The function that describes the graph is an exponential function
<h3>How to determine the function type?</h3>
From the graph, we have the following highlights:
- Initially, when x increases; y seem not to increase
- Then, x and y increase at the same time
- Finally, y increase and x seem not to increase
The above is the description of an exponential function
Hence, the function that describes the graph is an exponential function
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Answer:
The rate of the runner is 3.5 meters per second.
Step-by-step explanation:
To get this answer in meters per second, we first have to convert each of the terms into either meters or seconds. We can do that by multiplying by unit rates.
21 km * 1000 = 21,000 meters
1 hour * 3600 = 3,600 seconds
40 minutes * 60 = 2,400 seconds
Now we divide the meters by the total number of seconds to get the rate.
21,000 meters / (3,600 + 2,400) secs
21,000 meters / 6,000 secs
3.5 meters per second.
Answer:
x=28
Step-by-step explanation:
We can use similar triangles and proportions to solve this problem. Put the side of the small triangle over the same side of the larger triangle.
x 42
---------- = ----------
x+10 42+15
Simplify
x 42
---------- = ----------
x+10 57
Using cross products
57x = 42 (x+10)
Distribute
57x = 42x+420
Subtract 42x from each side
57x-42x = 42x-42x +420
15x = 420
Divide each side by 15
15x/15 = 420/15
x=28
Answer: The value of k for which one root of the quadratic equation kx2 - 14x + 8 = 0 is six times the other is k = 3.
Let's look into the solution step by step.
Explanation:
Given: A quadratic equation, kx2 - 14x + 8 = 0
Let the two zeros of the equation be α and β.
According to the given question, if one of the roots is α the other root will be 6α.
Thus, β = 6α
Hence, the two zeros are α and 6α.
We know that for a given quadratic equation ax2 + bx + c = 0
The sum of the zeros is expressed as,
α + β = - b / a
The product of the zeros is expressed as,
αβ = c / a
For the given quadratic equation kx2 - 14x + 8 = 0,
a = k, b = -14, c = 8
The sum of the zeros is:
α + 6α = 14 / k [Since the two zeros are α and 6α]
⇒ 7α = 14 / k
⇒ α = 2 / k --------------- (1)
The product of the zeros is:
⇒ α × 6α = 8 / k [Since the two zeros are α and 6α]
⇒ 6α 2 = 8 / k
⇒ 6 (2 / k)2 = 8 / k [From (1)]
⇒ 6 × (4 / k) = 8
⇒ k = 24 / 8
⇒ k = 3
Answer:
17%
Step-by-step explanation:
First: work out the difference (decrease) between the two numbers you are comparing. Then: divide the decrease by the original number and multiply the answer by 100.
First:
1,200,000 - 995,000 = 205,000
Then:
205,000 / 1,200,000 = 0.17
0.17 × 100% = 17%
