If a symmetric matrix can be inverted into a diagonal matrix using another matrix, then it is diagonalizable. Accordingly, it may be said that there is a matrix P that can be inverted such that P-1 * A * P = D, where D is a diagonal matrix and A is the symmetric matrix. The diagonal entries of D are the appropriate eigenvalues, while the columns of P are the eigenvectors of A.
The matrix P is the foundation of the vector space because its columns are linearly independent and it is invertible. The inner product of any two different eigenvectors is 0, as A's eigenvectors are orthogonal to one another due to its symmetry.
We can divide each eigenvector by its norm to get an orthonormal basis from this collection of eigenvectors. As a result, a group of eigenvectors that are orthonormal to one another and serve as the vector space's orthonormal basis are produced.
Therefore, A symmetric matrix is diagonalizable and has an orthonormal eigen basis consisting of orthonormal eigenvectors, which can be obtained by dividing each eigenvector by its norm.
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Find the dimensions of a rectangular lot whose length is 2km more than its width if the area is 24km²?
Answer:
4 km wide and 6 km long.
Step-by-step explanation:
Let the width be x, then the length is x+2 km.
Area = width * length
Substituting the given values:
24 = x(x + 2)
24 = x^2 + 2x
x^2 + 2x - 24 = 0
(x + 6)(x - 4) = 0
x = -6, 4
As x must be positive, then x = 4.
So, the dimensions are 4 and 4+2
= 4, 6,
Answer:
width = 3.46 km and length = 6.93 km
Step-by-step explanation:
let the width be : X km
then the length would be: 2X km
as area is length x width
therefore:
2X x X = 24
2X² = 24
X² = 24/2
X² = 12
X = [tex]\sqrt{12}[/tex]
X= 3.46
the width would be 3.46 km while the length would be 2X = (93.46) = 6.93 km
what is the approzimate surface area (including both side and base) of a 4m high right circular cone
The surface area is approximately 100.5m².
Surface Area = πrl + πr²
Where r is the radius of the base and l is the slant height.
Surface Area = π(2m)(4m) + π(4m)²
Surface Area = 100.5m²
The surface area of a right circular cone can be calculated by using the formula surface area = πrl + πr². In this particular case, the height of the cone is 4m and the radius of the base is 2m. Therefore the surface area of the cone is calculated as follows: π(2m)(4m) + π(4m)² = 100.5m². This surface area includes both the base and sides of the cone.
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solve for w
-5/2 + 1/4w = -5/8
Answer: 15/2
Step-by-step explanation: -5/2 + 1/4W = -5/8
- 1/4W = -5/8 + 5/2
- 1/4W = 15/8
- W = 15/8 × 4
- W = 15/2
Triangle ABC has AB = 13, BC = 14, and AC = 15. The points D, E, and F are the midpoints of AB, BC, and AC respectively. Let X ≠E be the intersection of the circumcircles of Δ BDE and Δ CEF. What is XA + XB + XC?a. 24b. 14√3c. 195/8d. 129√7/14e. 69√2/4
The answer is C) 195/8
First, we can use the fact that A, B, C, D, E, and F are concyclic and that D, E, and F are the midpoints of AB, BC, and AC respectively.
Let r be the radius of the circumcircle of triangle ABC. Then using the Pythagorean theorem, we can find that r = (151413) / (4*K) where K is the area of the triangle.
Now we can use the property that the perpendicular bisectors of any triangle pass through the circumcenter of the triangle. We know that the midpoint of a line segment is the foot of the perpendicular from that point to the other endpoint. Then we can use the property that the radius from the circumcenter of the triangle to the midpoint of a side is half the length of that side.
Therefore, the circumcenter of triangle BDE is located at X = (BD/2, DE/2) = (13/2, 7/2) and the circumcenter of triangle CEF is located at X = (CE/2, EF/2) = (15/2, 7/2).
So the coordinates of X are (13/2, 7/2) and since the circumcenter of a triangle is equidistant from each vertex of the triangle, we can find that XA = XB = XC = r = r = (151413) / (4*K)
Therefore, XA + XB + XC = 3r = 3(151413) / (4*K) = (195/8)
So the answer is c. 195/8.
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Containers of gochujang, a Korean chili sauce, are sold at a market. The scatter plot shows the relationship between the cost of different containers and the amount of sauce in each container. A line of best fit is drawn through the data. Based on the line of best fit, what is the approximate cost per ounce of a container of gochujang at the market?
