Answer:
0
Step-by-step explanation:
How many complex roots does the equation 0=3x5−x4−5x2+1 have?
The given polynomial equation 3x⁵ − x⁴ − 5x² + 1 = 0 has two complex roots.
What is a polynomial?A polynomial is defined as a mathematical expression that has a minimum of two terms containing variables or numbers. A polynomial can have more than one term.
The given polynomial equation below is:
0 = 3x⁵ − x⁴ − 5x² + 1
3x⁵ − x⁴ − 5x² + 1 = 0
The given polynomial equation is a polynomial of degree 5.
The simplest method is to solve it graphically using a graphing program.
Clearly, the polynomial equation is a degree 5 equation, hence it has a maximum of 5 roots.
We may now locate the roots of the equation using the graph.
Since there are 3 real roots, the remaining are two complexes, so there are 2 complex roots
Hence, the given polynomial equation 3x⁵ − x⁴ − 5x² + 1 = 0 has two complex roots.
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which statement is true about fiction
Answer:
The function is even because of symmetry over x axis
What is 9 squared?
Why?
Why do we call this "Squared"?
What is 5 cubed?
Why?
Why do we call this "Cubed"?
Answer:
The squared root of 9 is 3
Why - Half of 9 is 3
Why do we called this squared - It is the positive solution of the equation x2 = 9. The number 9 is a perfect square.
5 Cubed is equal to 125
Why - The number 125 on prime factorization gives 5 × 5 × 5. On combining the prime factors in groups of 3 gives 5
Why do we call this cubed = The cube of a number is that number times itself times itself. 5 cubed, denoted 53, is equal to 5×5×5, or 125.
Which ordered pair would form a proportional relationship with the point graphed below?
On a coordinate plane, a line goes through points (0, 0), (10, 40) and (negative 10, negative 40).
(40, 10)
(–5, –10)
(5, 20)
(–10, –20)
Answer:
(5,20)
Step-by-step explanation:
divide both sides of (10, 40) by the same number 2 and you will get (5,20). The points should all lie on the same straight line to form a proportional relationship.
Answer: 5,20
Step-by-step explanation:
(x - 4)/(x + 6) - (x - 6)/(x + 4)
Answer:
[tex]\frac{20}{(x+4)(x+6)}[/tex]
Step-by-step explanation:
assuming you require the expression simplified
[tex]\frac{x-4}{x+6}[/tex] - [tex]\frac{x-6}{x+4}[/tex]
multiply the numerator/denominator of the first fraction by (x + 4)
multiply the numerator/denominator of the second fraction by (x + 6)
= [tex]\frac{(x-4)(x+4)}{(x+4)(x+6)}[/tex] - [tex]\frac{(x-6)(x+6)}{(x+4)(x+6)}[/tex] ← expand and simplify numerators leaving the common denominator
= [tex]\frac{x^2-16-(x^2-36)}{(x+4)(x+6)}[/tex]
= [tex]\frac{x^2-16-x^2+36}{(x+4)(x+6)}[/tex]
= [tex]\frac{20}{(x+4)(x+6)}[/tex]
Which graph represents the function of f(x) = 4x^2-16/2x-4 ?
See the graph in the image.
y = (4x² - 16)/(2x - 4)y = [4(x-2)(x+2)]/[2(x-2)]y = 2(x+2), with a domain of all real numbers other than 2A function is a relationship between inputs where each input is related to exactly one output.
The graph of f(x) = (4x² - 16) / (2x - 4) is given below.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
Function:
f(x) = (4x² - 16) / (2x - 4)
This can be written as,
f(x) = (2x)² - 4² / (2x - 4) [ a² - b² = (a + b)(a - b) ]
f(x) = (2x - 4)(2x + 4) / (2x - 4)
f(x) = 2x + 4
Now,
We will find the coordinates from the function f(x) = 2x + 4
x = 0, f(x) = 4
(0, 4)
x = 1, f(x) = 6
(1, 6)
x = 3, f(x) = 10
(3, 10)
And so on.....
The graph is given below,
Thus,
The graph of f(x) = (4x² - 16) / (2x - 4) is given below.
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A boat leaves a dock and goes 240 miles in a direction of 290 degrees. It then turns and goes 50 miles in a direction on 30 degrees. How far is the boat from the dock and in what direction?
By Pythagorean theorem and trigonometric functions, the magnitude and direction of the boat are approximately 284.403 miles and 295.043° with respect to the east.
