Answers Algebra IIQuadratics, Complex Numbers, and Systems

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What is the solution set of the quadratic inequality f of x is less than or equal to 0 ?

start set x such that x is equal to 5 end set

varnothing

start set x such that x is equal to negative 5 end set

start set x such that x is in the real numbers end set

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What are the values of x in the equation x squared minus 6 x plus 9 is equal to 25 ?

x is equal to negative 2 or x is equal to 8

x is equal to 1 or x is equal to 11

x is equal to negative 1 or x is equal to negative 11

x is equal to 2 or x is equal to negative 8

Susan plans to use 120 feet of fencing to enclose a rectangular area for a garden. Which equation best models the area, y , of the rectangular garden that she creates if one side is x feet long? cap A is equal to l w

y is equal to open paren 60 minus x close paren times x

y is equal to open paren 60 minus x close paren times open paren 60 plus x close paren

y is equal to open paren 120 minus x close paren times x

y is equal to open paren 120 minus x close paren times open paren 120 plus x close paren

Which graph represents the solution set for the quadratic inequality x squared plus 2 x plus 1 is greater than 0 ?

Image with description A number line, labeled x, is marked with integers from negative 5 to 5. An open circle is at negative 1, and a thick line extends indefinitely in both directions with arrows at each end.

Image with description A number line, labeled x, is marked with integers from negative 5 to 5. An open circle is at 1, and a thick line extends from this point to the right, with an arrow indicating it continues indefinitely.

Image with description A number line, labeled x, is marked with integers from negative 5 to 5. A closed circle is at negative 1, and a thick line extends from this point to the right, with an arrow indicating it continues indefinitely.

Image with description A number line, labeled x, is marked with integers from negative 5 to 5. A closed circle is at negative 1, and a thick line extends from this point to the left, with an arrow indicating it continues indefinitely.

What is the greatest possible integer value of x for which square root of x minus 5 end root is an imaginary number?

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?

infinitely many

one

none

two

Which equation is the inverse of y is equal to 7 x squared minus 10 ?

y is equal to plus or minus square root of the fraction with numerator x plus 10 and denominator 7 end root

y is equal to the fraction with numerator plus or minus square root of x plus 10 end root and denominator 7

y is equal to the fraction with numerator plus or minus square root of x and denominator 7 plus or minus the fraction with numerator square root of 10 and denominator 7

y is equal to plus or minus square root of x over 7 plus 10 end root

What is one solution of the following system? 2 y minus 2 x is equal to 12 x squared plus y squared is equal to 36

open paren negative 2 comma 4 close paren

open paren 4 comma negative 2 close paren

open paren 0 comma negative 6 close paren

open paren negative 6 comma 0 close paren

What is the vertex of the graph of y plus 2 x plus 3 is equal to negative open paren x plus 2 close paren squared plus 1 ?

open paren 3 comma negative 24 close paren

open paren negative 3 comma 3 close paren

open paren 3 comma 21 close paren

open paren negative 3 comma negative 33 close paren

If the discriminant of a quadratic equation is 4, which statement describes the roots?

There are two real roots.

There are two complex roots.

There is one real root.

There is one complex root.

Which equation is the inverse of y is equal to x squared minus 36 ?

y is equal to plus or minus square root of x plus 36

y is equal to plus or minus square root of x squared plus 36 end root

y is equal to plus or minus square root of x plus 36 end root

y is equal to plus or minus square root of x plus 6

Which function is a quadratic function?

k times x is equal to negative x

g of x is equal to 5 x cubed

f of x is equal to 2 x squared

b times x is equal to negative 9 x to the 4th power

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 3 x squared plus 7 y 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 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

Which system is equivalent to the given system? y is equal to 9 x squared x plus y is equal to 5

5 minus x is equal to 9 x squared y is equal to 5 minus x

y is equal to 9 y squared minus 90 y plus 225 x is equal to y minus 5

y is equal to 3 x x plus 3 x is equal to 5

5 plus x is equal to 9 x squared y is equal to 5 plus x

Using the quadratic formula to solve 11 x squared minus 4 x is equal to 1 , what are the values of x ?

2 over 11 plus or minus the fraction with numerator 2 square root of 15 and denominator 11

2 over 11 plus or minus the fraction with numerator square root of 15 and denominator 11

2 over 11 plus or minus the fraction with numerator square root of 7 and denominator 11

2 over 11 plus or minus the fraction with numerator square root of 7 i and denominator 11

Use the zero product property to find the solutions to the equation x squared minus 9 is equal to 16

x is equal to 7 or x is equal to 1

x is equal to negative 5 or x is equal to 5

x is equal to negative 6 or x is equal to negative 3

x is equal to negative 3 or x is equal to 3

Which expression is equivalent to open paren 4 plus 6 i close paren squared ?

16 minus 36 i

negative 20 plus 48 i

8 plus 12 i

20 plus 48 i

Which equation is an example of the commutative property of multiplication?

open paren 4 plus 2 i close paren times open paren 3 minus 5 i close paren is equal to open paren 3 minus 5 i close paren times open paren 4 plus 2 i close paren

open paren 4 plus 2 i close paren is equal to open paren 2 i plus 4 close paren

open paren 4 plus 2 i close paren times open paren 3 minus 5 i close paren is equal to open paren 4 plus 2 i close paren times open paren 3 minus 5 i close paren times 1

open paren 4 plus 2 i close paren is equal to open paren 4 plus 2 i plus 0 close paren

Louis used a quadratic equation to model the height, y , of a falling object x seconds after it is dropped. Which ordered pair generated by this model should be discarded because the values are unreasonable?

open paren negative 4 comma 1 close paren

open paren 5 comma 3 halves close paren

open paren 6 comma 0 close paren

open paren 9 fourths comma 24 close paren

What is the value of i raised to the 20 plus 1 power ?

negative 1

negative i

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