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kykrilka [37]
3 years ago
11

Given f(x) and g(x) = k⋅f(x), use the graph to determine the value of k.

Mathematics
1 answer:
Rasek [7]3 years ago
6 0

Answer: -3.

Step-by-step explanation:

We are given that : g(x)=kf(x)      (1)

It means that f(x) and g(x) are proportional.

[Equation of direct variation: y=kx , where k= proportionality constant.]

From the given graph ,

At x= -3 , f(x)=1 and g(x) =-3

Put value of x=-3 in (1) , we get

g(-3)=kf(-3)  

\Rightarrow\ -3=k(1)  [∵ f(x)=1 and g(x) =-3]

\Rightarrow\ -3=k

i.e. The value of k = -3

Hence, the correct answer is -3.

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I think this is the answer ---->  8.7 (8.66 rounded)
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This question is not correctly written

Complete Question

The Henderson Hawks minor-league baseball team is giving away baseballs an

game. The balls cost $3 each and the towels cost $2 each. The team wants to give away 200 items and have 500 to spend. How many of each item should the team give away Show your

work or explain your reasoning.

Answer:

They should give away 100 balls and 100 towels

Step-by-step explanation:

Let the number of balls = x

Let the number of towels = y

x + y = 200........ Equation 1

y = 200 - x

$3 × x + $2 × y = $5000

3x + 2y = 5000...... Equation 2

3x + 2(200 - x)= 5000

3x + 400 - 2x = 5000

Collect like terms

3x - 2x = 500 - 400

x = 100

Number of balls to be given away = 100

Note:

y = 200 - x

y = 200 - 100

y = 100

Number of towels to be given away = 100

Therefore, they should give away 100 balls and 100 towels

3 0
3 years ago
Scarlett is practicing math fluency. She has 100 math operation flashcards with 42 addition problem cards, 56 subtraction cards,
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Answer:

C

Step-by-step explanation:

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4 0
3 years ago
21 The graph of an exponential function is shown on the grid.
morpeh [17]

Answer:

  • C The range is the set of all real numbers greater than 0.

Step-by-step explanation:

We see that the function has positive range and no restriction of domain.

A The range is the set of all real numbers less than 0.

  • Incorrect, positive values only

B The domain is the set of all real numbers greater than-4.

  • Incorrect, the domain can get any value

C The range is the set of all real numbers greater than 0.

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D The domain is the set of all real numbers less than-4.

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5 0
3 years ago
Find the distance from the origin to the graph of 7x+9y+11=0
Cerrena [4.2K]
One way to do it is with calculus. The distance between any point (x,y)=\left(x,-\dfrac{7x+11}9\right) on the line to the origin is given by

d(x)=\sqrt{x^2+\left(-\dfrac{7x+11}9\right)^2}=\dfrac{\sqrt{130x^2+154x+121}}9

Now, both d(x) and d(x)^2 attain their respective extrema at the same critical points, so we can work with the latter and apply the derivative test to that.

d(x)^2=\dfrac{130x^2+154x+121}{81}\implies\dfrac{\mathrm dd(x)^2}{\mathrm dx}=\dfrac{260}{81}x+\dfrac{154}{81}

Solving for (d(x)^2)'=0, you find a critical point of x=-\dfrac{77}{130}.

Next, check the concavity of the squared distance to verify that a minimum occurs at this value. If the second derivative is positive, then the critical point is the site of a minimum.

You have

\dfrac{\mathrm d^2d(x)^2}{\mathrm dx^2}=\dfrac{260}{81}>0

so indeed, a minimum occurs at x=-\dfrac{77}{130}.

The minimum distance is then

d\left(-\dfrac{77}{130}\right)=\dfrac{11}{\sqrt{130}}
4 0
4 years ago
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