What is the direction and magnitude of the resulting displacement with respect to the origin
In this problem we assume that the first angle is measured with respect to the east side and that the second angle is counterclockwise and measured with respect to the direction of the first vector. First, we need to determine the resulting vector by using trigonometric and vectorial formulas:
(x, y) = (240 · cos 290°, 240 · sin 290°) + (50 · cos 320°, 50 · sin 320°)
(x, y) = (120.387, - 257.666) [mi]
The magnitude is found by Pythagorean theorem:
[tex]r = \sqrt{(120.387\,mi)^{2}+(-257.666\,mi)^{2}}[/tex]
r ≈ 284.403 mi
The direction of the boat is obtained by inverse trigonometric functions:
θ = tan⁻¹ (- 257.666/120.387)
θ ≈ 295.043°
By Pythagorean theorem and trigonometric functions, the magnitude and direction of the boat are approximately 284.403 miles and 295.043° with respect to the east.
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The Law of Sines states that sin A/b = sin B/c = sin C/a
True
False
Step-by-step explanation:
hope you can understand
Yaqub, Angus and Iris share 18 slices of pizza in the ratio
1:3:2.
How many slices of pizza does Iris have?
Answer:
6 Slices
Step-by-step explanation:
Total units = 1 + 3 + 2 = 6 Units
6 Units = 18 Slices of Pizza
Iris shared 2 units.
1 Unit = 18/6 = 3 Slices of Pizza
2 Units = 2 * 3 = 6 Slices of Pizza
If p() = x2 - 1 and q(x) - 5(x-1), which expression is equivalent to (p - q)(x)?
Answer:
[tex]\text{If p(x) = x2 - 1 and q(x) = 5(x - 1), the expression which is equivalent to}[/tex] [tex]\text{ (p - q)(x) is (x2 - 1) - 5(x - 1).}[/tex]
Step-by-step explanation:
Given:
p(x) = 2x2 - 1q(x) = 3(x - 1)To find:
(p - q)(x)We know:
(p - q)(x) = p(x) - q(x)Substitute
(2x^2 - 1) - 3(x - 1)[tex]\text{Therefore, the expression equivalent to (p - q)(x) is (2x2 - 1) - 3(x - 1).}[/tex]
What is the solution to the following equation?
3(x-4)-5-x-3
A. x = 12
B. x=3
C. x=8
D. x = 7
Answer:
D. x = 7
Step-by-step explanation:
NOTE : there should be an equal sign somewhere in the given expression.
suppose the equation is the following:
3(x-4)-5 = x-3
………………………………………………………
3(x - 4) - 5 = x - 3
⇔ 3x - 12 - 5 = x - 3
⇔ 3x - 17 = x - 3
⇔ 3x - 17 + 17= x - 3 + 17
⇔ 3x = x + 14
⇔ 2x = 14
⇔ x = 14/2
⇔ x = 7
simplify (–2 – c )(–1)
The simplified expression of (-2 - c)(-1) is 2 + c
How to simplify the expression?We have:
(-2 - c)(-1)
Express as product
(-2 - c) * (-1)
Evaluate the product
2 + c
Hence, the simplified expression of (-2 - c)(-1) is 2 + c
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If 1=3 2=3 3=5 4=4 5=4 then 6=?
The value of the 6 is 3.
If you write 1 in word then you will write one and if you count the letter it will give you 3
Similarly, if you write the numbers 2,3,4,5 in word and count the number you will get 3,5,4,4 respectively.
What are the counting letters?counting Letters provides a perfect way to introduce number words to beginning readers, as well as discuss the concepts of letters and words.
So, if you write 6 in words you will write six and on counting the letter you will get 3.
Hence, 6 = 3 ans.
Therefore the value of the 6 is 3.
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please help i dont know how to do this
If the degree of a polynomial function is even and the leading coefficient is negative, then the end behavior of the function is?
Answer:
Its the last option.
Step-by-step explanation:
The function will rise from the left and descend to the right.
f(x) ---> -∝ as x ---> -∝ and f(x) ---> -∝ as x ---> ∝
Choose the correct simplification of the expression (2x7y)2(y5)3.
The correct simplification of the expression is 4x¹⁴y¹⁷
Given,
The expression is (2x⁷ y)² (y⁵)³
To distribute the exponent, apply the power rule (ab)ⁿ = aⁿbⁿ
Implement the product rule to (2x⁷y)².
Here, we have a = 2x⁷ , b = y and n = 2
=(2x⁷)² y²(y⁵)³
= 2²(x⁷)² y²(y⁵)³
= 4(x⁷)² y²(y⁵)³
Now exponents should be multiplied while using the product rule.
