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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.
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1) The slope of a line passing through (-3,5) and (2,1) can be determined using the slope formula: m=(Δy/Δx) which is (1-5)/(-3-2)=-4/5.
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3) A line parallel to the graph of 4x-2y=10 that passes through (2,1) has a slope of 2.
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2) Lines can be classified by their slope as having a positive, zero, negative, or undefined slope.
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Perform the indicated operation:
1. 19×2 - 13x + 31 - 12×2 - 24x - (16×2 - 27x + 25)
2. 7xy2(5×3 – 4x2y2 + 3xy4)
3. (13x + 5)(9x - 13)
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4. (25x - 12)2
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6. (25×4 - 35×3 + 45×2) / (5×2)
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8. 2x / (x + 5) – 150 / (x2 - 25) + 3x / (x – 5)
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9. x / (x - y) – y / (x + y)
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10. 5 / [sqrt(5) + sqrt(7)] – 7 / [sqrt(5) – sqrt(7)]
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sqrt(7)][ sqrt(5) + sqrt(7)]
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2x-3-
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x-
12. 125×2 -
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x-
x-
13. 8×2 + 6x - 5 -
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x-
14. 5×2 – 4x – 3 -
X-
X-
15. 24×2 + 32x - 96 -
3×2 + 4x – 12-
X-
X-
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X-
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X-
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Demo content and sample answers
Perform the indicated operation:
1. 19×2 - 13x + 31 - 12×2 - 24x - (16×2 - 27x + 25)
2. 7xy2(5×3 – 4x2y2 + 3xy4)
3. (13x + 5)(9x - 13)
-
-
-
4. (25x - 12)2
-
-
5. (13a + 15b)(13a - 15b)
-
-
6. (25×4 - 35×3 + 45×2) / (5×2)
-
-
-
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-
-
-
8. 2x / (x + 5) – 150 / (x2 - 25) + 3x / (x – 5)
-
-
-
-
-
-
-
9. x / (x - y) – y / (x + y)
-
-
-
-
10. 5 / [sqrt(5) + sqrt(7)] – 7 / [sqrt(5) – sqrt(7)]
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sqrt(7)][ sqrt(5) + sqrt(7)]
-
-
-
-
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11. (2x – 3)2 -
2x-3-
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x-
12. 125×2 -
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x-
x-
13. 8×2 + 6x - 5 -
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x-
14. 5×2 – 4x – 3 -
X-
X-
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This document contains examples of calculating slope and writing equations of lines from graphs and points. It includes the slope-intercept form equation, examples of finding the slope and y-intercept of lines from their graphs, writing equations of lines given their slope and y-intercept, and finding the slope between two points on a line. Formulas for calculating slope and identifying horizontal and vertical lines are also presented.
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2. It gives the equations for three example problems: a line with slope -3/4 through (8,3), a line through points (7,7) and (2,-2), and a line with slope 1/2 through (4,1).
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Factoring quadratics ex 3.1
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.
Factoring quadratics ex 5
The document shows the step-by-step factorization of the polynomial 3x^2 - 8x - 3. It factors the expression into (3x + 1)(x - 3) by first finding the greatest common factor of -9, then determining the signs of the factors based on the leading coefficient, and finally dividing both factors by the leading coefficient of 3 to complete the factorization.
Factoring quadratics ex 3
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).
Factoring quadratics ex 2
This document describes factorizing the quadratic expression x^2 + 1x - 20. It shows the steps of multiplying, finding the factors of -20, and determining that the expression can be fully factorized as (x - 4)(x + 5).
Factoring quadratics ex 1
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.
Ibnp
El documento contiene 12 conjuntos de ecuaciones lineales. Cada conjunto contiene dos ecuaciones lineales de la forma y=mx+b que representan rectas. Las ecuaciones varían en sus pendientes (m) y ordenadas al origen (b).
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.
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.
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Perp hints
- 1. m b y = -9x + 3 y = 1/9x + 3
- 2. m -9 1/9
- 3. m 1/9-9
- 4. m 1/9 = -1-9
- 5. m b y = -1x + 9 y = 1x – 1
- 6. m -1 1
- 7. m 1 = -1-1
- 8. m b y = -4/5x – 1 y = 5/4x – 7
- 9. m -4/5 5/4
- 10. m 5/4-4/5
- 12. If two lines are perpendicular, their slopes (m) will always have a product of -1