Answers Algebra IIModel and Reason with Equations and Inequalities: Part One

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The scatterplot shows the number of minutes spent reading, x , and the number of pages read, y , by each of seven students last night. Use the labeled points to create a linear model that predicts the number of pages that a typical student reads in x minutes. Which equation represents this linear model?

y is equal to 11 sevenths x minus 263 sevenths

y is equal to 11 sevenths x minus 43 sevenths

y is equal to 7 over 11 x plus 29 over 11

y is equal to 7 over 11 x plus 169 over 11

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A cell phone carrier offers two plans for text messaging. Plan cap A costs 20 dollars per month plus 0 point 0 5 dollars per text. Plan cap b costs 10 dollars per month plus 0 point 1 0 dollars per text. For how many text messages per month are the plans the same cost?

200

300

Which graph shows the solution set of the compound inequality 1 point 5 x minus 1 is greater than 6 point 5 or 7 x plus 3 is less than negative 25 ?

Image with description A number line lists negative 10 to 10 by 5. An open circle on negative 4 and another one on 5, and the arrows go in opposite directions.

Image with description A number line labeled from negative 10 to 10 in increments of 5 with tick marks every 1 unit. The graph consists of an open circle at 5 with a line extending to the right ending with an arrow pointing right.

Image with description A number line labeled from negative 10 to 10 in increments of 5 with tick marks every 1 unit. The graph consists of an open circle at negative 4 with a line extending to the left ending with an arrow pointing left.

Image with description A number line labeled from negative 10 to 10 in increments of 5 with tick marks every 1 unit. The graph consists of a horizontal line segment extending from an open circle at negative 4 to an open circle at 5.

Fuaad solved an absolute value inequality and expressed the solution as negative 12 is less than x comma x is less than 7 What is another way to show Fuaad’s solution?

left parenthesis negative 12 comma 7 right bracket

start set x such that negative 12 is less than x comma x is less than 7 end set

the union of open paren infinity close paren and open paren 7 close paren

start set x such that x is greater than negative 12 or x comma negative 12 or x is less than 7 end set

The constraints of a problem are listed. What are the vertices of the feasible region? 4 x plus 3 y is less than or equal to 12 2 x plus 6 y is less than or equal to 15 x is greater than or equal to 0 y is greater than or equal to 0

open paren 0 comma 0 close paren , open paren 0 comma 4 close paren , open paren 1 point 5 comma 2 close paren , open paren 7 point 5 comma 0 close paren

open paren 0 comma 2 point 5 close paren , open paren 1 point 5 comma 2 close paren , open paren 4 comma 3 close paren

open paren 0 comma 4 close paren , open paren 1 point 5 comma 2 close paren , open paren 7 point 5 comma 0 close paren

open paren 0 comma 0 close paren , open paren 0 comma 2 point 5 close paren , open paren 1 point 5 comma 2 close paren , open paren 3 comma 0 close paren

Which system of equations can be graphed to find the solution(s) to 4 x squared is equal to x squared plus 7 ?

y is equal to 4 x squared y is equal to x squared plus 7

y is equal to 3 x squared plus 7 y is equal to x squared plus 7

y is equal to 4 x squared y is equal to 4 x squared plus 7

y is equal to 3 x squared y is equal to x squared plus 7

Vicky is solving an equation where both sides are linear expressions. She sets each linear expression equal to y and graphs the resulting system. If the y -intercepts of the graphs are the same but the slopes are different, what is the greatest possible number of intersections for these graphs?

one

infinitely many

two

none

What is the solution to the equation negative 3 times open paren h plus 5 close paren plus 2 is equal to 4 times open paren h plus 6 close paren minus 9 ?

h is equal to negative 2

h is equal to negative 4

h is equal to 4

h is equal to 2

Which graph shows the solution to the inequality start absolute value x plus 3 end absolute value is greater than or equal to 2 ?

Image with description A number line marked as x ranges from negative 6 to 6 in intervals of 1. Closed circles are on negative 5 and negative 1 and are connected.

Image with description Number line extending indefinitely in both directions, indicated by arrows at each end. Solid points are marked at negative 5 and negative 1. A highlighted line begins at negative 5, passes through negative 1, and continues infinitely to the left and right. This represents all real numbers on the number line, with negative 5 and negative 1 included.

Image with description A number line marked as x ranges from negative 6 to 6 in intervals of 1. Closed circles are on 1 and 5 and are connected.

Image with description Number line extending indefinitely in both directions, indicated by arrows at each end. Solid points are marked at 1 and 5. The highlighted line extends from negative infinity to 1, and from 5 to positive infinity, with both endpoints included. This represents all numbers less than or equal to 1, or greater than or equal to 5.

Which statement is true about f of x plus 2 is equal to 1 sixth start absolute value x minus 3 end absolute value ?

The graph of f of x has a vertex of open paren negative 3 comma 2 close paren .

The graph of f of x opens downward.

The graph of f of x is a horizontal compression of the graph of the parent function.

The graph of f of x has range of f of x is greater than or equal to negative 2 .

It takes Franklin 14 hours to make a 200 -square-foot cement patio. It takes Scott 10 hours to make the same size patio. Which equation can be used to find x , the number of hours it would take Franklin and Scott to make the patio together?

