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Questions and Answers
Which equation represents a line with a slope of -4 that passes through the point (0, 2)?
Which equation represents a line with a slope of -4 that passes through the point (0, 2)?
- $y = 4x + 2$
- $y = 4x - 2$
- $y = -4x - 2$
- $y = -4x + 2$ (correct)
Determine the equation of a line passing through the points (-3, 4) and (5, -2).
Determine the equation of a line passing through the points (-3, 4) and (5, -2).
$y = -\frac{3}{4}x + \frac{7}{4}$
Simplify the expression $(5a^2b^5)^3$, ensuring all exponents are positive.
Simplify the expression $(5a^2b^5)^3$, ensuring all exponents are positive.
- $5a^6b^{15}$
- $5a^5b^8$
- $125a^6b^{15}$ (correct)
- $125a^5b^8$
When converting 0.000000002 meters to scientific notation, the result is $2 \times 10^{-9}$ meters.
When converting 0.000000002 meters to scientific notation, the result is $2 \times 10^{-9}$ meters.
To express a value of $4.3 \times 10^7$ in standard form, move the decimal point 7 places to the ____ .
To express a value of $4.3 \times 10^7$ in standard form, move the decimal point 7 places to the ____ .
Evaluate the polynomial expression $(3x^2 - 8x + 14) + (7x^2 + 3x - 2)$.
Evaluate the polynomial expression $(3x^2 - 8x + 14) + (7x^2 + 3x - 2)$.
Determine the product of the polynomials $(2x + 5)(3x - 6)$.
Determine the product of the polynomials $(2x + 5)(3x - 6)$.
Match the exponential expression simplification with the appropriate power rule.
Match the exponential expression simplification with the appropriate power rule.
Flashcards
Slope-Intercept Form
Slope-Intercept Form
A straight line on a graph represented by y = mx + b, where 'm' is the slope and 'b' is the y-intercept.
Horizontal Line
Horizontal Line
A line with a slope of zero. It's equation is in the form y = constant.
Vertical Line
Vertical Line
A line with an undefined slope. Its equation is in the form x = constant.
Vertical Intercept
Vertical Intercept
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Scientific Notation
Scientific Notation
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Exponent
Exponent
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Simplify
Simplify
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Distributive Property
Distributive Property
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Study Notes
- These notes cover graphing lines, finding equations of lines, working with exponents and polynomials, converting to scientific notation, and factoring polynomials
Review of Lines
- To graph y = -x + 2, locate the y-intercept at (0, 2), then use the slope of -1/3 to find additional points and draw the line
- To graph a line with slope m = 1/2 passing through (1, 2), plot the point (1, 2) and use the slope to find another point, then draw a line through them
- The equation y = -2 represents a horizontal line that intersects the y-axis at -2
- The equation x = 6 represents a vertical line that intersects the x-axis at 6
- To find the equation of the line with a slope of 1/2 passing through the point (1,2), use the point-slope form of a line
- To find the equation of the line passing through (-3, 4) and (5, -2), first calculate the slope and then use the point-slope form with either point
Interpreting Graphs of Lines
- The vertical intercept of a credit card debt graph represents the initial amount of debt at the beginning of the year
- The horizontal intercept represents the time when the debt is fully paid off
Exponents and Polynomials
- To simplify (-4x²y⁷)(7xy²), multiply the coefficients and add the exponents of like variables: -28x³y⁹
- To simplify (5a²b⁵)³, raise each factor inside the parentheses to the power of 3: 125a⁶b¹⁵
- To simplify (6x²y²)²(-5x²y)⁴, apply the power to power rule and then multiply the terms: 36x⁴y⁴ * 625x⁸y⁴ = 22500x¹²y⁸
- To simplify c⁴d⁻⁵ / c⁻²d³, subtract the exponents of like variables: c⁶d⁻⁸ = c⁶/d⁸
Scientific Notation Conversions
- 52,600,000,000 in scientific notation: 5.26 x 10¹⁰
- 0.000,000,002 in scientific notation: 2 x 10⁻⁹
- 4.3 x 10⁷ in standard form: 43,000,000
- 6.024 × 10⁻⁶ in standard form: 0.000006024
Operations in Scientific Notation
- -30(45.7 × 10⁻⁸) = -1371 x 10⁻⁸ = -1.371 x 10⁻⁵
- (1.5×10⁻¹²) / (3.0×10⁸) = 0.5 x 10⁻²⁰ = 5 x 10⁻²¹
Polynomial Operations
- (3x² - 8x + 14) + (7x² + 3x – 2) = 10x² - 5x + 12
- (5x² − 8x + 2) – (2x² – 8) = 3x² - 8x + 10
- 5x(7x + 8) = 35x² + 40x
- -8x(7x² + 2x - 4) = -56x³ - 16x² + 32x
- (2x + 5)(3x - 6) = 6x² + 3x - 30
- (3x + 7)² = 9x² + 42x + 49
- (x - 4)(x² + 5x − 3) = x³ + x² - 23x + 12
Factoring Polynomials
- 24x³ - 32x² = 8x²(3x - 4)
- 2y(x + 3) – 5(x + 3) = (2y - 5)(x + 3)
- 5m² + 10m – 7m – 14 = 5m(m + 2) - 7(m + 2) = (5m - 7)(m + 2)
- x² + 16x + 64 = (x + 8)(x + 8) = (x + 8)²
- x² - 4x - 21 = (x - 7)(x + 3)
- 2x² + 13x + 15 = (2x + 3)(x + 5)
- x² - 64 = (x + 8)(x - 8)
- x² + x + 3 is prime
- g³ - 8g² + 15g = g(g² - 8g + 15) = g(g - 3)(g - 5)
- 4xyz + 2xz - 24yz – 12z = 2z(2xy + x - 12y - 6) = 2z[x(2y + 1) - 6(2y + 1)] = 2z(x - 6)(2y + 1)
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Description
Review of graphing and interpreting lines, including slope-intercept and point-slope forms. Covers exponents, polynomials, scientific notation, and factoring polynomials. Includes finding equations of lines and vertical intercepts.
