The polynomials in factored form are listed below:
f(x) = (x - 3.043) · (x - 1.521 - i 1.716) · (x - 1.521 + i 1.716) f(x) = (x - 2.236) · (x - 2) · (x + 2.236) · (x + 4)f(x) = (x + 3) · (x - 5) · (x - 1)f(x) = (x - 4) · (x - 3) · (x - 1) · xHow to factor polynomialsIn this question we must factor polynomials as there are both numerical and analytical methods. Mathematically speaking, factoring polynomials is represented by the following formula:
[tex]\sum^{n}_{i = 0} \,c_{i}\cdot x^{i} = \prod^{n}_{i=1}(x-r_{i})[/tex], [tex]\forall\,x, r_{i}\in \mathbb{C}[/tex] (1)
Where:
[tex]c_{i}[/tex] - [tex]i[/tex]-th Coefficient[tex]r_{i}[/tex] - [tex]i[/tex]-th RootRegarding fourth order polynomials we can solve them by Ferrari's method and third order polynomials by Descartes' method. Then, the solutions of each polynomials are given below:
Polynomial 1 ([tex]f(x) = x^{3}-4\cdot x +16[/tex])f(x) = (x - 4) · (x - 3) · (x - 1) · x
Polynomial 2 ([tex]f(x) = x^{4}+2\cdot x^{3}-13\cdot x^{2}-10\cdot x + 40[/tex])f(x) = (x - 2.236) · (x - 2) · (x + 2.236) · (x + 4)
Polynomial 3 ([tex]f(x) = x^{3}-3\cdot x^{2}-13\cdot x +15[/tex])f(x) = (x + 3) · (x - 5) · (x - 1)
Polynomial 4 ([tex]f(x) = x^{4}-8\cdot x^{3}+19\cdot x^{2}-12\cdot x[/tex])f(x) = (x - 4) · (x - 3) · (x - 1) · x
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An angle that measures exactly 180° is known as a/an _____ angle
Answer:
An angle that measures exactly 180° is known as a straight angle
Step-by-step explanation:
A straight angle is basically just a line. It is equal to two right angles (which are 90 degrees) and it is also half of a circle.
I hope this was helpful! If you need any more information on straight angles or any other angles, let me know! Have a lovely day! :)
I’m trying to find the absolute Max and min, I can’t figure out how to do the derivative, thanks
Step-by-step explanation:
Step 1: Take the First Derivative This means only differentiate once.
Disclaimer: Since absolute value only take positve outputs and quadratics only take positve outputs, we can get rid of the absolute value signs so we now have
[tex]e {}^{ {x}^{2} - 1 } [/tex]
We have the function x^2-1 composed into the function e^x.
So we use chain rule
Which states the derivative of a function composed is the
derivative of the main function times the derivative of the inside function.
So the derivative of the main function is
[tex] \frac{d}{dx} (e {}^{x} ) = e {}^{x} [/tex]
Then we replace x with x^2-1
[tex]e {}^{ {x}^{2} - 1} [/tex]
Then we take the derivative of the second function which is 2x so qe multiply them
[tex]e { }^{ {x}^{2} - 1 } 2x[/tex]
Step 2: Set the equation equal to zero.
[tex]e {}^{x {}^{2} - 1} 2x = 0[/tex]
Since e doesn't reach zero. We can just set 2x=0.
[tex]2x = 0 = x = 0[/tex]
So the critical point is 0.
Since e^x will never reach zero
Since 0 is the only critical point, this where the max or min will occur at.
Next we pick any numbergreater than zero, and plug them in the derivative function which gives us a positve number.
Any pick less than zero will give us a negative number.
Since the function is decreasing then increasing, we have a minimum.
Since 0 is the only critical point, we have a absolute minimum at 0.
To find the y coordinate, plug 0 in the orginal function.
