Deck 8: Quadratic Equations

Question 1

Solve by factoring.

- $\mathrm{x}^{2}-\mathrm{x}-42=0$

A) $\{7,6\}$
B) $\{6,7\}$
C) $\{-6,-7\}$
D) $\{-6,7\}$

Answer 1

$\{-6,7\}$

Question 2

Solve by factoring.

- $x^{2}+7 x-18=0$

A) $\{9,2\}$
B) $\{2,9\}$
C) $\{-9,2\}$
D) $\{9,-2\}$

Answer 2

$\{-9,2\}$

Question 3

Solve by factoring.

- $x^{2}+10 x+24=0$

A) $\{4,-6\}$
B) $\{1,24\}$
C) $\{4,6\}$
D) $\{24,-1\}$

Answer 3

$\{4,-6\}$

Question 4

Solve by factoring.

- $x^{2}+3 x=10$

A) $\{5,2\}$
B) $\{5,-2\}$
C) $\{-5,2\}$
D) $\{-2,5\}$

Question 5

Solve by factoring.

- $x^{2}+48=16 x$

A) $\{4,12\}$
B) $\{48,-1\}$
C) $\{-4,-12\}$
D) $\{1,48\}$

Question 6

Solve by factoring.

- $x^{2}-81=0$

A) $\{9\}$
B) $\{9,0,9\}$
C) $\{9\}$ .
D) $\{-9,9\}$

Question 7

Solve by factoring.

- $\mathrm{x}(\mathrm{x}+3)+8(\mathrm{x}+3)=0$

A) $\{3,8\}$
B) $\{3,-8\}$ .
C) $\{3,-8\}$
D) $\{-3,8\}$

Question 8

Solve by factoring.

- $-15 x^{2}-15 x+300=0$

A) $\{4,5\}$
B) $\{4,-5\}$
C) $\{4,-5\}$ .
D) $\{-4,5\}$

Question 9

Solve by extracting square roots

- $x^{2}=49$

A) $\{8,-8\}$
B) $\{7,-7\}$
C) $\{7\}$
D) $\{24.5\}$

Question 10

Solve by extracting square roots

- $\mathrm{x}^{2}-64=0$

A) $\{34\}$
B) $\{8,-8\}$
C) $\{7,-7\}$
D) $\{8\}$

Question 11

Solve by extracting square roots

- $\mathrm{x}^{2}=8$

A) $\{64\}$
B) $\{\sqrt{8}\}$
C) $\{ \pm 4\}$
D) $\{ \pm 2 \sqrt{2}\}$

Question 12

Solve by extracting square roots

- $x^{2}=24$

A) $\{ \pm 12\}$
B) $\{ \pm 2 \sqrt{6}\}$
C) $\{ \pm 6 \sqrt{2}\}$
D) $\{576\}$

Question 13

Solve by extracting square roots

- $x^{2}=-64$

A) $\{ \pm 8 \mathrm{i}\}$
B) $\{ \pm 64 \mathrm{i}\}$
C) $\{ \pm \mathrm{i}\}$
D) $\{ \pm 8\}$

Question 14

Solve by extracting square roots

- $x^{2}+343=0$

A) $\{ \pm 14 \sqrt{7} i\}$
B) $\{ \pm 7 \sqrt{7}\}$
C) $\{ \pm 7 \sqrt{7} i\}$
D) $\{ \pm \sqrt{7} i\}$

Question 15

Solve by extracting square roots

- $(x+6)^{2}=5$

A) $\{6 \pm \sqrt{5}\}$
B) $\{6 \pm \sqrt{5} i\}$
C) $\{-6 \pm \sqrt{5} i\}$
D) $\{-6 \pm \sqrt{5}\}$

Question 16

Solve by extracting square roots

- $(x+16)^{2}-6=0$

A) $\{4 \pm \sqrt{6}\}$
B) $\{16 \pm \sqrt{6}\}$
C) $\{-16 \pm \mathrm{i} \sqrt{6}\}$
D) $\{10,22\}$

