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The given polynomial equation 3x⁵ − x⁴ − 5x² + 1 = 0 has two complex roots.

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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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]

Answer:

See below

Step-by-step explanation:

Next step is to gather 'like' terms

-x2 - 4x -3 = 2x + 5.

x^2 + (4x + 2x)   + (3+5)    = 0       then simplify

x^2 + 6x + 8     = 0        then factor

(x+4)(x+2) = 0  

so either of these terms = 0

x+4 = 0    means   x = -4

x+ 2 = 0 means  x = - 2          

Answer:

d

Step-by-step explanation:

Combine like terms onto one side of the equation.

Answer:

The function is even because of symmetry over x axis

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

Step-by-step explanation:

I have solve all the questions and your work is to match with that option

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.

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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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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Step-by-step explanation:

yo thara bhai joginder tu he ek bndr

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.

Answer:

a] 38.5$
b] 118.71$

Step-by-step explanation:

A)35$ was increased by 10%
So:
10% of 35$
10/100 x 35 ($)
3.5$
So 35$ was increased by 3.5$ and the new price is 38.5$
B)105.99$ was increased by 12%
So:
12% of 105.99$
12/100 x 105.99$
=12.7188$
Let's round it to the nearest hundredths:
12.72$

So 105.99$ was increased by 12.72$ and the new price is 118.71$

HOPE IT HELPS :D
Tip: "of" means multiplication in Maths.

Answer:

Step-by-step explanation:

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

See the graph in the image.

A 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.

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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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.

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 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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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

……………………………………………………

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:

Step-by-step explanation:

hope you can understand

The matching of definitions and terms are done below.

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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Answer:

[tex]\displaystyle{y=-3x-1}[/tex]

Step-by-step explanation:

I have two methods: standard-learning which will explain overall mathematically - basically formula, etc. - while the other one trick-tips method will rely on choices rather mathematical calculations but with explanation on why and how.

First, let’s pick two points that are integers since they are easily to be found via graphs. We see that (-1,2) and (0,-1) is a part of the graph so now we finally have picked two points for our calculations.

When we have finally picked two points, we will be using them for slope calculation. This part is crucial for finding an equation of a line because a line has to contain slope in its equation.

To calculate the slope, we use rise over run formula which is:

[tex]\displaystyle{\dfrac{\Delta y}{\Delta x} = \dfrac{y_2-y_1}{x_2-x_1}}[/tex]

Note that [tex]\displaystyle{\Delta}[/tex] is delta - in both mathematic and physics, it means changes in.

So, we will be using those two points that we have picked to substitute in the slope formula. Let’s determine that [tex]\displaystyle{(x_2,y_2)=(-1,2)}[/tex] and [tex]\displaystyle{(x_1,y_1)=(0,-1)}[/tex].

Therefore, our slope will be:

[tex]\displaystyle{m=\dfrac{2-(-1)}{-1-0}}\\\\\displaystyle{m=\dfrac{2+1}{-1}}\\\\\displaystyle{m=-3}[/tex]

Next, find the y-intercept. From the graph, we see that the graph intercepts at (0,-1) which is y-intercept so we will only use y-value. Hence, b = -1.

From the slope-intercept form:

[tex]\displaystyle{y=mx+b}[/tex]

Substitute m (slope) = -3 and b (y-intercept) = -1. Hence, the equation of line is:

[tex]\displaystyle{y=-3x-1}[/tex]

Relying on choices and knowledge of graph, notice that there are slopes of 3 and -3.

Keep in mind that if slope is negative, it will decrease down and if slope is positive, it will increase up.

Therefore, cut off all choices with positive slopes which are 1 and 3. We are now left with 2 and 4.

Next, look at the graph and tell its y-intercept. It intercepts y at y = -1 so we take value of -1.

So choice 4 is cut off and now we have choice 2 as the answer.

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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:

To find:

We know:

Substitute

[tex]\text{Therefore, the expression equivalent to (p - q)(x) is (2x2 - 1) - 3(x - 1).}[/tex]

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.

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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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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Answer:

8t - 15

Explanation:

⇒ 3(t+5)+5(t−6)

distribute inside parenthesis

⇒ 3(t) + 3(5) + 5(t) + 5(-6)

multiply the variables

⇒ 3t + 15 + 5t - 30

collect like terms

⇒ 3t + 5t + 15 - 30

add/ subtract like terms

⇒ 8t - 15

Solution: 8t-15

Detailed explanation:

First the problem asks us to expand

[tex]\tt 3(t+5)=3\cdot t +3\cdot5=3t+15[/tex]

Similarly

[tex]\tt 5(t-6)=5\cdot t -5\cdot 6=5t-30[/tex]

Therefore

[tex]\tt 3t+15+5t-30[/tex]

Upon combining like terms

[tex]\tt 8t+15-30[/tex]

Upon doing this further

[tex]\tt 8t-15[/tex]

Answer:

tgnjfgznjE XVNJ

Step-by-step explanation:

rtjtejWEJAREfnndzjt

Answer:

15. 2.66

16. - 18

17. Impossible

18. Impossible

19. - 1

20. - 8

21.

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