Find all zeros to the following polynomial function. f(x)= 5x^4 -10x^3 +4x^2 -8x.
Please answer in detailed steps I’m confused.
Answer:
Please check the explanation.
Step-by-step explanation:
Given the function
[tex]f(x)= 5x^4 -10x^3 +4x^2 -8x[/tex]
To determine the zeros, set f(x) = 0
[tex]0=\:5x^4\:-10x^3\:+4x^2\:-8x[/tex]
switch sides
[tex]5x^4-10x^3+4x^2-8x=0[/tex]
as
[tex]5x^4\:-10x^3\:+4x^2\:-8x=x\left(x-2\right)\left(5x^2+4\right)[/tex]
so the equation becomes
[tex]x\left(x-2\right)\left(5x^2+4\right)=0[/tex]
Using the zero factor principle:
[tex]\mathrm{\quad \:If}\:ab=0\:\mathrm{then}\:a=0\:\mathrm{or}\:b=0\:\left(\mathrm{or\:both}\:a=0\:\mathrm{and}\:b=0\right)[/tex]
[tex]x=0\quad \mathrm{or}\quad \:x-2=0\quad \mathrm{or}\quad \:5x^2+4=0[/tex]
so solving
[tex]x=0[/tex][tex]x-2=0[/tex]
[tex]x=2[/tex]
Therefore, the real zeros are:
[tex]x=0[/tex] and [tex]x=2[/tex]
[tex]5x^2+4=0[/tex] has all the imaginary zeros.
solving
[tex]5x^2+4=0[/tex]
[tex]5x^2=-4[/tex]
[tex]x^2=-\frac{4}{5}[/tex]
[tex]\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}[/tex]
[tex]x=\sqrt{-\frac{4}{5}},\:x=-\sqrt{-\frac{4}{5}}[/tex]
[tex]x=i\frac{2\sqrt{5}}{5},\:x=-i\frac{2\sqrt{5}}{5}[/tex] ∵ [tex]\sqrt{-1}=i[/tex]
Therefore, the total zeros are:
[tex]x=0,\:x=2,\:x=i\frac{2\sqrt{5}}{5},\:x=-i\frac{2\sqrt{5}}{5}[/tex]
As you can see I NEED HELP RIGHT NOW!
Answer:
Ten over two would be at the very right side of this number line. It would be located at the number 5. Negative nine over two would be located two segment or lines after negative five.
Step-by-step explanation:
Ten over two would come out to a positive and whole number of five. Negative nine over ten comes out so negative four wholes and one half. So this gets located two segments after negative five because it is not fully negative five but it is negative four and one half. I got these whole numbers by simplifying the numbers that we started off with. Hope you have an amazing day and do well on your assignments.
-Vizion
Geometry! Find the length of a-b. Give answer in simplest radical form.
Answer:
Length of AB is [tex]\sqrt{106}[/tex]
Step-by-step explanation:
Let us use the rule of the distance To find the length of AB
∵ A = (9, -3)
∵ B = (0, 2)
∴ x1 = 9 and y1 = -3
∴ x2 = 0 and y2 = 2
∵ AB = [tex]\sqrt{(x2-x1)^{2}+(y2-y1)^{2}}[/tex]
→ Substitute the values of x1, x2, y1, and y2 in the rule to find AB
∴ AB = [tex]\sqrt{(0-9)^{2}+(2--3)^{2}}[/tex]
∴ AB = [tex]\sqrt{(-9)^{2}+(2+3)^{2}}[/tex]
∴ AB = [tex]\sqrt{81+(5)^{2}}[/tex]
∴ AB = [tex]\sqrt{81+25}[/tex]
∴ AB = [tex]\sqrt{106}[/tex]
→ The square root of 106 is the simplest radical form
∴ Length of AB is [tex]\sqrt{106}[/tex]
Select the correct answer.
A school conducts 27 tests in 36 weeks. Assume the school conducts tests at a constant rate. What is the slope of the line that represents the
number of tests on the y axis and the time in weeks on the x-axls?
A. 3/4
B. 4/3
C. 3
D. 4
it should be A. 3/4
Math Trick
43 x 67 = ?
Answer:2881
Step-by-step explanation:
Answer:
2881
Step-by-step explanation:
Answer please, Ill give Brrainliest for right answer
Answer:
slope is 1/3
Step-by-step explanation:
rise over run
22.9885 rounded to the nearest 10th
Answer: 22.9890 is the answer
Answer:
23.0 will be your answer.
Step-by-step explanation:
When you round to the nearest tenth, you go one decimal place past the decimal. This is the number that will be rounded up or stays the same.
Then we go to 1 decimal place past that one. This number determines if the number will round up or stay. If the number is 5 and greater, then it will make the number before round-up. If the number is 4 or less, then the number will stay the same.
In this case, the 8 will make the 9 round up, resulting in the 9 become a "10", and that one gets added to the 2, or the next digit to the left.
