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3 years ago

Which is a counterexample for the conditional statement shown?

Mathematics

1 answer:

Arte-miy333 [17]3 years ago

7 0

Answer: First Option

The points have the same x-coordinate value.

Step-by-step explanation:

By definition, a relation is considered a function if and only if for each input value x there exists only one output value y.

So, the only way that the line that connects two points in the coordinate plane is not a function, is that these two points have the same coordinate for x.

For example, suppose you have the points (2, 5) and (2, 8) and draw a line that connects these two points.

The line will be parallel to the y axis.

Note that the value of x is the same x = 2. But when x = 2 then y = 5 and y = 8.

There are two output values (y = 8, y = 5) for the same input value x = 2.

In fact all the vertical lines parallel to the y-axis have infinite output values "y" for a single input value x. Therefore, they can not be defined as a function.

Then the correct option is:

The points have the same x-coordinate value.

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What is the distance between points (5, 13)

horrorfan [7]

You are going to treat this as a triangle so one side is 13 units long and the other is 22. And using the pythagorean theorem a²+b²=c².

13²+22²=c²

169+484=c²

653=c²

√653=√c²

25.55386...=c

Or, rounded to the nearest hundredth, 25.55

7 0

3 years ago

The radius of a circular pond is increasing at a constant rate, which can be modeled by the function , where t is time in months

horrorfan [7]

Answer:

B. A(r(t)) = 25πt²

Step-by-step explanation:

Find the completed question below

The radius of a circular pond is increasing at a constant rate, which can be modeled by the function r(t) = 5t where t is time in months. The area of the pond is modeled by the function A(r) = πr². The area of the pond with respect to time can be modeled by the composition . Which function represents the area with respect to time? A. B. C. D.

Given

A(t) = πr²

r(t) = 5t

We are to evaluate the composite expression A(r(t))

A(r(t)) = A(5t)

To get A(5t), we will replace r in A(t) with 5t and simplify as shown

A(5t) = π(5t)²

A(5t) = π(25t²)

A(5t) = 25πt²

A(r(t)) = 25πt²

Hence the composite expression A(r(t)) is 25πt²

Option B is correct.

5 0

3 years ago

How can you use a rate to compare the costs of two boxes of cereal that are different sizes

liraira [26]

By normally dividing it (the two different size of the boxes

7 0

3 years ago

Read 2 more answers

Please help, Algebra 1

Svetach [21]

3px = 2q(r-5x)
distribute
2qr - 10qx
3px = 2qr - 10qx

To solve for x
add 10qx to both sides
3px + 10qx = 2qr
factor out x
x(3p+10q) = 2qr
divide both sides by 3p+10q to isolate x
x = 2qr / (3p+10q)

Hope this helps :)

3 0

4 years ago

I need help with it I don't understand this .... Can someone please help ASAP

DIA [1.3K]

Answer:

a. h(t) = -16t^2 +12t + 4.

b. 5.04 ft

c. 6 ft.

d. 1 second.

Step-by-step explanation:

This is upward motion against the force of gravity. The acceleration due to gravity is 32 ft s-2.

An equation modelling this is

h(t) = ut + 1/2 gt^2 + 4 where h(t) = height of the birdie at time t, g = acceleration due to gravity, t = the time and u = the initial velocity.

u = 12 and g = -32 (because the flight is against gravity) so we have:

h(t) = 1/2 * -32 t^2 + 12t + 4

h(t) = -16t^2 + 12t + 4

b. At t = 0.1 seconds the height is 12(0.1) - 16(0.1)^2 + 4

= 1.2 - 0.16 + 4

= 5.04 ft.

c. At t = 0.25 the height is 12(0.25) - 16(0.25)^2 + 4

= 6 feet

d . When the birdie reaches the ground h will be 0 so

12t - 16t^2 + 4 = 0

-4t^2 + 3t + 1 = 0

(4t- 1)(-t - 1) = 0

t = -0.25, t = 1

t = 1 ( ignore the negative root).

t = 1 second.

6 0

4 years ago