The product rule is (aˣ)ⁿ = aˣⁿ
We apply this to (x⁷)² and (y⁵)³
So the expression becomes,
=4x⁷·² y² (y⁵·³)
= 4x¹⁴ y² y¹⁵
∵ In exponents we have a rule that if bases are same then powers are added i.e, aˣ aⁿ = aˣ⁺ⁿ
∴ 4x¹⁴ y¹⁵ ⁺ ²
= 4x¹⁴ y¹⁷
Hence we get the answer as 4x¹⁴ y¹⁷
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Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options.
2.3p – 10.1 = 6.4p – 4
2.3p – 10.1 = 6.49p – 4
230p – 1010 = 650p – 400 – p
23p – 101 = 65p – 40 – p
2.3p – 14.1 = 6.4p – 4
Answer:
2.3p – 10.1 = 6.49p – 4 [tex]\huge \checkmark[/tex]
230p – 1010 = 650p – 400 – p [tex]\huge \checkmark[/tex]
Step-by-step explanation:
……………………………………………
2.3p – 10.1 = 6.5p – 4 – 0.01p
⇔ 2.3p – 10.1 = (6.5p – 0.01p) – 4
⇔ 2.3p – 10.1 = (6.5 – 0.01)p – 4
⇔ 2.3p – 10.1 = (6.49)p – 4
⇔ 2.3p – 10.1 = 6.49p – 4
_______________________
_______________________
2.3p – 10.1 = 6.5p – 4 – 0.01p
⇔ 100 × (2.3p – 10.1) = 100 × (6.5p – 4 – 0.01p) multiply both sides by 100
⇔ 100 × (2.3p – 10.1) = 100 × (6.5p – 4 – 0.01p)
⇔ 230p – 1010 = 650p – 400 – p
……………………………………………………
Please Help
What does the missing angle in the triangle measure?
Answer:
x = 60
Step-by-step explanation:
The sum of the angles of a triangle is 180
95+25 +x = 180
120 +x = 180
Subtract 120 from each side
120+x-120 = 180-120
x = 60
Choose any set of Pythagorean triplets of your choice and illustrate them using graph sheet.
Example given below:
The required Pythagorean triplets are hypotenuse, perpendicular and base is 13, 12 and 5 respectively.
In a right angled triangle, its side, such as hypotenuse, perpendicular and base is Pythagorean triplets.
We have
Hypohypotenuse = 13
perpendicular = 12
base = 5
Which satisfies the condition of the Pythagorean theorem.
[tex]a^2+b^2=c^2\\12^2+5^2=c^2\\169=c^2[/tex]
and c = 13
Thus, the required value of Pythagorean triplets satisfies the Pythagorean theorem.
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A,B and C are points in the cartesian plane. the coordinates of A are (3,-2),BA=(4,-3)and AC=(4,9). Calculate
i. the coordinates of B and C
Match each inequality to the number line that represents its solution:
Step-by-step explanation:
I have solve all the questions and your work is to match with that option
Examine the nuclear reaction: superscript 1 subscript 1 h plus superscript 1 subscript 0 n right arrow superscript 2 subscript 1 h.. why is this classified as a nuclear reaction rather than a chemical reaction?
The given reaction is considered as nuclear reaction instead of chemical reaction as the change is coming in the nucleus.
A nuclear reaction is one in which the number of protons or neutrons changes as a result of collisions between two nuclei or an atom and a subatomic particle.
In the given reaction also which is superscript 1 subscript 1 h plus superscript 1 subscript 0 n right arrow superscript 2 subscript 1 h.
A neutron is added to the nucleus of a hydrogen atom here. As a result, it is a nuclear reaction.
A chemical reaction involves the acquisition or loss of electrons, which leads in the synthesis of a new molecule while leaving the nucleus of an atom unchanged.
Thus, we can give a conclusion that because a change in a nucleus happened, the described event is categorised as a nuclear reaction rather than a chemical reaction.
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Jose paid $1.12 for a dozen eggs at his local grocery store. Determine the cost of 18 eggs.
Answer:
$1.68
Step-by-step explanation:
1 dozen is 12.
18 is the same as 12 + 6
6 eggs is half of 12 eggs.
Since 12 eggs cost $1.12, then 6 eggs cost half of $1.12, or $1.12/2 = $0.56.
18 = 12 + 6, so
the price of 18 eggs = the price of 12 eggs + the price of 6 eggs.
price of 18 eggs = $1.12 + $0.56 = $1.68
Match the verbal expression (term) with its algebraic expression (definition).
