All categories

2 years ago

Graph the function.

Mathematics

1 answer:

Lera25 [3.4K]2 years ago

4 0

Answer:

Please review my interpretation of the written expression.

Step-by-step explanation:

f(x) = 5*(4/5)^x : Is this correct?

If so, see attached graph.

One can calculate several points and then draw the graph, or use an online, and free, graphing app (DESMOS in this case).

Since the exponent is the variable, I'll pick a few vaules that are easy (for me) to calculate:

f(0) = 5*(4/5)^0

Anything raised to the 0th power is equal to 1, so we get 5*1 or 5 to make the point (1,5).

When x = 1, the fraction (4/5) remains (4/5) and when multiplied by 5, reduces to simply 4. The second point is (1,4)

For the last point, I chose x to be 10. 5(4/5)^10 becomes 0.5. The third point is (10,0.5)

We can see the line approaches 0 as x increases.

You might be interested in

In a game of cornhole, Sasha tossed a bean bag and it landed at the edge of the hole. The hole can be represented by the equatio

Nitella [24]

In the game of cornhole, when Sasha tossed a bean bag to the edge of the hole, in which the equations of the hole and bean bag's path are x² + y² = 5 and y = 0.5x² + 1.5x - 4, respectively, she could have tossed her bean bag to the points (1, -2) or (2, 1).

To find the points in which she could have tossed her bean bag, we need to intersect the two equations of the function as follows.

The equation for the hole

$x^{2} + y^{2} = 5$ (1)

The equation for the path of the bean bag

$y = 0.5x^{2} + 1.5x - 4$ (2)

By entering equation (2) into (1) we have:

$x^{2} + (0.5x^{2} + 1.5x - 4)^{2} = 5$

$x^{2} + 0.25x^{4} + 1.5x^{3} - 4x^{2} + 2.25x^{2} - 12x + 16 = 5$

$0.25x^{4} + 1.5x^{3} - 0.75x^{2} - 12x + 11 = 0$

By solving for x, we have:

x₁ = 1

x₂ = 2

Now, for y we have (eq 2):

x₁ = 1

$y_{1} = 0.5(1)^{2} + 1.5(1) - 4 = -2$

x₂ = 2

$y_{2} = 0.5(2)^{2} + 1.5(2) - 4 = 1$

Therefore, the points are (1, -2) or (2, 1).

To find more about intersections, go here: brainly.com/question/4977725?referrer=searchResults

I hope it helps you!

8 0

3 years ago

Analyze the diagram below and complete the instructions that follow.

Maslowich

As QS bisects <RQT into 2 congruent triangles

therefore, <RQS = <SQT

4x-25= 2x+5

2x= 30

x= 15

<RQS = 4x-25

= 4(15) -25

=60-25

= 35

8 0

3 years ago

Can u pls help me with this

BabaBlast [244]

Answer:

Problem 1:

x=12, x=3, x=6

Problem 2:

18*3=54

54/18=3

Problem 3:

Part A: 36/4.5=? 4.5*x=36

Part B: 8

Step-by-step explanation:

7 0

3 years ago

Please help me <33333

mariarad [96]

Comment
You have to begin by declaring what g(f(x)) means. It means that wherever you see an x in g(x) you put in f(x).

It will look like this to start with
g(f(x)) = (f(x) + 5) / (f(x)

Now substitute into this for g(-3)

g(x^2 + 5) = (x^2 + 5 + 5)/(x^2 + 5) It's time to use some numbers.
g(- 3) = ((-3)^2 + 10)/( (-3)^2 +5)
g(-3) = ( 9 + 10 ) / ( 9 + 5)
g(-3) = (19)/14 <<<<<< answer.
C <<<< answer.

8 0

3 years ago

For a certain map, the scale shows that 1 cm on the map equals 2.50 km on earth's surface. two towns on the map are 4.75 cm apar

Julli [10]

In this problem, to find the answer we have to setup a series of ratios that relate the scale to real life distance. We know that 1cm = 2.50km, so that ratio would be 1cm/2.5km. For two towns that are 4.75cm apart on the map, we set a ration of 4.75cm/x km, where x is the actual distance. Now we set the ratios equal to each other and solve for x. 1/2.5=4.75/x where x = 4.75*2.5/1 = 11.875 and rounding up we get 11.88 km. The two towns are actually 11.88 km apart from each other.

3 0

3 years ago