Question 17

Solve by extracting square roots

- $2(x-7)^{2}+12=52$

A) $\{7 \pm 2 \sqrt{5}\}$
B) $\{7 \pm 2 \sqrt{5} i\}$
C) $\{-7 \pm 2 \sqrt{5}\}$
D) $\{-7 \pm 2 \sqrt{5} i\}$

Question 18

Solve by extracting square roots

- $\left(x-\frac{3}{4}\right)^{2}=-\frac{25}{16}$

A) $\left\{\frac{-3 \pm 5 i}{4}\right\}$

B) $\left\{\frac{-3 \pm 5 i}{16}\right\}$

C) $\left\{\frac{3 \pm 5 \mathrm{i}}{16}\right\}$

D) $\left\{\frac{3 \pm 5 \mathrm{i}}{4}\right\}$

Question 19

Find the term that should be added to the expression to form a perfect square trinomial. Write the resulting perfect square trinomial in factored form.

- $x^{2}+8 x$

A) $0 ;(x+4)^{2}$
B) $16 ;(x+4)^{2}$
C) $64 ;(x+8)^{2}$
D) $16 ;(x-4)^{2}$

Question 20

Find the term that should be added to the expression to form a perfect square trinomial. Write the resulting perfect square trinomial in factored form.

- $x^{2}+12 x$

A) $36 ;(x+6)^{2}$
B) 0 ; $(x+6)^{2}$
C) $144 ;(x+12)^{2}$
D) $36 ;(x-6)^{2}$

Question 21

Find the term that should be added to the expression to form a perfect square trinomial. Write the resulting perfect square trinomial in factored form.

- $x^{2}-2 x$

A) $1 ;(x+1)^{2}$
B) $1 ;(x-2)^{2}$
C) $0 ;(x-1)^{2}$
D) $1 ;(x-1,)^{2}$

Question 22

Find the term that should be added to the expression to form a perfect square trinomial. Write the resulting perfect square trinomial in factored form.

- $x^{2}-16 x$

A) $64 ;(x+8)^{2}$
B) $64 ;(x-16)^{2}$
C) 0 ; $(x-8)^{2}$
D) $64 ;(x-8)^{2}$

Question 23

Find the term that should be added to the expression to form a perfect square trinomial. Write the resulting perfect square trinomial in factored form.

- $x^{2}+3 x$

A) $0 ;(x+3)^{2}$
B) $\frac{9}{4} ;\left(x+\frac{3}{2}\right)^{2}$
C) $\frac{9}{4} ;\left(x-\frac{3}{2}\right)^{2}$
D) 0 ; $\left(x+\frac{3}{2}\right)^{2}$

Question 24

Find the term that should be added to the expression to form a perfect square trinomial. Write the resulting perfect square trinomial in factored form.

- $x^{2}-3 x$

A) $0 ;\left(x-\frac{3}{2}\right)^{2}$

B) $\frac{9}{4} ;\left(x-\frac{3}{2}\right)^{2}$

C) $\frac{9}{4} ;\left(x+\frac{3}{2}\right)^{2}$

D) $9 ;(x-3)^{2}$

Question 25

Find the term that should be added to the expression to form a perfect square trinomial. Write the resulting perfect square trinomial in factored form.

- $x^{2}-\frac{2}{3} x$

A) $\frac{1}{9} ;\left(x+\frac{1}{3}\right)^{2}$

B) $-\frac{2}{3} x ;\left(x-\frac{1}{3}\right)^{2}$

C) $9 ;\left(x-\frac{1}{3}\right)^{2}$

D) $\frac{1}{9} ;\left(x-\frac{1}{3}\right)^{2}$

Question 26

Find the term that should be added to the expression to form a perfect square trinomial. Write the resulting perfect square trinomial in factored form.

- $x^{2}+\frac{2}{5} x$

A) $\frac{1}{25} ;\left(x+\frac{1}{5}\right)^{2}$

B) $\frac{1}{25} ;\left(x-\frac{1}{5}\right)^{2}$

C) $25 ;\left(x+\frac{1}{5}\right)^{2}$

D) 0 ; $\left(x-\frac{1}{5}\right)^{2}$

Question 27

Find the term that should be added to the expression to form a perfect square trinomial. Write the resulting perfect square trinomial in factored form.