#teamtrees #WAP (Water And Plant)
In new York, the federal reserve gold vault is located at a depth of -80 feet below ground. the treasure at oak island is believed to at a depth of -134 feet which is farther below ground the gold vault or the oak island treasure.which is farther below ground the gold vault or the oak island treasure
Answer:
oak island treasure is deeper in the ground
A:1.7
B:2.7
C:2.8
D:6.6
(Ik it’s not C)
B:2.7
I added the numbers that we knew from the right side and subtracted it from 17
Anthony and Gordon are collecting clothes for a clothing drive. Gordon collected 1/2 as many clothes as Anthony did. If Anthony collected 1/3 of a bag of clothes, how many bags of clothes did Gordon collect?
Answer:
1/6
Step-by-step explanation:
hope this helped you!
Which equation is a point slope form equation for line AB?
y+2=−2(x−5)
y+5=−2(x−2)
y+6=−2(x−1)
y+1=−2(x−6)
Step-by-step explanation:
none of these are correct because beside the y it is a plus sign and it needs to be a minus sign but the awnser would be. y-6=-2(x-1) the way your supposed to set this up is y-y¹=slope(x-x¹) the only way their would be a addition sign in the equation is if one of the numbers in the parentheses that you put down is negative.
HOPE THIS HELPS!
srry if it confusing
3. An isosceles right triangle is a right triangle with congruent legs. If the length of each leg is represented by x, what algebraic expression can be used to represent the length of the hypotenuse? Explain your reasoning
please don't answer if you don't know
Answer:
Step-by-step explanation:
right triangle means Pythagorean theorem!
a^2+b^2=c^2
if each leg (a and b) = x, then
x^2+x^2=c^2
2x^2=c^2
solving for c by taking the square root of both sides leaves
c=x×sqrt(2)
c must be positive since its a length, so no need for a +- I. this case
Divide. Express your answer in simplest form.
11/12 ÷ 3/4
Answer:
11/9 = 1 2/9
Step-by-step explanation:
When divide by a fraction you multiply by the reciprocal, which in others words you flip the second fraction and then multiply straight across.
The reciprocal of 3/4 is 4/3 now just multiply straight across
11×4 / 12 × 3 = 44/36 this can be simplified to 11/9 because 4 goes into 44 and 36 evenly
Answer:
11/9
Step-by-step explanation:
What is an equation of the line that passes through the point (2,3) and is parallel to the line x+y=4
Answer:
The equation of required line is: [tex]\mathbf{x+y=5}[/tex]
Step-by-step explanation:
We need to find an equation of the line that passes through the point (2,3) and is parallel to the line x+y=4
For finding an equation of line, we need to find slope and y-intercept of the line.
Finding slope:
If the lines are parallel their slope is same
We are given: x+y=4
Writing in slope-intercept form: [tex]y=mx+b[/tex] where m is slope and b is y-intercept
[tex]x+y=4\\y=-x+4[/tex]
Comparing [tex]y=-x+4[/tex] with [tex]y=mx+b[/tex] the slope m is -1
So, slope of given line is -1
It is parallel with required line, so they have same slope.
The slope of required line is m=-1
Finding y-intercept
Using slope m=-1 and point(2,3) we can find y-intercept
Using slope-intercept form: [tex]y=mx+b[/tex]
[tex]y=mx+b\\3=-1(2)+b\\3=-2+b\\b=3+2\\b=5[/tex]
So, y-intercept is: b=5
The equation of required line having slope m=-1 and y-intercept b = 5 is
[tex]y=mx+b\\y=-1x+5\\y=-x+5\\x+y=5[/tex]
So, equation of required line is: [tex]\mathbf{x+y=5}[/tex]
The equation of the line that passes through the point (2,3) and is parallel to the line x+y=4 is y = -x + 5
Two equations are parallel if they have equal slope
For the equation x + y = 4
Rewrite the equation in the form y = mx + c
y = -x + 4
Compare y = -x + 4 with y = mx + c
The slope, m = -1
The equation parallel to x + y = 4 will also have a slope, m = -1
The line passes through the point (2, 3)
That is, x₁ = 2, y₁ = 3
The point-slope form of the equation of a line is:
y - y₁ = m(x - x₁)
Substitute x₁ = 2, y₁ = 3 into y - y₁ = m(x - x₁)
y - 3 = -1(x - 2)
y - 3 = -x + 2
y = -x + 2 + 3
y = -x + 5
The equation of the line that passes through the point (2,3) and is parallel to the line x+y=4 is y = -x + 5
Learn more here: https://brainly.com/question/19484034
which one could u guys consider? plz I need ur guys opinion
On Your Own
4. A puppeteer is making a triangular hat for a puppet. If two of the three
angles of the hat both measure 30°, what is the measure of the third angle?
Answer:
Step-by-step explanation:
E
First person to get it right gets brainliest
Answer:
4
Step-by-step explanation:
Segement JK joins J (-2,4) and K (3,-1). Which point is four times as far from K as it is from J?
