Answer:
The roots of the of the function are 2,3 and 4.
Step-by-step explanation:
The given function is
f(x) = x³ - 9x² + 26x - 24
It is given that x=2 is a root of the function. So (x-2) is a factor of f(x).
According to the remainder theorem if a function is divided by (x-c), then the remainder is equal to f(c). If f(c) is equal to 0, therefore c is the root of the function.
Use synthetic method to divide f(x) by (x-2).
f(x) = (x - 2) (x² - 7x + 12)
f(x)= (x - 2) (x² - 4x - 3x + 12)
f(x)= (x - 2) (x(x - 4) - 3(x - 4))
f(x)= (x - 2) (x - 4) (x - 3)
To find the roots equation the function equate the function equal to 0.
0 = (x - 2) (x - 4) (x - 3)
Equate each factor equal to 0.
x = 2,3,4
Therefore the roots of the function are 2,3 and 4.
(btw this is someone else's answer i found since i got a little confused myself heh)
Answer:
The roots of the of the function are 2,3 and 4.
Step-by-step explanation:
\The roots of the of the function are 2,3 and 4.
The table shows the results of a survey of 200 randomly selected people on whether they like watermelon,
cantaloupe, or both.
Which is the marginal relative frequency for the people who do not like cantaloupe?
A. 25/91
B. 66/200
C. 91/200
D. 66/91
Answer:
C
Step-by-step explanation:
Marginal relative frequency for the people who do not like cantaloupe is 0.455
or
91/100
Answer:
C is correct
Step-by-step explanation:
explain what it means to solve a system of equations
Answer:
um hope this helps :D
Step-by-step explanation:
A system of equations is a collection of two or more equations with a same set of unknowns. In solving a system of equations, we try to find values for each of the unknowns that will satisfy every equation in the system. The problem can be expressed in narrative form or the problem can be expressed in algebraic form.
A collection of two or more equations with the same set of unknowns is referred to as a system of equations. I
What is a system of equations?A system of equations is a collection of two or more equations with the same set of unknowns. In solving a system of equations, we try to find values for each of the unknowns that will satisfy every equation in the system. The problem can be expressed in narrative form or the problem can be expressed in algebraic form.
If the lines intersect, we identify the point of intersection. This is the solution to the system. The solutions of a system of equations are the values of the variables that make all the equations true.
To know more about a system of equations follow
https://brainly.com/question/13729904
#SPJ2
Find the sum.. -3/2 + 8/5
Answer: 0.1 or 1/10
Step-by-step explanation:
what are the names of three planes that contain Point G
Answer:
Points L, J, and K are collinear.
Step-by-step explanation:
brinlest plz
Answer:
ferns,gymnosperms, and flowering plants are all vascular plants
Step-by-step explanation:
Use substitution to show that 9+6(10-7x) is equivalent to 69-42x.
.
Answer:
hope this helps
Step-by-step explanation:
9+6(10-7x)
9+60-42x
69-42x
(HELP!!!) Please Factor Completely:
9x^2y^2-27x^2y-72y^2+216y
Answer:
Can u space them out so i know which ones are exponents
Step-by-step explanation:
Can somebody plz answer these 3 questions correct!!! Help
(WILL MARK BRAINLIEST
it increases 3° each hour
3*2= 6
6° after 2 hours
3*3= 9
9° after 3 hours
3*6= 18
18° after 6 hours
Angie and Kenny play online video games. Angie buys 1 software package and 1month of gameplay. Kenny buys 1 software package and 2 months of game play. Each software package costs $30. If their total cost is $90, what is the cost of one month of gameplay?
Answer: $10
Step-by-step explanation:
Angie buys = 1 software package and 1month of gameplay.
Kenny buys = 1 software package and 2 months of game play.
Cost of each software package = $30. Total cost = $90
The total cost is the addition of what Kenny and Angie bought. This will be:
(1 SF + 1 G) + (1 SF + 2 G) = 90
where,
SF = software package = 30
G = game
(1 SF + 1 G) + (1 SF + 2 G) = 90
30 + 1G + 30 + 2G = 90
60 + 3G = 90
3G = 90 - 60
3G = 30
G = 30/3
G = 10
One month of game play cost $10
18 + 19x = 10x + 54
can someone help me with this
Answer:
The answer is X= 4.
1. Label the Type of Slope
Answer:
positive slope
Step-by-step explanation:
Terrence took a total of 16 pages of notes during 8 hours of class. In all, how many hours will
Terrence have to spend in class before he will have a total of 18 pages of notes in his
notebook? Assume the relationship is directly proportional.
who can ask me a question about addition?
Find the y-intercept of a line that passes through the point (-5,-6) and has a slope of 2.
