Solve: x+2/x-4<0A 4 < x < 2B 2 < x < 4C 2 < x < 4D 4 < x < 2

Answer:B. -2 < x < 4Step-by-step explanation:The function is (x +2)/(x-4) and we are asked to determine the x interval when the inequality (x +2)/(x-4) < 0 is satisfied1. Find the critical pointsThe critical points are x = - 2 when the numerator becomes -2 + 2 = 0, and f(x) = 0andx = 4 when the denominator becomes 4 - 4 = 0 and (x + 2)/0 is undefinedSo critical points are -2 and 42. Use these critical points to divide the number line into intervalsThe intervals are - < x < -2, -2 < x < 4 and 4 < x < these can be re-written as x < -2, -2 < x < -4 and x > 43. For each of these intervals take a test point and see if it satisfies that inequality(a) - < x < -2 Take x = -3 which is less than -2We get f(-3) = (-3 + 2)/(-3 -4) = -1/-7 which is + 1/7 and does not satisfy the (x+2)/(x-4) < 0 inequality. So we can discard this interval(b) For interval -2 < x < 4, Let's take x = 0(0+2)/(0-4) = 2/(-4) = -1/2 = -0.5 which does satisfy the inequality (x+2)/(x-4) <0, so this is a valid interval(c) For interval x > 4, take x = 5(x+2)/(x-4 ) = (5 + 2)/(5-4) = 7/1 = 7 and does not satisfy (x+2)/(x-4 ) < 0So the interval which satisfies the inequality is -2 < x < 4

Mathematics High School

Solve: x+2/x-4<0
A –4 < x < –2
B –2 < x < 4
C –2 < x < –4
D –4 < x < 2

Answers

Answer 1

Answer:

B. -2 < x < 4

Step-by-step explanation:

The function is (x +2)/(x-4) and we are asked to determine the x interval when the inequality (x +2)/(x-4) < 0 is satisfied

1. Find the critical points

The critical points are

x = - 2 when the numerator becomes -2 + 2 = 0, and f(x) = 0

and

x = 4 when the denominator becomes 4 - 4 = 0 and (x + 2)/0 is undefined

So critical points are -2 and 4

2. Use these critical points to divide the number line into intervals
The intervals are -∞ < x < -2, -2 < x < 4 and 4 < x < ∞
these can be re-written as x < -2, -2 < x < -4 and x > 4

3. For each of these intervals take a test point and see if it satisfies that inequality
(a) -∞ < x < -2 Take x = -3 which is less than -2
We get f(-3) = (-3 + 2)/(-3 -4) = -1/-7 which is + 1/7 and does not satisfy the (x+2)/(x-4) < 0 inequality.

So we can discard this interval
(b) For interval -2 < x < 4, Let's take x = 0
(0+2)/(0-4) = 2/(-4) = -1/2 = -0.5 which does satisfy the inequality
(x+2)/(x-4) <0, so this is a valid interval

(c) For interval x > 4, take x = 5
(x+2)/(x-4 ) = (5 + 2)/(5-4) = 7/1 = 7 and does not satisfy (x+2)/(x-4 ) < 0

So the interval which satisfies the inequality is -2 < x < 4

Solve: X+2/x-4<0A 4 < X < 2B 2 < X < 4C 2 < X < 4D 4 < X < 2

Related Questions

3x3 what is the sum to this..?

Answers

Answer:

Step-by-step explanation:

3x3=9

Answer:

the sum is 9

Step-by-step explanation:

3×1=3

3×2=6

3×3=9

Square root of 9 =3=3=3 and 1 half + 1 half

Answers

Nah the square root of 9 is 3

Simplify.
2 + 8 - 2 [32 + 5 (1 + 2)]}

Answers

Your answer should be - 84.

Explanation:

Starting equation: [tex]2\:+\:8\:-\:2\:\left[32\:+\:5\:\left(1\:+\:2\right)\right][/tex]

-Calculate within parentheses [32 + 5 (1+2)] = 47.