Which gives us
[tex]e {}^{ {0}^{2} - 1 } = e {}^{ - 1} = \frac{1}{e} [/tex]
So the minimum occurs at
(0,1/e).
Rotate the given triangle 180° counter-clockwise about the origin. [ 0 -3 5 ] [0 1 2]
Answer:
[tex]\left[\begin{array}{ccc}0&3&-5\\0&-1&-2\end{array}\right][/tex]
Step-by-step explanation:
Rotation 180° (in either direction) about the origin causes each coordinate to have its sign changed. Effectively, the coordinate matrix is multiplied by -1.
__
Additional comment
This is equivalent to reflection across the origin.
The length of a rectangle is triple the width. If the area of the rectangle is 75 square inches, then find the length and width
Answer:
W = 5
L = 15
Step-by-step explanation:
Formula for Area of Rectangle is L × W
Since stated triple;
L = 3W
Area = L×W = 3W² = 75
It'll be:
3W² = 75
Divide both sides with 3:
3W² = 75
3 3
W² = 25
Then square root both sides:
w = 5
Again stated that length is triple the width:
L = 5 × 3
L = 15
Therefore;
W = 5
L = 15
Points P and Q are respectively 4m North and 3m East of point R. Calculate the distance between point P and Q
Apply Pythagorean theorem
PQ²=QR²+PR²PQ²=4²+3²PQ²=5²PQ=5mAnswer:
Distance between point P and Q = 5m
Step-by-step explanation:
Given
Point P is 4m north (↑) of Point RPoint Q is 3m east (→) of Point RUsing Pythagorean Theorem (applicable for only right triangles)
PQ = √4² + 3²PQ = √25PQ = 5 mHope it helped~
Solve by completing the square:
x2 + 2x-8= 0
-8
a.
x = -4 or 2
b. X= 4 or 2
-
=
c.
x= -4 or - 2
d. X= 4 or - 2
x
Rewrite the expression 2 square root X•4x^-5/2 in the form k•x^n
Answer:
(4x)
2
=16×x
2
Step-by-step explanation:
hope it's help
Gizmo eats 3 crickets per day. If there are 15 crickets in a container, what is the maximum number of days Ms. Evans can go before buying replacement crickets.
What is the area of this trapezoid? units 2
area of trapezoid: 153 units²
Here given information:
height : 9side 1 : 10side 2 : 7 + 10 + 7 = 24trapezium area = [tex]\sf \frac{1}{2}[/tex] * ( side 1 + side 2 ) * height
[tex]\hookrightarrow \sf \dfrac{1}{2} * ( 10 + 24) * 9[/tex]
[tex]\hookrightarrow \sf 153 \ units^2[/tex]
What is the outlier for the data set?
Heart Rate
5 0 7
6 3 5 6 8 8
7 0 2
8
9 0
5 0 = 50 beats per minute
40
50
68
90
Answer:
6 3 5 6 8 8
Step-by-step explanation:
farthest apart than any other number
Answer:
Your correct answer is 90 :)
Step-by-step explanation:
90 is the biggest number in the number set so therefore it is an outlier.
Have an amazing day!!
Please rate and mark brainliest!!
What length is X
3.0000
4.0000
Add. Simplify the answer and write the answer as a mixed number if appropriate 3/8+2/3
THINK SMARTER + Julianna is lining the inside of a basket with fabric.
The basket is in the shape of a rectangular prism that is 29 cm long,
19 cm wide, and 10 cm high. How much fabric is needed to line the
inside of the basket if the basket does not have a top? Explain your
strategy
2
Answer:
1,511 cm²
Step-by-step explanation:
We will find the surface area, but not include the top.
