The x-intercepts and the y-intercept of the cubic function f(x) = x³ - 9·x² + 20·x - 12 for which (x - 6) is a factor are;
The x-intercepts are; (6, 0), (2, 0), and (1, 0)The y-intercepts of the function is the point (0, -12)What is a function?A function is a rule that uniquely maps each value from the set of input variables to exactly one value in the set of the output variables.
The specified cubic function is; f(x) = x³ - 9·x² + 20·x - 12
A factor of f(x) = x - 6
The x-intercepts are the points on the graph of the function, where the value of the function, f(x) = 0, which are found as follows;
At the x-intercept, f(x) = x³ - 9·x² + 20·x - 12 = 0
x³ - 9·x² + 20·x - 12
Dividing the cubic function by the factor (x - 6), we get;
x² - 3·x + 2
(x - 6) | x³ - 9·x² + 20·x - 12
[tex]{}[/tex] x³ - 6·x²
[tex]{}[/tex] -3·x²
[tex]{}[/tex] -3·x² + 18·x
[tex]{}[/tex] 2·x
[tex]{}[/tex] 2·x - 12
[tex]{}[/tex] 0
The other factor of the cubic function is; x² - 3·x + 2
x² - 3·x + 2 = (x -2)·(x - 1)
Therefore;
f(x) = x³ - 9·x² + 20·x - 12 = (x - 6)·(x - 2)·(x - 1)
From which at the x-intercepts, we get;
f(x) = (x - 6)·(x - 2)·(x - 1) = 0
x = 6, x = 2, and x = 1
The x-intercepts are the points (6, 0), (2, 0), and (1, 0)The y-intercept are the points the x-values is zero, therefore, at the y-intercepts, we get;
f(0) = 0³ - 9·0² + 20·0 - 12 = -12
The y-intercept is the point (0, -12)Learn more on the graph of a cubic function here: https://brainly.com/question/29052227
#SPJ1
Mr.Heritage invests $6000 total into two diffent bank accounts. One account pays 8% interest annually. The second par 10% interest antally. If he earns $560 in interest after one year, how much did he put in each account?
The amount invested in the two different bank accounts which has a simple interest of $ 560 is $ 2000 and $ 4000 respectively
What is Simple Interest?Simple interest is a method of calculating interest that ignores the impact of compounding. While interest frequently compounds throughout the course of a loan's set periods, simple interest does not. Simple interest is calculated by multiplying the principal amount by the interest rate, times the number of periods.
Simple Interest = ( Principal Amount x Rate x Time Period ) / 100
Given data ,
Let the simple interest be represented as SI
The value of SI = $ 560
Now , the total amount A = $ 6000
Let the first bank account be A
Let the second bank account be B
The amount invested in the bank account A be = P
The amount invested in the bank account B be = ( 6000 - P )
The rate of interest of bank account A = 8 %
The rate of interest of bank account B = 10 %
Now ,
The SI of bank account A = ( Principal Amount x Rate x Time Period ) / 100
Substituting the values in the equation , we get
The SI of bank account A = ( P x 8 x 1 ) / 100
The SI of bank account A = 8P/100
And ,
The SI of bank account A = ( Principal Amount x Rate x Time Period ) / 100
Substituting the values in the equation , we get
The SI of bank account A = [ ( 6000 - P ) x 10 x 1 ] / 100
The SI of bank account A = ( 60000 - 10P ) /100
And , the total SI = $ 560
So ,
8P/100 + ( 60000 - 10P ) /100 = 560
Multiply by 100 on both sides of the equation , we get
8P + 60000 - 10P = 56000
On simplifying the equation , we get
-2P = -4000
Divide by -2 on both sides of the equation , we get
P = $ 4000
So , the amount invested in bank account A = $ 4000
And , the amount invested in bank account B = $ 2000
Hence , the amount invested is $ 4000 and $ 2000 respectively
To learn more about simple interest click :
https://brainly.com/question/17282817
#SPJ1
Find the values of k and m in the parallelogram?
Answer:
In order to find the values of k and m in a parallelogram, you would need to have additional information such as the coordinates of the points that make up the parallelogram and the formulas or equations that relate k and m to these points.
Here is one way to find the values of k and m in a parallelogram:
Label the four vertices of the parallelogram as A, B, C, and D with the opposite sides parallel to each other.
