Answer:
[tex]{ \bf{f(x) = {x}^{3} + {ax}^{2} - 1 }} \\ { \tt{f( - 1) : {( - 1)}^{3} + a {( - 1)}^{2} - 1 = 0}} \\ { \tt{f( - 1) : a - 2 = 0}} \\ a = 2[/tex]
The polynomial function [tex]$x^3 + ax^2 -1[/tex] will have -1 as a root at the value of
a = 2.
What is a polynomial function?A polynomial function exists as a function that applies only non-negative integer powers or only positive integer exponents of a variable in an equation like the quadratic equation, cubic equation, etc.
Given: A root exists at a value of x such that the polynomial exists equivalent to zero.
Let, the polynomial equation be [tex]$x^3 + ax^2 -1[/tex]
then [tex]$\mathbf{f}(\mathbf{x})=\mathbf{x}^{3}+a \mathbf{x}^{2}-\mathbf{1}$[/tex]
Put, x = -1, then we get
[tex]$\mathbf{f}(-1)=(-1)^{3}+\mathrm{a}(-1)^{2}-1=0$[/tex]
f(-1) = a - 2 = 0
a = 2
Therefore, the value of a = 2.
To learn more about polynomial function
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What is the mean absolute deviation? 6,5,7,2,4,8
Answer:
To find the mean absolute deviation of the data, start by finding the mean of the data set. Find the sum of the data values, and divide the sum by the number of data values. Find the absolute value of the difference between each data value and the mean: |data value – mean|
Step-by-step explanation:
Find the slope between the points (−3,−5) and (10,-5)
. Enter DNE if the slope between the points is undefined.
Answer:
0
Step-by-step explanation:
[tex] m = \dfrac{y_2 - y_1}{x_2 - x_1} [/tex]
[tex] m = \dfrac{-5 - (-5)}{-3 - 10} [/tex]
[tex] m = \dfrac{0}{-13} [/tex]
[tex] m = 0 [/tex]
from -3 to 10 are 13 steps to the right and from -5 to -5 0 steps up or down.
devide the steps up by the steps to the right
0 / 13 = 0
in this case it's obvious, but I hope you see the method how to do this. you would normally get a more interesting fraction as a slope.
subtract the following rational expressions
[tex] \frac{8k}{9k - 4} - \frac{3k^3}{2k + 7} [/tex]
please show all work
Answer:
-27k^4 +12k^3+16k^2+56k
---------------------
(9k-4)(2k+7)
Step-by-step explanation:
8k 3k^3
--------- - -----------
9k-4 2k+7
Get a common denominator
8k *(2k+7) 3k^3 *(9k-4)
--------- - -----------
(9k-4)(2k+7) (9k-4)(2k+7)
Combine
8k *(2k+7) -3k^3 *(9k-4)
---------------------
(9k-4)(2k+7)
Distribute
16k^2+56k -27k^4 +12k^3
---------------------
(9k-4)(2k+7)
-27k^4 +12k^3+16k^2+56k
---------------------
(9k-4)(2k+7)
PLEASE HELP! PLEASE SHOW WORK
Use the following expression to answer this three part question:
f(x) = 2x2 + 4x − 6
Part A: What are the x-intercepts of the graph of f(x)? Show your work.
Part B: Is the vertex of the graph of f(x) going to be a maximum or minimum? What are the coordinates of the vertex? Justify your answers and show your work.
Part C: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part A and Part B to draw the graph.
Answer:
Step-by-step explanation:
The graph of a quadratic function is a U-shaped curve called a parabola. One important feature of the graph is that it has an extreme point, called the vertex. If the parabola opens up, the vertex represents the lowest point on the graph, or the minimum value of the quadratic function.
The Students in a school can be arranged in 12, 15, 18 equal rows and also into a solid square. What is the lowest number of students that can be in the school? (Hint: find the LCM)
Answer:
180
Step-by-step explanation:
Find the measure of the third angle of a triangle if the measures of the other two angles are given.
102.9 and 40.4
Answer:
36.7
Step-by-step explanation:
180 - 102.9 - 40.4= 36.7
The measure of the third angle of the given triangle after applying the angle sum property of a triangle is 36.7 degrees.
