List the possible rational zeros for each function.
1. f(x)= 2x^3 - 3x^2 + 4x - 18
2. f(x) = x^4 - 3x^2 + 2x + 24
Find the zeros of each function
3. f(x)= 2x^3 + 2x^2 - 8x -8
4. f(x)= x^3 + x^2 - 10x + 8
Answers
9514 1404 393
Answer:
{±1/2, ±1, ±3/2, ±2, ±3, ±9/2, ±6, ±9, ±18}{±1, ±2, ±3, ±4, ±6, ±8, ±12 ±24}-2, -1, 2-4, 1, 2Step-by-step explanation:
Possible rational zeros are of the form ...
±{divisor of the constant term}/{divisor of the leading coefficient}
__
1. Rational zeros will be one of ±{1, 2, 3, 6, 9, 18}/{1, 2}, so will be ...
{±1/2, ±1, ±3/2, ±2, ±3, ±9/2, ±6, ±9, ±18}
__
2. Rational zeros will be one of {±1, ±2, ±3, ±4, ±6, ±8, ±12 ±24}.
__
3. The pairs of coefficients suggest factoring by pairs:
f(x) = (2x^3 +2x^2) -(8x +8) = 2x^2(x +1) -8(x +1) = 2(x^2 -4)(x +1)
f(x) = 2(x -2)(x +2)(x +1)
Zeros of f(x) are 2, -2, -1, values of x that make the factors zero.
__
4. The sum of coefficients is zero, so x=1 is a zero. Factoring that out by any of several means, you find ...
f(x) = (x -1)(x^2 +2x -8)
The quadratic is factored by looking for factors of -8 that have a sum of 2. (4 and -2 are those)
f(x) = (x -1)(x +4)(x -2)
Zeros of f(x) are 1, -4, 2.
_____
The attached graph confirms our factoring of the polynomials of questions 3 and 4. For cubic and higher degree, I find a graphing calculator to be quite helpful finding zeros.
Answer:
f(x)= 2x^3 + 2x^2 - 8x -8
4. f(x)= x^3 + x^2 - 10x + 8
Related Questions
Determine whether a quadratic model exists for each set of values. If so, write the model.
f(-2)=16, f(0)=0, f(1)=4
Answers
Answer:
[tex]f(x)=4x^2[/tex]
Step-by-step explanation:
Quadratic Model
The quadratic function can be expressed in the form:
[tex]f(x)=ax^2+bx+c[/tex]
Where a,b, and c are constants to be determined using the points through which the function passes.
We have the points (-2,16) (0,0) (1,4). To find the values of a,b,c we just substitute the values of x and y and solve the system of equations.
Point (0,0):
[tex]f(0)=a*0^2+b*0+c=0[/tex]
It follows that
c=0
Point (-2,16):
[tex]f(0)=a*(-2)^2+b*(-2)+c=16[/tex]
Operating:
[tex]a*(4)+b*(-2)+c=16[/tex]
Since c=0:
[tex]4a-2b=16[/tex]
Divide by 2:
[tex]2a-b=8\qquad\qquad [1][/tex]
Point (1,4):
[tex]f(1)=a*(1)^2+b*(1)+c=4[/tex]
[tex]a*(1)+b*(1)+c=4[/tex]
Since c=0:
[tex]a+b=4\qquad\qquad [2][/tex]
Adding [1] + [2]:
2a+a=12
3a=12
a=12/3=4
a=4
From [2]
b=4-a
b=4-4=0
b=0
The model is:
[tex]\boxed{f(x)=4x^2}[/tex]
An object travels in a straight line for 1200 m in 20 seconds. What is the average velocity? *
Answers
Answer:
Velocity is 20
Step-by-step explanation:
well you divide the meters traveled by the time it took and you should get your answer.
1. divide 1200 by 20
2 answer should be 60
I NEED HELP ASAP!!!! PLS HELP ME. WILL MARK THE FIRST ANSWER BRAINLIEST!!!
Answers
Answer:
I am too young for this type of math, but I suggest you try M-a-t-h w-a-y
b. Were you able to find the solution(s) of each Mathematical sentence? How did
you find the solution(s) of each Mathematical sentence?
pls,,, help me mga tol
Answers
Answer:
Evaluate each given numbers, expressions or equation.
Check the values or numbers.
Now in order to solve we proceed in the manner
Read the problem Analyze the problem Write the given variables Find the missing variables Write the equation Solve the equation
Find the measure of angle b.
Answers
Answer:
angle b=36
Step-by-step explanation:
angle b = 90-54=36 (given b+54+90)
HELPPP . sorry for cracked. screen.. Identify w as either rational or irrational
, and approximate to the tenths place. (4
points)
Answers
Answer:
Irrational: √2 = 1.4
Step-by-step explanation:
When finding the slope of a line using a slope triangle, the____
length is divided by the____
length.