Find the slope of the line segment AB by using the formula (y2-y1)/(x2-x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.
Let the slope of AB be represented by k.
Find the slope of the line segment AD by using the same formula and let it be represented by m.
The values of k and m are now found.
Please note that, this method is only applicable if the Parallelogram is not degenerate i.e, it is not a rectangle or a line.
It is also important to keep in mind that different formulas or equations may be used depending on the specific context of the problem. It is also important to check that the slopes of opposite sides are equal.
Step-by-step explanation:
The actual sum is
0
A i need help for this math please
Answer:
the answer is 0
Step-by-step explanation:
because the question you asked has no digits other than 0
PLEASE HELP ME ASAP IREADY
4 hundreds is 10 times as much as 4 thousandths
No, 4 hundreds is not 10 times as much as 4 thousandths.
How to compare 4 hundreds and 4 thousandths?Numbers in the tens are numbers that are multiples of 10, such as 10, 20, 30, 40, etc.
4 hundreds is equal to 4 × 100 = 400.
4 thousandths is equal 4/1000 = 0.004
To compare their magnitudes, we can divide 0.4 by 0.004:
400 ÷ 0.004 = 100000
So 4 hundreds (400) is significantly larger than 4 thousandths (0.004).
Therefore, 4 hundreds is 100000 times as much as 4 thousandths.
Learn more about Numbers in tens on:
brainly.com/question/23846183
#SPJ1
Ill give brainiest for the answer
Answer:
m∠10 = 41°
Step-by-step explanation:
If ∠9 and ∠10 are complementary. Then ∠7 and ∠8 are complementary as well. Complementary angles meameansns they sum up to 90 degrees.
m∠7 + m∠8 = 90
m∠7 + 41 = 90
m∠7 = 90 - 41 = 49°
Given that m∠7 ≅ m∠9. So m∠9 = 49° and m∠10 = 41°.
what is the solution to this equation?
[tex](\frac{1}{4})x^+{1}=32[/tex]
[tex]\cfrac{1}{4}x+1=32\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{4}}{4\left( \cfrac{1}{4}x+1 \right)=4(32)}\implies x+4=128\implies x=124[/tex]
Multiply the previous term by 3 and subtract 4 The second term of the sequence is 5. Find the difference between the first and fourth terms of the sequence.
Answer:
72
Step-by-step explanation:
Given that the second term of the sequence is 5, and that we are to multiply the previous term by 3 and subtract 4, we can use that as a recursive formula to find the other terms of the sequence.
The first term of the sequence is:
5*3-4 = 11
The third term of the sequence is:
53-4=11
113-4=29
The fourth term of the sequence is:
53-4=11
113-4=29
29*3-4=83
The difference between the first and fourth terms of the sequence is:
83-11 = 72
So the difference between the first and fourth terms of the sequence is 72.
I will give brainliest, if you get this correct
Answer: the estimated maintenance cost of cars when the age of cars is 12 years is 16.5 ( in 100 birr)
Step-by-step explanation:
To obtain the regression equation for costs related to age of cars, we can use the method of least squares. This method involves finding the line of best fit that minimizes the sum of the squared differences between the predicted values and the actual values.
The equation for a linear regression line is:
y = a + bx
where a is the y-intercept and b is the slope of the line.
To find the slope of the line (b), we can use the formula:
b = (n(∑xy) - (∑x)(∑y)) / (n(∑x^2) - (∑x)^2)
To find the y-intercept (a), we can use the formula:
a = (∑y - b(∑x)) / n
Given the data provided, we can calculate the following values:
∑x = 142
∑y = 150
∑xy = 2430
∑x^2 = 10304
n = 8
By substituting these values into the formulas for b and a, we can find the slope and y-intercept of the line:
b = (8(2430) - 142(150)) / (8(10304) - 142^2) = 0.5
a = (150 - 0.5(142)) / 8 = 13.5
Therefore, the regression equation for the costs related to age of cars is:
y = 13.5 + 0.5x
To estimate the maintenance cost of cars when the age of cars is 12 years, we can substitute x = 12 into the equation and solve for y:
y = 13.5 + 0.5(12) = 16.5
So the estimated maintenance cost of cars when the age of cars is 12 years is 16.5 ( in 100 birr)
How do you do this math problem involving csc? Can you do it on a ti-84 calculator?