The measures of the two angles of a triangle are 102.9 and 40.4.
We need to find the measure of the third angle.
What is the Angle Sum Property of a triangle?The angle sum property of a triangle states that the sum of all three interior angles of a triangle is 180 degrees.
If A, B, and C are the interior angles we have,
A + B + C = 180.
Consider the three interior angles to be A, B, and C.
We are given two angles 102.9 and 40.4.
Let A = 102.9, B = 40.4.
and C = angle to be measured.
Now,
Applying the angle sum property of a triangle.
We have,
A + B + C = 180
102.9 + 40.4 + C = 180
143.3 + C = 180
C = 180 - 143.3
C = 36.7 degrees.
After applying the angle sum property of a triangle we got the measure of the third angle as 36.7 degrees.
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HELP i need help on part b
Wilson is thinking about buying a house for $249,000. The table below shows the projected value of two different houses for three years.
Number of years 1 2 3
House 1 (value in dollars) 253,980 259,059.60 264,240.79
House 2 (value in dollars) 256,000 263,000 270,000
Part A: What type of function, linear or exponential, can be used to describe the value of each of the houses after a fixed number of years? Explain your answer. (2 points)
Part B: Write one function for each house to describe the value of the house f(x), in dollars, after x years. (4 points)
Part C: Wilson wants to purchase a house that would have the greatest value in 45 years. Will there be any significant difference in the value of either house after 45 years? Explain your answer, and show the value of each house after 45 years. (4 points)
Answer
Number of years 1 2 3
House 1 (value in dollars) 249,000 253,980 259,059.60
House 2 (value in dollars) 249,000 256,000 263,000
House 1: exponential function
House 2: linear function
House 1: f(x) = 249,000 * (1.02)^(x-1)
→ f(3) = 249,000 * (1.02)³⁻¹ = 249,000 * (1.02)² = 259,059.60
House 2: f(x) = 249,000 + 7,000(x-1)
→ f(3) = 249,000 + 7,000(3-1) = 249,000 + 7,000(2) = 249,000 + 14,000 = 263,000
House 1:
f(45) = 249,000 * (1.02)⁴⁵⁻¹ = 249,000 * (1.02)⁴⁴ = 249,000 * 2.39 = 595,110
House 2:
f(45) = 249,000 + 7,000(45-1) = 249,000 + 7,000(44) = 249,000 + 308,000 = 557,000
House 1 will have a greater value than House 2 after 45 years.
Step-by-step explanation:
Hope this helps, if not let me know and I will fix it.
Part A
The value for house 1 follows an exponential growth function since the value is increasing by 2% each year. This is because we multiply each value by 1.02 to get the next year's value.
249,000*1.02 = 253,980253,980*1.02 = 259,059.60259,059.60*1.02 = 264,240.792 = 264,240.79In contrast, house 2's value increases by the same amount each year (7000 per year)
249,000 + 7,000 = 256,000256,000 + 7,000 = 263,000263,000 + 7,000 = 270,000This fixed amount it increases directly leads to house 2 having linear growth.
-----------
Summary:House 1 = exponential functionHouse 2 = linear function=================================================
Part B
The equation for house 1's value is y = 249000(1.02)^x
This is in the form y = ab^x, where a = 249000 is the starting value and b = 1.02 is the growth rate factor.
We can think of 1.02 as 1+0.02 to represent the 2% growth.
In other words, 1.02 = 1+r solves to r = 0.02 = 2%
-----------
The equation for the second home's value is y = 7000x+249000
The slope m = 7000 tells us how the value is going up per year.
The y intercept b = 249000 is the original home value (when x = 0).
-----------
Summary:Equation for home 1 is f(x) = 249000(1.02)^xEquation for home 2 is f(x) = 7000x+249000=================================================
Part C
Let's plug x = 45 into each equation mentioned in part B
For home 1, we have
f(x) = 249000(1.02)^x
f(45) = 249000(1.02)^45
f(45) = 607,025.697
f(45) = 607,025.70
So that's the value of home 1 after 45 years of constant 2% growth per year
For the second home, we have,
f(x) = 7000x+249000
f(45) = 7000*45+249000
f(45) = 564,000
So there is a significant difference. This difference is 607,025.70 - 564,000 = 43,025.70 dollars.