- $x^{2}-\frac{5}{2} x$

A) $\frac{25}{4} ;\left(x-\frac{5}{4}\right)^{2}$

B) $\frac{25}{16} ;\left(x+\frac{5}{4}\right)^{2}$

C) $\frac{25}{16} ;\left(x-\frac{5}{4}\right)^{2}$

D) 0 ; $\left(x-\frac{5}{4}\right)^{2}$

Question 28

Approximate to the nearest tenth when necessary.

-The area of a square is 100 square centimeters. Find the length of a side of the square.

A) $25 \mathrm{~cm}$
B) $50 \mathrm{~cm}$
C) $10 \mathrm{~cm}$
D) $20 \mathrm{~cm}$

Question 29

Approximate to the nearest tenth when necessary.

-The area of a square is 185 square meters. Find the length of a side of the square.

A) $13.6 \mathrm{~m}$
B) $46.3 \mathrm{~m}$
C) $19.2 \mathrm{~m}$
D) $92.5 \mathrm{~m}$

Question 30

Approximate to the nearest tenth when necessary.

-The area of a circle is 90 square meters. Find the radius of the circle.

A) $9.5 \mathrm{~m}$
B) $5.4 \mathrm{~m}$
C) $16.8 \mathrm{~m}$
D) $28.6 \mathrm{~m}$

Question 31

Approximate to the nearest tenth when necessary.

-The area of a circle is $47 \pi$ square inches. Find the radius of the circle.

A) $12.2 \mathrm{in}$ .
B) $6.9 \mathrm{in}$ .
C) $47 \mathrm{in}$ .
D) $3.9 \mathrm{in}$ .

Question 32

Approximate to the nearest tenth when necessary.

-The area of a circle is $169 \pi$ square inches. Find the radius of the circle.

A) 23 in.
B) $169 \mathrm{in.}$
C) 13 in.
D) $40.8 \mathrm{in}$ .

Question 33

Approximate to the nearest tenth when necessary.

-The distance $d$ , in feet, that a free- falling object falls in $t$ seconds is given by the formula $d=16 t^{2}$ . Find the time that it takes for an object to fall 96 feet.

A) 2.7 seconds
B) 2.4 seconds
C) 39.4 seoonds
D) 39.2 seconds

Question 34

Approximate to the nearest tenth when necessary.

-The velocity $\mathrm{v}$ , in $\mathrm{ft} / \mathrm{s}$ , of a free falling object after $\mathrm{t}$ seconds is given by the formula v $32 \mathrm{t}$ until the object reaches terminal velocity. The terminal velocity $\mathrm{V}_{\mathrm{t}}$ of a free-falling object is the highest velocity that the object can attain, and it depends on the mass of the object as well as its projected area. The distance $d$ , in feet, that a free-falling object falls in $t$ seconds is given by the formula $\mathrm{d} e=16 \mathrm{t}^{2}$ until it reaches terminal velocity. After that occurs, the distance that it falls is found by multiplying the terminal velocity $\mathrm{V}_{\mathrm{t}}$ by the amount of time after it reaches terminal velocity. Find the distance that a parachutist travels in $\mathrm{t}=45$ seconds if she has the given terminal velocity $\mathrm{V}_{\mathrm{t}}=16 \mathrm{ft} / \mathrm{s}$ .

A) 512 feet
B) 716 feet
C) 720 feet
D) 480 feet

Question 35

The Hardy- Weinberg principle that states if $p$ is the frequency of the dominant allele $A$ in a gene pool and $q$ is the frequency of the recessive allele $a$ in the gene pool, then $p+q=1$ and $\mathrm{p}^{2}+2 \mathrm{pq}+\mathrm{q}^{2}=1$ .
*Portion of the population that is homozygous dominant (AA): $\mathrm{p}^{2}$
*Portion of the population that is heterozygous dominant (Aa): 2pq
*Portion of the population that is homozygous recessive (aa): $\mathrm{q}^{2}$
Sickle-cell anemia is a recessive genetic condition, meaning that a person only has the disease if both alleles are recessive. If $0.35 \%$ of a population has sickle- cell anemia, what percentage of the population is homozygous dominant and what percentage is heterozygous dominant? Round $\mathrm{q}$ and $\mathrm{p}$ to the nearest thousandth, and round percentages to the nearest tenth of a perœent.