The approximate cost per ounce of a container of gochujang at the market is given as follows:
$0.5.
How to obtain the cost per ounce?As we have the graph of the linear function, the best way to define it is in slope-intercept form, as follows:
y = mx + b.
For which the parameters are given as follows:
m is the slope, representing the rate of change of the output variable relative to the input variable.b is the intercept, representing the value of y when x = 0.The cost per ounce is represented by the slope.
From the graph, we have that the graph starts at the origin, and when the number of ounces increases by 4, the cost increases by 2, hence the slope representing the cost per ounce is given as follows:
m = 2/4
m = $0.5.
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Does 12/16 20 form a right triangle?
The sides given as 16cm , 12cm and 20cm forms a right triangle because the sides satisfies the condition of Pythagoras Theorem .
What is Pythagoras Theorem ?
The Pythagoras Theorem states that the square of the longest side (hypotnuse) is equal to the sum of the square of the other two sides .
The sides of the triangle are given as ⇒ 16cm , 12cm and 20cm ;
here the hypotnuse (longest side) is = 20 cm ;
According to Pythagoras theorem ,
⇒ [tex]20^{2} =12^{2} +16^{2}[/tex] ;
⇒ [tex]400 =144+256[/tex] ;
⇒ [tex]400=400[/tex] ;
So , The condition of Pythagoras theorem is satisfied .
Therefore , the given sides can form a Right Triangle .
The given question is incomplete , the complete question is
Does the sides 16cm , 12cm and 20cm form a right triangle ?
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Which represents the polynomial written in standard form?
8x2y2 – 3x3y + 4x4 – 7xy3
4x4 – 3x3y + 8x2y2 – 7xy3
4x4 – 7xy3 – 3x3y + 8x2y2
4x4 + 8x2y2 – 3x3y – 7xy3
–7xy3 – 3x3y + 8x2y2 + 4x4
Answer:
A) 4x4 – 3x3y + 8x2y2 – 7xy3
Step-by-step explanation:
The polynomial written in standard form is: 4x4 + 8x2y2 - 3x3y - 7xy3. Option C
Which represents the polynomial written in standard form?In standard form, a polynomial is written with the highest exponents first and positive numbers in front of each term.
This means that the term with the greatest power comes first, followed by the terms in decreasing order of powers.
The polynomial is organized in option C like this.
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HELP PLEASE^^ (10 points)
A customer at a shipping store is planning to send a package and is considering two options. The customer can send a package for $5, plus an additional $2 per pound. The cost, y, can be represented by the equation y = 5 + 2x, where x represents the amount of pounds of the package. Another option is that the customer can pay a one-time fee of $15 to send the box, represented by the equation y = 15.
Based on the graph of the system of equations, when will the cost of the two shipping options be the same?
A. A package that weighs 15 pounds will cost $35 for both options.
B. A package that weighs 15 pounds will cost $25 for both options.
C. A package that weighs 10 pounds will cost $15 for both options.
D. A package that weighs 5 pounds will cost $15 for both options.
The solution is, D: A package that weighs 5 pounds will cost $15 for both options.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
here, we have,
The customer can send a package for $5, plus an additional $2 per pound.
The cost, y, can be represented by the equation y = 5 + 2x,
where x represents the amount of pounds of the package.
Another option is that the customer can pay a one-time fee of $15 to send the box, represented by the equation y = 15.
so, we get,
2x + 5 = 15
x = 5
Hence, The solution is, D: A package that weighs 5 pounds will cost $15 for both options.
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Answer:
D: A package that weighs 5 pounds will cost $15 for both options.
Step-by-step explanation:
2x + 5 = 15
x = 5
Thus, the person above me is correct :)
Please helpp ive been stuck in this exercise for an hourrrr(mathh)
let's keep in mind that a conjugate is no more than the same "pair" but with a different sign between, so the conjugate of meow + quack is simply meow - quack, and so on, let's also recall that i² = -1.