Remaining equation: 2 + 8 - 2 x 47

-Multiply and divide (left to right) 2 x 47 = 94

Remaining equation: 2 + 8 - 94

-Add and subtract (left to right) 2 + 8 - 94 = -84

Your final answer is -84

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Hope this helps!

Have a great day and God bless! :)

Paul collects comic books. He has 20 books in his collection, and he adds 3 per month. In how many months will he have a total of 44 books in his collection?
F. 5
G. 6
H. 8
J. 15

Answers

In 8 months he will have a total of 44 books in his collection.

The correct answer is an option (H)

In this question,

Paul collects comic books. He has 20 books in his collection, and he adds 3 per month.

We need to find the number of months required to have a total of 44 books in his collection.

Let n be the required number of months.

From given information, we get an equation,

20 + 3n = 44

We solve above equation to find the required number of months.

20 + 3n - 20 = 44 - 20

3n = 24

n = 8

Therefore, in 8 months he will have a total of 44 books in his collection.

The correct answer is an option (H)

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Write each number as a percent.
1(2/5)

Answers

140% pretty straight and easy let me know if you need an explanation

Write a relationship for a function whose hx values are 6 less than the cube of x

Answers

The mathematical expression from the algebraic expression is a x^3 - 6.

According to the statement

We have to find that the expression of the statement in the mathematical form.

So, For this purpose, we know that the

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

From the given information:

The hx values are 6 less than the cube of x

Then

To convert into the mathematical form:

The cube of the x is in the mathematical form is a x^3

Then

And the 6 less than the cube

And in the mathematical form it becomes the

x^3 - 6.

So, The mathematical expression from the algebraic expression is a x^3 - 6.

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Problem: using the digits -9 to 9 at most one time each, place a digit on each box to create an equation whose solution is a positive whole number. ("_" is what i need to fill in and the "/" are fractions)
_/_(x)+_/_= _

Answers

Considering division signal rules, one possible example of an equation that results in a positive number is:

-9/-3 + 3/1 = 6.

When does a division results in a positive number?

A division(fraction) results in a positive numbers if the two terms have the same signal, either both positive or both negative.

Hence, to ensure an expression with a positive result in this problem, the terms in each division got to have the same signal, as the example that follows:

-9/-3 + 3/1 = 6.

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Determine whether each sequence is geometric. If so, find the common ratio. 10,4,1.6,0.64, . . . . .

Answers

The given sequence is geometric, with common ratio = 0.4.

What is a geometric progression?A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.

Now, Given: 10, 4, 1.6, 0.64, ....

Here, [tex]\frac{4}{10}=\frac{1.6}{4}=\frac{0.64}{1.6}=0.4[/tex]

That is, the given sequence follows the only necessary condition for a sequence to be geometric.

Hence, The given sequence is geometric, with common ratio = 0.4.

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Jan and Dinah both ran for 20 seconds, each at a constant speed. Jan ran 50 mefers and Dingh ran 60 meters. 1. Who was moving faster? Explain how you know. 2. How far did each person move in 1 second?

Answers

By calculating speed of each person we can find who is faster.

What is Speed?

Speed can be defined as the distance covered with respect to time. It is a scalar quantity. It is calculated as follows

Speed = Distance / Time taken

The time taken by each person is 20 seconds.

Distance covered by Jan = 50 meter

Speed of Jan = Distance / Time taken

Speed of Jan = 50 / 20

Speed of Jan = 2.5 meters per second

Distance covered by Dingh = 60 meter

Speed of Dingh = Distance / Time taken

Speed of Dingh = 60 / 20

Speed of Dingh = 3 meters per second

Since the speed of Dingh is more than Jan, we can say that Dingh is faster.

Distance = Speed × Time taken

Here, time taken = 1 second

This implies Distance Covered = Speed

Therefore, Jan covers 2.5 meters in one second while Dingh covers 3 meters in one second.

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Chen buys 11 books for $77. Each book has the same price. What is the price of each book? Show the multiplication or division fact you used to solve the problem?

Answers

Answer: $7 per book

Step-by-step explanation:

$77 for 11 books, so we do 77 ÷ 11 = 7

What is the value of this product

Answers

Answer:

The value of the product is 2²

how do i subtract inteargers

Answers

Answer:

You remove the difference between the two numbers from each other. E.g., 5-2=3, and 6-4=2.

Step-by-step explanation:

Number 7 is the one I need help with please

Answers

Answer:

Step-by-step explanation:

The answer is C 14-9=5

The larger of two numbers is 7 more than 5 times the smaller. If the sum of the two numbers is 31, what are the two numbers

Answers

Answer: x=27 y=4

Step-by-step explanation:

Let the larger of two numbers is x and the smaller of two numbers is y

Hence,

[tex]\displaystyle\left \{ {x-5y=7} \atop {x+y=31}} \right.\\\\\left \{ {{x-5y=7} \atop {x+y-y=31-y}} \right. \\\\\left \{ {{x-5y=7\ \ \ \ \ (1)} \atop {x=31-y}\ \ \ \ (2)} \right. \\[/tex]

Substitute equation (2) into equation (1):

[tex]31-y-5y=7\\31-6y=7\\31-6y+6y=7+6y\\31=7+6y\\31-7=7+6y-7\\24=6y\\[/tex]

Divide both parts of the equation by 6:

[tex]4=y\\Hence,\\x=31-4\\x=27[/tex]

Record your answers on the answer sheet provided by your teacher or on a sheet of paper.
Suppose line l contains points A, B , and C , If A B=7 inches, A C=32 inches, and point B is between points A and C , what is the length of BC? Express your answer in inches.

Answers

Length of BC is 25 inches.

Here,

Line l contains points A, B and C.

A B =7 inches, A C = 32 inches, and point B is between points A and C.

We have to find the length of BC in inches.

What are Collinear points?

If two or more points are lie on a straight line then points are called Collinear points.

Now,

Line l contains points A, B and C.

Point B is between points A and C.

Length of A B = 7 inches and A C = 32 inches

Hence, Length of BC = Length of AC - Length of A B

= 32 - 7 = 25 inches.

Therefore, Length of BC is 25 inches.

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I Need help pls i forgot what to do with this math problem

Answers

Answer:

-8^3/7^3 = -512/343

Step-by-step explanation:

3√ (-512/343) = 3√-(8/7)^3 = -8/7

-8^3/7^3 = -512/343

The telephone company offers two billing plans for local calls. Plan 1 charges $30 per month for unlimited calls and Plan 2 charges $13 per month plus $0.04 per call.

a. Use an inequality to find the number of monthly calls for which Plan 1 is more economical than Plan 2.

b. Explain the meaning of the answer to part a.

Answers

Answer:

Step-by-step explanation:

The telephone company offers two billing plans for local calls. Plan 1 charges $30 per month for unlimited calls and Plan 2 charges $15 per month plus $0.04 per call.

a. Use an inequality to find the number of monthly calls for which Plan 1 is more economical than Plan 2.

b. Explain the meaning of the answer to part

50 points
add and write the fraction in its simplest form.
-7/8 + (-2 1/6) =

Answers

Answer:-3 1/24

Step-by-step explanation:

You want to buy a new iPhone 50 that costs $1330 including taxes(13%). How many hours will you have to work to be able to buy this new phone if you make minimum wage which is $14.25 per hour?

Answers

Answer:

105.47 hours

Step-by-step explanation:

1300x0.13=172.9

172.9+1300=1502.9

1502.9/14.25=105.47

Write two absolute value functions such that they have a common vertex in Quadrant III and one is the reflection of the other in a horizontal line.

Answers

The functions

y = -|x + 4| - 5y=−∣x+4∣−5

y = |x + 4| - 5y=∣x+4∣−5

Both these functions have got a common vertex in the third Quadrant.

They are the reflections of each other in a horizontal line.

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Determine the following attributes of the graph below please i only have 8 mins to turn this in 20 points pleaseeee

Answers

For the following function, we have that:

The domain is 0 < x ≤ 4.The range is -2 ≤ y ≤ 2.The x-intercepts are x = 1 and x = 3, that is, points (1,0) and (3,0).The y-intercept is y = 2, that is, point (0,2).The maximum value on the interval [1,4] is of 2, at point (4,2).The minimum value on the interval [1,4] is of -2, at point (2,-2).

What are the domain and the range of a function?

The domain of a function is the set that contains all the values of the input.The range of a function is the set that contains all the values of the output.

In a graph:

The domain is given by the x-values, the horizontal axis.The range is given by the y-values, the vertical axis.

Hence, for the graph in this problem, we have that:

The domain is 0 < x ≤ 4.The range is -2 ≤ y ≤ 2.

What are the intercepts of a function?

The x-intercept of a function is given by the value of x when f(x) = 0, that is, the value of x when the function crosses the x-axis.The y-intercept of a function is given by the value of f(x) when x = 0, that is, the value of y when the function crosses the y-axis.

Hence:

The x-intercepts are x = 1 and x = 3, that is, points (1,0) and (3,0).The y-intercept is y = 2, that is, point (0,2).

What is the maximum and the minimum value?

We have to look at the values of y on the interval, hence:

The maximum value on the interval [1,4] is of 2, at point (4,2).The minimum value on the interval [1,4] is of -2, at point (2,-2).

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Write a coordinate proof to prove that Δ A B C is an isosceles triangle if the vertices are A(0,0), B(a, b) , and C(2 a, 0) .

Answers

An isosceles triangle is one with two equal-length sides. ΔABC is an isosceles triangle.

What is the distance between two points ( p,q) and (x,y)?

The shortest distance (length of the straight line segment's length connecting both given points) between points ( p,q) and (x,y) is:

D = √[(x-p)² + (y-q)²] units.

Given that the coordinates of the vertices of the triangle are A(0,0), B(a, b), and C(2a, 0). Now, to prove that the given triangle is an isosceles triangle we need to find the length of each side of the triangle.

AB = √[(x₂-x₁)² + (y₂-y₁)²]

= √[(a - 0)² + (b - 0)²]

= √(a² + b²)

BC = √[(x₂-x₁)² + (y₂-y₁)²]

= √[(2a - a)² + (0 - b)²]

= √(a² + b²)

AC = √[(x₂-x₁)² + (y₂-y₁)²]

= √[(2a - 0)² + (0 - 0)²]

= √4a²

= 2a

Since the length AB and BC are the same, while the length of AC is different, therefore, ΔABC is an isosceles triangle.

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The average professional hockey player makes $2.78 million a year.
They play an average of 82 games.
How much does the average hockey player make per game?

A. $33,900.00
B. $3,390.00
C. $34,000.00
D. $3,400.00
E. None of the above

Answers

Answer:

$34,000.00

Step-by-step explanation:

[tex]2,780,000/82 = 33,902.439\\33,902.439 ~ 34,000.00[/tex]

The average hockey player makes per game is an amount of $34,000.00 which is the correct option would be option (A).

What is the division operation?

In mathematics, divides left-hand operands into right-hand operands in the division operation. The primary purpose of the division is to generate equal groupings or to determine how many people are in each category after a fair distribution.

For example 4/2 = 2

The average professional hockey player makes $2.78 million a year.

$2.78 million = $2,780,000

They play an average of 82 games.

The average hockey player makes per game = 2,780,000 / 82

Apply the division operation to get the answer.

The average hockey player makes per game = 33,902.439

The average hockey player makes per game = $33,900.00

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Write the equation of the circle that passes through the given point and has a center at the origin. (Hint: You can use the distance formula to find the radius.) (-2,3)

Answers

The equation of the circle that passes through the point (-2 , 3) and has a center at the origin is x^2 + y^2 = 13.