A) homozygous dominant: $86.2 \%$ , heterozygous dominant: $12.8 \%$
B) homozygous dominant: $94.1 \%$ , heterozygous dominant: $5.9 \%$
C) homozygous dominant: 94.5\%, heterozygous dominant: $5.5 \%$
D) homozygous dominant: 88.5\%, heterozygous dominant: $11.1 \%$

Question 36

Solve the equation by completing the square

- $\mathrm{x}^{2}-4 \mathrm{x}-5=0$

A) $\{ \pm \sqrt{-5}\}$
B) $\{5,-1\}$
C) $\{-4,-1\}$
D) $\{-5,1\}$

Question 37

Solve the equation by completing the square

- $x^{2}+4 x+68=0$

A) $\{6,-10\}$
B) $\{2 \pm 8 \mathrm{i}\}$
C) $\{2 \pm 2 \sqrt{17} i\}$
D) $\{2 \pm 8 \mathrm{i}\}$ .

Question 38

Solve the equation by completing the square

- $x^{2}-12 x+17=0$

A) $\{-6 \pm \sqrt{19}\}$

B) $\{6 \pm \sqrt{19}\}$ .

C) $\{12+\sqrt{17}\}$

D) $\{6 \pm \sqrt{17}\}$

Question 39

Solve the equation by completing the square

- $x^{2}+3 x=40$

A) $\{8,5\}$
B) $\{-8,-5\}$
C) $\{-8,5\}$ .
D) $\{-5,8\}$

Question 40

Solve the equation by completing the square

- $\mathrm{x}^{2}+90=19 \mathrm{x}$

A) $\{-9,-10\}$
B) $\{-90,-1\}$
C) $\{9,10\}$
D) $\{1,90\}$

Question 41

Solve the equation by completing the square

- $\mathrm{x}^{2}+5 \mathrm{x}-5=0$

A) $\left\{\frac{-5-3 \sqrt{5}}{2}\right\}$

B) $\left\{\frac{-5 \pm 3 \sqrt{5}}{2}\right\}$

C) $\left\{\frac{5+3 \sqrt{5}}{2}\right\}$

D) $\{-5 \pm 3 \sqrt{5}\}$

Question 42

Solve the equation by completing the square

- $\mathrm{x}^{2}+4 \mathrm{x}=3$

A) $\{-2 \pm 2 \sqrt{7}\}$
B) $\{2+\sqrt{7}\}$
C) $\{-2 \pm \sqrt{7}\}$
D) $\{-1 \pm \sqrt{7}\}$

Question 43

Find a quadratic equation with integer coefficients that has the given solution set.

- $\{8,-5\}$

A) $x^{2}-40 x-3=0$
B) $x^{2}+3 x-40=0$
C) $x^{2}-3 x-40=0$
D) $x^{2}-40 x+3=0$

Question 44

Find a quadratic equation with integer coefficients that has the given solution set.

- $\{0,2\}$

A) $x^{2}-4=0$
B) $x^{2}+2 x=0$
C) $x^{2}-2 x=0$
D) $x^{2}+2 x+4=0$

Question 45

Find a quadratic equation with integer coefficients that has the given solution set.

- $\left\{-\frac{2}{3}, \frac{9}{2}\right\}$

A) $6 x^{2}+23 x-18=0$
B) $6 x^{2}-18 x+6=0$
C) $6 x^{2}+6 x-18=0$
D) $6 x^{2}-23 x-18=0$

Question 46

Find a quadratic equation with integer coefficients that has the given solution set.

- $\{6,-6\}$

A) $x^{2}-12 x+36=0$
B) $x^{2}+36=0$
C) $x^{2}+12 x+36=0$
D) $x^{2}-36=0$

Question 47

Find a quadratic equation with integer coefficients that has the given solution set.