Answer:
The y intercept is 4
Step-by-step explanation:
Given:
-Given point: (-5,-6)
-Slope of 2
1) Put the equation into point-slope form y - y1 = m(x - x1)
With the given, we can plug it all in using this formula!
-y1 = -6
-x1 = -5
m = 2
(you would change these negative numbers into positives because the equation shows them being subtracted! remember that two negatives make one positive!)
y+6= 2(x+5)
2) Simplify
y+6= 2(x+5)
y+6=2x+10
y=2x+4
With y=2x+4, set x to 0 because the y intercept is where x is equal to 0 and you get 4!
NEED HELP ASAP
Given: (DE) is a midsegment of triangle ABC.
Find the value of x and y.
What is the length of (AC)?
Answer:
X=13. y=5 AC=20
Step-by-step explanation:
To do this we first have to find the value of x... giving the fact that DE is a mid segment, We know that the length of BC is double the length of DE this means that the length of BC equals 16. So, to equal 16 x will have to equal 13 so 13 + 3 = 16. Now we will find the value of y. We do this by looking at the length of ae and ec. AE equals EC so now that we know x equals 13 we can do 13 minus 3 equals 10 for AE. since EC has to equal 10 we can do 10 minus 5 which equals 5. We now know that y equals 5. We can now add this all up to find the length of AC. We would do 10 + 10 = 20. Hope this helps!
The length of AC from the diagram is 25
To get the value of x and y, we will use the similarity theorem of a triangle
BC = 2DE
x + 3 = 2(8)
x + 3 = 16
x = 16 - 3
x = 13
Hence BC = 16
From the given figure;
AE/DE = AC/BC
x-3/8 = (x-3+y+5)/x+3
10/8 = 15+y/13
130 = 8(15+y)
130 = 120 + y
y = 10
Get the length of AC
AC = 13-3+10+5
AC = 25
Hence the length of AC from the diagram is 25
Learn more here: https://brainly.com/question/23961310
Use the formula (n−2)×180◦ figure out the sum of the angle measures of the Trapezoid.
Answer: 360 degrees
Step-by-step explanation: There are 4 sides in an angle. Substitute that value in for n and u have: (4-2) x180. After doing that, subtract inside the parenthesis and multiply your difference by 180. You should get 360 degrees. I hoped this helped.
Answer:
360!!!!!!!!!!!!!!!!!!!! ;)
Step-by-step explanation:
The amount that Ronnie earns, E, in terms of the number of hours that he works, h, is shown in the graph below.
What is the constant of proportionality,
E/H, for this situation?
+/-
.
Answer:
Pay Rate = Constant of Proportionality = E/h
Step-by-step explanation:
Recall this formula: Total Pay = (Hourly Pay Rate)*(Number of Hours Worked)
Apparently there was a graph associated with this problem; it's up to you to share all instructions and other info that comes with your question.
Rewriting Total Pay = (Hourly Pay Rate)*(Number of Hours Worked), using E for total earnings and h for the number of hours worked, we get:
E = (Hourly Pay Rate)*h
The relevant constant of proportionality is found by dividing E by h:
Pay Rate = Constant of Proportionality = E/h
I will give Brainlyest to the first person
A family gathered 12 seashells from the beach bringing the total number of seashells in their collection to 86
Which equation can be used to find, x, the number of seashells in the collection before the 12 were added?
Answer:
The first selection is the answer.
Step-by-step explanation:
x+12=86
The equation that can be used to find x is x + 12 = 86
A linear equation is of the form:
y = mx + b;
where y, x are variables, m is the slope of the line and b is the y intercept.
Let x represent the number of seashells in the collection before the 12 were added. Hence to find x, we use the equation:
x + 12 = 86
The equation that can be used to find x is x + 12 = 86
Find out more at: https://brainly.com/question/13911928
Help please I will give Brainliest!!!!
Josiah invested $96,000 in an account paying an interest rate of 3.5% compounded continuously. Assuming no deposits or withdrawals are made, how long would it take, to the nearest year, for the value of the account to reach $153,400?
The number of years it will take for the value of the money in the account to reach $153,400 would be = 17 years.
What is simple interest?Simple interest is defined as the amount of money that is received as an extra cash based on an investment made in an account.
The principal amount of money invested= $96,000
The rate of interest = 3.5%
The total interest on the principal amount = $153,400- $96,000 = $57,400
The time for this investment= ?
Using the formula for simple interest= p×T×R/100
57,400 = 96,000 ×T× 3.5 /100
Make T the subject of formula;
T = 57,400×100/96,000×3.5
T = 5740000/336000
T = 17 years (approximately)
Learn more about simple interest here:
https://brainly.com/question/25793394
#SPJ1
Given: 3x + 2y + 7 = 5x +3y +10
Prove: m = -2
please help im very confused :)
also make sure to include the statements and reasonings as shown in the screenshot!
