Nadia owns a chain of restaurants that operated 200 stores in 1999. If the rate of increase is 8% annually, how many stores does she operate in 2007?The first step to solving this question would be:

years after 1999 | stores 1999 0 | 200 2000 1 | 1.08(200)

years after 1999 | stores 1999 0 | 200 2000 1 | 8+(200)

years after 1999 | stores 1999 0 | 200 2000 1 | (200)x8

Nadia owns a chain of restaurants that operated 200 stores in 1999. If the rate of increase is 8% annually, how many stores does she operate in 2007?which of the following statements is true?

if the rate of increase is 8% then I convert it to 1.08 and multiply it to 200 the number of stores

if the rate of increase is 8% then I convert it to 0.08 and multiply it to 200 the number of stores

if the rate of increase is 8% then I convert it to 8 and multiply it to 200 the number of stores

7.6(6.6) And 8.1(7.1) Solving Radical Equations And Exponential Graphs

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Salgm

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Quizzes Created: 5 | Total Attempts: 3,720

Questions: 16 | Attempts: 286 | Updated: Mar 20, 2023

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7.6(6.6) And 8.1(7.1) Solving Radical Equations And Exponential Graphs - Quiz

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Questions and Answers

1.

Is the given x-value a solution of the equation 4(x-5)^1/2 = 28x=12
- A.
  
  Yes
- B.
  
  No
Correct Answer
B. No

Explanation
The given x-value is not a solution of the equation because the equation is written incorrectly. There is an extra "=" sign after 28x, which is not necessary. Therefore, the equation should be written as 4(x-5)^1/2 = 28x - 12.

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2.

4 x^(3/4) = 108

Correct Answer
81

Explanation
The equation 4 x (3/4) means multiplying 4 by the fraction 3/4. When we multiply a whole number by a fraction, we can simplify the calculation by canceling out common factors between the numerator and denominator. In this case, the common factor is 4. By canceling out the 4 in both the numerator and denominator, we are left with 1 x 3, which equals 3. Therefore, the correct answer is 3.

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4
3.

X ^(2/3) + 15 = 24
- A.
  
  27
- B.
  
  No real solutions
- C.
  
  -3
Correct Answer
A. 27

Explanation
To solve the equation, we need to isolate the variable x. First, we can subtract 15 from both sides of the equation: x (2/3) = 9. Then, we can multiply both sides by the reciprocal of 2/3, which is 3/2, to get x = 9 * (3/2) = 27/2 = 13.5. Therefore, the correct answer is 27.

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4.

Sqrt (2x-1) = sqrt (x+4)
- A.
  
  5
- B.
  
  6
- C.
  
  7
Correct Answer
A. 5

Explanation
sqrt means the square root sign

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5.

sqrt x = 8
- A.
  
  64
- B.
  
  8
- C.
  
  2 sqrt 2
Correct Answer
A. 64

Explanation
The given equation states that the square root of x is equal to 8. We need to find the value of x that satisfies this equation. By squaring both sides of the equation, we get x = 64. Therefore, the correct answer is 64.

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6.

x ^1/3 +10 = 16
- A.
  
  6
- B.
  
  18
- C.
  
  216
Correct Answer
C. 216
7.

(y-9)^1/4 +4 = 0

Correct Answer
no real roots
no solution

Explanation
The given equation is a fourth root equation. When we isolate the variable, we get (y-9)^(1/4) = -4. However, taking the fourth root of a number will always result in a real number, and since there is no real number that, when raised to the fourth power, equals -4, there are no real roots for this equation. Therefore, there is no solution.

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4
8.

(6u-5)^1/3 + 2 = -3
- A.
  
  -225
- B.
  
  -125
- C.
  
  -20
Correct Answer
C. -20

Explanation
To solve the equation (6u-5)^(1/3) + 2 = -3, we need to isolate the term with u. First, we subtract 2 from both sides of the equation, giving us (6u-5)^(1/3) = -5. Next, we cube both sides of the equation to eliminate the cube root, resulting in 6u-5 = -125. Finally, we add 5 to both sides of the equation, giving us 6u = -120. Dividing both sides by 6, we get u = -20. Therefore, the correct answer is -20.

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9.

Sqrt (4x-6) = sqrt x
- A.
  
  10
- B.
  
  2
- C.
  
  8
Correct Answer
B. 2

Explanation
The correct answer is 2 because when both sides of the equation are squared, the square root cancels out and we are left with 4x-6 = x. Solving for x, we get x = 2.

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10.

The velocity of a roller coaster is 10 m/s. Find the radius of the roller coaster loop if g=9.8 m/s2. Given v=sqrt(rg) Round to 1 decimal place.

