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2 years ago

10

GEOMETRY: Official doubles tennis court has a length of 78 feet and the width of 36 feet. How many times greater is the length t

hen the width of the court to the nearest tenth?

1 answer:

Sever21 [200]2 years ago

7 0

Basically 78 / 36 use the calculator. I have 2.1666666666667 then round it to 2.2
<span>Piece of cak</span>

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If the units for x are years, and x = 5 represents the year 2015, what is the y-value for 2010?

Darya [45]

<u>Given</u>:

The given graph passes through the points (-3,4) and (3,2)

The x - axis represents the years. The value x = 5, year 2015.

We need to determine the y - value for 2010.

<u>Slope</u>:

The slope of the line can be determined using the formula,

$m=\frac{y_2-y_1}{x_2-x_1}$

Substituting the points (-3,2) and (3,2), we get;

$m=\frac{2-4}{3+3}$

$m=\frac{-1}{3}$

Thus, the slope of the line is $m=\frac{-1}{3}$

<u>y - intercept:</u>

The y - intercept in the graph is the point in the line that crosses the y - axis.

Thus, from the graph, it is obvious that the y - intercept is b = 3.

<u>Equation of the line:</u>

The equation of the line can be determined using the formula,

$y=mx+b$

Substituting the values, we have;

$y=-\frac{1}{3}x+3$

Thus, the equation of the line is $y=-\frac{1}{3}x+3$

<u>The y - value for 2010:</u>

Since, it is given that x = 5 represents 2015 and 2010 is 5 years before 2010.

Hence, the value of x for 2010 is given by

$x=5-5=0$

Thus, x = 0 represents the year 2010.

To determine the y - value, let us substitute x = 0 in the equation $y=-\frac{1}{3}x+3$ , we have;

$y=-\frac{1}{3}(0)+3$

$y=3$

Thus, for 2010 the value of y is 3.

5 0

2 years ago

Park rangers tagged fish in a state park to track their population. The function f(x)=200(1.05)x can be used to find the populat

Sedbober [7]

The given exponential function can be used to determine the

population of the fish at different times.

Response:

1. 200

2. 0.05

3. Please find attached the graph of the exponential function and the table

$\begin{array}{|c|c|c}x&f(x)\\0&200 & y-intercept\\1&210\\3&231.525\\4&243.1\\5&255.26\end{array}$

4. Range; [0, ∞)

Domain: [200, ∞)

5. 346 fishes (approximate value)

<h3>How is the population of the fish obtained from the exponential function?</h3>

The given function is f(x) = 200·(1.05)ˣ

1. The initial population is given by the value of the function when x = 0,

which is given as follows;

At x = 0, f(0) = 200·(1.05)⁰ = 200

The initial population of the fish is <u>200</u>

2. The rate of growth of the fish from the exponential function is given as follows;

The growth factor = 1.05

The growth rate =<u> 0.05</u>

3. Please find attached the graph of the exponential function created

with MS Excel.

The asymptote of the exponential function is the line, <u>y = 0</u>

The table of values is presented as follows;

$\begin{array}{|c|c|c}x&f(x)\\0&200 & y-intercept\\1&210\\3&231.525\\4&243.1\\5&255.26\end{array}$

4. The domain is the possible x-values which is; 0 ≤ x < ∞

The range is the possible y-values which is; 200 ≤ f(x) < ∞

Which gives;

Domain; [0, ∞)

Range: [200, ∞)

5. The population of the fish after 11 years is f(11) = 200·(1.05)¹¹

f(11) = 200 × (1.05)¹¹ ≈ 342

The population of the fish after 11 years is <u>346 (fishes)</u>

Learn more about exponential function here:

brainly.com/question/15662160

3 0

2 years ago

(3х2 + 6х+7) – (6х2 – 5х – 7) =

juin [17]

Answer:

OD.-3×2+11×++4

Step-by-step explanation:

ttc gtfbdjwnjdnhwjhbdjsk

4 0

3 years ago

Annabelle’s bicycle has a wheel radius of 13 inches. She places a sticker on the wheel so that its minimum height above the grou

Alchen [17]

Answer:

$y=12.5 sin(180\pi x-\frac{\pi}{2})+13$

Step-by-step explanation:

In order to solve this we can start by drawing a sketch of the problem (see attached picture)

So fist, let's take the general form of a sinusoidal movement:

$y=Asin(\omega x+\phi)+b$

where:

A= amplitude

$\omega$ = angular frequency

x= time

$\phi$ = horizontal shift

b= vertical shift.

In this case, the amplitude will be the maximum distance between the center of the wheel and the highest or lowest point of the trajectory, in this case:

A= 13in - 0.5in =12.5 in

The angular frequency is how many radians the wheel will turn in a minute, so we get:

$\omega=\frac{90 rev}{min}*\frac{2\pi rad}{1 rev}$

$\omega=180\pi rad/min$

Generally, the sin function will start at the center of the circular movement. In this case, since it starts on the lowest point, we can say that the graph moves right by $\frac{\pi}{2} rad$ , so in this case:

$\phi=-\frac{\pi}{2}$

and finally, the vertical shift is the distance between the center of the circular movement and the ground so in this case:

b=13in

so when putting it all together we get our equation to be:

$y=12.5 sin(180\pi x-\frac{\pi}{2})+13$

4 0

3 years ago

Find the value of 22/2+9-4^2+18. Then change one operation sign and add one set of grouping symbols so that the value of the exp

Leokris [45]

Okay,
First, we solve our problem.
22/2 = 11 + 9 = 20-16(4^2)= 4+18= 22

Now, we change our operation sign -22 and add an expression that will give us 36.
Which would be, -22(-2)-8= 36

7 0

2 years ago