Answer:
See Below.
Step-by-step explanation:
1) Given:
[tex]3x+2y+7=5x+3y+10[/tex]
2) Subtraction Property of Equality (subtract 2y from both sides):
[tex]3x+7=5x+y+10[/tex]
3) Subtraction Property of Equality (subtract 5x from both sides):
[tex]-2x+7=y+10[/tex]
4) Subtraction Property of Equality (subtract 10 from both sides):
[tex]-2x-3=y[/tex]
5) Symmetric Property:
[tex]y=-2x-3[/tex]
6) Slope-intercept form:
[tex]y=mx+b\text{, where $m$ is slope and $b$ is y-intercept.}[/tex]
7) Substitution:
[tex]m=-2[/tex]
What is the slope of the linear function?
Answer:
the slope is [tex]\frac{7}{4}[/tex]
Step-by-step explanation:
Given: 4y - 7x = 10; solve y
4y - 7x = 10; add 7x to both sides to isolate the 4y variable
4y = 7x + 10; now divide by 4
y = [tex]\frac{7}{4}[/tex]x + [tex]\frac{10}{4}[/tex]; reduce the fraction
y = [tex]\frac{7}{4}[/tex]x + [tex]\frac{5}{2}[/tex]; the slope is
Answer:
m= 7/4
Step-by-step explanation:
2 cartons of juice in the month of January. In the month of February, she drank twice as many cartons of juice as in
January. How many cartons of juice did she drink in February?
Answer:
She drank 4 cartons in February.
Step-by-step explanation:You multiply 2x2 because it doubles.
Sean adds up all the even integers from 2 to 500, inclusive. Julie adds up all the integers from 1 to 250, inclusive. What is Sean's sum divided by Julie's sum?
Answer:
Sean's sum divided by Julie's sum is 2.
Step-by-step explanation:
The sum of an arithmetic sequence is:
[tex]\frac{n}{2}(2a+(n-1)d)[/tex]
In Sean's sequence, a = 2, n = 250, and d = 2
In Julie's sequence, a = 1, n = 250, and d = 2
[tex]\frac{\frac{250}{2}(2(2)+(250-1)2)}{\frac{250}{2}(2(1)+(250-1)1)}\\= 2[/tex]
The Sean's sum divided by Julie's sum gives the 2.
What is arithmetic sequence?An arithmetic sequence is sequence of integers with its adjacent terms differing with one common difference.
If the initial term of a sequence is 'a' and the common difference is of 'd', then we have the arithmetic sequence as:
a, a + d, a + 2d, ... , a + (n+1)d, ...
Its nth term is ; T_n = a + (n-1)d
(for all positive integer values of n)
And thus, the common difference is T_{n+1} - T_n for all positive integer values of n
The sum of an arithmetic sequence is;
[tex]= \dfrac{n}{2}[2a + (n-1)d ][/tex]
In Sean's sequence, a = 2, n = 250, and d = 2
[tex]= \dfrac{250}{2}[2(2) + (250-1)2 ]\\[/tex]
In Julie's sequence, a = 1, n = 250, and d = 2 then;
[tex]= \dfrac{250}{2}[2(1) + (250-1)2 ]\\[/tex]
Therefore, the Sean's sum divided by Julie's sum gives the 2.
Learn more about arithmetic sequence here:
https://brainly.com/question/3702506
#SPJ2
Choose the linear equation written in slope-intercept
form that matches each graph.
Answer:A
Step-by-step explanation:
The line touches the y axis at -1. The line then goes up 1 over 2 but since it’s on the bottom part of the graph it has the be negative. Y=-1/2X-1
Answer:
Slope = rise/run
= -1/2 (negative because the slope is decreasing)
y - intercept = -1
Option A
y = -1/2x-1
When translating the point (3,5) 5 units up and 3 units to the left, we should get:
Answer:
(0, 10 )
Step-by-step explanation:
5 units up means add 5 to the y- coordinate
3 units left means subtract 3 from the x- coordinate
Translation rule is
(x, y ) → (x - 3, y + 5 ) , thus
(3, 5 ) → (3 - 3, 5 + 5 ) → (0, 10 )
Write an equation of the line that passes through the points ( 4, 2), (0, -6) *
9514 1404 393
Answer:
y = 2x -6
Step-by-step explanation:
One form you can use for this purpose is ...
(x2 -x1)(y -y1) = (y2 -y1)(x -x1)
Filling in the given point values, this is ...