This means we will have five sides to calculate for, see attached. Please note that the area of a rectangle can be found with A = L * W
[1] 19 cm * 10 cm = 190 cm²
[2] 19 cm * 10 cm = 190 cm²
[3] 29 cm * 10 cm = 290 cm²
[4] 29 cm * 10 cm = 290 cm²
[5] 19 cm * 29 cm = 551 cm²
Add them all together:
190 cm² + 190 cm² + 290 cm² + 290 cm² + 551 cm² = 1,511 cm²
Classify each of the following statements as true or false.
a 4 × n can be written as 4n. say if it is true or false thanks smarties
b n × 3 can be written as 3n.
c 4 × b can be written as b + 4.
d a × b can be written as ab.
e a × 5 can be written as 50a.
Step-by-step explanation:
a- true
b- true
c- false, it can be written 4b
d- true
e- false, 5a
Answer:
A.true B.true C.False D.true E.False
The cards below have a mean of 25. What is the missing number?: ? 19, 22, 31
Answer: Its 28.
Step-by-step explanation:
The missing number in the card s 28
How to determine the missing number?Represent the missing number with x.
So, we have:
x, 19, 22 and 31
The mean of a dataset is:
Mean = Sum/Count
So, we have:
25 = (x + 19 + 22 + 31)/4
Multiply both sides by 4
100 = x + 19 + 22 + 31
Evaluate the sum
100 = x + 72
Subtract 72 from both sides
x = 28
Hence, the missing number is 28
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can someone help me please
Answer:
y=x-5
Step-by-step explanation:
try that my good sir
"The sum of a number and 20 is multiplied by 6 and the result is 26."
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
Consider the number as x
let's solve ~
[tex]\qquad \sf \dashrightarrow \:6(x + 20) = 26[/tex]
[tex]\qquad \sf \dashrightarrow \:6x + 120 = 26[/tex]
[tex]\qquad \sf \dashrightarrow \:6x = - 120 + 26[/tex]
[tex]\qquad \sf \dashrightarrow \:6x = -94[/tex]
[tex]\qquad \sf \dashrightarrow \:x = - 94 \div 6[/tex]
[tex]\qquad \sf \dashrightarrow \:x = \dfrac{ - 47}{3} [/tex]
・ ．━━━━━━━†━━━━━━━━━．・
Answer:
[tex](x + 20) 6 = 26[/tex]
[tex]6x + 120 = 26[/tex]
[tex]6x = 26 - 120[/tex]
[tex]6x = - 94[/tex]
[tex] \displaystyle \: x = \frac{ - 94}{6} [/tex]
[tex] \displaystyle{x = \frac{ - 47}{3} }[/tex]
[tex]\red {\rule{35pt}{2pt}} \green{ \rule{35pt}{2pt}}\orange{ \rule{35pt}{2pt}}\pink{ \rule{35pt}{2pt}}\blue{ \rule{35pt}{2pt}}\purple{ \rule{35pt}{2pt}}\red{ \rule{35pt}{2pt}}[/tex]
[tex] \bold{ \displaystyle{x = - \frac{47}{3} }}[/tex]
Michelle is fishing from a small boat. A fish swimming at the same depth as the hook at the end of her fishing line is 16 meters away from the hook. If Michelle is 20 meters away from the fish, how far below Michelle is the hook?
Answer:
12 meters
Step-by-step explanation:
You have to use the inverse of the pythagorean theorem to do this so you do square root of (20x20-16x16) which is 12
which fraction is larger: 3/10 or 2/7
Plot on a number line
Answer:
3/10 is bigger
Step-by-step explanation:
covert into a decimal so 0.3 is bigger than 0.2857
Can someone solve this question to me.i will mark brainliest. :)
Answer:
Parent Function: [tex]y=\sqrt{x}[/tex]Horizontal shift: right 3 unitsVertical shift: up 3 unitsReflection about the x-axis: noneVertical strech: strechedStep-by-step explanation:
assume that [tex]y=\sqrt{x}[/tex] is [tex]f(x)=\sqrt{x}[/tex] and [tex]y=\sqrt{-2x+6}+3[/tex] is
[tex]g(x)=\sqrt{-2x+6}+3\\ f(x)=\sqrt{x} \\g(x)=\sqrt{-2x+6}+3[/tex]
The transformation from the first equation to the second equation can be found by finding a,h and k for each equation.