- $\{8 \mathrm{i},-8 \mathrm{i}\}$

A) $x^{2}-64=0$
B) $x^{2}+64=0$
C) $x^{2}+64 i=0$
D) $x^{2}-16 i x+64=0$

Question 48

Solve by using the quadratic formula

- $\mathrm{x}^{2}-\mathrm{x}-56=0$

A) $\{7,8\}$
B) $\{-8,7\}$
C) $\{-7,-8\}$
D) $\{-7,8\}$

Question 49

Solve by using the quadratic formula

- $x^{2}+2 x-48=0$

A) $\{-8,-6\}$
B) $\{-8,6\}$
C) $\{-6,8\}$
D) $\{8,6\}$ .

Question 50

Solve by using the quadratic formula

- $x^{2}+21 x+110=0$

A) $\{-10,-11\}$
B) $\{10,11\}$
C) $\{-110,-1\}$
D) $\{1,110\}$

Question 51

Solve by using the quadratic formula

- $x^{2}+x+6=0$

A) $\left\{\frac{-1 \pm \sqrt{23}}{2}\right\}$

B) $\left\{\frac{1 \pm \sqrt{23} \mathrm{i}}{2}\right\}$

C) $\left\{\frac{-1 \pm \sqrt{23} \mathrm{i}}{2}\right\}$

D) $\left\{\frac{1 \pm \sqrt{23}}{2}\right\}$

Question 52

Solve by using the quadratic formula

- $\mathrm{x}^{2}-25=0$

A) $\{-5\}$
B) $\{-5,0,5\}$
C) $\{5\}$
D) $\{-5,5\}$

Question 53

Solve by using the quadratic formula

- $x^{2}+72=18 x$

A) $\{12,6\}$
B) $\{-12,-6\}$
C) $\{-72,-1\}$
D) $\{1,72\}$

Question 54

Solve by using the quadratic formula

- $x^{2}-24=0$

A) $\{ \pm 12\}$
B) $\{\pm6 \sqrt{2}\}$
C) $\{ \pm 2 \sqrt{6}\}$
D) $\{576\}$

Question 55

Solve by using the quadratic formula

- $6 x^{2}-3 x-9=0$

A) $\left\{\frac{2}{3}, 1\right\}$

B) $\left\{\frac{2}{3},-1\right\}$

C) $\left\{\frac{2}{3}, 0\right\}$

D) $\left\{\frac{3}{2},-1\right\}$

Question 56

Solve by using the quadratic formula

- $x^{2}-\frac{4}{3} x+\frac{7}{6}=0$

A) $\left\{0,-\frac{7}{8} \mathrm{i}\right\}$

B) $\left\{\frac{4}{3} \mathrm{i}, 0\right\}$

C) $\left\{\frac{-4 \pm \sqrt{26} \mathrm{i}}{6}\right\}$

D) $\left\{\frac{4 \pm \sqrt{26} i}{6}\right\}$

Question 57

Solve by using the quadratic formula

- $2 x^{2}+10 x=-4$

A) $\left\{\frac{-10 \pm \sqrt{17}}{2}\right\}$

B) $\left\{\frac{-5 \pm \sqrt{33}}{2}\right\}$

C) $\left\{\frac{-5 \pm \sqrt{17}}{2}\right\}$

D) $\left\{\frac{-5 \pm \sqrt{17}}{4}\right\}$

Question 58

For the given quadratic equation, use the discriminant to determine the number and type of solutions.

- $x^{2}-6 x+5=0$

A) One real
B) Two nonreal complex
C) Two real

Question 59

For the given quadratic equation, use the discriminant to determine the number and type of solutions.

- $x^{2}+4 x+7=0$

A) Two nonreal complex
B) One real
C) Two real

Question 60

For the given quadratic equation, use the discriminant to determine the number and type of solutions.

- $7 z^{2}+7 z+4=0$

A) Two real
B) One real
C) Two nonreal complex

Question 61

For the given quadratic equation, use the discriminant to determine the number and type of solutions.

