Question 1

Solve the problem.
-George and Matt have a painting business. George has less experience and it takes him 3 hours more to paint a medium sized room than it takes Matt. Working together they can paint a medium sized room in 6 hours. How long does it take each of them working individually? Round to the nearest tenth of an hour.

Accepted Answer

A)  George: 12.0 hours, Matt: 9.0 hours
B)  George: 14.5 hours, Matt: 11.5 hours
C)  George: 12.9 hours, Matt: 9.9 hours
D)  George: 13.7 hours, Matt: 10.7 hoursE) C) and D)
F) A) and B)

Question 2

Solve the polynomial inequality. Express the solution in interval notation.
-  0">(x+4) (x−4) (x−5) >0( x + 4 )  ( x - 4 )  ( x - 5 )  > 0(x+4) (x−4) (x−5) >0

Accepted Answer

A)    (−4,4) ∪(5,∞) ( - 4,4 )  \cup ( 5 , \infty ) (−4,4) ∪(5,∞)  
B)    (−∞,4) ( - \infty , 4 ) (−∞,4)  
C)    (−∞,−4) ∪(4,5) ( - \infty , - 4 )  \cup ( 4,5 ) (−∞,−4) ∪(4,5)  
D)    (5,∞) ( 5 , \infty ) (5,∞) E) B) and C)
F) C) and D)

Question 3

Solve the three-part linear inequality. Graph the solution set on a number line, and express the solution using interval notation.
- 0≤3x+43<40 \leq \frac { 3 x + 4 } { 3 } < 40≤33x+4​<4

Accepted Answer

A)    [−43,83]\left[ - \frac { 4 } { 3 } , \frac { 8 } { 3 } \right][−34​,38​] 
B)    (−43,83) \left( - \frac { 4 } { 3 } , \frac { 8 } { 3 } \right) (−34​,38​)  
C)    [−43,83]\left[ - \frac { 4 } { 3 } , \frac { 8 } { 3 } \right][−34​,38​] 
D)    [−43,83]\left[ - \frac { 4 } { 3 } , \frac { 8 } { 3 } \right][−34​,38​]  E) A) and B)
F) A) and C)

Question 4

Perform the desired operation. Write the answer in the form a + bi.
- (−2+i) (−2−i) ( - 2 + i )  ( - 2 - i ) (−2+i) (−2−i)

Accepted Answer

A)    −2- 2−2 
B)    −3- 3−3 
C)   4
D)   5 E) A) and B)
F) C) and D)

Question 5

Solve the linear inequality. Express the solution in set-builder notation.
- 2x+6<142 x + 6 < 142x+6<14

Accepted Answer

A) 4 \}">{x∣x>4}\{ x \mid x > 4 \}{x∣x>4} B) {x∣x<4}\{ x \mid x < 4 \}{x∣x<4} C) {x∣x≤4}\{ x \mid x \leq 4 \}{x∣x≤4} D) {x∣x≥4}\{ x \mid x \geq 4 \}{x∣x≥4}E) A) and D) F) B) and D)

Question 6

Solve the equation after making an appropriate substitution.
- 3(x+1) 2+13(x+1) +4=03 ( x + 1 )  ^ { 2 } + 13 ( x + 1 )  + 4 = 03(x+1) 2+13(x+1) +4=0

Accepted Answer

A)    {−43,−4}\left\{ - \frac { 4 } { 3 } , - 4 \right\}{−34​,−4} 
B)    {0,3⟩\{ 0,3 \rangle{0,3⟩ 
C)    {−13,−5}\left\{ - \frac { 1 } { 3 } , - 5 \right\}{−31​,−5} 
D)    {−43,−5}\left\{ - \frac { 4 } { 3 } , - 5 \right\}{−34​,−5}E) A) and B)
F) All of the above

Question 7

Solve the equation by completing the square.
- 9x2+36x+20=09 x ^ { 2 } + 36 x + 20 = 09x2+36x+20=0

Accepted Answer

A)    {23,103}\left\{ \frac { 2 } { 3 } , \frac { 10 } { 3 } \right\}{32​,310​} 
B)    {−103,103}\left\{ - \frac { 10 } { 3 } , \frac { 10 } { 3 } \right\}{−310​,310​} 
C)    {−23,−103}\left\{ - \frac { 2 } { 3 } , - \frac { 10 } { 3 } \right\}{−32​,−310​} 
D)    {−29,−109}\left\{ - \frac { 2 } { 9 } , - \frac { 10 } { 9 } \right\}{−92​,−910​}E) B) and D)
F) None of the above

Question 8

Solve the problem.
-Two friends decide to meet in Chicago to attend a Cub's baseball game. Rob travels 126 miles in the same time that Carl travels 120 miles. Rob's trip uses more interstate highways and he can average 3 mph more than Carl. What is Rob's average speed?

