The possible rational roots are ±1, ±3, ±5, ±9, ±15, and ±45.
The actual roots ordered from least to greatest are?
Answers
The actual roots of the function P(x) = x^4 - 4x^3 - 4x^2 + 36x - 45 are its real roots
The actual roots ordered from least to greatest are -3 and 3
How to determine the actual roots?From the complete question, the polynomial function is:
P(x) = x^4 - 4x^3 - 4x^2 + 36x - 45
Expand the above equation
P(x) = x^4 - 4x^3 + 5x^2 - 9x^2 + 36x - 45
Factorize the equation
P(x) = x^2(x^2 - 4x + 5) - 9(x^2 - 4x + 5)
Factor out x^2 - 4x + 5
P(x) = (x^2- 9)(x^2 - 4x + 5)
Express x^2 - 9 as a difference of two squares
P(x) = (x + 3)(x - 3)(x^2 - 4x + 5)
The expression (x^2 - 4x + 5) cannot be factorized.
So, we have:
P(x) = (x + 3)(x -3)
Equate to 0
(x + 3)(x -3) = 0
Expand
x + 3 = 0 or x - 3 = 0
Solve for x
x = -3 or x = 3
Hence, the actual roots ordered from least to greatest are -3 and 3
Read more about polynomial functions at:
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Answer:
answer in picture
Step-by-step explanation:
Related Questions
find the equation of line that passes through the point (4,-5) and the slope 5/4
Answers
Answer:
[tex]\boxed{\sf{y=\dfrac{5}{4}x-10 }}[/tex]
Step-by-step explanation:
To find the equation of line, you have to use a slope and slope-intercept formula.
Slope formula:
[tex]\Longrightarrow:\sf{\dfrac{y_2-y_1}{x_2-x_1} }[/tex]
Slope-intercept formula:
[tex]\Longrightarrow:\sf{y=mx+b}[/tex]
M represents the slope.B represents the y-intercept.So, the slope is 5/4.The y-intercept is -10.Rewrite the problem down.
y=5/4x-10
So, the correct answer is y=5/4x-10.I hope this helps you! Let me know if my answer is wrong or not.
Odds in favor of drawing a face card
Answers
Answer:
y blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah
12 face cards
->12/52
=3/13
(a) Write down the angle between the vector i + j and the vector i- j.
(6) Calculate the angle between the vector 2i + 5j and the vector 4i.
(2)
(c) Two forces, A = (14i +2j) N and B = (2i - 6j) N, act on a ball.
Show that the magnitude of A is Root k times larger than the magnitude of B, where k is
an integer
(3)
Answers
(i + j) • (i - j) = ||i + j|| ||i -j|| cos(θ)
We also recall that for any vector x,
||x||² = x • x
We have
(i + j) • (i - j) = (i • i) + (j • i) + (i • (-j)) + (j • (-j))
= (i • i) + (j • i) + (i • (-j)) + (j • (-j))
= ||i||² + (i • j) - (i • j) - ||j||²
= 1 + 0 - 1
= 0
and
||i + j|| = √(1² + 1²) = √2
||i - j|| = √(1² + (-1)²) = √2
So,
0 = 2 cos(θ)
cos(θ) = 0
θ = arccos(0) = 180°
(b) By the same process, we find
(2i + 5j) • 4i = 8
||2i + 5j|| = √(2² + 5²) = √29
||4i|| = 4
Then if θ is the angle between 2i + 5j and 4i, we have
8 = 4√29 cos(θ)
cos(θ) = 2/√29
θ = arccos(2/√29) ≈ 68.1986°
(c) Compute the magnitudes:
||A|| = √(14² + 2²) = √200 = 10√2
||B|| = √(2² + (-6)²) = √40 = 2√10
Now we can write
||B|| = 2√10 = 2 √(5 × 2) = 2√5 × √2 = 1/√5 × 10 √2 = 1/√5 ||A||
or
||A|| = √5 ||B||
so that k = 5.
Need help ASAP due today! I will give brainlisted for correct answer!
Answers
Answer: 15.
Step-by-step explanation: To find the slope, you need to use rise/run which is done below if you need a visual look at what I'm saying. Before we use rise/run, we need two points on the line. We'll use (2, 80), and (6, 140). We need to go 60 up and 4 to the right to make the points meet. Going up or down is the rise and left or right is the run. Our rise/run is 60/4 or 15 when you divide. Therefore, 15 is your slope for this equation of a line.
Have a great day! :)
Differentiate y = tan²x from first principle
Answers
Answer:
[tex]y'=2sec^2(x)tan(x)[/tex]
Step-by-step explanation:
A circle with radius of 1 cm sits inside a 11 cm x 12 cm rectangle.
What is the area of the shaded region?
