All categories

3 years ago

Given:

Mathematics

1 answer:

jekas [21]3 years ago

4 0

Answer:

we conclude that:

If 4x - 6≠4, then 2x–5≠5 is the contrapositive of a conditional statement if 2x -5=5, then 4x-6=14.

Step-by-step explanation:

We know that the contrapositive of a conditional statement of the form "If p then q" is termed as "If ~q then ~p".

In other words, it is symbolically represented as:

' ~q ~p is the contrapositive of p q '

For example, the contrapositive of "If it is a rainy day, then they suspend the match" is "If they do not suspend the match, then it won't be a rainy day."

Given

p: 2x -5=5

q: 4x-6=14

As the contrapositive of a conditional statement of the form "If p then q" is termed as "If ~q then ~p

Thus, we conclude that:

If 4x - 6≠4, then 2x–5≠5 is the contrapositive of a conditional statement if 2x -5=5, then 4x-6=14.

You might be interested in

Hector's service club is raising money by wrapping presents in the mall. The function f\left(x\right)=3xf(x)=3x describes the am

mestny [16]

Given:

The function f(x) describes the amount of money, in dollars, the club will earn for wrapping x presents.

$f(x)=3x$

To find:

The f(658).

Solution:

We have,

$f(x)=3x$

Substitute x=658 to find the value of f(658).

$f(658)=3(658)$

$f(658)=1974$

It means, the club will earn $1974 for wrapping 658 presents.

Therefore, $f(658)=1974$ .

7 0

3 years ago

The function f(x)=(x-5)^2 +2 is not one-to-one. Identify a restricted domain that makes the function one-to-one, and find the in

Anon25 [30]

We have been given a quadratic function $f(x)=(x-5)^{2} +2$ and we need to restrict the domain such that it becomes a one to one function.

We know that vertex of this quadratic function occurs at (5,2).

Further, we know that range of this function is $[2,\infty)$ .

If we restrict the domain of this function to either $(-\infty,5]$ or $[5,\infty)$ , it will become one to one function.

Let us know find its inverse.

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

Upon interchanging x and y, we get:

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

Let us now solve this function for y.

$(y-5)^{2}=x-2\\
y-5=\pm \sqrt{x-2}\\
y=5\pm \sqrt{x-2}\\$

Hence, the inverse function would be $f^{-1}(x)=5+\sqrt{x-2}$ if we restrict the domain of original function to $[5,\infty)$ and the inverse function would be $f^{-1}(x)=5-\sqrt{x-2}$ if we restrict the domain to $(-\infty,5]$ .

8 0

3 years ago

There are 32 students in a class. Of the class, 3/8 of the students bring their own lunches. How many students bring their lunch

OverLord2011 [107]

Answer:

The number of students that bring their lunches is 12

Step-by-step explanation:

Let

x -----> the number of students that bring their lunches

y -----> the total number of students in a class

we know that

The number of students that bring their lunches divided by the total number of students in a class must be equal to 3/8

$\frac{x}{y}=\frac{3}{8}$

$x=\frac{3}{8}y$ -----> equation A

$y=32$ -----> equation B

substitute the value of y in equation A and solve for x

$x=\frac{3}{8}(32)$

$x=12$

therefore

The number of students that bring their lunches is 12

6 0

3 years ago

HELP MEEEEE........

Alex787 [66]

Answer:

Maybe Dependent

Step-by-step explanation:

3 0

3 years ago

**Solve by Elimination<br> 3 + 2x - y = 0<br> -3-7y = 10x<br> 7) x =<br> 8) y =

timofeeve [1]

Answer:

Explanation:

3 + 2x - y = 0
Or 2x - y = -3 (1)

-3-7y = 10x
Or -10x - 7y = 3 (2)

2x - y = -3 (1)
-10x - 7y = 3 (2)
———————

Multiply 5 to (1)

5(2x - y = -3)
-10x - 7y = 3
———————
10x - 5y = -15
-10x - 7y = 3
———————
-12y = -12
y = -12/-12
y = 1

Plug y value in (1)

2x - 1 = -3
2x = -3 + 1
2x = -2
x = -2/2 = -1

Therefore, x = -1 and y = 1

7 0

2 years ago