[tex]y=a\sqrt{x-h}+k[/tex]
factor a 1 out of the absolute value to make the coefficient of x equal to 1
[tex]y=\sqrt{x}[/tex]
factor a 2 out of the absolute value to make the coefficient of x equal to 1
[tex]y=\sqrt{2}\sqrt{x-3}+3[/tex]
find a, h and k for [tex]y=\sqrt{2}\sqrt{x-3}+3[/tex]
[tex]a=1.41421356\\ h=3\\k=3[/tex]
the horizontal shift depends on the value of h when [tex]h > 0[/tex], the horizontal shift is described as:
[tex]g(x)=f(x+h)[/tex] - the graph is shifted to the left h units
[tex]g(x)=f(x-h)\\[/tex] - the graph is shifted to the right h units
the vertical shift depends on the value of k
A city has a population of 380,000 people. Suppose that each year the population grows by 6.5%. What will the population be after 10 years?
Round your answer to the nearest whole number.
If the volume of a cuboid is 120 cm' and it has a length of 10cm, a height of 4cm, the width of the cuboid is ?
cm,
Answer:
3cm
Step-by-step explanation:
V = L * W * H
V = 10 * W * 4
10 * 4 = 40
120 / 40 = 3
W = 3
How do I solve for X?
The value of x in the special right triangle is 39.60 ft.
Right angle triangleRight angle triangle has one of its angles as 90 degrees. The side and angles can be found using trigonometric ratios.
Therefore, let's find the base of the triangle with 30 degrees.
sin 30° = opposite / hypotenuse
1 / 2 = 7 / b
b = 14 ft
Let's use the value(14 ft) to find the height of the biggest triangle.
sin 30 = opposite / hypotenuse
sin 30 = 14 / h
0.5h = 14
h = 14 / 0.5
h = 28 ft
Therefore, let's find the value of x .
sin 45° = 28 / x
x = 28 / 0.70710678118
x = 39.5979797464
x = 39.60 ft
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Use the Pythagorean Theorem to find the missing length and then round the
result to the nearest tenth.
Answer:2 squared +3 squared and the square root of that number
Step-by-step explanation:
Select ALL the expressions that have the same value as the expression 0.5 ÷ 0.25
A. 1,200 ÷ 60
B. 1.2 ÷ 0.6
C. 0.012 ÷ 0.06
D. 2.5 ÷ 2.25
E. 0.05 ÷0.025
Answer:
B and E
Step-by-step explanation:
0.5 ÷ 0.25 = 2
A. NO because it's 20
B. Yes
C. NO because it's 0.2
D. NO because it's 1.1 repeating
E. Yes
A T.V. se was bought for Rs. 13950, when 10% discount is given. , calculate the marked price of the T.V.
Answer:
15500
Step-by-step explanation:
Solution
here
price of tv after discount: 13950
discount : 10%
now,
price of tv without discount= 13950÷90×100price of tv without discount= Rs15500Need Help Please!!
Determining the price for a product can be tricky! Companies often have to juggle several variables in order to find the price that maximizes their revenue. Currently, the price of a product is set at $100. The company is getting about 20 customers per week at this rate. The company has done some research and found that they lose two customers for every $5 they increase their price.
Let the variable ”x” represent the number of times the company increases the price by $5. What is the price of the product when x= 3?
Check the picture below.
