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2 years ago

(2x+3y+4z)(4x^2+9y^2+16z^2-6xy-12yz-8zx)

1 answer:

6 0

1.1 Factoring: 4x2+9y2+16z2-6xy-12yz-8xz

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1: -6xy-12yz
Group 2: 16z2-8xz
Group 3: 4x2+9y2

Pull out from each group separately :

Group 1: (x+2z) • (-6y)
Group 2: (x-2z) • (-8z)
Group 3: (4x2+9y2) • (1)

Looking for common sub-expressions :

Group 1: (x+2z) • (-6y)
Group 3: (4x2+9y2) • (1)
Group 2: (x-2z) • (-8z)

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each of 4 family members uses 175 minutes or fewer of their combined family cell phone plan. at the end of the month, the family

Mamont248 [21]

Answer:

x = ± ∜175 = ± 3.6371

Step-by-step explanation:

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

x^4-(175)=0

Step by step solution :

STEP

Trying to factor as a Difference of Squares:

1.1 Factoring: x4-175

Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =

A2 - AB + BA - B2 =

A2 - AB + AB - B2 =

A2 - B2

Note : AB = BA is the commutative property of multiplication.

Note : - AB + AB equals zero and is therefore eliminated from the expression.

Check : 175 is not a square !!

Ruling : Binomial can not be factored as the difference of two perfect squares.

Polynomial Roots Calculator :

1.2 Find roots (zeroes) of : F(x) = x4-175

Polynomial Roots Calculator is a set of methods aimed at finding values of x for which F(x)=0

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers x which can be expressed as the quotient of two integers. The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient

In this case, the Leading Coefficient is 1 and the Trailing Constant is -175.

The factor(s) are:

of the Leading Coefficient : 1

of the Trailing Constant : 1 ,5 ,7 ,25 ,35 ,175

Let us test ....

P Q P/Q F(P/Q) Divisor

-1 1 -1.00 -174.00

-5 1 -5.00 450.00

-7 1 -7.00 2226.00

-25 1 -25.00 390450.00

-35 1 -35.00 1500450.00

-175 1 -175.00 937890450.00

1 1 1.00 -174.00

5 1 5.00 450.00

7 1 7.00 2226.00

25 1 25.00 390450.00

35 1 35.00 1500450.00

175 1 175.00 937890450.00

Polynomial Roots Calculator found no rational roots

Equation at the end of step

x4 - 175 = 0

STEP

Solving a Single Variable Equation:

2.1 Solve : x4-175 = 0

Add 175 to both sides of the equation :

x4 = 175

x = ∜ 175

The equation has two real solutions

These solutions are x = ± ∜175 = ± 3.6371

Two solutions were found :

x = ± ∜175 = ± 3.6371

4 0

2 years ago

Read 2 more answers

Normal probability Density Function Use a graphing utility to graph the model probability density function with µ = 0 and ð = 2,

Nuetrik [128]

Answer:

Step-by-step explanation:

Hello!

The standard deviation (δ) is a measure of variability, this means, it shows how dispersed the data set is with respect to the mean. The population mean (μ) is a measurement of position. The three graphics have the same position μ=0 but their standard deviations change, this means, the form of their bells is different. The greater the value of the standard deviation, the more dispersed the data is you can see this graphically because the width of the bell will be greater.

Graph attached.

I hope it helps!

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3 years ago

The area of a circle is given by πr2, where r is the radius of the circle. If we use rounding to the nearest whole number, what

Makovka662 [10]

Answer:

75cm^2

Step-by-step explanation:

Check attachment

4 0

3 years ago

Svp aidez moi )

34kurt

Answer:

Dans 3 ans l’âge du père sera le triple de celui de sa fille

Step-by-step explanation:

X= années qui doivent passer

3(12+X ) = 42 +X

36+ 3X = 42 +X

2X = 6

X = 3

La fille 15 ans

Le père 45 ans (15x3=45)

3 0

3 years ago

Jared creates a number sequence that has a first term of 2 and a second of term of 5. Each term after the second is created by s

dexar [7]

The rule for the sequence is S(n) = 2S(n-1) - S(n-2)

Alternative form: S(n) = S(n-1) + 3

Step-by-step explanation:

In this problem, we know the first two terms of the sequence:

S(1) = 2

S(2) = 5

We are told that each term after the second is created by subtracting the term before the previous term from twice the previous term. In other words, if we call:

S(n) the current term

S(n-1) the previous term

S(n-2) the term before the previous term

This statement translates into the following sequence:

S(n) = 2S(n-1) - S(n-2)

Because we are subtracting the term before the previous term, S(n-2), from twice the previous term, 2S(n-1).

We can apply now the rule to find the first few terms of the sequence after S(1) and S(2):

$S(3) = 2S(2) - S(1) = 2(5)-2=10-2 = 8$