-----------
Summary:Home 1's value = $607,025.70Home 2's value = $564,000This is a difference of $43,025.70 which is fairly significant. It's better to go with home 1.Which ordered pair is a solution of 2x+4y=6x-y
Answer:
5y=4x
Step-by-step explanation:
Write the solution set of the equation x2 – 4=0 in roster form
Answer:
Step-by-step explanation:
x²-4=0
(x+2)(x-2)=0
x=-2,2
solution is x∈{-2,2}
Uma madeira clandestina corta 325 árvores por dia em quantos dias eles devastaram uma área com 1625 árvores
Answer:
Se necesitarían 5 días para talar 1625 árboles a este ritmo
Step-by-step explanation:
1625 dividido por 325 iguales 5, así que otra forma de averiguar esto es multiplicar 325 por 5, 325 Multiplicado por 5 iguales 1625.
Someone please help me ASAP please
Answer:
hey mate
plz mark it as brainliest
Which expression is equivalent to this polynomial?
16x2 + 4
A.
(4x + 2i)(4x − 2i)
B.
(4x + 2)(4x − 2)
C.
(4x + 2)2
D.
(4x − 2i)2
Answer:
A.
Step-by-step explanation:
C and D do not create any x² terms when doing the multiplications. so, they are out.
B stands for (a+b)×(a-b) = a² - b².
so, that would give us a "-4" at the end and is not fitting to the "+4" term at the end of the original expression.
that leaves us with A.
let's verify :
(4x+2i)(4x-2i)
it follows the same rule as B :
(a+b)(a-b) = a² - b²
a = 4x
b = 2i
you remember, i = sqrt(-1).
so, we get
(4x)² - (2i)² = 16x² - 4×(sqrt(-1))² = 16x² - 4×(-1) = 16x²+4
bingo !
Answer:
Step-by-step explanation:
the answer is A
• Work out
3 1/2 X 1 3/5
Give
your answer as a mixed number in its simplest form
Answer:
5 3/5
Step-by-step explanation:
3 1/2 * 1 3/5
Change to improper fractions
(2*3+1)/2 * (5*1+3)/5
7/2 * 8/5
56/10
Change back to a mixed number
50/10 +6/10
5 +3/5
5 3/5
A jewellery shop is having a sale. A bracelet is now reduced to £420. This is 70% of the original price. Work out the original price of the bracelet.
Answer:
Step-by-step explanation:
x is the original price.
420/x = 70% = 0.7
x = 420/0.7 = 600
Original price of bracelet was £600
luis tiene 3 años más que
Ines. La edad de Antonio
suma de las edades de ambos.
¿ Cuales Son las edades de Luis
e Ine's si antonio tiene 15 años?
Answer:
NMHGJMHBNKJ6T76 5745
Step-by-step explanation:
7657457657776767
A local hamburger shop sold a combined total of 688 hamburgers and cheeseburgers on Thursday. There were 62 fewer cheeseburgers sold than hamburgers How many hamburgers were sold on Thursday?
Answer:
626
Step-by-step explanation:
So 62 fewer right so 688 combined- 62 cheeseburger =626 hamburger
Help please guys if you don’t mind
Step-by-step explanation:
Step 2:
[tex] ({15x}^{2} - 9x) + (5x - 3)[/tex]
Stepc3:
[tex]3x(5x - 3)[/tex]
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
Find the area of the triangle.
8
9
Square units
Reset
Next
Answer:
36 spuare units
Step-by-step explanation:
A= 1/2 b*h
b=8
h=9
A=1/2(8*9)
A=1/2(72)
A=36
1. Paul uses a coordinate plane to design
his model town layout.
Paul moves the market 2 units left and 3
units down. He says the ordered pair for
the new location of the market is (0,6).
Explain Paul's mistake and write the
correct ordered pair for the new location of
the market.
PLZ ALSO INCLUDE WHAT HIS MISTAKE WAS!
ANSWER FOR Brainiest!!!