Explanation:
The TI-84 calculator is fairly powerful and can handle things like this, but it's not needed to be honest. Any calculator will do.
"csc" is shorthand for "cosecant". It's the reciprocal of sine.
csc = 1/sin
Recall that
sin = opposite/hypotenuse
which means
csc = 1/sin = hypotenuse/opposite
What we'll need are the hypotenuse and opposite sides. Plot the points (0,0) and (-20,21). Draw a segment between them. This forms the hypotenuse of the right triangle shown below. This triangle is in the quadrant Q2 in the upper left corner. The hypotenuse 29 is found using the pythagorean theorem a^2+b^2 = c^2.
Use a = 20 and b = 21 to find c = 29.
According to that diagram, we can then say:
csc = hypotenuse/opposite = 29/21
7Mr's sharma spends 17/25 parts of her earning of her children education. how many childrene percent does she spends on her daughter education How many percent does she save.
If Mrs. Sharma spends 17/25 parts of her earnings on her children's education, then she is spending (17/25) x 100 = 68% of her earnings on her children's education.
If the number of children is the same, she spends 68%/number of children on her daughter education.
If she spends 68% of her earnings on her children's education, then she is saving 100 - 68 = 32% of her earnings.
So, she spends 68% on her daughter education and she saves 32% of her earning.
She drove a total distance of 86,028.8 yd on a race track. He drove 13 laps where each lap was the same lefty. what was the length to if each lap? Write your answer in miles.
each of the lap is of length 6617.6 miles.
What are Distance and velocity?
a velocity is a unit of measurement for the Distance an object travels in a
the predetermined period of time. Here is a word equation that illustrates the
connection between space, speed, and time: velocity is calculated by
dividing the total Distance traveled by the journey time.
Diane and Douglas both drive at an average rate of 50 miles per hour. So if they travel for the same time they will end up covering the same distance as well.
As we know velocity = rate of change of displacement or
She drove a total distance of 86,028.8 yd on a race track.
He drove 13 laps where each lap was the same lefty.
each lap is 86028.8/13 = 6617.6
Hence each of the lap is of length 6617.6 miles.
Learn more about Distance and velocity , by the following link.
brainly.com/question/4931057
#SPJ1
To which set does the number
11 belong. Choose the most descriptive answer.
O rational
O irrational
O whole
O natural
Answer:
Step-by-step explanation:
The number 11 belongs to the set of natural numbers. Natural numbers are the set of all positive whole numbers, including 0, and the number 11 is a positive whole number.
3) You inherit $2,500 and decide to invest it in an account that earns 1.5% interest
compounded monthly.
a) Write an equation to model this scenario.
b) How much money is in the account 15 years after you first invested?
Therefore , the solution of the given problem of interest comes out to be
A = $3,130.37 is the amount after 15 years.
What exactly is meant by interest?Simple interest is calculated by dividing the principal by the borrowing cost, the remaining time, and other elements. The simple return formula in marketing is principal + interest plus hours. Utilizing this method is the simplest way to calculate interest. As a percentage of the principle sum is the most frequent way to calculate income. For instance, he will only pay his portion of the 100% cost if he borrows $100 from a friend and agrees to pay the loan back with 5% interest.. You have to pay interest on money you borrow, and you have to charge interest on money you lend.
Here,
Given :
a ) the equation that can be formed is
2500x - 1.5y = 30
b)
Using compound formula :
=> Then solve the equation for A
A = P(1 + r/n)nt
A = 2,500.00(1 + 0.015/12)(12)(15)
A = 2,500.00(1 + 0.00125)(180)
A = $3,130.37
To know more about interest visit:
https://brainly.com/question/28792777
#SPJ1
$2750 is invested at an interest rate of 3.5% APR compounded quarterly. Determine the amount after 7 years. Round your answer to the nearest hundredth.
Answer:
The compound interest formula is A = P(1 + r/n)^(nt) where A is the final amount, P is the principal (initial deposit), r is the annual interest rate (expressed as a decimal), n is the number of times interest is compounded per year, and t is the number of years.
In this case, P = 2750, r = 0.035, n = 4 (because interest is compounded quarterly) and t = 7 (because we are trying to find the balance after 7 years).
