All categories

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.

You might be interested in

Mrs. Fowler has 28 students in her class, and 16 of them are boys.

Elan Coil [88]

We subtract 28 - 16 and get the number of girls
so lets do that
28 - 16 = 12
now we know the unsimplified ratio os 12 to 16
simplifed girls 12 ÷ 4 = 3
simplified boys 16 ÷ 4 = 4
since it says (girls to boys) we put girls first then boys
so it would become 3 : 4
Or the answer is B.) 3 : 4

5 0

3 years ago

Simplify the following expression: 48⋅47

xxTIMURxx [149]

Answer:

2256

Step-by-step explanation:

you simply multiply the two together

8 0

3 years ago

C represents the commission on her sales.

vlabodo [156]

First simplify the expression.
1/3(1,650+0.15c)
550+0.05c
Answer is A
Hope this helps!

3 0

3 years ago

Find the obtuse angle the line y-2x=7 makes with the x- axis

Kazeer [188]

In analytical geometry, there are already derived equations to find the distance of lines and points as well as the angle made between two lines. As special case is when the other line is one of the coordinate axis. Then, the formula can be simplified to

tan θ =m, where m is the slope of the equation

In the next step, we also incorporate operations of calculus. Since the slope is equal to Δy/Δx, this is equivalent to dy/dx in calculus. Therefore, you can find the slope by differentiating the equation in terms of x.

y-2x=7
y = 2x+7
dy/dx = 2 =m

So,

tan θ = 2
θ = tan⁻¹(2)
θ = 63.43°

5 0

3 years ago

A club is choosing 2 members to serve on a committee. The club has nominated 2 women and 4 men. Based on chance alone, what is t

tekilochka [14]

Answer:

53.33% probability that one woman and one man will be chosen to be on the committee

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

The order in which the members are chosen is not important, so we use the combinations formula to solve this question.

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

What is the probability that one woman and one man will be chosen to be on the committee?

Desired outcomes:

One woman, from a set of 2, and one man, from a set of 4. So

$D = C_{2,1}*C_{4,1} = \frac{2!}{1!1!}*\frac{4!}{1!3!} = 8$

Total outcomes:

Two members from a set of 2 + 4 = 6. So

$T = C_{6,2} = \frac{6!}{2!4!} = 15$

Probability:

$p = \frac{D}{T} = \frac{8}{15} = 0.5333$

53.33% probability that one woman and one man will be chosen to be on the committee

5 0

3 years ago