Accepted Answer

A)  55 mph
B)  71 mph
C)  60 mph
D)  63 mphE) B) and C)
F) A) and B)

Question 9

Solve the problem.
-A chemist needs 190 milliliters of a 66% solution but has only 42% and 99% solutions available. Find how many milliliters of each that should be mixed to get the desired solution.

Accepted Answer

A)  80 mL of 42%; 110 mL of 99%
B)  110 mL of 42%; 80 mL of 99%
C)  70 mL of 42%; 120 mL of 99%
D)  120 mL of 42%; 70 mL of 99%E) A) and C)
F) B) and C)

Question 10

Solve the equation.
-9x - (3x - 1) = 2

Accepted Answer

A)    {112}\left\{ \frac { 1 } { 12 } \right\}{121​} 
B)    {16}\left\{ \frac { 1 } { 6 } \right\}{61​} 
C)    {−16}\left\{ - \frac { 1 } { 6 } \right\}{−61​} 
D)    {−112}\left\{ - \frac { 1 } { 12 } \right\}{−121​}E) A) and D)
F) B) and D)

Question 11

Perform the indicated operations and write the result in standard form.
- −6−−1806\frac { - 6 - \sqrt { - 180 } } { 6 }6−6−−180​​

Accepted Answer

A)    1+i51 + i \sqrt { 5 }1+i5c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ 
B)    −1−i5- 1 - i \sqrt { 5 }−1−i5c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ 
C)    −1+i5- 1 + \mathrm { i } \sqrt { 5 }−1+i5c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ 
D)    −1−i6- 1 - i \sqrt { 6 }−1−i6c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​E) None of the above
F) A) and C)

Question 12

Solve the three-part linear inequality. Graph the solution set on a number line, and express the solution using interval notation.
- −13≤7x−16<13- \frac { 1 } { 3 } \leq \frac { 7 x - 1 } { 6 } < \frac { 1 } { 3 }−31​≤67x−1​<31​

Accepted Answer

A)    [−521,13]\left[ - \frac { 5 } { 21 } , \frac { 1 } { 3 } \right][−215​,31​] 
B)    (−17,37) \left( - \frac { 1 } { 7 } , \frac { 3 } { 7 } \right) (−71​,73​)  
C)    [−17,37]\left[ - \frac { 1 } { 7 } , \frac { 3 } { 7 } \right][−71​,73​] 
D)    [−17,37]\left[ - \frac { 1 } { 7 } , \frac { 3 } { 7 } \right][−71​,73​]  E) B) and D)
F) A) and D)

Question 13

Solve the equation after making an appropriate substitution.
- x1/2−9x1/4+18=0x ^ { 1 / 2 } - 9 x ^ { 1 / 4 } + 18 = 0x1/2−9x1/4+18=0

Accepted Answer

A)    {81,1296}\{ 81,1296 \}{81,1296} 
B)    {9,36}\{ 9,36 \}{9,36} 
C)    {−3,−6}\{ - 3 , - 6 \}{−3,−6} 
D)    {3,6}\{ 3,6 \}{3,6}E) None of the above
F) B) and C)

Question 14

Determine whether the equation is linear or nonlinear.
- 9x+1=7\frac { 9 } { x } + 1 = 7x9​+1=7

Accepted Answer

A)  linear
B)  nonlinear C) A) and B)
D) undefined

Question 15

Find the real solutions, if any, of the equation. Use the quadratic formula.
-3x2 + 12x + 1 = 0

Accepted Answer

A)   {−6−393,−6+393} \left\{\frac{-6-\sqrt{39}}{3}, \frac{-6+\sqrt{39}}{3}\right\} {3−6−39c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​,3−6+39c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​} 
B)   {−6−336,−6+336} \left\{\frac{-6-\sqrt{33}}{6}, \frac{-6+\sqrt{33}}{6}\right\} {6−6−33c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​,6−6+33c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​} 
C)   {−6−333,−6+333} \left\{\frac{-6-\sqrt{33}}{3}, \frac{-6+\sqrt{33}}{3}\right\} {3−6−33c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​,3−6+33c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​} 
D)   {−12−333,−12+333} \left\{\frac{-12-\sqrt{33}}{3}, \frac{-12+\sqrt{33}}{3}\right\} {3−12−33c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​,3−12+33c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​}E) A) and B)
F) C) and D)

Question 16

Solve the problem.
-A ball is thrown vertically upward from the top of a building 144 feet tall with an initial velocity of 128 feet per second. The distance s (in feet) of the ball from the ground after t seconds is s = 144 + 128t - 16t2. After how many seconds will the ball pass the top of the building on its way down?

