Question 1

In the vicinity of a bonfire the temperature T in ${ } ^ { 0 } C$ 
at a distance of x meters from the center of the fire was given by $T = \frac { 800,000 } { x ^ { 2 } + 400 }$ 
. At what range of distances from the fire's center was the temperature less than 400 ${ } ^ { 0 } C$ 
?

Accepted Answer

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Question 2

Determine which of the given choices is a solution of the equation.  2−5x=8+x2 - 5 x = 8 + x2−5x=8+x

Accepted Answer

A)   1
B)   - 1
C)   0
D)   2
E)   none of these F) C) and D)
G) All of the above

Question 3

Solve the equation.  ∣x+11∣=∣2x+5∣| x + 11 | = | 2 x + 5 |∣x+11∣=∣2x+5∣

Accepted Answer

A)    x=8x = 8x=8  and  x=−185x = - \frac { 18 } { 5 }x=−518​ 
B)    x=3x = 3x=3  and  x=−134x = - \frac { 13 } { 4 }x=−413​ 
C)    x=6x = 6x=6  and  x=−163x = - \frac { 16 } { 3 }x=−316​ 
D)    x=±6x = \pm 6x=±6 
E)    x=6x = 6x=6  F) A) and B)
G) B) and D)

Question 4

Using calculus, it can be shown that if a ball is thrown upward with an initial velocity of 16 ft/s from the top of a building 256 ft high, then its height h above the ground t seconds later will be $h = 256 + 16 t - 16 t ^ { 2 }$ 
. During what time interval will the ball be at least 64 ft above the ground

Accepted Answer

The answer of Using calculus, it can be shown that...

Question 5

Solve the equation.  10x−12+9x+12=126x2−144\frac { 10 } { x - 12 } + \frac { 9 } { x + 12 } = \frac { 126 } { x ^ { 2 } - 144 }x−1210​+x+129​=x2−144126​

Accepted Answer

A)    −12- 12−12 
B)   12
C)   144
D)   6
E)   10 F) B) and E)
G) A) and B)

Question 6

Evaluate the expression $( 5 + 10 i ) ( 7 - 9 i )$  and write the result in the form a + bi.

Accepted Answer

The answer of Evaluate the expression \(( 5 + 10...

Question 7

Al paints with watercolors on a sheet of paper 22 inches wide by 17 inches high. He then places this sheet on a mat so that a uniformly wide strip of the mat shows all around the picture. The perimeter of the mat is 102 inches. How wide is the strip of the mat showing around the picture?

Accepted Answer

The answer of Al paints with watercolors on a sheet...

Question 8

Evaluate the expression  414−5i\frac { 41 } { 4 - 5 i }4−5i41​  and write the result in the form a + bi

Accepted Answer

A)   4 + 5i
B)   4 - 5i
C)   - 5 - 4i
D)   5 + 4i
E)   none of these F) A) and B)
G) B) and E)

Question 9

Catalina paints with watercolors on a sheet of paper a = 22 inches wide by b = 17 inches high. She then places this sheet on a mat so that a uniformly wide strip of the mat shows all around the picture. The perimeter of the mat is 102 inches. How wide is the strip of the mat showing around the picture?

Accepted Answer

The answer of Catalina paints with watercolors on a sheet...

Question 10

Determine whether the given value is a solution of the equation. $\frac { 1 } { x } - \frac { 1 } { x - 4 } = 1$  , $x = 2$

Accepted Answer

The answer of Determine whether the given value is a...

Question 11

Find all real solutions of the equation.  5x+9+3=x\sqrt { 5 x + 9 } + 3 = x5x+9​+3=x

Accepted Answer

A)   0
B)   0,11
C)   11
D)   1,0
E)    −11- 11−11  F) C) and D)
G) A) and E)

Question 12

Use the discriminant to determine the number of real solutions of the equation.x2 - 5.66x + 2.52 = 0

Accepted Answer

The answer of Use the discriminant to determine the number...