[tex] \rm \sum_{n = 1}^{ \infty } \frac{( - {1)}^{n + 1} }{n \binom{2n}{n} } \\ [/tex]
Recall the well-known series
[tex]\displaystyle 2 \arcsin^2(x) = \sum_{n=1}^\infty \frac{(2x)^{2n}}{n^2 \binom{2n}n}[/tex]
Replace x with √x :
[tex]\displaystyle 2 \arcsin^2(\sqrt x) = \sum_{n=1}^\infty \frac{(4x)^n}{n^2 \binom{2n}n}[/tex]
Differentiate both sides:
[tex]\displaystyle -\frac{\arcsin(\sqrt x)}{2\sqrt{x-x^2}} = \sum_{n=1}^\infty \frac{(4x)^n}{n \binom{2n}n}[/tex]
Multiply by 4x :
[tex]\displaystyle -\frac{4x \arcsin(\sqrt x)}{2\sqrt{x-x^2}} = \sum_{n=1}^\infty \frac{(4x)^{n+1}}{n \binom{2n}n}[/tex]
All the series I've mentioned converge for |x| < 1, so we can take x = -1/4 to find the value of the sum we want.
[tex]\displaystyle \sum_{n=1}^\infty \frac{(-1)^{n+1}}{n \binom{2n}n} = -\frac{4 \times \left(-\frac14\right) \arcsin\left(\sqrt{-\frac14}\right)}{2\sqrt{-\frac14-\left(-\frac14\right)^2}} = -\frac{\arcsin\left(\frac i2\right)}{\frac{\sqrt5\,i}2}} = \boxed{\frac2{\sqrt5} \mathrm{arsinh}\left(\frac12\right)}[/tex]
where
[tex]\arcsin\left(\frac i2\right) = z \iff 2\sin(z) = -2i\sinh(iz) = i \implies z = i \, \mathrm{arsinh}\left(\frac12\right)[/tex]
The area of a square slice of cheese is 25 square inches. The perimeter of the slice of cheese is
Choose...
inches.
Answer:
As Per Provided Information
Area of given square slice of cheese is 25 square inches .
We have been asked to determine the perimeter of the slice of cheese .
First we will find the side of square slice of cheese .
Let us assume the side of square slice of cheese be s .
Now Let's Solve
[tex] \boxed{\bf \:Area_{(Square)} = {Side}^{2}}[/tex]
Substituting the value and we obtain
[tex] \sf \longrightarrow \: 25 = {s}^{2} \\ \\ \\ \sf \longrightarrow \: \sqrt{25} = s \\ \\ \\ \sf \longrightarrow \: s \: = 5 \: inch[/tex]
So, the side of square slice cheese is 5 inch
Now let's calculate the Perimeter of cheese
[tex] \boxed{\bf \: Perimeter_{(Square)} = 4 \times side}[/tex]
Substituting the value we obtain
[tex] \longrightarrow \sf \: Perimeter_{(Square)} = 4 \times 5 \\ \\ \\ \longrightarrow \sf \: Perimeter_{(Square)} =20 \: inches[/tex]
Therefore,
Perimeter of square slice of cheese is 20 inches .If you have 100 feet of fencing and want to enclose a rectangular area up against a long, straight wall, what is the largest area you can enclose
Answer: 1250 square feet!
Step-by-step explanation:
A (25)=25•(100-2•25)=25•50=1250 Sq Ft
If you have 100 feet of fencing and want to enclose a rectangular area up against a long, straight wall, The largest area you can enclose will be 1250 sq Ft.
What is a rectangle?It is defined as two-dimensional geometry in which the angle between the adjacent sides is 90 degrees. It is a type of quadrilateral. The area occupied by the rectangle in two-dimensional planner geometry.
The area of a rectangle can be calculated using the following formula:
Rectangle area = length x width
It is given that if you have 100 feet of fencing and want to enclose a rectangular area up against a long, straight wall.
Any rectangle's length and width differences must be as small as possible for the area to be maximized.
The largest area you can enclose
A =25×(100-2•25)
A=25•50
A=1250 Sq Ft
Thus, if you have 100 feet of fencing and want to enclose a rectangular area up against a long, straight wall, The largest area you can enclose will be 1250 sq Ft.
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