Accepted Answer

A)  10 sec
B)  8 sec
C)  7 sec
D)  144 secE) A) and B)
F) A) and C)

Question 17

Solve the equation.
- x(x2+8) =3+x3x \left( x ^ { 2 } + 8 \right)  = 3 + x ^ { 3 }x(x2+8) =3+x3

Accepted Answer

A)    {38}\left\{ \frac { 3 } { 8 } \right\}{83​} 
B)    {3}\{ 3 \}{3} 
C)    {8}\{ 8 \}{8} 
D)    {83}\left\{ \frac { 8 } { 3 } \right\}{38​}E) B) and C)
F) None of the above

Question 18

Write the power of i as i, -1, -i, or 1.
- i18\mathrm { i } ^ { 18 }i18

Accepted Answer

A)  -i
B)  1
C)  -1
D)  i E) A) and B)
F) A) and C)

Question 19

Solve the problem.
-The length of a vegetable garden is 3 feet longer than its width. If the area of the garden is 54 square feet, find its dimensions.

Accepted Answer

A)  6 ft by 9 ft
B)  5 ft by 8 ft
C)  7 ft by 10 ft
D)  5 ft by 10 ftE) None of the above
F) All of the above

Question 20

Solve the problem.
-The product of 6 and the square of a number is 24. Find the number(s) .

Accepted Answer

A)    −26,26- 2 \sqrt { 6 } , 2 \sqrt { 6 }−26c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​,26c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ 
B)    262 \sqrt { 6 }26c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ 
C)    −2,2- 2,2−2,2 
D)   2 E) A) and B)
F) None of the above

Exam 1: Equations, Inequalities, and Applications

Solve the equation. - $x \left( x ^ { 2 } + 8 \right) = 3 + x ^ { 3 }$

Correct Answer
verified

Correct Answer
verified

Perform the indicated operations and write the result in standard form. - $\frac { - 6 - \sqrt { - 180 } } { 6 }$

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Solve the equation after making an appropriate substitution. - $x ^ { 1 / 2 } - 9 x ^ { 1 / 4 } + 18 = 0$

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Correct Answer
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Solve the problem. -Two friends decide to meet in Chicago to attend a Cub's baseball game. Rob travels 126 miles in the same time that Carl travels 120 miles. Rob's trip uses more interstate highways and he can average 3 mph more than Carl. What is Rob's average speed?

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Determine whether the equation is linear or nonlinear. - $\frac { 9 } { x } + 1 = 7$

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Solve the problem. -A chemist needs 190 milliliters of a 66% solution but has only 42% and 99% solutions available. Find how many milliliters of each that should be mixed to get the desired solution.

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Correct Answer
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Solve the problem. -The product of 6 and the square of a number is 24. Find the number(s) .

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Write the power of i as i, -1, -i, or 1. - $\mathrm { i } ^ { 18 }$

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Solve the problem. -The length of a vegetable garden is 3 feet longer than its width. If the area of the garden is 54 square feet, find its dimensions.

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Solve the equation after making an appropriate substitution. - $3 ( x + 1 ) ^ { 2 } + 13 ( x + 1 ) + 4 = 0$

Correct Answer
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Solve the equation by completing the square. - $9 x ^ { 2 } + 36 x + 20 = 0$

Correct Answer
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Find the real solutions, if any, of the equation. Use the quadratic formula. -3x² + 12x + 1 = 0

Correct Answer
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Correct Answer
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Solve the polynomial inequality. Express the solution in interval notation. - $( x + 4 ) ( x - 4 ) ( x - 5 ) > 0$

Correct Answer
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Solve the equation. -9x - (3x - 1) = 2

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Solve the linear inequality. Express the solution in set-builder notation. - $2 x + 6 < 14$

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Perform the desired operation. Write the answer in the form a + bi. - $( - 2 + i ) ( - 2 - i )$

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Exam 1: Equations, Inequalities, and Applications

Solve the equation. - x(x2+8) =3+x3x \left( x ^ { 2 } + 8 \right) = 3 + x ^ { 3 }x(x2+8) =3+x3

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Perform the indicated operations and write the result in standard form. - −6−−1806\frac { - 6 - \sqrt { - 180 } } { 6 }6−6−−180​​

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Solve the equation after making an appropriate substitution. - x1/2−9x1/4+18=0x ^ { 1 / 2 } - 9 x ^ { 1 / 4 } + 18 = 0x1/2−9x1/4+18=0

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Solve the problem. -Two friends decide to meet in Chicago to attend a Cub's baseball game. Rob travels 126 miles in the same time that Carl travels 120 miles. Rob's trip uses more interstate highways and he can average 3 mph more than Carl. What is Rob's average speed?

