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Answer:

Using Descartes' Rule of Signs, we observe whether each consecutive term has a + or - sign:

f(x) = 3x4 − 5x3 − x2 − 8x + 4

Signs are: + - - - +

There are 2 sign changes (from +3 to -5, then from -8 to +4). This means that there are either 2 or 0 positive roots. (We take the number of sign changes, which is 2, and subtract by 2s to get all possible numbers of positive roots.)

For negative roots, we first invert all the odd-powered terms in f(x):

3x4 + 5x3 − x2 + 8x + 4

Signs are: + + - + +

There are 2 sign changes, from +5 to -1, and from -1 to +8. Therefore, there are either 2 or 0 negative roots.

Since the overall degree of f(x) is 4, the total number of roots must sum up to 4. There are either 2 or 0 positive roots, and 2 or 0 negative roots, and everything that remains will be a complex root. The possibilities are:

2 positive, 2 negative, 0 complex

2 positive, 0 negative, 2 complex

0 positive, 2 negative, 2 complex

0 positive, 0 negative, 4 complex.

Therefore we can have either 0, 2, or 4 complex roots.

The correct answer is the last choice.

Answer:

<

Step-by-step explanation:

Answer:

x + y = 11

Step-by-step explanation:

You would need to substitute the numbers into the expression.

Evaluate means that we need to work out what the answer would be.

x + y is equivalent to 9 - - 2.

- - is equivalent to +.

Therefore you would do 9 + 2, which equals 11.

Hope this helps :)

The quadrilateral with vertices at the  points: (0,0), (3,2), (6,0), (3,-2) is a square

The vertices (or coordinates) of the quadrilateral is given as:

[tex](x,y) = (0,0), (3,2), (6,0), (3,-2)[/tex]

Calculate the distance between subsequent points, using the following distance formula

[tex]d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2}[/tex]

So, we have:

[tex]AB = \sqrt{(0 -3)^2 + (0 -2)^2}[/tex]

[tex]AB = \sqrt{13}[/tex]

[tex]BC = \sqrt{(3 -6)^2 + (2 -0)^2}[/tex]

[tex]BC = \sqrt{13}[/tex]

[tex]CD = \sqrt{(6 -3)^2 + (0 --2)^2}[/tex]

[tex]CD = \sqrt{13}[/tex]

[tex]DA = \sqrt{(3 -0)^2 + (-2 -0)^2}[/tex]

[tex]DA = \sqrt{13}[/tex]

Notice that the sides of the quadrilateral are congruent.

Hence, the quadrilateral is a square

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Answer:

it's not a

Step-by-step explanation:

Step-by-step explanation:

We know that in kinematics we can write the formula for uniformly accelerated bodies:

s = 1/2 a t^2 + v0 t + s0

In our case s0 (initial deployment)  = 0m and v0 (initial velocity) = 0

So:

s = 1/2 a t^2

Now we isolate t:

t = [tex]\sqrt[2]{\frac{2s}{a} }[/tex]

All proportionalities are obvious.

Note: I forgot to say that a, the acceleration, is the gravitational acceleration. It can be g or -g depending on how you'll choose the reference system.

The required distance is 11.4 rounded to the tenth

If light intensity (I) is proportional (a) to the inverse square of distance (d) of a subject from a light  source, this is expressed as:

If a light intensity (I) is 516 lumens at the source and 4 lumens at a specific distance from the  source, the distance is calculated as:

l = a/d²

d² = a/l

d² = 516/4

d = √129

d = 11.4

Hence the required distance is 11.4 rounded to the tenth

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Answer:

the slope is 8

Step-by-step explanation:

since , x = 8 is a vertical line ,so the slope is undefined

Answer:

26.18 units

Step-by-step explanation:

You could use distance formula three times to calculate the length of each side. Add the three lengths to find the perimeter. However, (see image) if you look at a graph of these points, two of the sides are the hypotenuse of a right triangle that have known, integer values--Pythagorean triples. The sides are 3-4-5 and the other is 6-8-10. We use the Pythagorean theorem to find the third side. See image.

11.18 + 5 + 10

= 26.18 units

The perimeter of triangle is 26.18.

A triangle is 2-dimensional closed curve. which has 3 sides, 3 angles and 3 vertices.

According to the question,

Triangle ABC has coordinates A(-6,2), B(-3,6), C(5,0).

Distance formula: √(x₂-x₁)² + (y₂-y₁)².

Points A and B are (-6,2) and (-3,6)

= √(-3-(-6))² + (6-2)²

= √9+16

= √25

=5.

Thus, point A and B has distance, S₁ = 5.

Points B and C are (-3,6) and (5,0)

Distance formula: √(x₂-x₁)² + (y₂-y₁)²

= √(5-(-3))² + (0-6)²

= √(8)² + (-6)²

= √(64+36)

=√100

=10.