[tex]\textit{difference of squares} \\\\ (a-b)(a+b) = a^2-b^2 \\\\[-0.35em] ~\dotfill\\\\ -1-\sqrt{5}i\hspace{5em}\stackrel{conjugate}{-1+\sqrt{5}i} \\\\\\ (-1-\sqrt{5}i)(-1+\sqrt{5}i)\implies (-1)^2~~ - ~~(\sqrt{5}i)^2\implies (-1)^2~~ - ~~(\sqrt{5})^2 i^2 \\\\\\ 1~~ - ~~(\sqrt{5^2})i^2\implies 1~~ - ~~(5)(-1)\implies 1-(-5)\implies 1+5\implies \text{\LARGE 6}[/tex]
in early 2019, the us rate of recycling plastic water bottles was only 23%. a government agency designs an expensive program to increase the recycling rate. the program will be tested in texas and, if successful, it will be used nationally. a hypothesis test is conducted with h0: the proportion of water bottles that are recycled is still 23% after the program, and ha: the proportion of water bottles that are recycled is more than 23% after the program. what is a type i error and its consequence in this context?
A type I error, also known as a false positive, is when a test incorrectly rejects the null hypothesis. In this context, a type I error would mean that the test incorrectly concludes that the proportion of water bottles that are recycled is more than 23% after the program, when in reality it is still 23%.
1. Calculate the means of the two samples.
2. Calculate the standard deviation of the two samples.
3. Calculate the degrees of freedom (df) by subtracting 1 from the total
number of samples.
4. Calculate the t-statistic by subtracting the means of the two samples, dividing the result by the standard deviation, and then dividing that result by the square root of the degrees of freedom.
5. Calculate the critical value of t from the t-distribution table for the degrees of freedom and the chosen level of significance.
6. Compare the calculated t-statistic with the critical value of t.
7. Make a decision – accept or reject the null hypothesis.
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In what ratio is the line segment joining the points (- 3 2 and 6'1 is divided by Y axis?
Y-axis divides the line segment formed by the points ( -3 ,2) and ( 6,1) in the ratio equals to 1 :2.
As given in the question,
Coordinates of the line segment is given by :
( x₁ , y₁ ) = (-3, 2)
(x₂ , y₂ ) = ( 6,1)
Let the ratio of the given line segment divided by the y -axis that is ( x, y) = ( 0, y ) be m : n given by the formula:
( x, y ) = [ ( mx₂ + nx₁) /(m +n) , (my₂ + ny₁ ) / ( m + n ) ]
Substitute the values we get,
( 0 ,y ) = [ ( 6m -3n) /(m +n) , (1m + 2n ) / ( m + n ) ]
⇒ ( 6m -3n) /(m +n) = 0
⇒ 6m -3n = 0
⇒ 6m = 3n
⇒m : n = 1 : 2
Therefore, y-axis divides the given line segment into the ratio 1 : 2.
The above question is incomplete, the complete question is :
In what ratio is the line segment joining the points (- 3 2) and (6,1) is divided by Y-axis?
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Sydney invests $100 every month into an account that pays 0.8% annual interest, compounded monthly. Benny invests $80 every month into an account that pays 2.2%
annual interest rate, compounded monthly.
a. Determine the amount in Sydney's account after 10 years.
b. Determine the amount in Benny's account after 10 years.
c. Who had more money in the account after 10 years? Sydney
d. Determine the amount in Sydney's account after 30 years. $40,672.12
e. Determine the amount in Benny's account after 30 years.
f. Who had more money in the account after 30 years? Benny
For Sydney with $100 at 5%, monthly, for 10 year we get 229050.
What is meant by annual interest rate?Annual percentage rate (APR) refers to the yearly interest generated by a sum that's charged to borrowers or paid to investors. APR is expressed as a percentage that represents the actual yearly cost of funds over the term of a loan or income earned on an investment.
The interest rate is the amount a lender charges a borrower and is a percentage of the principal—the amount loaned. The interest rate on a loan is typically noted on an annual basis known as the annual percentage rate (APR).
Let the equation be
A = [ p(1 + r/n)nt ] + [ PMT ((( 1 + r/n)nt - 1) / (r / n)) ]
For Sydney with $100 at 5%, monthly, for 10 year
A = [ 100(1 + 0.05/12)(12)(10) ] + 100 (((1 + 0.05/12)(12)(10) - 1) / (0.05 / 12)) ]
= 229050
Therefore, the correct answer is 229050.
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1. what is the equation in slope-intercept form of a line whose slope is 9 and whose y-intercept is -3?
The equation in slope-intercept form of a line whose slope is 9 and whose y-intercept is -3 is equals to the y = 9x-3.
Slope intercept form of an equation : The slope intercept form is one of method to determine the equation of a straight line in the coordinate plane. The equation of a straight line is a relation which:
the coordinates of any point must be satisfied if point on the line.the coordinates of any point can't satisfied if point not on the line.Let us assume a straight line of slope 'm' and y-intercept 'b'. The equation of slope intercept form for a straight line with slope, say, 'm', and the y-intercept, 'b', is
y = mx + b
Now, the slope of line , m = 9
y-intercept of line, b = - 3
As we know slope intercept form of a line is, y = mx + b , so plugging the known values of slope and y-intercept in it,
=> y = 9x - 3
So, required equation in slope intercept form of line is y = 9x - 3.
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jason is a skilled rapper. he has already rapped a 40-word intro to a song and continues to rap 5 words per second
write an inequality to determine how many more seconds t he will rap to complete the song if the total song, including the intro, is at least 500 words.
drag each numbers or symbol into each box to correctly complete the inequality
hint
500
40
3
>
500
40
+
check
de toch
o
Answer:
500 > 40 + 5t
Step-by-step explanation:
At least 500
40 intro = initial, constant
t = time in seconds
5 words per second
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The scatter plot above shows the average rent (in dollars) for a 111-bedroom apartment in New York City each year between 200020002000 and 201320132013. Which of the following is the best estimate of the average change in rent each year
The best estimate of the average change in rent each year include the following: C. $40.
How to determine the average change in rent each year?Mathematically, the rate of change is also referred to as slope or gradient and it can be calculated by using this formula;
Rate of change, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Rate of change, m = (y₂ - y₁)/(x₂ - x₁)
Next, we would determine the rate of change of the value of y with respect to the value of x on the scatter plot, which represents a line that is passing through the points (0, 800) and (10, 1200):
Rate of change, m = (1200 - 800)/(10 - 0)
Rate of change, m = 400/10
Rate of change, m = 40.
Based on the scatter plot, we can reasonably infer and logically deduce that the average rate of change in rent each year is equal to 40 dollars.
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Complete Question:
The scatter plot below shows the average rent (in dollars per month) for a 1-bedroom apartment in New York City each year between 2000 and 2013.
Which of the following is the best estimate of the average change in rent each year?
answer choices
$0.5
$1
$40
$400
Paige has a cell phone plan that charges $0. 06 per minute plus a monthly fee of $15. 0. She budgets $25. 50 per month for
her total cell phone expenses without taxes.
What is the maximum number of minutes Paige could use her phone each month and still stay within her budget?
Therefore , the solution of the given problem of linear equation comes out to be 550 minutes she can use her cell phone.
The definition of a linear equation.A linear regression model is one that conforms to the algebraic equation y=mx+b. The slope is B, and the y-intercept is m. The previous clause is usually referred to as an "mathematical equation having two variables because both y and x are unique parameters. Two variables make up bivariate linear equations. Linear equations have a variety of applications, all of which have a zero outcome. Y=mx+b, where m stands for the gradient and b for the y-intercept, is the formula for a linear equation.
Here,
Given : 55=0.1(m-500)+50
where m is the number of minute
=> 55=0.1(m-500)+50
=> 55=0.1m-50+50
=>55=0.1m-0
=>55-0=0.1
=>55=0.1
=>0.1=0.1
=>550=m
Therefore , the solution of the given problem of linear equation comes out to be 550 minutes she can use her cell phone.
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Answer the following:-
[tex]\sf 4\div 2+33-2+5[/tex]
Answer:
38
Step-by-step explanation:
4/2+33-2+5=2+33-2+5=35-2+5=33+5=38
What are real numbers?
Is the quotient of two real numbers an integer?
Answer:
real number, in mathematics, a quantity that can be expressed as an infinite decimal expansion. Real numbers are used in measurements of continuously varying quantities such as size and time, in contrast to the natural numbers 1, 2, 3, …, arising from counting
Step-by-step explanation:
The quotient of any two integers is an integer.
A real number is a number that can be measured and represented on a number line; this includes fractions, decimals, irrational numbers, rational numbers, and basically every number you encounter. With that in mind, the quotient of 2 real numbers is not necessary an interger as 2.01/ 1 is not an integer
on an old-fashioned bicycle the front wheel has a radius of 2.5 feet and the back wheel has a radius of 4 inches. if there is no slippage, how many revolutions will the back wheel make while the front wheel makes 100 revolutions?