So the formula becomes:
A = 2750(1 + 0.035/4)^(4*7)
By plugging the number into the formula we can find the final amount after 7 years
A = $3,974.23
So the amount of money in the account at the end of 7 years is $3,974.23, rounded to the nearest hundredth.
Does anyonw know how to solve:
cos2a=4/5?
The value of a is 18.43°
What are trigonometric ratios?The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).
Given that, cos2a=4/5
cos 2a = 4/5
2a = cos⁻¹(4/5)
2a = 36.86°
a = 18.43°
Hence, the value of a is 18.43°
Learn more about trigonometric ratios, click;
https://brainly.com/question/25122825
#SPJ1
9 cm Find the area of the square. Remember A = s² Area of the square cm 2
identify the vertex of the parabola
I WILL MARK BRAINLIEST
Answer:(1,0) which is the second one in the picture
Step-by-step explanation:The vertex is in (1,0).
Maureen bought a new car worth $26,525 one year ago. She knows that her car's value will depreciate each year. She uses an online calculator to find that her car is worth $24,403 today. Write an exponential equation in the form y = a(b) that can model the value, y, of Maureen's car x years after purchase. Use whole numbers, decimals, or simplified fractions for the values of a and b.
The exponential equation that models the function of Maureen's car is 26,525 (0.92)
a = 26,525 and b = 0.92
What is an exponential function?Exponential function is a type of function of the form: f(x) = a(b)^x. It is made up of 3 main parts
a = the starting value
b = the base function
x = the exponents
Considering the problem,
the starting = $26,525
the base = depreciation
the exponents = x
A year ago hence x = 1
$24,403 = $26,525(b)¹
b = 24,403 / 26,525
b = 0.92
hence we can say that a = 26,525 and b = 0.92
Learn more about exponential function here:
https://brainly.com/question/29716012
#SPJ1
solve the inequality:
||x-3|-2|≤1
Answer:
-1 ≤ x ≤ 5
Step-by-step explanation:
-1 ≤ x ≤ 5 is the answer
Two alien spaceships start traveling toward each other from space stations that are 710,000 km apart. The first spaceship started an hour before the second spaceship and is traveling at 110,000 km/hr. In how many hours will the two spaceships meet if the second spaceship is traveling at 90,000 km/hr?
Answer:
They will meet after 4 hours from the departure------------------------
The distance is 710000 km and the first spaceship has travelled 110000 km in the first hour.
The remainder of the distance is reducing by:
110000 + 90000 = 200000 km an hourTime to travel before they meet:
(710000 - 110000)/200000 = 600000/200000 = 3 hoursAdd the first hour to this to get total travel time of 4 hours.
As of 2018, the population of Turks and Caicos is 37,910 people. The Locust Grove football field is 120
yd. x 54 yd. If each person takes up 2 square feet, can the entire population of Turks and Caicos fit on
our football field?
Answer:
Step-by-step explanation:
No, the entire population of Turks and Caicos would not be able to fit on the football field. The total area of the football field is 6,480 square yards, which is equivalent to 13,728 square feet. Since each person takes up 2 square feet, this means that only 6,864 people could fit on the field. Therefore, the population of Turks and Caicos is more than double the amount of people that could fit on the football field.
Cyprian was allowed a discount of 11% for goods at sh 800 and a discount of 8.6% for worth 17000.What percentage discount was he allowed altogether
The percentage discount that Cyprian was allowed altogether was 8.21%.
What is the percentage discount?The percentage discount is a portion of the sales price that reduces the amount the purchaser or customer pays for their purchase.
Percentages are ratios of a value or variable compared to another or the whole matter.
We express Percentages as the quotients of the division operations multiplied by 100.
In this situation, the overall percentage discount is worked out step by step as follows:
Discount on goods worth Sh. 800 = 11%
= Sh. 88 (Sh. 800 x 11%)
Discount on goods worth Sh. 17,000 = 8.6%
= Sh. 1,462
The total value of goods = Sh. 17,800 (Sh. 800 + Sh. 17,000)
Percentage discount = 8.21% (Sh. 1,462/Sh. 17,800 x 100)
Thus, overall, the total discount based on the full value of goods Cyprian bought was 8.21%.
Learn more about percentage discounts at https://brainly.com/question/843074
#SPJ1
Need help for 50 points.
Answer:
Step-by-step explanation:
Answer:
The Graph is Below
Step-by-step explanation:
Please help to solve this
Hope it helps.