Answers
Answer:
Hope the picture will help you.................
un classeur contient des feuilles de couleurs différents les deux tiers des feuilles sont blanches le un sixieme des feuilles sont bleues et 12 feuilles restantes sont jaunes determiner le nombre des feuilles dans le classeur
Answers
Answer:
Step-by-step explanation:
bonjour :
soit x le nombre des feuilles dans le classeur
les deux tiers des feuilles sont blanches veut dire : (2/ 3)x
un sixieme des feuilles sont bleues veut dire : (1/6)x
on compose cette équation : (2/ 3)x + (1/6)x +12 = x
rsolvont cette équation : multiplions les deux membres par : 6
4x+x+72 =6x
4x-6x+x+72=6x-6x
-x+72=0
x=72
verification :(2/3)(72)+(1/6)(72)+12=144/3 +72/6 +12 =48+12+12=72
Find the area of the square.
pls help!!
Answers
Answer:
Area of square: 9/16 m²
Step-by-step explanation:
We are given:
Side length of square: 3/4 metersThe area of the square is the side multiplied by the same side. Therefore,
⇒ Area of square: (3/4) × (3/4)⇒ Area of square: (3/4)²Using the exponents property, [(a/b)² = (a²/b²)]:
⇒ Area of square: (3²/4²)⇒ Area of square: (9/16) m²Therefore, the area of the square is 9/16 m².
Answer:
[tex]\huge\boxed{\bf{Area_{square} = \frac{9}{16}m^2}}[/tex]
Step-by-step explanation:
Given : -
Slide length of square = [tex]\frac{3}{4}[/tex]m.To Find : -
Area of squareAns : -
$\sf \to Area_{square} = (side\:length)^2$
$\sf \to Area_{square} = (\frac{3}{4}m)^2$
$\sf \to Area_{square} = (\frac{3}{4}m*\frac{3}{4})$
$\sf \to Area_{square} = (\frac{3*3}{4*4}m^2)$
$\sf \to Area_{square} = \frac{9}{16}m^2$
[tex]\:[/tex]
$\huge\colorbox{skyblue}{BlackPain}$
Help picture below problem 9
Answers
Answer:
i think the answer might be E.
the answer is A option that is Angle M
Please Expand the following y( y + 2)
Answers
Answer:
[tex]y^{2} + 2y[/tex]
Step-by-step explanation:
y times y is [tex]y^{2}[/tex]
2 times y is 2y
PLEASE HELP ASAP
Reginald Wallace's gross weekly salary is $515. His weekly federal withholding is $55. The Social Security tax is 6.2% of the first $97,500 he earns. The Medicare tax is 1.45% of gross pay. The state tax is 1.5% of gross pay. Each week he pays $12.40 for medical insurance. How much is deducted from Reginald's weekly wages for state tax and Medicare tax?
Answers
Answer:
$15.20
Step-by-step explanation:
Had the same question last year and found the answer in some flashcards. You can browse the question too.
Find the equation of the line joining the points (4, 9) and (-1, 0)
Answers
The equation of the line joining the points (4, 9) and (-1, 0) is y = 9/5 x + 9/5
How to find the equation of a line?The formula for calculating the equation of a line is expressed as:
y = mx + b
m is the slope
b is the intercept
Determine the slope:
Slope = 0-9/-1-4
Slope = -9/-5
Slope = 9/5
Determine the y-intecept
0 = 9/5(-1) + b
b = 9/5
Hence the equation of the line is y = 9/5 x + 9/5
Learn more on equation of a line here: https://brainly.com/question/13763238
Write the equation of the line through the points (-6, -19) and (2, 5).
Answers
Answer:
y = 3x - 1
Step-by-step explanation:
The slope of a line passing through the two points
P = (x1. y1) and Q = (x2, y2) is given by
m= (y2-y1)/(x2-x1)
We have that x1= -6, y1= -19, x2= 2, y2= 5
m=3
Now, the y-intercept is b=y1 - mx1 (or b= y2 - mx2, the result is the same).
b= -19-(3)(-6)
b= -1
y = 3x - 1
Evaluate the expression 5p for p=2
Answers
Answer:
10
Step-by-step explanation:
when p=5
substituting p=5 into 5p.
5p = 5×2 =10
The roof of one building is 400 feet below the roof of another building. A person standing on the lower roof sees another person standing on the higher roof at a 35o angle of elevation. Approximately how far apart are the buildings? Round to the nearest foot.
Answers
Since the roof of one building is 400 feet below the roof of another building, the buildings are 571 ft apart.
The required triangleThe line of sight of the lower building to the taller building, the distance of the buldings apart, D and the height of the lower building below the taller building, h form a right angled triangle with angle Ф = 35° = angle of elevation of taller building and opposite side, h.
From trigonometric ratios, we have that
tanФ = h/D
So, D = h/tanФ
Since
h = 400 ft and Ф = 35°,Distance of building apartSubstituting the values of the variables into the equation, we have
D = h/tanФ
D = 400 ft/tan35°
D = 400 ft/0.7002
D = 571.27 ft
D ≅ 571 ft to the nearest foot
So, the roof of one building is 400 feet below the roof of another building, the buildings are 571 ft apart.
Learn more about distance of building apart
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I WILL MARK BRAINLIEST
Is an antacid polar or non-polar?
Answers
Answer:
Antacid tablets react with water but not oil so its polar
Rewrite the expression ^3 square root of x^8 using rational exponents.
