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3 years ago

What is x? -4(x+2)=4(2-2x)

Mathematics

1 answer:

ivann1987 [24]3 years ago

7 0

Answer:

x = 4

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Step-by-step explanation:

Step 1: Define Equation

-4(x + 2) = 4(2 - 2x)

Step 2: Solve for x

Divide -4 on both sides: -(x + 2) = 2 - 2x
Distribute negative: -x - 2 = 2 - 2x
Add 2x on both sides: x - 2 = 2
Add 2 on both sides: x = 4

Step 3: Check

Plug in x into the original equation to verify it's a solution.

Substitute in x: -4(4 + 2) = 4(2 - 2(4))
Multiply: -4(4 + 2) = 4(2 - 8)
Add/Subtract: -4(6) = 4(-6)
Multiply: -24 = -24

Here we see that -24 does equal -24.

∴ x = 4 is the solution to the equation.

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A fourth-order polynomial passes through the five points for which the independent and dependent variables, x and y, respectivel

Sladkaya [172]

Answer:

The fourth-order polynomial that passes through the points is $P(x)=2x^4+x^3+3x^2+2x+5$

Step-by-step explanation:

A fourth-order polynomial has this general form:

$P(x)=ax^4+bx^3+cx^2+dx+e$

We need to replace the given points one by one, which leads to a system of 5 equations and 5 variables (namely a,b,c,d,e)

$37=a(-2)^4+b(-2)^3+c(-2)^2+d(-2)+e\\7=a(-1)^4+b(-1)^3+c(-1)^2+d(-1)+e\\5=a(0)^4+b(0)^3+c(0)^2+d(0)+e\\13=a(1)^4+b(1)^3+c(1)^2+d(1)+e\\61=a(2)^4+b(2)^3+c(2)^2+d(2)+e$

We can rewrite this system as follows:

$16a-8b+4c-2d+e=37\\a-b+c-d+e=7\\e=5\\a+b+c+d+e=13\\16a+8b+4c+2d+e=61$

We can use the Gaussian Elimination to solve this system of equations. To use the Gaussian Elimination we need to express the system of linear equations in matrix form (the matrix equation Ax = b).

The coefficient matrix (A) for the above system is

$\left[\begin{array}{ccccc}16&-8&4&-2&1\\1&-1&1&-1&1\\0&0&0&0&1\\1&1&1&1&1\\16&8&4&2&1\end{array}\right]$

the variable matrix (x) is

$\left[\begin{array}{c}a&b&c&d&e\end{array}\right]$

and the constant matrix (b) is

$\left[\begin{array}{c}37&7&5&13&61\end{array}\right]$

The augmented matrix for this system, it is obtained by appending the columns of the coefficient matrix and the constant matrix.

$\left[\begin{array}{ccccc|c}16&-8&4&-2&1&37\\1&-1&1&-1&1&7\\0&0&0&0&1&5\\1&1&1&1&1&13\\16&8&4&2&1&61\end{array}\right]$

The augmented matrix can be transformed by a sequence of elementary row operations to the reduced row echelon form.

$\left[\begin{array}{ccccc|c}1&0&0&0&0&2\\0&1&0&0&0&1\\0&0&1&0&0&3\\0&0&0&1&0&2\\0&0&0&0&1&5\end{array}\right]$

Therefore the solutions are:

$\left\begin{array}{c}a=2&b=1&c=3&d=2&e=5\end{array}\right$

And the polynomial P(x) is:

$P(x)=2x^4+x^3+3x^2+2x+5$

We can check our solution plotting the polynomial and checking that it passes through the points.

4 0

3 years ago

Braxton loves downloading new music he originally had 41 songs but plans to purchase 4 new songs each week. he wants to know how

ycow [4]

Answer:

$a_110=41+(110-1)4$

Step-by-step explanation:

He already has songs = 41

Since we are given that he purchase four songs every week .

So, in first week he purchase songs = 4

Initially he already has 41 songs

So, total songs after 1 week = $41+(4\times1)=45$

After 2 weeks he will have songs = $41+(4\times 2)=49$

This forms an arithmetic sequence : 41,45,49......

Formula of nth term in A.P. : $a_n=a+(n-1)d$

a = first term = 41

d = common difference = 45-41=49-45=4

Since we are required to find the new songs after110 weeks

So, n =110

Substituting values :

$a_110=41+(110-1)4$

Thus Option A is correct.

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Step-by-step explanation:

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Answer:

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C) Null hypothesis: mean <55 vs. Alternative hypothesis :mean =55

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Step-by-step explanation:

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The mean is ;

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if specifically, the mean time to finish their standard test course should be less than 55 seconds for a former Olympic champion, then the null hypothesis is correct

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Alternative hypothesis :mean =55

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3 years ago