Therefore , the solution of the given problem of circle comes out to be 100 rotations of the front tire will be made by the back wheel.
What does a circle represent?Each point in the plane whose distance from that other point is a certain value forms a circle (center). It is therefore a curve composed of vertices that are spaced apart from one another in the plane by a specific amount. Furthermore, it is symmetrical about the center at all angles in terms of rotation. The closed, two-dimensional plane of a circle has all pairs of endpoints equally separated from the "center." When a line is drawn through the circle, a circle symmetry line is created. Furthermore, it rotates equally from all angles about the center.
Here,
The circle of the rear wheel is equal to circle = diameter x π, or 2.5 feet by 12 inches, or 30 inches.
The length of the front axle is 30 x 2 = 60 inches.
The diameter of the front wheel, C, is equal to 60 x Pi, or 60π, in inches.
The diameter of a back wheel is 4 x 2 = 8 inches.
The circumference of back wheel is C = 8 x Pi = 8π in inches.
750 revolutions are equal to
100 × [60Pi/8π] = 6,000π/8π.
100 rotations of the front tire will be made by the back wheel.
Therefore , the solution of the given problem of circle comes out to be 100 rotations of the front tire will be made by the back wheel.
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Is all real numbers infinity?
Yes, the set of all real numbers is uncountably infinite but "infinity" is not a member of the set of real numbers.
Basically, The real numbers R is the set of "all the numbers" on the number line that includes the rationals and irrationals together.
The real numbers are an uncountably infinite set – there actually are far more real numbers than there are natural numbers, and there is no way to line up the reals and the naturals so that we are assigning exactly one real number to each natural number. Hence there is no possible way of counting the number it can be considered in the category of uncountably infinite. If the domain of a function is all real numbers, you can represent this using interval notation as (−∞,∞), however "infinity" is not a member of the set of real numbers.
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four ambassadors and one advisor for each of them are to be seated at a round table with 12 chairs numbered in order 1 to 12. each ambassador must sit in an even-numbered chair. each advisor must sit in a chair adjacent to his or her ambassador. there are $n$ ways for the 8 people to be seated at the table under these conditions. find the remainder when $n$ is divided by $1000$.
Therefore , the solution of the given problem of combination comes out to be 479001.6.
Combination : What is it?Combinations are mathematical procedures that count the number of possible configurations from a set of items, where the selection direction is immaterial. You can select any arrangement of the parts in any combination. It's possible to mix together combinations and permutations.
Here,
Given : four ambassadors and one advisor for each of them are to be seated at a round table with 12 chairs numbered in order 1 to 12..
and n ways for seating 8 people.
Thus , to find this permutation- combination arrangement .
So,
nPr => 6 P 6 and * 12P6
nPr => 665280 * 720
nPr = > 47,90,01,600
and divide it by 1000 .
So ,
=> 479001600/1000
=> 479001.6
Therefore , the solution of the given problem of combination comes out to be 479001.6.
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1) 77.2 - 43.778 =
2) 2.072 ÷ 5.6 =
3) 6.811 × 4.997 =
4) 27.001 - 7.5 =
5) 4.23 × 9 =
6) 19.2 + 31.82 =
7) 97.68 - 32.3 =
8) 0.468 ÷ 6.5 =
9) 0.6144 ÷ 1.6 =
10) 4.4 × 2.727 =
11) 20.97 + 85.62 =
12) 48 + 58.1 =
Add computations
Adding 3 points with computation
Answer:
1) 33.422
2) 0.37
3) 34.034567
4) 19.501
5) 38.07
6) 51.02
7) 65.38
8) 0.072
Cheers
Complete the system of equations with a linear equation so that the graphs of the equations intersect at their x- and y-intercepts.
y=x^3+4x+3x+12
y=?
The required system of equation is given as y = 3x + 12 and y=x³+4x²+3x+12.
What is the equation?The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.
Given equation,
y=x³+4x²+3x+12
To determine the x-intercept put equation y = 0
0 = x³+4x²+3x+12
Factorize the above equation
0=(x²+3)(x+4)
One of the factors from above is given as
x+4=0
x = -4
The x-intercept is (-4,0)
For the y-intercepts, x=0 and solve.
y = 12
y = 12
The y-intercept is (0,12)
Now equation of the line passing these points is given as.
m = (y₂ - y₁) / (x₂ - x₁)
m = 12/3
m = 3
C, we already have C=12
So the equation of the line is
y = mx + c
y=3x+12
Thus, the required system of equation is given as y = 3x + 12 and y=x³+4x²+3x+12.
