Real life examples
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Este documento presenta varias ecuaciones lineales de la forma y = mx + b, incluyendo y = 3x + 4, y = 5x + 1, y = 2/3x + 6, y = -3/2x - 8, y = 2x + 6 y y = 7x + 3.
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This document shows the step-by-step work of solving the equation (3x - 6) = 24 for x. It begins with distributing the -1, then combining like terms and solving for x by first adding 6 to both sides and then dividing both sides by -3, resulting in the solution of x = 6.
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This document discusses factorizing the quadratic expression 1x^2 - 2x - 24. It shows the steps of multiplying the expression by 1, finding the factors of -24, and determining that the factors that combine to give -24 are (x-6)(x+4), following the sign of the larger number. The expression is therefore factorized as (x-6)(x+4).
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This document appears to be an outline or agenda containing numbered sections and subsections. It includes topics such as CFL (compact fluorescent light), thermostats, and other unspecified subjects that are broken down into further subpoints. The document structure suggests it may be used to organize information across several topics for a meeting, presentation, or other discussion.
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El documento presenta una serie de ecuaciones lineales de la forma y=mx+b que representan rectas. Cada par de ecuaciones corresponde a dos rectas distintas. En total hay 12 pares de ecuaciones lineales que definen 24 rectas diferentes.
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This document contains 10 linear equations in the form of y=mx+b. The equations represent lines with different slopes and y-intercepts, except for the last two lines which are coincident since they have the same slope of -4 and y-intercept of 0.
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This document describes factoring the quadratic expression 1x^2 - 12x + 32. It shows the steps of multiplying the expression by 1, combining like terms, identifying the factors of the constant term 32 as 1 x 32 and 2 x 16, and determining that the factors of the expression are (x - 4)(x - 8) which results in the fully factored form.
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This document shows the step-by-step algebraic manipulation of the equation 9x + 7y - 1 = 0. Through adding 1 to both sides and subtracting 9x, the equation is transformed into y = -9x/7 + 1/7, representing the line that satisfies the original equation.
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The document provides examples of solving linear equations in three steps: 1) combining like terms, 2) using the inverse operation to isolate the variable, and 3) dividing to solve for the variable. In example 1, the equation 2x + 6x = -24 is solved to get x = -3. In example 2, the equation 8a + 3 - 2a = -17 is solved to get a = -10/3.
Sol4
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Sol3
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Dp ex3
The document shows the step-by-step working of the expression 4(2x - 7), which equals 8x - 28 when fully simplified. It cautions that a common mistake is forgetting that the minus sign belongs to the 7 term, and not treating 2x - 7 as a single term.
Dp ex2
This document shows the step-by-step working of distributing a negative sign when multiplying a number by a binomial expression. It starts with the expression -3(6x + 1) and through distributing the negative sign, arrives at the equivalent expression -18x - 3 in 3 lines.
Dp ex1
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Solving 2 step equations examples
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This document provides step-by-step work to factor the expression 1x^2 - 9. It begins with the expression, multiplies -9 to both sides, then factors -9 into 3*3. This leads to factoring the entire expression as (x-3)(x+3), showing the two factors that multiply to the original expression.
Factoring quadratics ex 2
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This document shows the step-by-step factorization of the expression 1x^2 + 6x + 8. It begins with the original expression and shows multiplying and adding like terms. The expression is then factored into (x + 2)(x + 4), showing the work and reasoning for combining the factors.
Perp hints
Two lines are perpendicular if their slopes have a product of -1. The slopes of perpendicular lines will always satisfy the property of having a product of -1.
Perp
El documento contiene varias ecuaciones de líneas. Cada sección presenta dos ecuaciones de líneas, una en función de y = mx + b y la otra en función de y = bx + m. Las ecuaciones describen líneas con diferentes pendientes y ordenadas al origen.
Para hints
The document presents several pairs of lines with the same slope (m) but different y-intercepts (b), demonstrating that parallel lines have the same slope but different y-intercepts. It includes 10 pairs of lines in standard y=mx+b form to illustrate that while the m term is the same between parallel lines, the b term can vary between each pair without affecting their parallel nature.
Parallel
El documento contiene varias ecuaciones lineales de la forma y=mx+b con diferentes pendientes m y ordenadas al origen b. Cada par de ecuaciones tiene la misma pendiente m pero diferente ordenada al origen b, indicando líneas paralelas.