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Jet001 [13]
3 years ago
10

The function below shows the number of car owners f(t), in thousands, in a city in different years t: f(t) = 0.25t2 − 0.5t + 3.5

The average rate of change of f(t) from t = 2 to t = 6 is ______ thousand owners per year. Answer for Blank 1:
Mathematics
1 answer:
N76 [4]3 years ago
5 0
We solve this by the definition of slope in analytical geometry. The definition of slope is the rise over run. In equation, that would be

m = Δy/Δx = (y₂-y₁)/(x₂-x₁)

The x-coordinates here are the t values, while the y-coordinates are the f(t) values. So, let's find the y values of the boundaries.

At t=2: f(t)= 0.25(2)²<span> − 0.5(2) + 3.5 = 3.5
Point 1 is (2, 3.5)
At t=6: </span>f(t)= 0.25(6)² − 0.5(6) + 3.5 = 9.5
Point 2 is (6, 9.5)

The slope would then be

m = (9.5-3.5)/(6-2)
m = 1.5

Hence, the slope is 1.5. Interpreting the data, the rate of change between t=2 and t=6 is 1.5 thousands per year.
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PLEASE HELP!!!
Paladinen [302]

Answer:

d (w) = 0.1w² – w+ 5

Step-by-step explanation:

d(w) = c(w) - a(w)

= -0.3w²+2w+13 -(-0.4w²+3w+8)

= -0.3w²+0.4w²+2w-3w+13-8

= 0.1w²-w+5

4 0
3 years ago
Ryan and Sarah collect baseball cards. Ryan has 150 baseball cards and collects 10 cards per week. Sarah has 200 baseball cards
Nadusha1986 [10]

Answer:

<h2>10 weeks </h2>

Step-by-step explanation:

Step one:

given data

Ryan

number of baseball cards=150

number collected per week= 10

let the number of weeks be x

and the total be y

y=10x+150-----------------1

Sarah

number of baseball cards=200

number collected per week= 5

let the number of weeks be x

and the total be y

y=5x+200------------2

Step two:

Required

the number of weeks where both total will be the same

10x+150=5x+200

10x-5x=200-150

5x=50

divide both sides by 5

x=50/5

x=10 weeks

3 0
2 years ago
1. Define: Capacity
xeze [42]

1. C) The amount that something can hold.  Usually means volume, such as milliliters (ml) or liters (l) in Metric, or pints or gallons in Imperial.

It is the amount something can hold.

3 0
3 years ago
Read 2 more answers
Which function is the inverse of f Superscript negative 1 Baseline (x) = negative one-fifth x minus four-fifths?
DedPeter [7]

Answer:

f(x) = -5x - 4

Step-by-step explanation:

We want to get the inverse of the following function:

f^-1(x) = (-1/5)x - 4/5

To do that, we have to replace x with f(x) and f^-1(x) with x, as follows:

x = (-1/5)f(x) - 4/5

And then solve for f(x), the inverse of f^-1(x).

x + 4/5 = (-1/5)f(x)

f(x) = -5x + (-5)4/5

f(x) = -5x - 4

To check our result we compute a pair (x, f(x))

x   f(x)

1   -5*1 - 4 = -9

which has to be equivalent to (-9, 1) in the original function

x      f^-1(x)

-9     (-1/5)*(-9) - 4/5 = 1

5 0
3 years ago
Read 2 more answers
How would I graph a line that contains the point (6,5) and has a slope of - 2/3 ?​
ddd [48]

Answer:

y=-2/3x+9

Step-by-step explanation:

Use point-slope formula:

y-y1 = m(x-x1)

y-5=-2/3(x-6)

y-5=-2/3x+4

y=-2/3x+9

You would then proceed to graphing this equation, as it is in slope intercept form now.

HTH :)

6 0
3 years ago
Read 2 more answers
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