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Which point is located at 4, -2?
Answer:
B
Step-by-step explanation:
the 4 is how far along you go on the x-axis (horizontal line).
the -2 is saying it needs to be 2 boxes below 0 on the y-axis (vertical line).
therefore the answer is b
Leslie has comprehensive insurance with a $500 deductible on her van. On Halloween her van is vandalized, and the damages total $1,766. Leslie submits a claim to her
insurance company.
a. How much must Leslie pay for the repair?
b. How much must the insurance company pay?
Answer:
a. Leslie must pay the first $500 of the repair costs, as that is her comprehensive insurance policy's deductible.
b. The insurance company must pay the remaining $1,266 of the repair costs, as that is the total cost of the repairs ($1,766) minus Leslie's portion of the cost (the $500 deductible).
2. ALGEBRA On April 14, Mikos Souvakis borrowed $100,000 to remodel
his restaurant kitchen with a single-payment loan at 10. 5% ordinary
interest. If his loan's maturity value was $104,375, when does Mikos
have to pay it back?
and
We may apply the simple interest formula to find the due date for repayment from Mikos is 5 months.
I = P*r*t, where I represents interest, P the principal (initial sum), r the interest rate, and t the period of time in years.
The maturity value formula can be used to calculate interest given that the loan's principal is $100,000 and its maturity value is $104,375:
Where MV is the maturity value, P is the principal, and I is the interest, the formula is: MV = P + I.
With the above data, we obtain: 104,375 = 100,000 + I
I = 4,375.
Now we can use this value of I to find the time t in years:
I = P*r*t
4,375 = 100,000 (0.105) t
t = 4.375 / (100,000 x 0.105)
t = 4.375 / 10,500
t = 0.417 years or approximately 5 months
So, it takes approximately 5 months to repay the pay back amount .
Therefore, Mike must repay the amount by April 14, which is around five months after the day he took out the loan.
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what is the total number of points of intersection of the graphs of the equations y 5 ex and xy 5 20 ?
A. The total number of points of intersection of the graphs of the equations y = 5e^x and xy = 20 is two.
To find the points of intersection, we must solve the two equations for x and y.
For the first equation, y = 5e^x, we can solve for x by taking the natural logarithm of both sides and getting x = ln(y/5).
For the second equation, xy = 20, we can solve for y by dividing both sides by x and getting y = 20/x.
We can then substitute the expression for x in terms of y into the expression for y in terms of x and solve for y to get y = 20/(ln(y/5)). This is a nonlinear equation that must be solved numerically.
By using numerical methods, we can solve the equation and find the two points of intersection, which are (x, y) = (3.68, 4.64) and (x, y) = (0.87, 22.95).
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Colin deposited $1,230 in an account that pays 3.19% simple interest for three years.a. What will the interest be for the three years?
b. What will be the new balance after three years?
[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$1230\\ r=rate\to 3.19\%\to \frac{3.19}{100}\dotfill &0.0319\\ t=years\dotfill &3 \end{cases} \\\\\\ A = 1230[1+(0.0319)(3)] \implies \stackrel{balance}{\boxed{A \approx 1347.71}}~\hfill \underset{interest}{\stackrel{1347.71~~ - ~~1230}{\boxed{117.71}}}[/tex]
Which set of ordered pairs does not represent a function?
A company models its net income, in thousands of dollars, with the function f(x) = 9x2 – 54x – 144, where x is the number of units of its product sold. How many units of its product does the company need to sell in order for the net income to equal $0?
Solving the quadratic equation, it is found that the company needs to sell 8 products for the net income to be equal $0.
What is the quadratic equation for the net income of the company?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
here, we have,
It is given by:
f(x) = 9x² - 54x - 144.
It can be simplified as follows:
f(x) = 9(x² - 6x - 16)
Then:
f(x) = 9[(x + 2)(x - 8)]
It has a net income equals to 0 when:
f(x) = 0,
hence:
x + 2 = 0 -> x = -2.
x - 8 = 0 -> x = 8.
The amount of products sold is positive, hence, the company needs to sell 8 products for the net income to be equal $0.
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