Find the product. x 3(x 2 5x 1) x 6 5x 4 x 3 x 5 5x 4 x 3 x 5 5x 3 x 3

Answers

Answer 1

Answer: $x^(3) ( x^(2) +5x+1)= x^(5) +5 x^(4) + x^(3)$

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Solve each quadratic equation. (2x-1)(x+7)=1

Answers

So you foil out the problem and get

According to Rational Root Theorem, which statement about fox) 66x4 2x3 11x2 +35 is true?the O Any rational root of foo) a factor of 35 divided by a factor of 66.is Any rational root of f(x) is a multiple of 35 divided by a multiple of 66Any rational root of f() is a factor of 66 divided by a factor of 35.Any rational root of f(x) is a multiple of 66 divided by a multiple of 35

Answers

Answer:

Any rational root of f(x) is a factor of 35 divided by a factor of 66.

Step-by-step explanation:

The Rational Root Theorem states that:

If P(x) is a Polynomial with integer coefficients and if there exist a rational root of the polynomial i.e. of the form p/q then p is the factor of the constant term and q is a factor of leading coefficient of the polynomial function P(x).

Here we have:

$P(x)=66x^4-2x^3+11x^2+35$

So, according to the Rational Root Theorem the statement that holds true is:

Any rational root of f(x) is a factor of 35 divided by a factor of 66.

Answer:

Any rational root of f(x) a factor of 35 divided by a factor of 66.

Step-by-step explanation:

Rational Root Theorem-

$a_(n)x^(n)+a_(n-1)x^(n-1)+\cdots +a_(0)=0$

If $a_(0)$ and $a_(n)$ are nonzero, then each rational solution x will be,

$x=\pm \frac{\text{Factors of }a_0}{\text{Factors of }a_n}$

The given polynomial is,

$66x^4-2x^3+11x^2 +35$

Here,

$a_(0)=35$ and $a_(n)=66$

Applying the theorem,

$x=\pm \frac{\text{Factors of }35}{\text{Factors of }66}$

You can find the product of any two binomials using the _____ property.

Answers

distributive property

If the eccentricity of an ellipse is 0.43 and the length of its major axis is 11 units, how far from the center are the foci located?

Answers

Answer:

2.365 unit far away the center are the foci located.

Step-by-step explanation:

Given : If the eccentricity of an ellipse is 0.43 and the length of its major axis is 11 units.

To find : How far from the center are the foci located?

Solution :

The eccentricity of an ellipse is defined as

$e=(c)/(a)$

Where, e is the eccentricity

c is the distance from center to focus

a is the distance between focus to vertex.

We have given,

Eccentricity of an ellipse is 0.43 i.e. e=0.43

The distance between focus to vertex is the half of the length of its major axis.

i.e. $a=(11)/(2)$

Substitute in the formula,

$0.43=(c)/((11)/(2))$

$c=0.43* (11)/(2)$

$c=2.365$

Therefore, 2.365 unit far away the center are the foci located.

You have 6 different video games. How many different ways can you arrange the games side by side on a shelf?

Answers

36 ways to stack 6+6+6+6+6+6

There are a total of 20 lions, tigers and bears. If the number of tigers is 2 more than the number of lions and the number of bears is 1 more than the number of tigers, find the number of each.

Answers

Number of tiguers: x + 2
Number of Lions: x
Number of bears:(x+2)+1=(x+3)

We can suggest this equation:
(x+2) + (x)+(x+3)=20

3x+5=20
3x=20-5
3x=15
x=15/3
x=5.

Therefore:
Number of tiguers: x + 2=5+2=7
Number of Lions: x=5
Number of bears:(x+2)+1=(x+3)=5+3=8.

Answer: there are 7 tiguers, 5 lions and 8 bears.

Final answer:

In the problem, if we denote the number of lions as x, the number of tigers as x+2, and the number of bears as x+3, and considering that the total of all these animals is exactly 20, we can form and solve a simple algebraic equation. We will find that there are 5 lions, 7 tigers, and 8 bears.

Explanation:

This is a problem of simple algebra. According to the problem, let's represent the number of lions as x, the total number of tigers as x + 2 (since it's two more than the lions), and the number of bears as x + 3 (1 more than the number of tigers).

The problem states the total number of all these animals as 20, so we can set up the following equation: x + x + 2 + x + 3 = 20.

Solving this algebra equation gives you:

3x + 5 = 20

Subtracting 5 from both sides gives us:

3x = 15

Dividing both sides by 3 gives us:

x = 5

So, the number of lions is 5, the number of tigers is 7 (5 + 2), and the number of bears is 8 (7 + 1).

Learn more about Algebra here:

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