Question 13

Find all real solutions of the equation.  x2−29x+1=0x ^ { 2 } - \sqrt { 29 } x + 1 = 0x2−29​x+1=0

Accepted Answer

A)    x=12,x=−17/2x = 12 , x = - 17 / 2x=12,x=−17/2 
B)    x=29/2,x=17/2x = \sqrt { 29 } / 2 , x = \sqrt { 17 } / 2x=29c-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'/>​/2,x=17c-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'/>​/2 
C)    x=19/2,x=−17/2x = \sqrt { 19 } / 2 , x = - \sqrt { 17 } / 2x=19c-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'/>​/2,x=−17c-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'/>​/2 
D)    x=29−52,x=29+52x = \frac { \sqrt { 29 } - 5 } { 2 } , x = \frac { \sqrt { 29 } + 5 } { 2 }x=229c-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'/>​−5​,x=229c-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'/>​+5​ 
E)   none of these F) A) and D)
G) A) and E)

Question 14

Solve the equation. $$\frac { 7 } { x - 8 } + \frac { 7 } { x + 8 } = \frac { 154 } { x ^ { 2 } - 64 }$$

Accepted Answer

The answer of Solve the equation. \[\frac { 7 }...

Question 15

Solve the equation by factoring.  6w2=11w−36 w ^ { 2 } = 11 w - 36w2=11w−3

Accepted Answer

A)    w=3/2,w=3/5w = 3 / 2 , w = 3 / 5w=3/2,w=3/5 
B)    w=1/5,w=1/3w = 1 / 5 , w = 1 / 3w=1/5,w=1/3 
C)    w=3/11,w=3/2w = 3 / 11 , w = 3 / 2w=3/11,w=3/2 
D)    w=3/2,w=1/3w = 3 / 2 , w = 1 / 3w=3/2,w=1/3 
E)   none of these F) A) and B)
G) C) and E)

Question 16

Find all real solutions of the equation.  1x−4−25x2=0\frac { 1 } { x - 4 } - \frac { 25 } { x ^ { 2 } } = 0x−41​−x225​=0

Accepted Answer

A)    x=0,x=20x = 0 , x = 20x=0,x=20 
B)    x=5,x=20x = 5 , x = 20x=5,x=20 
C)    x=0,x=−25x = 0 , x = - 25x=0,x=−25 
D)    x=20,x=80x = 20 , x = 80x=20,x=80 
E)   none of these F) A) and B)
G) C) and D)

Question 17

Determine which of the given choices is a solution of the equation.  2−5x=8+x2 - 5 x = 8 + x2−5x=8+x

Accepted Answer

A)   1
B)    −1- 1−1 
C)   0
D)   2
E)   none of these F) A) and E)
G) A) and B)

Question 18

Solve the equation. $5 x - 3 = 6 x + 4$

Accepted Answer

The answer of Solve the equation. \(5 x - 3...

Question 19

A pasture is four times as long as it is wide. Its area is $230,400 \mathrm { ft } ^ { 2 }$ How wide is the pasture?

Accepted Answer

The answer of A pasture is four times as long...

Question 20

Grain is falling from a chute onto the ground, forming a conical pile whose diameter is always three times its height. How high is the pile (to the nearest hundredth of a foot)  when it contains  1200ft31200 \mathrm { ft } ^ { 3 }1200ft3  of grain?

Accepted Answer

A)    6.99ft6.99 \mathrm { ft }6.99ft 
B)    7.88ft7.88 \mathrm { ft }7.88ft 
C)    6.28ft6.28 \mathrm { ft }6.28ft 
D)    7.5ft7.5 \mathrm { ft }7.5ft 
E)   none of these F) D) and E)
G) C) and D)

Exam 1: Equations and Graphs

Use the discriminant to determine the number of real solutions of the equation.x2 - 5.66x + 2.52 = 0

Correct Answer
verified

A pasture is four times as long as it is wide. Its area is $230,400 \mathrm { ft } ^ { 2 }$ How wide is the pasture?

Correct Answer
verified

Determine which of the given choices is a solution of the equation. $2 - 5 x = 8 + x$

Correct Answer
verified

In the vicinity of a bonfire the temperature T in ${ } ^ { 0 } C$ at a distance of x meters from the center of the fire was given by $T = \frac { 800,000 } { x ^ { 2 } + 400 }$ . At what range of distances from the fire's center was the temperature less than 400 ${ } ^ { 0 } C$ ?

