State whether the equation represents exponential growth, exponential decay, or neither.
yequals4 times 1.31 Superscript x
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Part 1
Choose the correct answer below.
Exponential growth
Exponential decay
Neither
11 answers
This equation represents exponential growth.
At a local fitness center, members pay an $8 membership fee and $5 for each aerobics class. Nonmembers pay $6 for each aerobics class. For what number of aerobics classes will the cost for members and nonmembers be the same?
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Part 1
Thus, for
enter your response here aerobics classes, the cost will be the same for members and nonmembers.
(Type a whole number.)
Question content area bottom
Part 1
Thus, for
enter your response here aerobics classes, the cost will be the same for members and nonmembers.
(Type a whole number.)
For what number of aerobics classes will the cost for members and nonmembers be the same?
Let x be the number of aerobics classes.
For members: Cost = $8 + $5x
For nonmembers: Cost = $6x
So, we need to find the value of x for which $8 + $5x = $6x.
$8 + $5x = $6x
$8 = $6x - $5x
$8 = $x
Therefore, for 8 aerobics classes, the cost will be the same for members and nonmembers.
Let x be the number of aerobics classes.
For members: Cost = $8 + $5x
For nonmembers: Cost = $6x
So, we need to find the value of x for which $8 + $5x = $6x.
$8 + $5x = $6x
$8 = $6x - $5x
$8 = $x
Therefore, for 8 aerobics classes, the cost will be the same for members and nonmembers.
Tell whether the system has one solution, infinitely many solutions, or no solution.
10yequalsminus4xplus20
2xplus5yequals10
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Part 1
Choose the correct answer below.
A.
The system has no solution.
B.
The system has infinitely many solutions.
C.
The system has one solution.
10yequalsminus4xplus20
2xplus5yequals10
Question content area bottom
Part 1
Choose the correct answer below.
A.
The system has no solution.
B.
The system has infinitely many solutions.
C.
The system has one solution.
The system of equations:
10y = -4x + 20
2x + 5y = 10
has one solution.
This can be determined since the system has two linear equations with two variables, which can be represented graphically as two lines that intersect at a unique point, representing the solution to the system.
10y = -4x + 20
2x + 5y = 10
has one solution.
This can be determined since the system has two linear equations with two variables, which can be represented graphically as two lines that intersect at a unique point, representing the solution to the system.
Gabe Amodeo, a nuclear physicist, needs 50 liters of a 60% acid solution. He currently has a 20 % solution and a 70 % solution. How many liters of each does he need to make the needed 50 liters of 60% acid solution?
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Part 1
Gabe needs
enter your response here liters of the 20% solution.
Part 2
He also needs
enter your response here liters of the 70% solution.
Question content area bottom
Part 1
Gabe needs
enter your response here liters of the 20% solution.
Part 2
He also needs
enter your response here liters of the 70% solution.
Let's represent the amount of 20% solution Gabe needs with x liters and the amount of 70% solution with y liters.
The total amount of the 60% acid solution needed is 50 liters.
We can set up the following system of equations based on the information given:
1. x + y = 50 (Total liters of solution)
2. 0.20x + 0.70y = 0.60(50) (Total acid content required)
Solving the system of equations:
From equation 1, we can express x in terms of y:
x = 50 - y
Substitute x = 50 - y into equation 2 and solve for y:
0.20(50 - y) + 0.70y = 0.60(50)
10 - 0.20y + 0.70y = 30
0.50y = 20
y = 40
Now, substitute y = 40 back into x = 50 - y to find x:
x = 50 - 40
x = 10
Therefore, Gabe needs 10 liters of the 20% solution and 40 liters of the 70% solution to make the needed 50 liters of 60% acid solution.
The total amount of the 60% acid solution needed is 50 liters.
We can set up the following system of equations based on the information given:
1. x + y = 50 (Total liters of solution)
2. 0.20x + 0.70y = 0.60(50) (Total acid content required)
Solving the system of equations:
From equation 1, we can express x in terms of y:
x = 50 - y
Substitute x = 50 - y into equation 2 and solve for y:
0.20(50 - y) + 0.70y = 0.60(50)
10 - 0.20y + 0.70y = 30
0.50y = 20
y = 40
Now, substitute y = 40 back into x = 50 - y to find x:
x = 50 - 40
x = 10
Therefore, Gabe needs 10 liters of the 20% solution and 40 liters of the 70% solution to make the needed 50 liters of 60% acid solution.
The area of a rectangular rug is given by the trinomial r squared minus 5 r minus 14. What are the possible dimensions of the rug? Use factoring.
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Part 1
The length and the width of the rectangle are
enter your response here.
(Use a comma to separate answers as needed.)
Question content area bottom
Part 1
The length and the width of the rectangle are
enter your response here.
(Use a comma to separate answers as needed.)
To find the possible dimensions of the rug, we need to factor the trinomial \(r^2 - 5r - 14\).
The factored form of the trinomial is \((r - 7)(r + 2)\).
Therefore, the possible dimensions of the rug are 7 by -2 or -7 by 2 (the negative values indicate that one of the dimensions can be negative, which may not make sense in a real-life scenario, but mathematically they are still valid factors). The length can be 7 or -7 and the width can be 2 or -2.
The factored form of the trinomial is \((r - 7)(r + 2)\).
Therefore, the possible dimensions of the rug are 7 by -2 or -7 by 2 (the negative values indicate that one of the dimensions can be negative, which may not make sense in a real-life scenario, but mathematically they are still valid factors). The length can be 7 or -7 and the width can be 2 or -2.
IS IT NEGATIVE OR POSITIVE?
I apologize for the oversight in the previous response. Let's correct that:
The factored form of the trinomial \( r^2 - 5r - 14 \) is \( (r - 7)(r + 2) \).
This means that the possible dimensions of the rug are 7 by -2. This is because the length would be \( r - 7 \) and the width would be \( r + 2 \), so the length can be 7 and the width can be -2.
The factored form of the trinomial \( r^2 - 5r - 14 \) is \( (r - 7)(r + 2) \).
This means that the possible dimensions of the rug are 7 by -2. This is because the length would be \( r - 7 \) and the width would be \( r + 2 \), so the length can be 7 and the width can be -2.
1 answer