- $x^{2}+6 x+9=0$

A) One real
B) Two nonreal complex
C) Two real

Question 62

For the given quadratic equation, use the discriminant to determine the number and type of solutions.

- $x^{2}+2 x-5=0$

A) Two nonreal complex
B) One real
C) Two real

Question 63

For the given quadratic equation, use the discriminant to determine the number and type of solutions.

- $4 x^{2}+8 x+4=0$

A) Onereal
B) Two nonreal complex
C) Two real

Question 64

Solve the quadratic equation using the most efficient technique (factoring, extracting square roots, completing the square, or the quadratic formula).

- $x^{2}+x+9=0$

A) $\left\{\frac{-1 \pm \sqrt{35}}{2}\right\}$

B) $\left\{\frac{-1 \pm \sqrt{35} \mathrm{i}}{2}\right\}$

C) $\left\{\frac{1 \pm \sqrt{35}}{2}\right\}$

D) $\left\{\frac{1 \pm \sqrt{35} i}{2}\right\}$

Question 65

Solve the quadratic equation using the most efficient technique (factoring, extracting square roots, completing the square, or the quadratic formula).

- $6 x^{2}+6 x+1=0$

A) $\left\{\frac{-3 \pm \sqrt{3}}{6}\right\}$

B) $\left\{\frac{-3 \pm \sqrt{15}}{6}\right\}$

C) $\left\{\frac{-3 \pm \sqrt{3}}{12}\right\}$

D) $\left\{\frac{-6 \pm \sqrt{3}}{6}\right\}$

Question 66

Solve the quadratic equation using the most efficient technique (factoring, extracting square roots, completing the square, or the quadratic formula).

- $x^{2}+5 x-84=0$

A) $\{12,7\}$ .
B) $\{-12,1\}$
C) $\{12,-7\}$
D) $\{-12,7\}$

Question 67

Solve the quadratic equation using the most efficient technique (factoring, extracting square roots, completing the square, or the quadratic formula).

- $(6 \mathrm{x}+9)^{2}=16$

A) $\left\{-\frac{5}{6}, 0\right\}$

B) $\left\{\frac{5}{6}, \frac{13}{6}\right\}$

C) $\left\{-\frac{5}{6},-\frac{13}{6}\right\}$

D) $\left\{\frac{7}{6}\right\}$

Question 68

Solve the quadratic equation using the most efficient technique (factoring, extracting square roots, completing the square, or the quadratic formula).

- $6 x^{2}-3 x-9=0$

A) $\left\{\frac{2}{3}, 1\right\}$

B) $\left\{\frac{2}{3}, 0\right\}$

C) $\left\{\frac{2}{3},-1\right\}$

D) $\left\{\frac{3}{2},-1\right\}$

Question 69

Solve the quadratic equation using the most efficient technique (factoring, extracting square roots, completing the square, or the quadratic formula).

- $(4 \mathrm{x}+1)^{2}=17$

A) $\left\{\frac{ \pm \sqrt{16}}{4}\right\}$

B) $\left\{\frac{ \pm \sqrt{17}+1}{4}\right\}$

C) $\left\{\frac{-1 \pm \sqrt{17}}{4}\right\}$

D) $\{-1 \pm \sqrt{17}\}$

Question 70

Solve the quadratic equation using the most efficient technique (factoring, extracting square roots, completing the square, or the quadratic formula).

- $\mathrm{x}^{2}-14 \mathrm{x}+65=0$

A) $\{7 \pm 4 i\}$
B) $\{11,3\}$
C) $\{14 \pm 8 \mathrm{i}\}$
D) $\{7 \pm 4 \mathrm{i}\}$

Question 71

Solve the quadratic equation using the most efficient technique (factoring, extracting square roots, completing the square, or the quadratic formula).

- $\frac{3}{4} x^{2}+\frac{1}{2} x+\frac{1}{12}=0$

A) $\left\{\frac{-1+\sqrt{2}}{3}, \frac{-1-\sqrt{2}}{3}\right\}$

B) $\left\{\frac{1}{3},-\frac{1}{3}\right\}$

C) $\left\{\frac{1}{3}\right\}$

D) $\left\{-\frac{1}{3}\right\}$

Question 72

Round your answer to the nearest tenth, when appropriate.