Answer:
P( - 1, 3)
Step-by-step explanation:
J(- 2, 4), P(x, y), K(3, -1)
KP = 4JP and KP + JP = JK
5JP = JK
JP = [tex]\frac{1}{5}[/tex] JK
JK = 5√2
JP = √2
KP = 4√2
2 = (x + 2)² + (y - 4)²
32 = (x - 3)² + (y + 1)²
P( - 1, 3)
That's what I need help with and I need the steps to it, please. Its the fraction one.
Answer:
27
Step-by-step explanation:
27/3 = 9, 27/9 = 3. so
9-3= 3+3
6=6
solve for w and simplify this fraction 3/2w=-20
Answer:
4 2/3
Step-by-step explanation:
Answer:
w = -1.3 (.3 repeating)
Step-by-step explanation:
3/2w = -20
3/2w time 2/3 (flip to get rid of fraction)
- 20 time 2/3 (what you do to one side, you must do to the other side)
w = 1.3 (.3 repeating)
1.3 as a fraction is 4/3
What is the image of (−3,9) after a reflection over the line y = x?
Answer:(9,-3)
Step-by-step explanation:
You just have to flip the numbers
Point P is a point on a circle with center point O. Point P is also a point on PQ←→, which is tangent to circle O.
Which of the following describes the relationship between radius OP and tangent PQ←→?
A.) OP and PQ←→ are sometimes perpendicular
B.) OP and PQ←→ are always perpendicular
C.) OP and PQ←→ are never perpendicular.
D.) The relationship is dependent on the placement of point P on the circle.
The radius of the circle and tangent of the circle are perpendicular to each other. Then the correct option is B.
What is a circle?It is the centre of an equidistant point drawn from the centre. The radius of a circle is the distance between the centre and the circumference.
Point P is a point on a circle with a center point O. Point P is also a point that lies on line PQ, which is tangent to circle O.
Then the relationship between radius OP and tangent PQ will be
We know that the radius of the circle and tangent of the circle are perpendicular to each other.
More about the circle link is given below.
https://brainly.com/question/11833983
#SPJ2
Please help me out!
At the point of tangency, the functions value and the local linear approximation of a function have the same value
True or false
Use the compound interest formula to find the present value P, for the following given values.
A = $25,000
i = 0.038
n=81
(Round to the nearest cent.)
PLEASE ANSWER WILL MARK BRAINLIEST
|4k|=12
Answer:
k = 3 or k = -3
Step-by-step explanation:
|4k|=12
There is a positive and a negative solution
4k =12 or 4k = -12
k = 3 or k = -3
Answer:
±3
Step-by-step explanation:
4k=12
-4k=12
k = 3
k = -3
k = ±3
What is the equation in slope-intercept form of the line that passes through the points ( -4 , 2) and (12, 6)?
Group of answer choices
y = 0.25x − 4.5
y = 4x − 42
y = 4x + 18
y = 0.25x + 3
Step-by-step explanation:
let the equation be y = mx + b.
m = (6 - 2)/(12 - (-4)) = 1/4
sub (12, 6):
6 = 1/4(12) + b
b = 3
therefore, equation of the line is y = 1/4x + 3, aka option 4
Topic: coordinate geometry
If you like to venture further, feel free to check out my insta (learntionary). I'll be constantly posting math tips and notes! Thanks!
Answer:
y = 0.25x + 3
Step-by-step explanation:
solve for slope:
(6-2)/(12+4) = 1/4
solve for b:
6 = 12(1/4) + b
6 = 3 + b
b = 3
equation can also be y = 1/4x + 3
plz help idk what is the answer will give a good review
Answer:
Step-by-step explanation:
I can't read it very well. If it says
5(6n-4)+2=68
30n-20+2=68
30n=86
n= 43/15 or 2 13/15
If it says
5(6n-4)-2=68
30n-20-2=68
30n=90
n= 3
Algebra
S.4 Find the slope from two points M05
Learn with an example
Find the slope of the line that passes through (5, 6) and (7, 7).
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Submit
!!URGENT!!
Camila has had a collection of sports cards for several years. If the time in years since the collection started is represented by t, and the number of cards in the collection is represented by B, match each of the statements below with an equation that models the function described. Camila had started her collection with 250 cards and her collection decreased by 60 cards each year. Camila didn't have any cards when she started her collection, but her collection grew by 60 cards each year.
Answer:
1). 250 - 60t
2). 60t
Step-by-step explanation:
"Camila started her collection with 250 cards and decreased by 60 cards each year"
Starting number of cards with Camila = 250
Decrease in number of cards each year = 60
Decrease in number of cards after 't' years = 60t
Number of cards after 't' years = 250 - 60t
"Camila didn't have any card when she started her collection, but her collection grew by 60 cards each year."
Number of cards with Camila = 0
Number of cards grew each year = 60
Number of cards after 't' years = 60t + 0 = 60t