1 over 14 x minus 1 tenth x is equal to 1

14 x minus 10 x is equal to 200

14 x plus 10 x is equal to 200

1 over 14 x plus 1 tenth x is equal to 1

The formula to determine energy is cap e is equal to 1 half m v squared What is the formula solved for v ?

v is equal to plus or minus square root of 2 cap e over m end root

v is equal to 2 cap e minus m

v is equal to plus or minus square root of m over 2 cap e end root

v is equal to plus or minus square root of 2 cap e minus m end root

A health club charges non-members 5 dollars per day to swim and 9 dollars per day for an exercise class. Members pay a yearly fee of 300 dollars plus 4 dollars per day to attend an exercise class and no swim fee. If Robert swims and takes an exercise class every time he goes to the gym, which equation shows the number of days, d , he must use the gym to make the membership worthwhile?

5 d plus 9 d is equal to 300 plus 4 d

the fraction with numerator 5 d plus 9 d and denominator 300 is equal to 4 d

the fraction with numerator 5 d plus 9 d and denominator 4 d is equal to 300

5 d plus 9 d is equal to 300 minus 4 d

Which graph shows all the values that satisfy 2 ninths x plus 3 is greater than 4 and 5 ninths ?

Image with description A number line shows integers from negative 10 to 10. An open circle is at negative 7, with a thick line extending from it to the left, ending in an arrow.

Image with description A number line lists negative 10 to 10 by 5. An open circle is on 7. An arrow goes to the right of 7.

Image with description A number line lists negative 10 to 10 by 5. An open circle is on 7. An arrow goes to the left of 7.

Image with description A number line lists negative 10 to 10 by 5. An open circle is on negative 7. An arrow goes to the right of negative 7.

Celo used the simple interest formula cap A is equal to cap p times open paren 1 plus r t close paren to calculate the interest he earned on his savings last month. Which equation is equivalent to the simple interest formula?

cap p is equal to the fraction with numerator 1 plus r t and denominator cap A

cap p is equal to cap A plus open paren 1 plus r t close paren

cap p is equal to the fraction with numerator cap A and denominator 1 plus r t

cap p is equal to cap A minus open paren 1 plus r t close paren

Which of the following is the graph of f of x is equal to 3 start absolute value x minus 4 end absolute value plus 1 ?

Image with description On a Cartesian coordinate system, the x-axis labeled from negative 8 to 2 in increments of 1 and y-axis labeled from negative 3 to 7 in increments of 1. A v shaped curve is plotted. The curve's vertex is at (negative 4 comma negative 1). From this point, the curve opens upwards, with its left branch passing through (negative 5 comma 2) and (negative 6 comma 5), and its right branch passing through (negative 3 comma 2) and (negative 2 comma 5).

Image with description On a Cartesian coordinate system, the x-axis labeled from negative 3 to 7 in increments of 1 and y-axis labeled from negative 7 to 3 in increments of 1. A v shaped curve is plotted. The curve's vertex is at (4 comma negative 1). From this point, the curve opens downwards, with its left branch passing through (3 comma negative 4) and (2 comma negative 7), and its right branch passing through (5 comma negative 4) and (6 comma negative 7).

Image with description On a Cartesian coordinate system, the x-axis labeled from negative 9 to 1 in increments of 1 and y-axis labeled from negative 7 to 3 in increments of 1. A v shaped curve is plotted. The curve's vertex is at (negative 4 comma 1). From this point, the curve opens downwards, with its left branch passing through (negative 5 comma negative 2) and (negative 6 comma negative 5), and its right branch passing through (negative 3 comma negative 2) and (negative 2 comma negative 5).

Image with description On a coordinate plane, the scale on the x axis ranges from negative 1 to 9 in increments of 1, and the scale on the y axis ranges from negative 3 to 7 in increments of 1. The V-shaped graph opening upward has a vertex at (4 comma 1) and the graph passes through the points (3 comma 4) and (5 comma 4).

The constraints of a problem are listed. What are the vertices of the feasible region? x plus y is less than or equal to 5 y is less than or equal to 3 x is greater than or equal to 0 y is greater than or equal to 0

open paren 0 comma 0 close paren , open paren 0 comma 5 close paren , open paren 2 comma 3 close paren , open paren 5 comma 0 close paren

open paren 0 comma 0 close paren , open paren 0 comma 3 close paren , open paren 2 comma 3 close paren , open paren 5 comma 0 close paren

open paren 0 comma 0 close paren , open paren 2 comma 3 close paren , open paren 5 comma 0 close paren

open paren 0 comma 3 close paren , open paren 0 comma 5 close paren , open paren 2 comma 3 close paren

Layna can paint a 350 -square foot room in 4 hours. It takes Bebe 7 hours to paint the same room. Which equation can be used to find the time in hours, t , it takes Layna and Bebe to paint the room together? Rate (Rooms per Hour) Time (Hours) Fraction Completed Layna 1 fourth Bebe 1 seventh

1 fourth t times 1 seventh t is equal to 1

4 t minus 7 t is equal to 1

4 t plus 7 t is equal to 1

1 fourth t plus 1 seventh t is equal to 1

What is the point of intersection when the system of equations is graphed on the coordinate plane? negative x plus y is equal to 4 6 x plus y is equal to negative 3

open paren negative 1 comma 3 close paren

open paren 1 comma 3 close paren

open paren negative 1 comma negative 3 close paren

open paren 1 comma negative 3 close paren

The scatterplot shows the number of minutes Tyler played in his last eight basketball games and the points he scored in each game. Estimate the location of the line of best fit. About how many points would Tyler score if he played for 40 minutes?

18 points

22 points

27 points

40 points

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