If you have any query, feel free to ask.
The function is defined below. (Will give brainliest.)
H(x)= x+2/x^2+4x+4
Find all values of that are NOT in the domain of H.
If there is more than one value, separate them with commas.
The value of x that is not in the domain of the function is given as follows:
x = -2.
What is the domain of a function?The domain of a function is the set that contains all the possible input values for the function.
The function in this problem is defined as follows:
H(x) = (x + 2)/(x² + 4x + 4).
The function is a fractional function, meaning that the denominator cannot assume a value of zero.
Hence the values of x that are not in the domain of the function are obtained as follows:
x² + 4x + 4 = 0
(x + 2)² = 0
x + 2 = 0
x = -2.
Hence the value of x = -2 does not belong to the domain of the function H(x), as it would make the denominator assume a value of zero.
More can be learned about the domain of a function at https://brainly.com/question/10687170
#SPJ1
what is the solution to -82-3(2x+4)=2(7x+1)-3(2x+4)
Answer:
according to BODMAS RULE
first step is to open the bracket , and solve
-82 - 6x - 12= 14x + 2 -6x -12
-82=14x + 2
-84 = 14x
x= -6
Find the set (A n C)'. U= (1, 2, 3, 4, 5, 6, 7, 8) A = (1, 2, 3, 4) C=1,2,3,6,8
1234 in. set A and 1234 in set B and 1234 in set C so the answer is (1234)
The value of the set ( A ∩ C )' = A' ∪ C' = { 4 , 5 , 6 , 7 , 8 }
What is Set Theory Formula?The set formula is given in general as n(A∪B) = n(A) + n(B) - n(A⋂B), where A and B are two sets and n(A∪B) shows the number of elements present in either A or B and n(A⋂B) shows the number of elements present in both A and B.
Given data ,
Let the universal set be represented as U
The value of U = { 1, 2, 3, 4, 5, 6, 7, 8 }
Let the value of set A = { 1 , 2 , 3 , 4 }
Let the value of set C = { 1 , 2 , 3 , 6 , 8 }
Now , the equation of set is ( A ∩ C )'
The value of ( A ∩ C )' = A' ∪ C'
Substituting the values in the equation , we get
A' = U - A
A' = { 1, 2, 3, 4, 5, 6, 7, 8 } - { 1 , 2 , 3 , 4 }
A' = { 5 , 6 , 7 , 8 }
And ,
C' = U - C
C' = { 1, 2, 3, 4, 5, 6, 7, 8 } - { 1 , 2 , 3 , 6 , 8 }
C' = { 4 , 5 , 7 }
So , ( A ∩ C )' = A' ∪ C'
Substituting the values in the equation , we get
( A ∩ C )' = { 4 , 5 , 6 , 7 , 8 }
Hence , the set ( A ∩ C )' is { 4 , 5 , 6 , 7 , 8 }
To learn more about sets click :
https://brainly.com/question/26397859
#SPJ2
In ΔXYZ, x = 89 cm, z = 84 cm and ∠Z=70°. Find all possible values of ∠X, to the nearest degree.
The value of angle X Is 85° ( nearest degree)
What is sine rule?The sine rule states that if a, b and c are the lengths of the sides of a triangle, and A, B and C are the angles in the triangle; with A opposite a, etc., then a/sinA=b/sinB=c/sinC.
the law of sines is used to solve the triangle, when we know two angles and one side or two angles and one included side. It means that the law of sines can be used when we have ASA (Angle-Side-Angle) or AAS (Angle-Angle-Side) criteria.
therefore x/sin X = z/sinZ
89/sinX = 84/sin 70
89sin70 = 84sin X
= 89× 0.94 = 84sinX
=83.66 = 84sin X
sin X = 83.66/84
sinX = 0.996
X = sin^-1 0.996
X = 85° ( nearest degree)
learn more about sine rule from
https://brainly.com/question/20839703
#SPJ1
what’s the numerator for the rational expression?
The numerator of the rational expression will be 6.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the expression is 1 / b + 5 / b = x / b.
The expression will be solved as below,
E = (1/b) + (5/b)
E = ( 1 + 5 ) / b
E = 6 / b
Hence, the numerator will be equal to 6.
To know more about an expression follow
https://brainly.com/question/28134715
#SPJ1