(0 -4)(y -2) = (-6 -2)(x -4)
-4y +8 = -8x +32
Generally, we like the equation to have coefficients with no common factors. All of these coefficients can be divided by -4.
y -2 = 2x -8
This can be rearranged to any form you may like--or left as is.
y = 2x -6 . . . . . slope-intercept form
Which graph represents a proportional relationship?
Answer:
If the relationship between two quantities is a proportional relationship, this relationship can be represented by the graph of a straight line through the origin with a slope equal to the unit rate. For each point (x, y) on the graph, ž is equal to k, where k is the unit rate. The point (1, k) is a point on the graph.
a restaurant starts with 10 dozen pieces of cornbread.every order receives 2 piece of cornbread.At the end of their lunch rush,there are 28 pieces of cornbread left.How many orders did the restaurant take?
Twelve less than two-thirds a number is 48.What is the number?
Can you please help me with those two questions and don’t only do 1 if you don’t know the answer dont comment
Answer:
32 ordersStep-by-step explanation:
10 dozen = 120120 - 28x2=28x2=56120 - 56=6464 divided by 2= 32what is the range and domain of this question? im unsure
Answer:
Step-by-step explanation:
Domain is the independent variable (x)
Range is the dependent variable (y)
For each of these you would just put what x and y are equal to
For the Domain you would put:
0<=x<=3
<= is less than or equal to
For the Range you would put
1<=y<=4
The line is a function
Evaluate each value expression for the given value of x: x-5 , x - =22
pls fast
Answer:
-18
Step-by-step explanation:
-18
brainlest please
Congruent Triangle Combination
Answer:
1) ΔABC ≅ ΔDBC by Side-Angle-Side (SAS)
2) ΔABC ≅ ΔCDB by Side-Side-Side (SSS)
3) ΔABC ≅ ΔDBE by Angle-Angle-Side (AAS)
4) m∠Y = 53°
5) y = 3
6) ΔABC ≅ ΔEDC by Side-Angle-Side (SAS)
7) ΔABC ≅ ΔADC by Angle-Angle-Side (AAS)
8) ΔABC ≅ ΔADC by Side-Angle-Side (SSS)
Step-by-step explanation:
1) Side AC ≅ Side BD [tex]{}[/tex] given
Side BC ≅ Side BC [tex]{}[/tex] reflexive property
∠DBC ≅ ∠ACB [tex]{}[/tex] given
Therefore ΔABC ≅ ΔDBC by Side-Angle-Side (SAS)
2) Side AC ≅ Side BD [tex]{}[/tex] given
Side DC ≅ Side BA [tex]{}[/tex] given
Side BC ≅ Side BC [tex]{}[/tex] reflexive property
Therefore, ΔABC ≅ ΔCDB by Side-Side-Side (SSS)
3) ∠BAC ≅ ∠DEB [tex]{}[/tex] given
Side BC ≅ Side BD [tex]{}[/tex] given
∠ABC ≅ ∠DBE [tex]{}[/tex] vertically opposite angles
Therefore, ΔABC ≅ ΔDBE by Angle-Angle-Side (AAS)
4) ΔXYZ ≅ ΔABC [tex]{}[/tex] given
m∠A = 44°, and m∠C = 83°
m∠B = 180 - (44 + 83) = 53° [tex]{}[/tex] Sum of angles in a triangle
m∠Y = m∠B = 53° [tex]{}[/tex] Corresponding Parts of Congruent Triangles are Congruent (CPCTC)
5) Given that Triangle GHK is congruent to Triangle TZK
GH ≅ XT, KG ≅ KT, and HK ≅ ZK by the definition of congruency
Therefore, GH = 4 = XT = 3y - 2
4 = 3y - 2
3y - 2 = 4
3y = 4 + 2 = 6
y = 6/2 = 3
y = 3
6) Side BC ≅ Side EC [tex]{}[/tex] given
Side AC ≅ Side DC [tex]{}[/tex] given
∠ACB ≅ ∠DCE [tex]{}[/tex] vertically opposite angles
Therefore, ΔABC ≅ ΔEDC by Side-Angle-Side (SAS)
7) ∠BAC ≅ ∠DAC [tex]{}[/tex] given
∠ADC ≅ ∠ABC [tex]{}[/tex] given
Side AC ≅ Side AC [tex]{}[/tex] reflexive property
Therefore, ΔABC ≅ ΔADC by Angle-Angle-Side (AAS)
8) Side AD ≅ Side BC [tex]{}[/tex] given
Side AC ≅ Side AC [tex]{}[/tex] reflexive property
Side AB ≅ Side DC [tex]{}[/tex] given that the included angle between the two legs side AD and side AC and side AC and side BC are both acute, the third sides side AB and side DC are equal
Therefore, ΔABC ≅ ΔADC by Side-Angle-Side (SSS)