-A ball is thrown downward from a window in a tall building. Its position at time $t$ in seconds is given by $h(t)=16 t^{2}+32 t$ , where $s$ is in feet. How long will it take the ball to fall 94 feet?

A) $1.4 \mathrm{sec}$
B) $1.6 \mathrm{sec}$
C) $2.6 \mathrm{sec}$
D) $2.4 \mathrm{sec}$

Question 73

Round your answer to the nearest tenth, when appropriate.


-A toy rocket is shot vertically upward from the ground. Its distanœe in feet from the ground in $t$ seconds is given by $h(t)=-16 t^{2}+133 t$ . At what time or times will the ball be 146 feet from the ground?

A) $8.3 \mathrm{sec}$
B) $129.1 \mathrm{sec}, 136.9 \mathrm{sec}$
C) $1.3 \mathrm{sec}, 7 \mathrm{sec}$
D) $4.2 \mathrm{sec}$

Question 74

Use the table below for values of $\cos (\theta)$ and $\sin (\theta)$ .
$\begin{array}{|c|c|c|}\hline \theta(\text { degrees }) & \cos (\boldsymbol{\theta}) & \sin (\boldsymbol{\theta}) \\\hline 10 & 0.985 & 0.174 \\\hline 20 & 0.940 & 0.342 \\\hline 30 & 0.866 & 0.500 \\\hline 40 & 0.766 & 0.643 \\\hline 45 & 0.707 & 0.707 \\\hline 50 & 0.643 & 0.766 \\\hline 60 & 0.500 & 0.866 \\\hline 70 & 0.342 & 0.940 \\\hline 80 & 0.174 & 0.985 \\\hline\end{array}$

A projectile is launched with an initial velocity of $500 \mathrm{ft} / \mathrm{s}$ at an angle of $45^{\circ}$ above the horizontal, from the roof of a building 92 feet above the ground.
A. How long will it take for the projectile to land on the ground? Round to the nearest hundredth of a second.
B. How far did the projectile travel horizontally before landing on the ground?

A) a) 15.98 seconds, b) 7901 feet
B) a) 15.98 seconds, b) 5588 feet
C) a) 22.35 seconds, b) 5588 feet
D) a) 22.35 seconds, b) 7901 feet

Question 75

Use the table below for values of $\cos (\theta)$ and $\sin (\theta)$ .
$\begin{array}{|c|l|l|}\hline \theta(\text { degrees }) & \cos (\boldsymbol{\theta}) & \sin (\boldsymbol{\theta}) \\\hline 10 & 0.985 & 0.174 \\\hline 20 & 0.940 & 0.342 \\\hline 30 & 0.866 & 0.500 \\\hline 40 & 0.766 & 0.643 \\\hline 45 & 0.707 & 0.707 \\\hline 50 & 0.643 & 0.766 \\\hline 60 & 0.500 & 0.866 \\\hline 70 & 0.342 & 0.940 \\\hline 80 & 0.174 & 0.985 \\\hline\end{array}$

A projectile is launched with an initial velocity of $150 \mathrm{ft} / \mathrm{s}$ from a height of 30 feet above the ground.
a) Complete the table by filling in the time required for the projectile to land. Round to the nearest hundredth of a second.
$\begin{array}{|l|l|}\hline \boldsymbol{\theta} \text { (degrees) } & \text { Time }(s) \\\hline 10 & \\\hline 30 & \\\hline 50 & \\\hline 70 & \\\hline\end{array}$

b) What launch angle gives the projectile the longest time in the air?
c) Complete the table by filling in the distance traveled horizontally by the projectile. Use the times found in part a. Round to the nearest hundredth of a foot.
$\begin{array}{|l|l|}\hline \boldsymbol{\theta} \text { (degrees) } & \text { Distance }(\text { ft }) \\\hline\end{array}$

d) What launch angle gives the greatest horizontal distance?