Answers
Answer:
X^8/3
Step-by-step explanation:
When transforming radical expressions to rational exponents, the radicand (8) becomes the numerator of the rational exponent. And the index, or root (3) of the radical becomes the denominator of the rational exponent.
How much on average did she make a week, if she worked 15 hours a week at $11/hour? (Rounded to the nearest whole dollar. Do NOT put the dollar sign.)
Answers
Answer:
1265 i think
Step-by-step explanation:
add 11 15 times
Answer:165
Step-by-step explanation:
Factorise fully 21a-7a²
Answers
-7(a-3)a
hope it helps...!!!!
(12 points) Let X = (1,2,3,4,5).
(a) Find the number of sequences of length 7 over X.
(b) A palindrome of length kis a sequence aja2 ... 0 such that alk-1...0,01 = 0102 ...k-101ka Find the number of palindromes of length 7 over X.
(c) How many three digit odd positive integers with distinct digits can you write using only the numbers in X?
Answers
The answer is C
If I am wrong, please come after me, I am not perfect
if 8 pieces are 220 calories how many calories is 1 piece
Answers
Step-by-step explanation:
8 pieces = 220 colories
1 piece = 220/8 = 27.5 calories
Answer:
27.5
Step-by-step explanation:
8 divided by 220 = 27.5
Sorry about the fisrts time i put the 8 in frunt and 220 in the back so it was all back werds Sorry about that
And Hope This Helps
A system of equations is shown below.
Equation A: 4x - y = -5
Equation B: x + 2y = 1
Which method eliminates one of the variables?
1.
Multiply equation A by 2 and add the result to equation B.
2.
Multiply equation B by 4 and add the result to equation A.
3.
Multiply equation A by 2 and equation B by 4, and add the results toge
4.
Multiply equation B by 2 and equation A by 4, and add the results toge
Answers
Answer:
this one has to be answer 1
Step-by-step explanation:
4x - y = -5
x + 2y =1
8x - 2y = -10
x + 2y = 1
9x = -9
How did the structure of the Han dynasty reflect Confucianism? Increasing rebellions represented the emphasis on warfare. Crowning a new emperor reflected the importance of loyalty. The multiple levels of bureaucracy reflected the belief in social order. The need for new leaders highlighted the importance of self-promotion.
Answers
Answer:
the multiple levels of bureaucracy reflected the belief in social order
Step-by-step explanation:
Simplify the following expression. 23 + 13 + 63 × 63 ÷ 6 =
Answers
Answer:
Here is the answer
Step-by-step explanation:
Find the measure of ∠b.
A. 110∘
B. 102∘
C. 111∘
D. 121∘
Answers
Answer:
110 :)
Step-by-step explanation:
Triangle total angle measurement: 180
Now lets solve!
28 + 42 + ? = 180
70 + ? = 180
Now we have to subtract!!
180 - 70 = 110
Have an amazing day!!
Please rate and mark brainliest!!
28 + 42 + ∠b = 180
70 + ∠b = 180
∠b = 180 - 70
∠b = 110
Lin's grandmother ordered needles that were 0.3125 inches. The pharmacist sent her 0.6875 inches needles. How longer were these needles than the ones she ordered?
Answers
Answer:
0.375
Step-by-step explanation:
0.6875-0.3125 = 0.375
A cylinder has a diameter of 6 cm and a height of 3 cm. What is the surface area of the cylinder? Enter your answer, in exact form, in the box.
Answers
If the diameter and height of the cylinder are 6 cm and 3 cm. Then the surface area of the cylinder is 56.55 square cm.
What is a cylinder?A cylinder is a closed solid that has two parallel circular bases connected by a curved surface.
A cylinder has a diameter of 6 cm and a height of 3 cm.
Then the surface area of the cylinder will be
[tex]\rm SA = \pi d h[/tex]
We have
d = 6 cm
h = 3 cm
Then the surface area will be
[tex]\rm SA = \pi \times 6 \times 3 \\\\SA = 56.55[/tex]
More about the cylinder link is given below.
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distribute to create an equivalent expression with the fewest symbols possible 1/5(15+10k)=
Answers
Answer:
[tex]3+2k[/tex]
Step-by-step explanation:
[tex]\frac{1}{5}(15+10k)=\frac{1}{5}(15)+\frac{1}{5}(10k)=3+2k[/tex]
Answer:
3 + 2k
Step-by-step explanation:
Given that:
⅕ (15+10k)
Using the distributive property which is:
a × (b + c) = a × b + a × c
Which also means: Remove Parentheses
Thus we have:
⅕ (15+10k)
⇒ ⅕ × 15+⅕ ×10k
⇒ ¹⁵⁄₅ + ¹⁰ᵏ⁄₅
⇒ 3 + 2k
Hence, the answer to equivalent expression is 3 + 2k.
Kavinsky
HELP
Which speed is equivalent to 1/2 mile per hour?
Answers
evelyn invests $3200.00 in an account for 9 months at a 5% annual interest rate, what is evelyns total amount in her account at the end of the term?
Answers
Answer:
3320
Step-by-step explanation:
So, 9 months is 9/12 of a year which is 3/4.
Each month they get 5/12% of their total money, so 9x5/12=3.75%.
3320