Thus, point B and C has distance, S₂ = 10.

Points C and A are (5,0) and (-6,2)

Distance formula: √(x₂-x₁)² + (y₂-y₁)²

= √(-6-(5))² + (2-0)²

= √((-11)² + (2)²)

=√(121+4)

=√125

=5√5

Thus, point C and A has distance, S₃= 5√5.

Perimeter of triangle = S₁ + S₂+S₃

= 5 + 10 + 5√5

=15+5√5

=15+5(2.23606)

=15+11.1803

=26.1803 ≈ 26.18

Hence, the perimeter of triangle is 26.18.

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Answer:

A and C

Step-by-step explanation:

Answer:

24x^5

Step-by-step explanation:

3 x 8 = 24

x multiplied by x^4 = x^5

(the exponents add to each other when multiplied)

Answer: u < 6

Step-by-step explanation: 2 + u < 8

u < (8-2)

u < 6

Answer:

Answer: 375 adult tickets were sold and 125 children tickets were sold.

Answer:

  x² +3x -50 = 0

Step-by-step explanation:

The area expression you got in part (a) is ...

  A = (x +8)(x -5) = x² +3x -40

If the area is to be 10, then x must satisfy the equation ...

  10 = x² +3x -40

  x² +3x -50 = 0 . . . . . . subtract 10 and put in standard form

Answer:

[tex]c=\frac{81}{4}[/tex]

I hope this is the right answer and I hope this helps

The value of the variable 'c' to convert the expression as the square of a binomial will be 81 / 4.

A perfect square trinomial formulation can be created by taking the binomial equation's squared. If and then only if a trinomial satisfying the criterion b² = 4ac has the form ax² + bx + c, it is indeed a perfect square.

The expression is given below.

⇒ x² + 9x + c

The value of the variable 'c' to convert the expression as the square of a binomial will be given as,

c = (9/2)²

c = 81 / 4

The value of the variable 'c' to convert the expression as the square of a binomial will be 81 / 4.

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Step-by-step explanation:

Hope it will help you...

Answer:

6 13/28

Step-by-step explanation:

Hope this helps!

Answer:

82/12

Step-by-step explanation:

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Answer:

[tex]\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1[/tex]

Answer:

x ∈ 〈-∞,-5/2]∪[3,+∞〉

Step-by-step explanation:

2x²-x-15 ≥ 0

2x²+5x-6x-15 ≥ 0

x(2x+5)-3(2x+5) ≥ 0

(2x+5)(x-3) ≥ 0

so

2x+5 ≥ 0

x-3 ≥ 0

2x+5 ≤ 0

x-3 ≤ 0

solve the equation

x ≥ -5/2

x ≥ 3

x ≤ -5/2

x ≤ 3

x ∈ [3,+∞〉

x ∈ 〈-∞,-5/2]

so x ∈ 〈-∞,-5/2]∪[3,+∞〉

Answer: A

Step-by-step explanation:

Answer:

Step-by-step explanation:

As x goes up, so does y. That immediately makes B incorrect.

The others (C and D) are incorrect because they points are not plotted correctly.

That leaves you with A.

Answer:

64 in 2 is it the answers im not shure

Answer:

Step-by-step explanation:

x = 3y

x + y = 180°

3y + y = 180° ⇒ y = 45° = a

x = 3( 45° ) ⇒ x = 135° = b

The sizes of angles represented by a and b​ are 45 and 135 degrees.

An angle requires two straight line/ line segments/rays, such that they're connected on one of their endpoints.

The point of their joint is called vertex of that angle.

Those two line segments forming it are called arms of that angle.

The angle is the degree of rotation that it will take for the moving side to go from initial side to the position it is currently on.

We are given that

x = 3y

Since we know that the linear pair is

x + y = 180°

Therefore, 3y + y = 180°

y = 45° = a

x = 3( 45° )

x = 135° = b

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The expression for the total number of fish and plants in all the sets is 24x + 18y.

The given parameters:

Let the total number of fish and plants = T

Let the total number of fish in all the sets = 24x

Let the total number of plants in all the sets = 18y

The expression for the total number of fish and plants in all the sets is calculated as follows;

T = 24x + 18y

Thus, the expression for the total number of fish and plants in all the sets is 24x + 18y.

The complete question is below:

Insert images of the plant and the fish in the space provided to arrange the 24 fish and the 18 plants into sets so that each set has the same number of fish and the same number of plants and none are left over. (In each set, the number of plants does not have to be equal to the number of fish.) Write an expression for the total number of fish and plants in each set

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Answer:

18

Step-by-step explanation:

since the equation of AC is y=x-4 then the length of CB and AB must be the same. therefor its (6*6)/2

Answer:

Preserve angles

Step-by-step explanation:

i think sorry if its wrong

Answer:

to preserve angles

Step-by-step explanation: