Solve 4/(x + 1) - 1/x = 1 over the real numbers.

Answers

Answer 1

Answer: $( 4)/(x + 1) - (1)/(x) = 1 \n \nx+1\neq 0 \ \ \ and \ \ \ x\neq 0 \n \nx\neq -1 \ \ \ and \ \ \ x\neq 0 \n \nD=R\setminus \left \{ -1,0 \right \}$

$( 4x- (x+1))/(x(x + 1)) = 1 \n \n( 4x- x-1 )/(x^2+ x)=1 \n \n( 3x -1 )/(x^2 + x) = 1 \n \n3x-1=x^2+x\n \n x^2+x-3x+1=0$

$x^2-2x+1=0 \n \n (x-1)^2=0 \n \nx-1=0 \n \nx=1$

Answer 2

Answer: Ok sorry I guessed this one but it was x = 1
4/(1+1) - 1/1 = 1
2 - 1 = 1
And it's right :)

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Jeanne babysits for $6 per hour. She also works as a reading tutor for $10 per hour. She is only allowed to work 20 hours per week. This week, her goal is to make at least $75. A. Use a system of inequalities to model the scenario above. Let x represent babysitting hours and y represent tutoring hours.
B. Use the model created in part A to create a graph representing Jeanne’s probable income earned and possible number of hours worked this week.
C. Analyze the set of coordinate values that represent solutions for the model created in part A. Choose one of the coordinates within the solution and algebraically prove that the coordinate represents a true solution for the model.

Answers

For the answer to the question above, I would start with a simple equation 6x+10y is more than or equal to 75
A.
If we let x represent babysitting hours and y represent tutoring hours:
x+ y ≤ 20
6x + 10y ≥ 75

B. The inequality: x+ y ≤ 20 can be graphed by graphing the line x + y = 20 and shading the area below the line.
The inequality 6x + 10y ≥ 75 can be graphed by graphing the line 6x + 10y = 75 and shading the area above the line.

C. The area where the two shaded regions from the two inequalities overlap are the possible number of hours for tutoring and for babysitting. Algebraically:
x ≤ 20 - y
6(20 - y) +10y ≥ 75
y ≤ 11.25
x ≤ 8.75

Answer:

x+y≤20

6x+10y ≥ 75

Step-by-step explanation:

Let the number of hours of babysitting be x and that for tutoring be y

As per the given conditions

The total no of hours of work must be less than or equal to 20

Hence

x+y≤20

Also Her target is to earn atleast $75

Hence the second inequation will be

6x+10y≥75

Hence our system of inequatlites representing above conditions are

x+y≤20

6x+10y≥75

Now in order to graph them , we first graph the lines x+y=20 and 6x+10y=75 and shade the region which satisfies the respective inequality by taking a coordinate (0,0) .

Please refer to the graph attached with this.

The shaded region gives us the set of coordinates probably the solution to above inequations.

Let us pick one coordinate (10,5) from the shaded region and check for the solution.

put (10,5) in two inequations and see if they are true for them.

10+5≤20

15≤20 True

6(10)+10(5) ≥75

60+50≥75

110≥75 true

Hence checked , both stands true for (10,5)

A sample of 50 11th graders were asked to select a favorite pattern out of 6 choices. the following display shows what their favorite color patterns were. blue on gray 4
green 9
pink polka dots ?
purple 11
red and orange stripes 9
yellow 3

the counts have been recorded in the accompanying table according to pattern and the number of students who selected the pattern. what is missing value in the table?

Answers

There a total of 50 11th graders who had to choose between 6 different color patterns. Among the 6 patterns, only the students who had chosen the pink polka dots are missing. To look for this missing value, simply subtract 50 to the sum of all of the known values of the 5 other colors to obtain the number of students who had picked pink polka dots. This is shown below:

50 - 4 - 9 - 11 - 9 - 3 = x
X = 14

Therefore, there were 14 students who chose pink polka dots.

Answer: 14

Step-by-step explanation:

A P E X

A trampoline has an area of 49 pi square feet. what is the diameter of the trampoline?

Answers

The area of a circle is pi times the radius squared. Set up the equation pi x r squared = 49 pi square feet. Divide both sides of the equation by pi.
r squared = 49 square feet. Take the square root of both sides. r = 7 feet.
The diameter of the trampoline is double the radius which is 14 feet.

Most financial advisors say you'll need about 50 percent of your pre-retirement earnings to comfortably maintain your pre-retirement standard living. True or false

Answers

Answer:

This is false.

Step-by-step explanation:

The correct answer is 70%.

Most financial advisors say you'll need about 70 percent of your pre-retirement earnings to comfortably maintain your pre-retirement standard living.

false ..............................

What the equation x/35 what is the value of x

Answers

The equation x/35=7

x/35 =7
(x/35) *35 = 7 * 35 {multiply both sides by 7}
x = 7 * 35
x =

Line OP has an equation of a line y = 6x − 5, and line QR has an equation of a line y = 6x + 3. These two equations represent

Answers

The two equations represent parallel lines, since they both have the same slope which is equal to 6. Line OP intersects the y-axis at (0,-5), and line QR intersects the Y axis at (0,3).

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