Answers
Answer:
rise, run
Step-by-step explanation:
When finding the slope of a line using a slope triangle, the RISE length is divided by the RUN length. (I think. Sometimes the "divided by" makes me confused about which is on top, but I'm pretty sure this is right.)
In parallelogram ABCD, if AO = 4x + 12 and OC = 5x – 6 what is the
****length of AC (be careful)
Answers
Answer:
Step-by-step explanation:
The sides of a parallelogram are equal. If O is the midpoint of its diagonal AC, them AO+OC = AC
Given
AO = 4x + 12 and
OC = 5x – 6
Required
AC
AC = 4x+12 + 5x-6
AC = 4x+5x+12-6
AC = 9x+6
Hence the length of AC is 9x+6
Jordan weighed two buckets of sand for a geology project. The first bucket weighed 26.31 pounds. The other bucket weighed 4.39 pounds. How much do the two buckets of sand weigh all together?
Answers
Answer:
30.7
Step-by-step explanation:
15 is what percent of 90
Answers
a stock has a price of $58.63. This is $5.92 less than the price of stock yesterday. Write and solve an equation to find the price p (in dollars) of the stock yesterday.
Answers
Answer:
$52.71
Step-by-step explanation:
Today's price= $58.63
Yesterday's price= y
Difference= $5.92
y+5.92 = 58.63
y = 58.63 - 5.92
= $52.71
greatest common factor of 24, 36, and 50
Answers
Answer:
The greatest common factor of 24, 36, and 50 is 2.
Step-by-step explanation:
Factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24
Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36
Factors of 50 are 1, 2, 5, 10, 25, 50
Therefore the GCF is 2.
We can see that 2 is the only common factor, hence the greatest common factor of 24, 36, and 50 is 2
For us to get the greatest common factor of 24, 36, and 50, we need to get their individual factor first as shown:
24 = 2 * 12
36 = 2 * 18
50 = 2 * 25
From all the factors, we can see that 2 is the only common factor, hence the greatest common factor of 24, 36, and 50 is 2
Learn more: https://brainly.com/question/219464
find the value of x of given figure and solve this question step by step plzz help question number D
Answers
Answer:
x=15 cm
Step-by-step explanation:
The two triangles in the diagram are:
ABC and BDC
First we have to find the third side (hypotenuse) of BDC so that we can use it to find the value of x.
Hypotenuse is the largest side of a triangle which is usually in front of the right angle.
So in BDC
[tex]Base = BD =10cm\\Hypotenuse = BC = ?\\Perpendicular = CD = 2\sqrt{11}cm[/tex]
Applying Pythagoras theorem:
[tex](Hypotenuse)^2 = (Base)^2 + (Perpendicular)^2\\BC^2 = BD^2 + CD^2\\BC^2 = (10)^2 + (2\sqrt{11})^2\\BC^2 = 100+(2^2 * 11)\\BC^2 = 100+(4*11)\\BC^2 = 100+44\\BC^2 = 144\\\sqrt{BC^2} = \sqrt{144}\\BC = 12cm[/tex]
Solving for triangle ABC
[tex]Base = BC = 12 cm\\Perpendicular = AB = 9 cm\\Hypotenuse = AC = x\\[/tex]
Applying Pythagoras theorem
[tex]AC^2 = BC^2+AB^2\\x^2 = (12)^2 + (9)^2\\x^2 = 144+81\\x^2 = 225\\\sqrt{x^2} = \sqrt{225}\\x = 15cm[/tex]
Hence,
x=15 cm
Elias’s teacher has given him a rectangle that is 15 feet by 20 feet. She has asked him to create a new rectangle using a scale factor of 8/3. Elias says that will be a reduction because the scale factor is a fraction. Is he correct?
Answers
Answer:
Yes
Step-by-step explanation:
Because for every 8 feet of the original rectangles, it will be 3 feet on the scale model, therefore it is reducing.
Answer:
Elias is not correct, A scale factor of 8/3 is an enlargement because it is greater than 1.
A reduction has a scale factor between
0 and 1.
(Verified answer)
(W+4)(3w-2) please solveeed
Answers
Step-by-step explanation:
[tex]{:}\longrightarrow[/tex][tex]\sf (w+4)(3w-2)[/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf w(3w-2)+4 (3w-2)[/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf 3w^2-2w+12w-8[/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf 3w^2+10w-8 [/tex]
Simplify to 3w^2+ 10 -8 is the answer
What is the answer to x - 10 + -6 + 4
Answers
Answer: x-12
Step-by-step explanation:
Simplify.
x
−
1
0
−
6
+
4
x−10−6+4
2 Collect like terms.
x
+
(
−
1
0
−
6
+
4
)
x+(−10−6+4)
3 Simplify.
x
−
1
2
x−12
PLS HELP THX PLS jrkdkekmc
Answers
Answer: No
Step-by-step explanation:
The c kind of cut off, but you can use slopes to figure it out. The rule for a perpendicular slope is the opposite reciprocal. Assuming that C is the right angle, since right triangles typically work that way, we can figure out the slopes for ac and bc. The slopes are not reciprocals:
AC= -5/2
BC= -1/3
This isn't a right triangle because the lines are not perpendicular.
