Answers HCVA - AL-Algebra II with Statistics--Helms - Q13 SEMESTER VERSIONUnit Test

Unit Test — Unit test Answers

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Which values of x and y would make the following expression represent a real number?(4 + 5i)(x + yi)

x = 4, y = 5

x = –4, y = 0

x = 4, y = –5

x = 0, y = 5

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A rectangular pan has a length that is the width. The total area of the pan is 432 in.2. What is the width of the cake pan?A = lw

10.4 in.

13.9 in.

18 in. ✓ Correct

24 in.

Solve for in the equation .

x = 6 plus-or-minus 3 StartRoot 10 EndRoot

x = 6 plus-or-minus 2 StartRoot 7 EndRoot

x = 12 plus-or-minus 3 StartRoot 22 EndRoot

x = 12 plus-or-minus 3 StartRoot 10 EndRoot

Which statement about the following equation is true?2x2 – 9x + 2 = –1

The discriminant is less than 0, so there are two real roots.

The discriminant is less than 0, so there are two complex roots.

The discriminant is greater than 0, so there are two real roots.

The discriminant is greater than 0, so there are two complex roots.

Which function has the domain ?

y = StartRoot x + 11 EndRoot + 5

y = StartRoot x minus 11 EndRoot + 5

y = StartRoot x + 5 EndRoot minus 11

y = StartRoot x + 5 EndRoot + 11

A box is to be constructed with a rectangular base and a height of 5 cm. If the rectangular base must have a perimeter of 28 cm, which quadratic equation best models the volume of the box? V = lwhP = 2(l + w)

y = 5(28 – x)(x)

y = 5(28 – 2x)(x)

y = 5(14 – x)(x)

y = 5(14 – 2x)(x)

Which equation is the inverse of ?

y = one-sixth x squared minus four-thirds x + StartFraction 43 Over 9 EndFraction

y = 4 plus-or-minus StartRoot 6 x minus StartFraction 34 Over 3 EndFraction EndRoot

y = negative 4 plus-or-minus StartRoot 6 x minus StartFraction 34 Over 3 EndFraction EndRoot

negative (x minus 4) squared minus two-thirds = negative 6 y + 12

Using the quadratic formula to solve 4x2 – 3x + 9 = 2x + 1, what are the values of x?

StartRoot 1 plus-or-minus StartRoot 159 EndRoot i Over 8 EndFraction

StartRoot 5 plus-or-minus StartRoot 153 EndRoot i Over 8 EndFraction

StartRoot 5 plus-or-minus StartRoot 103 EndRoot i Over 8 EndFraction

StartRoot 1 plus-or-minus StartRoot 153 EndRoot Over 8 EndFraction

Which phrase best describes the translation from the graph y = (x – 5)2 + 7 to the graph of y = (x + 1)2 – 2?

6 units left and 9 units down

6 units right and 9 units down

6 units left and 9 units up

6 units right and 9 units up

The sum of two complex numbers, where the real numbers do not equal zero, results in a sum of 34i. Which statement must be true about the complex numbers?

The complex numbers have equal imaginary parts.

The complex numbers have equal real parts.

The complex numbers have opposite imaginary parts.

The complex numbers have opposite real parts.

If x2 + mx + m is a perfect-square trinomial, which equation must be true?

x2 + mx + m = (x – 1)2

x2 + mx + m = (x + 1)2

x2 + mx + m = (x + 2)2

x2 + mx + m = (x + 4)2

Which equation is y = 9x2 + 9x – 1 rewritten in vertex form?

y = 9 (x + one-half) squared minus thirteen-fourths

y = 9 (x + one-half) squared minus 1

y = 9 (x + one-half) squared + five-fourths

y = 9 (x + one-half) squared minus five-fourths

Which equation demonstrates the multiplicative identity property?

(negative 3 + 5 i) + 0 = negative 3 + 5 i

(negative 3 + 5 i ) (1) = negative 3 + 5 i

(negative 3 + 5 i) (negative 3 + 5 i) = negative 16 minus 30 i

(negative 3 + 5 i) (3 minus 5 i) = 16 + 30 i

Which equation represents a graph with a vertex at (–3, 2)?

y = 4x2 + 24x + 38

y = 4x2 – 24x + 38

y = 4x2 + 12x + 2

y = 4x2 + 16x + 13

Which expression demonstrates the use of the commutative property of addition in the first step of simplifying the expression (–1 + i) + (21 + 5i)?

(–1 + i) + (21 + 5i) + 0

–1 + (i + 21) + 5i

(–1 + 21) + (i + 5i)

–(1 – i) + (21 + 5i)

Which statement about the following equation is true?3x2 – 8x + 5 = 5x2

The discriminant is less than 0, so there are two real roots.

The discriminant is greater than 0, so there are two real roots.

The discriminant is less than 0, so there are two complex roots.

The discriminant is greater than 0, so there are two complex roots.

Stacey has a square piece of cloth. She cuts 3 inches off of the length of the square and 3 inches off of the width. The area of the smaller square is the area of the original square. What was the side length of the original square?A = s2

1 in.

2 in.

6 in.

12 in.

The graph below shows the height of a projectile t seconds after it is launched. If acceleration due to gravity is –16 ft/s2, which equation models the height of the projectile correctly?h(t) = at2 + vt + h0