211 base x is equal to 10110 base 2
Hello,
[tex](211)_x=(10110)_2\\\\2*x^2+x+1=22\\\\2x^2+x-21=0\\\Delta=1+4*2*21=169=13^2\\x=\dfrac{-1+13}{4}= 3\\or\\x=\dfrac{-1-13}{4}\ may\ not\ be\ negative\\\\[/tex]
x=3
What is the value of x to the nearest tenth?
A) 29.5
B)18.5
C)37.0
D)40.8
Can someone help me with this math homework please!
Answer:
See step by Step
Step-by-step explanation:
Both are correct. As long as we undo the operations that was given from the original term to both sides until we get the variable by itself., any way can be applied.
Both, Spencer and Jeremiah are correct. We can verify this by testing their methods.
Spencer's method:
[tex]6x - 2 = - 4x + 2[/tex]
[tex]6x - 2 + 4x= - 4x + 2 + 4x[/tex]
[tex]10x - 2 = 2[/tex]
[tex]10x = 2 + 2[/tex]
[tex]10x = 4[/tex]
[tex]x = \frac{4}{10} [/tex]
[tex]x = 0.4[/tex]
Jeremiah's method:
[tex]6x - 2 = - 4x + 2[/tex]
[tex]6x - 2 - 6x = - 4x + 2 - 6x[/tex]
[tex] - 2 = - 10x + 2[/tex]
[tex] - 2 - 2 = - 10x[/tex]
[tex] - 4 = - 10x[/tex]
[tex] \frac{ - 4}{ - 10} = x[/tex]
[tex]0.4 = x[/tex]
As seen, we get the correct answer by using Spencer's and Jeremiah's method. So, we can say that they both are correct.
In the diagram below ,
Answer:
it doesn't show anything
225 students appeared at an examination. Among them, the ratio of the number of students who passed in the first and in the second division were 4.5. If 25 students passed in the third division and 29 students failed in the examination, find (i) the number of students who passed in the first and in the second division (ii) The ratio of the number of students who passed in the first second and in the third division.
(i) the number of students who passed in the first and in the second division
76+95=171 students
(ii) The ratio of the number of students who passed in the first second and in the third division.
RATIO is 4:5:(25/19) or 4:5: 1.3157894…….
225-29=196 (29students failed)
196-25=171. (Subtract 25 students from the 3rd division)
4x+5x= 171 (171 students from 1st and second division)
9x=171
X=19
4x19=76 5x19= 95 1.31578.....x19= 25
If you like peanut butter and chocolate, then you will love Reese's.
What is the converse of the statement?
Answer:
Reese's love peanut butter and chocolate
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In 2005, there were 1000 rabbits on an island. The population grows 8% per year. AT this rate, how many
rabbits will there be on the island by 2020?
Answer: 3172
Step-by-step explanation:
According to class 8 please solve
Answer:
i) The value of x is 3.
ii) TE = 20cm
RN = 20cm
Step-by-step explanation:
According to the properties of rectangles,
The diagonals of rectangles are equal and bisect each other at 90°.
As per this,
OR = OT
[tex]2x + 4 = 3x + 1[/tex]
[tex]4 - 1 = 3x - 2x[/tex]
[tex]3 = x[/tex]
TE = 2OT
TE = 2(3x + 1)
= 6x + 2
= 6(3) + 2
= 18 + 2
= 20
RN = 2OR
RN = 2(2x + 4)
= 4x + 8
= 4(3) + 8
= 12 + 8
= 20
Can you help me with this question? It’s in the photo
Answer:
Option (d), (e) and (f) are correct.
Step-by-step explanation:
In triangle MNP, angle P = 90 degree
Cos M = 7 / 12
Now according to the right angle triangle
[tex]NP^2 = NM^2 - PM^2\\\\NP^2 = 12^2 - 7^2\\\\NP = \sqrt95[/tex]
Now
[tex]Sin M = \frac{sqrt95}{12}\\\\Cos N = \frac{95}{12}[/tex]
the theater sells two types of tickets: adult tickets for $6 and child tickets for 5$. last night, the theatre sold a total of 375 tickets for a total of $2153. How many adult tickets did the theatre sell
Answer:
358
Step-by-step explanation:
Pls help this set question
1: True
2: False
3: False
4: True
5: False
6: True