Using the distance formula, get the radius of the circle by solving for the distance between the center and the point (-2 , 3).

radius = distance = √(x2 - x1)^2 + (y2 - y1)^2

radius = √(-2 - 0)^2 + (3 - 0)^2

radius= √4 + 9

radius = √13

The standard form of the equation of the circle is given by (x - h)^2 + (y - k)^2 = r^2, where (h , k) is the location of the center and r is the radius of the circle.

Given the radius and center of the circle, substitute these values to the standard form of the equation of the circle.

(x - h)^2 + (y - k)^2 = r^2

where (h , k) = (0 , 0)

r = √13

(x - 0)^2 + (y - 0)^2 = (√13)^2

x^2 + y^2 = 13

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Add or subtract as indicated.
25.32 + 109.2 + 8.574

Answers

25.32+109.2 is equal to 134.52 then add 8.574 and your total is 143.09

Evaluate x³ for x = 2.
06
02
08

Answers

Answer:

Step-by-step explanation:

x³; x = 2

2³ or 2 × 2 × 2 = 8

I hope this helps!

Answer is 8, because you multiply 2 by 3 times since there is a “3” exponent

Tyrone needs 50 volunteers for a concert.
Tyrone has 20% more volunteers than
he needs. Tyrone assigns 15% of the total
volunteers to the stage area. How many
volunteers does Tyrone assign to the
stage area?

Answers

Answer:

Step-by-step explanation:

i don't understand this shirty app

Answer: 9

Step-by-step explanation:

20% of 50 is 10. So, he has a total of 60 volunteers. He uses 15% of that for the stage area, and 15% of 60 is 9. So, Tyrone assigned 9 volunteers to the stage area.

What can you say about and based on the sum of their angles? How are the angles related?

Answers

Answer: Do you have a picture of the problem so it will be more sense?

Step-by-step explanation:

Two tents are in the shape of hemispheres, with circular floors. The ratio of their floor areas is 9: 12.25 . If the diameter of the smaller tent is 6 feet, what is the volume of the larger tent? Round to the nearest tenth.

Answers

The volume of the larger tent in the shape of hemispheres, with circular floors, is 89.8 cubic feet.

If the diameter of the smaller tent is 6 feet, then its radius is 3 feet. Solving for the area of its circular floor,

A = πr^2

A = π(3 feet)^2

A = 9π square feet

Using the ratio of the floor areas of the two tents, calculate the area of the circular floor of the larger tent.

9 : 12.25 = 9π square feet : x

where x = area of the circular floor of the larger tent

9x = 12.25(9π)

x = 12.25 π square feet

If the area of the circular floor of the larger tent is 12.25 π square feet, then solving for its radius,

A = πr^2

12.25 π square feet = πr^2

r = 3.5 feet

Hemisphere refers to half of a sphere and its volume is given by the formula V = 2/3πr^3, where r is the radius.

V = 2/3πr^3

V = 2/3 π (3.5 feet)^3

V = 89.79719002 cubic feet

Rounding off to the nearest tenth.

V = 89.8 cubic feet

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The geometric mean of a number and four times the number is 22 . What is the number?

Answers

If 22 is the geometric mean of a number and four times the number, then the number is 11.

Geometric mean, like arithmetic mean, is a kind of average and a measure of central tendency.

To solve for the geometric mean, we multiply the numbers together and then take a square root (for two numbers), cube root (for three numbers) etc. In other words, geometric mean is the nth root of the product of n values.

The formula for the geometric mean is given by:

GM = n√x1 x2 . . . xn

Let x = x1 = unknown number

y = x2 = four times the number = 4x

Using the formula in solving geometric mean, plug in the values and variables.

GM = n√x1 x2 . . . xn

22 = √xy

22 = √x(4x)

22 = √4x^2

22 = 2x

x = 11

y = 4x

y = 44

Hence, the number is 11. 22 is the geometric mean of 11 and 44.

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Solve: x+2/x-4<0 A –4 < x < –2 B –2 < x < 4 C –2 < x < –4 D –4 < x < 2

Answers

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Solve: x+2/x-4<0
A –4 < x < –2
B –2 < x < 4
C –2 < x < –4
D –4 < x < 2