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irina [24]
3 years ago
9

Don’t worry, this is just practice. I need help please!!

Mathematics
1 answer:
Helen [10]3 years ago
6 0
Is it any choices because i got 2 solutions
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Which of the following represents the graph of f(x) = 2x − 3? graph begins in the second quadrant near the line equals negative
Snezhnost [94]

Answer:

The second choice: graph begins in the second quadrant near the axis and increases slowly while crossing the ordered pair 3, 1. The graph then begins to increase quickly throughout the first quadrant.


Explanation:


1) As per the set of choices, the function is:


f(x)=2^{x-3}


2) Therefore it is an exponential function with these characteristics:

  • Since, the bases is greater than 1 (2), the function is growing in all the domain.
  • The domain is all real numbers (- ∞, ∞).
  • To know where the function starts, calculate the limit of f(x) as x trends to negative infinity:

\lim_{x \to \infty} 2^{x-3}=0^{+}

         That means that the range is y > 0, and so the graph starts in the second quadrant.

  • You can find the y-intersection making x = 0, which is 2⁰ ⁻ ³ = 2 ⁻³ = 1/8 = 0.25. So, the graph cross the y axis at y = 0.25.
  • That tells you, that the function increases slowly, at least, until that point (0, 0.25).
  • The other bullet point is when x = 3: 2 ³ ⁻ ³ = 2⁰ = 1. Therefore, the graph passes through the point (3, 1).
  • From that point, the function starts to increase rapidly (since it is exponential).
  • Those are the characteristics given by the second choice: graph begins in the second quadrant near the x-axis and increases slowly while crossing the ordered pair 3, 1. The graph then begins to increase quickly throughout the first quadrant.

You surely will find useful to watch the graph that I have attached.

4 0
3 years ago
After a year of weight training, Harold's weight changed from 172 pounds to 185 pounds. What is his percent increase in weight t
Lemur [1.5K]

Answer:

70.2%

Step-by-step explanation:

Given data

Initial weight =172 pounds

Final weight = 185 pounds

% increase= Final - Initial / final  *100

% increase=185 - 172 / 185 *100

% increase= 13 / 185 *100

% increase=0.0702*100

% increase=70.2%

Hence the increase is 70.2%

8 0
3 years ago
Solve the problem: -4/9 -8/9
Trava [24]

Answer:

\frac{-4}{3}

Step-by-step explanation:

When subtracting fractions with the same denominator (bottom number[s]) you can treat the numerators (top number[s]) like subtraction with whole numbers.

-4-8 is equal to -12. Therefore,\frac{-4}{9} - \frac{8}{9} will equal \frac{-12}{9}. But we're not there yet - this fraction can be simplified. We need to find the GCF, or greatest common factor, of -12 and 9. This would be another number that can be divided evenly into these two numbers. The first possible GCF that comes to mind is 3. Let's test that out:

-12/3 = -4

9/3 = 3

It works! Now we can use this information to simplify the fraction. We replace -12 with -4 and replace 9 with 3. This gives us our final answer, \frac{-4}{3}.

7 0
4 years ago
If the Math Olympiad Club consists of 15 students, how many different teams of 5 students can be formed for competitions?
seropon [69]

Answer:

  • 3003

Step-by-step explanation:

Teams of 5 from the total of 15 students.

<u>Combination of 5 is:</u>

  • nCr = n!/(n-r)!*r!
  • 15C5 = 15!/10!5! = 15*14*13*12*11/(2*3*4*5) = 3003 teams
4 0
3 years ago
The variable z is directly proportional to x, and inversely proportional to y. When x is 6 and y is 6, z has the value 12.
dalvyx [7]

z is directly proportional to x: z = kx.

If z is directly proportional to x and inversely proportional to y, then z = Kx/y.

When x= 6 and y = 6, z is 12. Find the constant of proportionality, K:

12 = K(6/6), or K = 12

Then, in general, z = 12x/y.

What is z when x=13 and y=10? z = 12(13)/(10) = 15.6 (answer)

3 0
4 years ago
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