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Determine whether the equation is linear or nonlinear. - 9x+1=7\frac { 9 } { x } + 1 = 7x9​+1=7

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Solve the problem. -A chemist needs 190 milliliters of a 66% solution but has only 42% and 99% solutions available. Find how many milliliters of each that should be mixed to get the desired solution.

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Solve the three-part linear inequality. Graph the solution set on a number line, and express the solution using interval notation. - 0≤3x+43<40 \leq \frac { 3 x + 4 } { 3 } < 40≤33x+4​<4

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Solve the problem. -The product of 6 and the square of a number is 24. Find the number(s) .

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Write the power of i as i, -1, -i, or 1. - i18\mathrm { i } ^ { 18 }i18

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Solve the problem. -The length of a vegetable garden is 3 feet longer than its width. If the area of the garden is 54 square feet, find its dimensions.

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Solve the equation after making an appropriate substitution. - 3(x+1) 2+13(x+1) +4=03 ( x + 1 ) ^ { 2 } + 13 ( x + 1 ) + 4 = 03(x+1) 2+13(x+1) +4=0

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Solve the equation by completing the square. - 9x2+36x+20=09 x ^ { 2 } + 36 x + 20 = 09x2+36x+20=0

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Find the real solutions, if any, of the equation. Use the quadratic formula. -3x2 + 12x + 1 = 0

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Solve the three-part linear inequality. Graph the solution set on a number line, and express the solution using interval notation. - −13≤7x−16<13- \frac { 1 } { 3 } \leq \frac { 7 x - 1 } { 6 } < \frac { 1 } { 3 }−31​≤67x−1​<31​

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Solve the polynomial inequality. Express the solution in interval notation. - (x+4) (x−4) (x−5) >0( x + 4 ) ( x - 4 ) ( x - 5 ) > 0(x+4) (x−4) (x−5) >0

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Solve the equation. -9x - (3x - 1) = 2

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Solve the linear inequality. Express the solution in set-builder notation. - 2x+6<142 x + 6 < 142x+6<14

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Perform the desired operation. Write the answer in the form a + bi. - (−2+i) (−2−i) ( - 2 + i ) ( - 2 - i ) (−2+i) (−2−i)

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Solve the equation. - $x \left( x ^ { 2 } + 8 \right) = 3 + x ^ { 3 }$

Correct Answer
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Correct Answer
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Perform the indicated operations and write the result in standard form. - $\frac { - 6 - \sqrt { - 180 } } { 6 }$

Correct Answer
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Solve the equation after making an appropriate substitution. - $x ^ { 1 / 2 } - 9 x ^ { 1 / 4 } + 18 = 0$

Correct Answer
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Correct Answer
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Correct Answer
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Determine whether the equation is linear or nonlinear. - $\frac { 9 } { x } + 1 = 7$

Correct Answer
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Correct Answer
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Correct Answer
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Correct Answer
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Write the power of i as i, -1, -i, or 1. - $\mathrm { i } ^ { 18 }$

Correct Answer
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Correct Answer
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Solve the equation after making an appropriate substitution. - $3 ( x + 1 ) ^ { 2 } + 13 ( x + 1 ) + 4 = 0$

Correct Answer
verified

Solve the equation by completing the square. - $9 x ^ { 2 } + 36 x + 20 = 0$

Correct Answer
verified

Find the real solutions, if any, of the equation. Use the quadratic formula. -3x² + 12x + 1 = 0

Correct Answer
verified

Correct Answer
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Solve the polynomial inequality. Express the solution in interval notation. - $( x + 4 ) ( x - 4 ) ( x - 5 ) > 0$

Correct Answer
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Correct Answer
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Solve the linear inequality. Express the solution in set-builder notation. - $2 x + 6 < 14$

Correct Answer
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Perform the desired operation. Write the answer in the form a + bi. - $( - 2 + i ) ( - 2 - i )$

Correct Answer
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