Correct Answer
10.2 m
10.2m

Explanation
don't forget the unit!

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4
11.

X^1/2 = 9
- A.
  
  3
- B.
  
  9
- C.
  
  81
Correct Answer
C. 81

Explanation
The equation x1/2 = 9 means that x raised to the power of 1/2 (or square root of x) is equal to 9. By squaring both sides of the equation, we can find the value of x. Thus, x = 9^2 = 81.

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12.

Correct the error:The error is in the ____ step.
- A.
  
  1st step
- B.
  
  2nd step
- C.
  
  3rd step
- D.
  
  4th step
Correct Answer
B. 2nd step

Explanation
The given answer suggests that the error is in the 2nd step. However, without any context or information about the specific error or process being referred to, it is difficult to provide a more detailed explanation.

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13.

The graph of y=3^x approaches the negative x-axis but does not touch it. True or False?
- A.
  
  True
- B.
  
  False
Correct Answer
A. True

Explanation
The graph of y=3x represents a straight line with a positive slope of 3. As x approaches negative infinity, y approaches negative infinity as well, but it never actually touches the negative x-axis. Therefore, the statement is true.

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14.

What's y when x=0 in y=3^x?
- A.
  
  0
- B.
  
  1
- C.
  
  3
Correct Answer
B. 1

Explanation
When x=0 in the equation y=3x, it means that the value of x is 0. When we substitute x=0 into the equation, we get y=3(0), which simplifies to y=0. Therefore, when x=0, the value of y is 0.

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15.

Nadia owns a chain of restaurants that operated 200 stores in 1999. If the rate of increase is 8% annually, how many stores does she operate in 2007?The first step to solving this question would be:
- A.
  
  Years after 1999 | stores 1999 0 | 200 2000 1 | 8+(200)
- B.
  
  Years after 1999 | stores 1999 0 | 200 2000 1 | (200)x8
- C.
  
  Years after 1999 | stores 1999 0 | 200 2000 1 | 1.08(200)
Correct Answer
C. Years after 1999 | stores 1999 0 | 200 2000 1 | 1.08(200)
16.

Nadia owns a chain of restaurants that operated 200 stores in 1999. If the rate of increase is 8% annually, how many stores does she operate in 2007?which of the following statements is true?
- A.
  
  If the rate of increase is 8% then I convert it to 1.08 and multiply it to 200 the number of stores
- B.
  
  If the rate of increase is 8% then I convert it to 0.08 and multiply it to 200 the number of stores
- C.
  
  If the rate of increase is 8% then I convert it to 8 and multiply it to 200 the number of stores
Correct Answer
A. If the rate of increase is 8% then I convert it to 1.08 and multiply it to 200 the number of stores

Explanation
The correct answer is if the rate of increase is 8% then I convert it to 1.08 and multiply it to 200 the number of stores. This is because to calculate the number of stores in 2007, we need to increase the initial number of stores by 8% annually. To do this, we convert 8% to its decimal form, which is 1.08, and then multiply it by the initial number of stores, which is 200. This will give us the number of stores Nadia operates in 2007.

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Current Version
Mar 20, 2023

Quiz Edited by
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Apr 22, 2010

Quiz Created by
Salgm

7.6(6.6) And 8.1(7.1) Solving Radical Equations And Exponential Graphs

Is the given x-value a solution of the equation 4(x-5)^1/2 = 28x=12

4 x(3/4) = 108

X (2/3) + 15 = 24

Sqrt (2x-1) = sqrt (x+4)

sqrt x = 8

x 1/3 +10 = 16

(y-9)1/4 +4 = 0

(6u-5)1/3 + 2 = -3

Sqrt (4x-6) = sqrt x

The velocity of a roller coaster is 10 m/s. Find the radius of the roller coaster loop if g=9.8 m/s2. Given v=sqrt(rg) Round to 1 decimal place.

X1/2 = 9

Correct the error:The error is in the ____ step.

The graph of y=3x approaches the negative x-axis but does not touch it. True or False?

What's y when x=0 in y=3x?

Nadia owns a chain of restaurants that operated 200 stores in 1999. If the rate of increase is 8% annually, how many stores does she operate in 2007?The first step to solving this question would be:

Nadia owns a chain of restaurants that operated 200 stores in 1999. If the rate of increase is 8% annually, how many stores does she operate in 2007?which of the following statements is true?

4 x^(3/4) = 108

X ^(2/3) + 15 = 24

x ^1/3 +10 = 16

(y-9)^1/4 +4 = 0

(6u-5)^1/3 + 2 = -3

X^1/2 = 9

The graph of y=3^x approaches the negative x-axis but does not touch it. True or False?

What's y when x=0 in y=3^x?