distance between two points (a, b) and (c, d) is given by:
= √(c - a)² + (d - b)²
The length between A and B:
= √(2 - 2)² + (3 +7)²
= √100
= 10
The length of C and D:
= √(-4 + 4)² + (-5 - 0)²
= √25
= 5
Thus,
The length of the line AB is 10
The length of the line CD is 5
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this is for advanced math
Answer:
I don't think it is proportional
Step-by-step explanation:
i can't explain it bc it's like hard to explain so u gotta do that on ur own
Amy and Betty roll a fair cubical die numbered from 1 to 6. Find the probability that Amy rolls a higher number than Betty?
Answer: 5/12
Step-by-step explanation:
6x6=36
36 is all possible values.
1+2+3+4+5=15
The higher the number betty rolls there will be one less possible value that will be bigger than hers.
15/36=5/12
A basketball team played 15 games and won 80% of them.if the teamhow many more games must it win to finish the season with a 90% winning percentage
Answer:
1.5 more games to win 90% which would mean a total of 13.5 games.
80% of 15 = 12
10% of 15 = 1.5
12+1.5=13.5
In 1992, the moose population in a park was measured to be 3590. By 1999, the population was measured again to be 4500. If the population continues to change linearly
A.) Find a formula for the moose population, P, in terms of t, the years since 1990.
P(t)= ____
B.) What does your model predict the moose population to be in 2006?
Answer:
A.) P(t) = 130t +3330
B.) P(16) = 5410
Step-by-step explanation:
Given the ordered pairs (t, P(t)) = (2, 3590) and (9, 4500), you want a linear model that describes the relation. You also want the value of P(16).
A.) Linear modelWe can write the formula for P(t) starting with the point-slope equation for P in terms of t. To do that, we need the slope:
m = (P2 -P1)/(t2 -t1)
m = (4500 -3590)/(9 -2) = 910/7 = 130
The point-slope equation will be ...
P -P1 = m(t -t1)
P -3590 = 130(t -2)
Solving for P, we find ...
P = 130t -260 +3590 . . . . . eliminate parentheses, add 3590
P(t) = 130t +3330
B.) PredictionThe value of P(16) will be ...
P(16) = 130(16) +3330 = 2080 +3330 = 5410
The moose population is predicted to be 5410 in 2006.
__
Additional comment
The value of t is years since 1990, so the relevant values are ...
1992: t = 1992 -1990 = 2
1999: t = 1999 -1990 = 9
2006: t = 2006 -1990 = 16
Values of moose population by linear model A.) P(t) = 130t +3330 B.) P(16) = 5410
What does the term "linear model" mean?
In a linear model, the terms are added rather than multiplied, divided, or provided as a non-algebraic function, as has been the case thus far in this section. A linear model is not just a straight line or its higher dimensional equivalent.Given the ordered pairs (t, P(t)) = (2, 3590) and (9, 4500), you want a linear model that describes the relation. You also want the value of P(16).
A.) Linear model
We can write the formula for P(t) starting with the point-slope equation for P in terms of t. To do that, we need the slope:
m = (P2 -P1)/(t2 -t1)
m = (4500 -3590)/(9 -2) = 910/7 = 130
The point-slope equation will be
P -P1 = m(t -t1)
P -3590 = 130(t -2)
Solving for P, we find
P = 130t -260 +3590 . . . . . eliminate parentheses, add 3590
P(t) = 130t +3330
B.) Prediction
The value of P(16) will be
P(16) = 130(16) +3330 = 2080 +3330 = 5410
The moose population is predicted to be 5410 in 2006.
(B) The value of t is years since 1990, so the relevant values are
1992: t = 1992 -1990 = 2
1999: t = 1999 -1990 = 9
2006: t = 2006 -1990 = 16
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