A)
a)
$\begin{array}{|l|l|}\hline \theta \text { (degrees) } & \text { Time }(\mathbf{s}) \\\hline 10 & 3.72 \\\hline 30 & 6.19 \\\hline 50 & 8.93 \\\hline 70 & 9.41 \\\hline\end{array}$
b) $70^\circ$
c)
$\begin{array}{|l|l|}\hline \theta \text { (degrees) } & \text { Distance }(\mathrm{ft}) \\\hline 10 & 411.87 \\\hline 30 & 698.63 \\\hline 50 & 571.08 \\\hline 70 & 493.77\\\hline \end{array}$
d) $30^\circ$

B)
a) $\begin{array}{|l|l|}\hline \theta \text { (degrees) } & \text { Time }(\mathbf{s}) \\\hline 10 & 10.86 \\\hline 30 & 8.64 \\\hline 50 & 7.43 \\\hline 70 & 5.83 \\\hline\end{array}$
b) $10^\circ$
c)
$\begin{array}{|l|l|}\hline \theta \text { (degrees) } & \text { Distance }(\mathrm{ft}) \\\hline 10 & 676.55 \\\hline 30 & 732.71 \\\hline 50 & 786.62 \\\hline 70 & 825.83 \\\hline\end{array}$
d) $70^\circ$

C)
a)
$\begin{array}{|l|l|}\hline \theta \text { (degrees) } & \text { Time }(\mathbf{s}) \\\hline 10 & 1.68 \\\hline 30 & 3.81 \\\hline 50 & 3.96 \\\hline 70 & 1.95\\\hline\end{array}$
b) $50^\circ$
c)
$\begin{array}{|l|l|}\hline \theta \text { (degrees) } & \text { Distance }(\mathrm{ft}) \\\hline 10 & 683.07 \\\hline 30 & 521.65 \\\hline 50 & 519.96 \\\hline 70 & 417.38 \\\hline\end{array}$
d) $10^\circ$

D)
a)
$\begin{array}{|l|l|}\hline \theta \text { (degrees) } & \text { Time }(\mathbf{s}) \\\hline 10 & 2.41 \\\hline 30 & 5.06 \\\hline 50 & 7.43 \\\hline 70 & 9.02 \\\hline\end{array}$
b) $70^\circ$
c)
$\begin{array}{|l|l|}\hline \theta \text { (degrees) } & \text { Distance }(\mathrm{ft}) \\\hline 10 & 356.08 \\\hline 30 & 657.29 \\\hline 50 & 716.62 \\\hline 70 & 462.73 \\\hline\end{array}$
d) $50^circ$

Question 76

Solve by making a u-substitution

- $x^{4}-6 x^{2}+8=0$

A) $\{2, \sqrt{2}\}$
B) $\{ \pm 2, \pm 2 \sqrt{2}\}$
C) $\{ \pm 2, \pm 2\}$
D) $\{ \pm 2, \pm \sqrt{2}\}$

Question 77

Solve by making a u-substitution

- $x^{4}-33 x^{2}+32=0$

A) $\{ \pm 1, \pm 4 \sqrt{2}\}$
B) $\{ \pm 2, \pm 4\}$
C) $\{ \pm 1, \pm 4 \sqrt{3}\}$
D) $\{ \pm 1, \pm \sqrt{2}\}$

Question 78

Solve by making a u-substitution

- $\mathrm{x}-11 \sqrt{\mathrm{x}}+30=0$

A) $\{-5,6\}$
B) $\{5,6\}$ .
C) $\{25,36\}$
D) $\{-25,36\}$ .

Question 79

Solve by making a u-substitution

- $\mathrm{x}-13 \mathrm{x}^{1 / 2}+42=0$

A) $\{36,49\}$
B) $\{-36,49\}$ .
C) $\{6,7\}$
D) $\{-6,7\}$ .

Question 80

Solve by making a u-substitution

- $x^{6}+26 x^{3}-27=0$

A) $\{-3,1\}$ .
B) $\{-3,-1\}$
C) $\{3,-1\}$ .
D) $\{3,1\}$