How many solutions <br> does -3(x-14)+9x=6x+42 have

Which situation could be represented by the graph?

Ymorist [56]

The correct option which resembles with the given graph is $\fbox{\begin\\\ optionA and optionC\\\end{minispace}}$ .

Further explanation:

From the given graph the it is observed that the interval is $[8,11)$ which is a half open interval or it can be said that it is a half closed interval.

A half closed or a half open interval is an interval in which one end point of the interval is included but the other point is not included.

For example:

In an interval of the form $[a,b)$ the point $a$ is included in the set but the point $b$ is not included in the set.

Similarly, in the interval $[8,11)$ the point $8$ is included in the set but the point $11$ is not included in the set.

In order to determine the correct option which resembles with given graph form interval for each option.

Option A:

As per the statement in option A the age of the student must be at least $8$ years and not more than $11$ years that is the age of the student is either $8$ years or greater than $8$ years and less than $11$ years.

As per the above statement the interval formed is $\fbox{\begin\\\ [8,11)\\\end{minispace}}$ in which $8$ is included in the set and $11$ is not included which means it is a half closed or half opoen interval.

Therefore, $\fbox{\begin\\\ optionA\\\end{minispace}}$ is a correct option.

Option B:

As per the statement in option B the amount of money the babysitter can earn is between $\$8$ and $\$11$ per hour.

As per the above statement the interval formed is $\fbox{\begin\\\ (8,11)\\\end{minispace}}$ in which both of the end points are not included in the set which means that it is an open interval.

Therefore, $\fbox{\begin\\\ optionB\\\end{minispace}}$ is an incorrect option.

Option C:

As per the statement in option C the time required to complete a program in college cannot be less than $8$ hours and the time must be less than $11$ hours.

From the above statement it is concluded that the time required can be $8$ hours or more than $8$ hours but it has to be less than $11$ hours.

So, as per the above the statement the interval formed is $\fbox{\begin\\\ [8,11)\\\end{minispace}}$ .

Therefore, $\fbox{\begin\\\ optionC\\\end{minispace}}$ is a correct option.

Option D:

As per the statement in option D the age of the dogs is either $8$ years old or below $8$ years and age of the dog must be greater than $11$ tears.

As per the above statement the interval formed is $\fbox{\begin\\\ (-\infty,8) \bigcup(11,\infty)\\\end{minispace}}$ .

Therefore, the $\fbox{\begin\\\ optionD\\\end{minispace}}$ is an incorrect option.

So, $\fbox{\begin\\\ optionA and optionC\\\end{minispace}}$ are the correct options which resembles with the given graph.

Learn more:

A problem on composite function brainly.com/question/2723982
A problem to find radius and center of circle brainly.com/question/9510228
A problem to determine intercepts of a line brainly.com/question/1332667

Answer details:

Grade: High school

Subject: Mathematics

Chapter: Sets

Keywords: Interval, set, open interval, closed interval, half open interval, half closed interval, set theory, program, community college, babysitters, veterinary clinic, ages, students.

5 0

3 years ago

Read 2 more answers

Using the Multiplication Property of -1

Papessa [141]

A. -(a+5)

Because the negative sign is outside the parenthesis, multiplying by -1 just removes the negative sign:

-(a+5) * -1 = a+5

B. -(-x+31)

Apply the distributive property:

-(-x+31) becomes (- -x +31) which simplifies to (x+31)

multiply that by -1 to get -x+31

C. -(4x+12)

Because the negative sign is outside the parenthesis, multiplying by -1 just removes the negative sign:

-(4x+12) * -1 = 4x+12

7 0

3 years ago

What is the slope of the line?

Salsk061 [2.6K]

Answer:

-3

Step-by-step explanation:

or -3x if youre writing an equation

5 0

3 years ago

Need help asap plzzzzzzzzzzzzzzzzz

tankabanditka [31]

I think your answer is the second one

best of luck

4 0

3 years ago

find the surface areas of the larger cone and the smaller cone in terms of pi. compare the surface areas using a percent. (the m

serious [3.7K]

ANSWER :

Surface area of larger cone : 24π units^2

Surface area of smaller cone : 6π units^2

The surface area of the smaller cone is 25% of that of the larger cone.

EXPLANATION :

From the given problem,

AB = 3 is the radius of the larger cone and the slanted height is BC = 5

DE = 1.5 is the radius of the smaller cone and the slanted height is EC = 2.5

Recall the surface area of the cone :

$A=\pi r^2+\pi rL$

where r = radius and L = slanted height.

For the larger cone, r = 3 and L = 5

$\begin{gathered} A=\pi(3)^2+\pi(3)(5) \\ A=24\pi \end{gathered}$

For the smaller cone, r = 1.5 and L = 2.5

$\begin{gathered} A=\pi(1.5)^2+\pi(1.5)(2.5) \\ A=6\pi \end{gathered}$

Comparing the surface areas :

The area of the smaller cone compared to the larger cone is :

$\begin{gathered} \frac{smaller}{larger}\times100=\frac{6\pi}{24\pi}\times100 \\ \\ =25\% \end{gathered}$

3 0

1 year ago

How many solutions does -3(x-14)+9x=6x+42 have