Correct Answer
verified

...
View Answer

Solve the equation. $5 x - 3 = 6 x + 4$

Correct Answer
verified

Determine whether the given value is a solution of the equation. $\frac { 1 } { x } - \frac { 1 } { x - 4 } = 1$ , $x = 2$

Correct Answer
verified

Correct Answer
verified

Grain is falling from a chute onto the ground, forming a conical pile whose diameter is always three times its height. How high is the pile (to the nearest hundredth of a foot) when it contains $1200 \mathrm { ft } ^ { 3 }$ of grain?

Correct Answer
verified

Solve the equation. $\frac { 10 } { x - 12 } + \frac { 9 } { x + 12 } = \frac { 126 } { x ^ { 2 } - 144 }$

Correct Answer
verified

Solve the equation by factoring. $6 w ^ { 2 } = 11 w - 3$

Correct Answer
verified

Solve the equation. $\frac { 7 } { x - 8 } + \frac { 7 } { x + 8 } = \frac { 154 } { x ^ { 2 } - 64 }$

Correct Answer
verified

Solve the equation. $| x + 11 | = | 2 x + 5 |$

Correct Answer
verified

Find all real solutions of the equation. $\frac { 1 } { x - 4 } - \frac { 25 } { x ^ { 2 } } = 0$

Correct Answer
verified

Correct Answer
verified

Find all real solutions of the equation. $\sqrt { 5 x + 9 } + 3 = x$

Correct Answer
verified

Find all real solutions of the equation. $x ^ { 2 } - \sqrt { 29 } x + 1 = 0$

Correct Answer
verified

Evaluate the expression $\frac { 41 } { 4 - 5 i }$ and write the result in the form a + bi

Correct Answer
verified

Evaluate the expression $( 5 + 10 i ) ( 7 - 9 i )$ and write the result in the form a + bi.

Correct Answer
verified

Al paints with watercolors on a sheet of paper 22 inches wide by 17 inches high. He then places this sheet on a mat so that a uniformly wide strip of the mat shows all around the picture. The perimeter of the mat is 102 inches. How wide is the strip of the mat showing around the picture?

Correct Answer
verified

Determine which of the given choices is a solution of the equation. $2 - 5 x = 8 + x$

Correct Answer
verified

Exam 1: Equations and Graphs

Use the discriminant to determine the number of real solutions of the equation.x2 - 5.66x + 2.52 = 0

Correct AnswerverifiedShow Answer

A pasture is four times as long as it is wide. Its area is 230,400ft2230,400 \mathrm { ft } ^ { 2 }230,400ft2 How wide is the pasture?

Correct AnswerverifiedShow Answer

Determine which of the given choices is a solution of the equation. 2−5x=8+x2 - 5 x = 8 + x2−5x=8+x

Correct AnswerverifiedShow Answer

Correct Answerverified ...View AnswerShow Answer

Solve the equation. 5x−3=6x+45 x - 3 = 6 x + 45x−3=6x+4

Correct AnswerverifiedShow Answer

Determine whether the given value is a solution of the equation. 1x−1x−4=1\frac { 1 } { x } - \frac { 1 } { x - 4 } = 1x1​−x−41​=1 , x=2x = 2x=2

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Grain is falling from a chute onto the ground, forming a conical pile whose diameter is always three times its height. How high is the pile (to the nearest hundredth of a foot) when it contains 1200ft31200 \mathrm { ft } ^ { 3 }1200ft3 of grain?