How can I isolate the variable f in f/3 + 22 = 17
Answers
Answer: First You Have To Simplify The Equation From Both Sides Then Thats how You Will Determine what f is. F = -15
Variable [tex]f[/tex] is isolated as [tex]\boldsymbol{f=-15}[/tex] in the expression [tex]\frac{f}{3}+22=17[/tex].
VariableA variable is a symbol and placeholder for a changing amount or any mathematical object.
An algebraic expression is one that is composed of integer constants, variables, and algebraic operations.
Given expression is [tex]\frac{f}{3}+22=17[/tex]
Transpose [tex]22[/tex] to the right side of the equation.
[tex]\frac{f}{3}=17-22\\\frac{f}{3}=-5[/tex]
[tex]f=-15[/tex]
So, variable [tex]f[/tex] is isolated as [tex]\boldsymbol{f=-15}[/tex]
Find out more information about algebraic expression here:
https://brainly.com/question/2945451?referrer=searchResults
How to solve m(2x-5) = 9x-k STEP BY STEP
Answers
if y⁻⁴ = 256 then y will be
Answers
Answer:
y = 1/4
Step-by-step explanation:
y⁻⁴ = 256
(1/y)⁴ = 256
y⁴ = 1/256
y = ⁴√1/256
y = 1/4
Thus, The value of y is 1/4
-TheUnknownScientist
4(x+8)+9(6-2x)
plz explain me step by step plz answer me fast
Answers
Ans is 86 - 14x
Steps in image :-
Answer:
86-14x
Step-by-step explanation:
4(x+8)+9(6-2x)
4x-18x+54
4x-18x+86
-14x+86
86-14x
Solve the Inequality:
Answers
Answer:
z > 4
Step-by-step explanation:
- 2z - 3 < 5
- 2z < 5 + 3
- 2z < 8
z > - 4
Answer:
z > -4
Step-by-step explanation:
Please see the following attachment for step by step
three examples of equations where there will be no solution.
Answers
Answer:
5x = 3x
4+8t-y=y-t+8
98/r=34t
Step-by-step explanation:
hope this helps!
mark me brainliest plz!
2r-7 = r + 15,
Find R
Answers
Answer: 22
Step-by-step explanation:
2r - 7 = r + 15
2r - r = 15 + 7
2r = 22
r = 22/2
r = 11
An estimate for - ✓ 72 is
A.- 8.1
b. - 8.5
c. -9.1
d. -9.5
Answers
Jeremy's password is the combination of letters and numbers shown below. He
wants to know the ratio of letters to numbers in this password. Use Jeremy's
password to write the ratio THREE different ways. (Hint: think about the different
formats) 27 R Q A58 E 3 (plz help I know the problem mightseem long but not really)
Answers
Answer:
numbers:letters
5:4 (numbers:letters form)
Step-by-step explanation:
There are 5 numbers in the password and 4 letters
Hopefully this helps :)
Addition and Subtraction of Mixed Numbers.
8 7/8+(7 5/6−2 1/3)
Answers
Answer:
14 1/3
Step-by-step explanation:
First, you need to do what's in the parenthesis by finding a common denominator, which is 6. Multiply the 1 by 2 because that is what you multiply 3 by to get 6. You end up with 8 7/8 + 5 3/6. You then have to find the common denominator again, which is 24. Now the problem is 8 21/24 + 5 12/24. you get 13 32/24, which is equal to 14 8/24. Simplify, and you have 14 1/3.
Will someone help me please please please please :D
Answers
Answer:
I believe it's C, 0.4 x 0.7
Step-by-step explanation:
So it’s 0.4 x 0.7
Given the function f(x) = 4 - 2x: If the domain is {-4,0, 5), find the range.
A)
{-4, 4,-6)
B)
{-4, 4, 14)
C)
{12, 4, -6}
D)
{12, 4, 14)
Answers
Answer:
C) -4,4,-6
Step-by-step explanation:
domain is x so plug the domain numbers into the function
4-2(-4)=12
4-2(0)=4
4-2(5)=-6
Therefore Range is (-4,4,-6)
What is (1.7x10^4)x(8.5x10^-2) in standard form
Answers
Answer:
1.445 × 10³
Step-by-step explanation:
Standard form is a way of writing a small number or a large number easily.
We should give the final answer in standard form.
1) (1.7 × 10⁴) × (8.5 × 10⁻²)
We enter this directly into the calculator to obtain a solution.
= 1445
We write this in standard form we have :
1.445 × 10³
Answer:
1.445 × 10³ hope it helped goodluck!