Match Term Definition
d
Some number increased by two A) a ÷ 2
c
A variable decreased by two B) y2
e
Product of an unknown value and two C) x − 2
2
Quotient of some number and two D) b + 2
b
An unknown value squared E) 2z
The matching of definitions and terms are done below.
Some number increased by two ⇒ b + 2A variable decreased by two ⇒ x – 2Product of an unknown value and two ⇒ 2zQuotient of some number and two ⇒ a ÷ 2An unknown value squared ⇒ y²What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
Match the verbal expression (term) with its algebraic expression (definition).
Some number increased by two ⇒ b + 2
A variable decreased by two ⇒ x – 2
Product of an unknown value and two ⇒ 2z
Quotient of some number and two ⇒ a ÷ 2
An unknown value squared ⇒ y²
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2x + 5y = 17 6x - 5y = -9
Answer:
Step-by-step explanation:
Horizontal lines n and m are intersected by lines q and p. At the intersection of lines q and n, the uppercase right angle is angle 4. At the intersection of lines q and m, the uppercase left angle is angle 1. At the intersection of lines p and n, the bottom left angle is angle 3. At the intersection of lines p and m, the uppercase left angle is angle 2.
If angle 1 is 110°, what would the other angle measures have to be in order for m || n and
q || p?
Angle 2 = °
Angle 3 = °
Angle 4 = °
The values of the angles based on the information will be:
Angle 2 = 110°Angle 3 = 70°Angle 4 = 70°How to calculate the angles?From the information given, angle 1 is 110° and the horizontal lines n and m are intersected by lines q and p.
In this case, it should be noted that opposite angles are equal. Hence, angle 2 is also 110°.
Angle 3 will be:
= 180° - 110° = 70° (angle on a straight line).
Angle 4 will also be 70° as opposite angle to angle 3.
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Use the fraction model to multiply: three multiplied by five sevenths. Leave your answer as an improper fraction. (1 point)
three fraction models, each model is partitioned into seven equal parts, with five parts shaded in each model
eight sevenths
eight tenths
fifteen twenty ones
fifteen sevenths
The product of three and five-sevenths is given by (D) Fifteen sevenths.
In fraction multiplication, we multiply the corresponding position like we multiply numerator with numerator and denominator with another denominator.
The denominator for a whole number is always 1.
Here given the numbers are three and five-sevenths, that is [tex]3,\frac{5}{7}[/tex].
So here since 3 is a whole number then the denominator of it is 1.
We can write 3 as [tex]\frac{3}{1}[/tex].
So product [tex]=\frac{5}{7}\times\frac{3}{1}=\frac{5\times3}{7\times1}=\frac{15}{7}[/tex]
Using the fraction model we get,
Here we can see that there are three bars with seven divisions in which fives are shaded.
So in multiplication with three we have to take the shaded region as the numerator and have to all the shaded and total bar for once.
here a total number of divisions in one bar is 7, so the denominator of the product is 7.
A total number of shaded divisions is 15, so the numerator of the product is 15.
So the product is [tex]\frac{15}{7}[/tex], that is fifteen sevenths.
Hence the correct option is (D) Fifteen sevenths.
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HELP !!!
Which of the following best describes the slope of the line below?
• A. Negative
O B. Zero
• C. Positive
D. Undefined
Question 1 of 10
Solve 10x+16 ≥ 6x+ 20.
O A. x29
OB. x≤ 1
OC. x2 1
OD. x≤ 9
Mr. McMillan and Ms. Burke are teaching their classes how to write in cursive. Mr. McMillan has already taught his class 8 letters. The students in Ms. Burke's class, who started the unit later, currently know how to write 12 letters. Mr. McMillan plans to teach his class 4 new letters per week, and Ms. Burke intends to cover 3 new letters per week. Eventually, the students in both classes will know how to write the same number of letters. How long will that take? How many letters will the students know?
The number of weeks by which the students in both classes will know how to write the same number of letters will be 4 weeks.
What is the linear system?A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
Mr. McMillan and Ms. Burke are teaching their classes how to write in cursive.
Mr. McMillan has already taught his class 8 letters.
The students in Ms. Burke's class, who started the unit later, currently know how to write 12 letters.
Mr. McMillan plans to teach his class 4 new letters per week.
Ms. Burke intends to cover 3 new letters per week.
Eventually, the students in both classes will know how to write the same number of letters.
Then the number of weeks by which the students in both classes will know how to write the same number of letters will be
Let x be the number of the weeks and y be the total number of the letters.
Then the equation will be
y = 4x + 8 …1
y = 3x + 12 …2
Then by solving the equations 1 and 2, we have
x = 4 and y = 24
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