Correct AnswerverifiedShow Answer

Solve the equation. 10x−12+9x+12=126x2−144\frac { 10 } { x - 12 } + \frac { 9 } { x + 12 } = \frac { 126 } { x ^ { 2 } - 144 }x−1210​+x+129​=x2−144126​

Correct AnswerverifiedShow Answer

Solve the equation by factoring. 6w2=11w−36 w ^ { 2 } = 11 w - 36w2=11w−3

Correct AnswerverifiedShow Answer

Solve the equation. 7x−8+7x+8=154x2−64\frac { 7 } { x - 8 } + \frac { 7 } { x + 8 } = \frac { 154 } { x ^ { 2 } - 64 }x−87​+x+87​=x2−64154​

Correct AnswerverifiedShow Answer

Solve the equation. ∣x+11∣=∣2x+5∣| x + 11 | = | 2 x + 5 |∣x+11∣=∣2x+5∣

Correct AnswerverifiedShow Answer

Find all real solutions of the equation. 1x−4−25x2=0\frac { 1 } { x - 4 } - \frac { 25 } { x ^ { 2 } } = 0x−41​−x225​=0

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Find all real solutions of the equation. 5x+9+3=x\sqrt { 5 x + 9 } + 3 = x5x+9​+3=x

Correct AnswerverifiedShow Answer

Find all real solutions of the equation. x2−29x+1=0x ^ { 2 } - \sqrt { 29 } x + 1 = 0x2−29​x+1=0

Correct AnswerverifiedShow Answer

Evaluate the expression 414−5i\frac { 41 } { 4 - 5 i }4−5i41​ and write the result in the form a + bi

Correct AnswerverifiedShow Answer

Evaluate the expression (5+10i)(7−9i)( 5 + 10 i ) ( 7 - 9 i )(5+10i)(7−9i) and write the result in the form a + bi.

Correct AnswerverifiedShow Answer

Al paints with watercolors on a sheet of paper 22 inches wide by 17 inches high. He then places this sheet on a mat so that a uniformly wide strip of the mat shows all around the picture. The perimeter of the mat is 102 inches. How wide is the strip of the mat showing around the picture?

Correct AnswerverifiedShow Answer

Determine which of the given choices is a solution of the equation. 2−5x=8+x2 - 5 x = 8 + x2−5x=8+x

Correct AnswerverifiedShow Answer

Correct Answer
verified

A pasture is four times as long as it is wide. Its area is $230,400 \mathrm { ft } ^ { 2 }$ How wide is the pasture?

Correct Answer
verified

Determine which of the given choices is a solution of the equation. $2 - 5 x = 8 + x$

Correct Answer
verified

Correct Answer
verified

...
View Answer

Solve the equation. $5 x - 3 = 6 x + 4$

Correct Answer
verified

Determine whether the given value is a solution of the equation. $\frac { 1 } { x } - \frac { 1 } { x - 4 } = 1$ , $x = 2$

Correct Answer
verified

Correct Answer
verified

Grain is falling from a chute onto the ground, forming a conical pile whose diameter is always three times its height. How high is the pile (to the nearest hundredth of a foot) when it contains $1200 \mathrm { ft } ^ { 3 }$ of grain?

Correct Answer
verified

Solve the equation. $\frac { 10 } { x - 12 } + \frac { 9 } { x + 12 } = \frac { 126 } { x ^ { 2 } - 144 }$

Correct Answer
verified

Solve the equation by factoring. $6 w ^ { 2 } = 11 w - 3$

Correct Answer
verified

Solve the equation. $\frac { 7 } { x - 8 } + \frac { 7 } { x + 8 } = \frac { 154 } { x ^ { 2 } - 64 }$

Correct Answer
verified

Solve the equation. $| x + 11 | = | 2 x + 5 |$

Correct Answer
verified

Find all real solutions of the equation. $\frac { 1 } { x - 4 } - \frac { 25 } { x ^ { 2 } } = 0$

Correct Answer
verified

Correct Answer
verified

Find all real solutions of the equation. $\sqrt { 5 x + 9 } + 3 = x$

Correct Answer
verified

Find all real solutions of the equation. $x ^ { 2 } - \sqrt { 29 } x + 1 = 0$

Correct Answer
verified

Evaluate the expression $\frac { 41 } { 4 - 5 i }$ and write the result in the form a + bi

Correct Answer
verified

Evaluate the expression $( 5 + 10 i ) ( 7 - 9 i )$ and write the result in the form a + bi.

Correct Answer
verified

Correct Answer
verified

Determine which of the given choices is a solution of the equation. $2 - 5 x = 8 + x$

Correct Answer
verified