1 m = P Choices A, C, and D are incorrect and are likely the result of conceptual or computation are substituted in 2y − x = −19, the value of the left side of the equation does not equal as shown in the figure below, where sin(x°) is equal
SAT Math Prep Practice Test Answer Key Explanations
Choices A, C, and D are incorrect because when the given values of x and y are substituted These are possible values for n, the number of sides of a or −1 Thus, an equation of the second line can be written in the form y = −x + d, where d is amount of trash in the landfill is at (equal to) or above (greater than) capac-
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If k> 0 and x = 7 in the equation above, what is the value of k ? A) 2 x +3 following? 5 5(1)-2, 3 > 561)-2 What is the sum of all values of m that satisfy 2m² - 16m +8 = 0 bonus were awarded, what is one possible number of $250 bonuses
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any available space in your test booklet for scratch work NOTES value 108 in this equation? -1 1,200 (x²y – 3y2 + 5xy?)-(-x+y + 3xy2 – 3y27 Which of the following is equivalent to the In the equations above, b and c represent the price
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following equations can be used to find the value of x? A) x 2 + 48x − 3,960 = methods (below) until you are comfortable with all of them 1 Factoring 2 Completing the ______ x + 44 What are all possible solutions to the given equation?
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the number of years after 2014, which of the following functions f gives the number of miles the next integer, and so the least possible value of n is 28 What is the solution (x, y) to the system of equations above? A) (1, 2) B) (1, −2) C) (−1
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y=x+y Which of the following ordered pairs (x,y) satisfies both equations y = x² + 3x – 4 and x = y-4 ? inequality represents all possible values of the total 1 ISSU D) 5,030 5 X 5 5,040 In the figure above, which of the following ratios has
PSAT Practice Test Answer
The density of tap water varies with temperature as shown in the table below: x models the estimated home value after x years Which statement is the Which equation could be used to determine the maximum or minimum of this function? A f ( x ) Which of the following values are possible solutions for the inequality: ?
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B) \*+1+1 C) 11-x] + 1 D) x-11+1 3(2x + 1)(4x+1) Which of the following is equivalent to the expression For what real value of x is the equation above true ?
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Consider the two mathematical statements below to answer the equations that follow Ifp(x) = Vx2 + 2x, then what is the value of p(f(1))? Show your work Sketch a possible graph of a function, H(x), which satisfies each of the conditions
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Alternatively the equation x + y = 0 can be rewritten as x = ?y
If (x y) is a solution to the system of equations above
C) 1 b = -2. D) 7 f(-²) = 3(-8) - 2. -5 x=6 y. 4(y + 1) = x. If (x y) is the solution to the system of equations above
CROSS MULTIPLY. 160. Page 1 of 3. = 5?. A++. SLICK! In the equation above a is a constant. If no value of = PARALLEL x satisfies the equation
In the equation above which of the following is a possible value of x +1 ? A) 1? 2. B). 2. C) 2. D) 4.
hours spent cutting a lawn what are all the values of x for which Taylor's The equation above is used to model the relationship between the number.
1. Which of the following expressions is equal to 0 for if x=0 some value of x ? above? ?x-a =x- - 4. 2 what is the solution set of the equation.
Dividing each side of the equation 3r = 18 by 3 gives These equations do not correctly relate ... possible values of x are x = 1 and x = 2.
above. Which of the following statements must be true? (D) The graph of ƒ has a point of inflection at x=1.not necessarily don't know about values.
If -1 <y< 0 which of the following is not between -1 and 0? A) -1 - y If x satisfies the equation above
1 : tangent line equation (c) Vertical tangent lines occu r at points on the curve where y3 +=10 (or 1y =?) and 1 x ?? On the curve 1y =? implies that xx2 ++?=2145 so 4x =? or 2 x = Vertical tangent lines occur at the points ()??4 1 and ()2 1 ? 3 : 1 : 1 1 : substitutes 1 into the equation of the curve 1 : answer y y ? =?
Part (b) asked for an equation of the line tangent to the graph of f at the point where x =?3 Students needed to find the derivative at this point to determine the slope of the tangent line the y-coordinate of the graph of f at this point and then combine this information to provide an equation for the line
f are given for selected values of x in the table above (a) Write an equation for the line tangent to the graph of f at x = 1 Use this line to approximate f ()1 4 (b) Use a midpoint Riemann sum with two subintervals of equal length and values from the table to approximate () 1 4 1 f ? xdx Use the approximation for () 1 4 1
at a nearby value of x Students needed to recognize that the slope of the tangent line is the value of the derivative given in the differential equation at the given point Part (c) asked for the particular solution to the differential equation that passes through the given point
X (b)Let y = f(x) be the panicular solution to the given differential equation with initial condition f(l) = 0 Write an equation for the line tangent to the graph of y = f (x) at x = 1 Use your equation to approximate f (0 7) -:; l/ / [>Z-!) Ro1) Y/3 ( 0 +---1) Unauthorized copying or reuse of any part of this page Is Illegal 41 1( -fo)
curate approximations to the roots of the following quadratic equations Compute the relative error a) 1 3x 2 ? 123 4 x+ 1 6 =0; b) 1 002x2 +11 01x+0 01265 = 0 Solution: The quadratic formula states that the roots of ax2 +bx+c = 0 are x12 = ?b± ? b2 ?4ac 2a a) The roots of 1 3x 2 ? 123 4 x+ 1 6 = 0 are approximately x1 =92
What is the panicular solution of a differential equation?
f(x) be the panicular solution to the given differential equation with initial condition f(l) = 0. Write an equation for the line tangent to the graph of y = f (x) at x = 1.
Which function satisfies the differential equation and the given initial condition?
So, the function y(x) that satis?es the differential equation and the given initial condition is: y(x) = 11e?x+x? 1. 5 1.1.45SupposeapopulationP ofrodentssatis?esthedifferentialequation dP/dt = kP2.
What is the value of Y (X) that represents the differential equation?
Solving for C we get: 10 = y(0) = Ce?0+0?1, ? C = 11. So, the function y(x) that satis?es the differential equation and the given initial condition is: y(x) = 11e?x+x? 1. 5
What is x(t) if x(0) = 0?
If x(0) = 0this implies C = 0, so x(t) = a(2t? sin(st)). On the other hand, we have y(t) = 2asin2t = 2a 1?cos(2t) 2 = a(1? cos(2t)). So, combining what we’ve derived we get: x(t) = a(2t?sin(2t)) y(t) = a(1? cos(2t)).
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