Explain why the solution set of the inequality |x|<5 is the intersection of two sets, while the solution set of the inequality |x|>5 is the union of two sets.The solution of |x|<5 is the set of numbers that makes either of two inequalities true. The solution set of |x|>5 is the set of numbers that makes both of two inequalities true. The solution of |x|<5 is the set of numbers between 5 and 5. The solution set of |x|>5 is the set of numbers greater than 5. The solution of |x|<5 is the set of numbers that makes both of two inequalities true. The solution of |x|>5 is the set of numbers that makes either of two inequalities true. The solution of |x|<5 is the set of numbers less than 5. The solution of |x|>5 is the set of numbers between 5 and 5.

Answer:The solution of |x|<5 is the set of numbers that makes both of two inequalities true. The solution of |x|>5 is the set of numbers that makes either of two inequalities true.Step-by-step explanation:

Mathematics High School

Explain why the solution set of the inequality |x|<5 is the intersection of two sets, while the solution set of the inequality |x|>5 is the union of two sets.The solution of |x|<5 is the set of numbers that makes either of two inequalities true. The solution set of |x|>5 is the set of numbers that makes both of two inequalities true. The solution of |x|<5 is the set of numbers between −5 and 5. The solution set of |x|>5 is the set of numbers greater than 5. The solution of |x|<5 is the set of numbers that makes both of two inequalities true. The solution of |x|>5 is the set of numbers that makes either of two inequalities true. The solution of |x|<5 is the set of numbers less than −5. The solution of |x|>5 is the set of numbers between −5 and 5.

Answers

Answer 1

Answer:

The region of the $|x|<5$ is the common area between -5 and 5.

But there is no common area for the solution of $|x|>5$.

Step-by-step explanation:

Given two modulus functions:

$1.\ |x|<5\\2.\ |x|>5$

Let us have a look at the definition of modulus function first:

$|x|=\left \{ {-{x}\ if\ x<0 \atop {x}\ if\ x>0} \right.$

Now, solving the above given modulus functions one by one using the definition of modulus function.

Solution 1 :

$\pm x <5\\\Rightarrow x<5, -x<5\\OR\\\Rightarrow x<5, x>-5$

Kindly refer to the attached diagram for solution.

The area shaded in the green color shows the solution for this equation.

Solution 2 :

$\pm x >5\\\Rightarrow x>5, -x>5\\OR\\\Rightarrow x>5, x<-5$

Kindly refer to the attached diagram for solution.

The area shaded in the blue color shows the solution for this equation.

We can clearly observe that the region of the first equation is the common area between -5 and 5.

But there is no common area for the solution of the second equation.

Therefore, solution of $|x|<5$ has intersection and

solution of $|x|>5$ has union.

Explain Why The Solution Set Of The Inequality |x|<5 Is The Intersection Of Two Sets, While The Solution

Answer 2

Answer:

The solution of |x|<5 is the set of numbers that makes both of two inequalities true. The solution of |x|>5 is the set of numbers that makes either of two inequalities true.

Step-by-step explanation:

Related Questions

Suppose your soccer coach is ordering duffel bags online for your team. The online store charges $16.49 per bag plus $10.50

for shipping and handling of the order. Suppose x is the number of bags ordered and go is the total cost of the bags. Select

the function that models the relationship. Then select the cost of buying 12 bags.

Answer: g(x)=16.49x+10.50

Total cost of 12 bags

$208.38

Answers

Answer:

g(x) = $16.49x + $10.50

$208.38

Step-by-step explanation:

Given the following:

Cost per bag = $16.49

Shipping and handling fee = $10.50

Number of bags ordered = x

If g(x) = total cost of bags

Bag cost = cost per bag × number of bags ordered

Bag Cost = $16.49 * x = $16.49x

Shipping and handling fee = $10.50

Total cost of bags = Bag cost + shipping and handling fee

g(x) = $16.49x + $10.50

Where x is the number of bags ordered.

Therefore, total cost of 12 bags equals ;

g(12) = $16.49(12) + $10.50

g(12) = $197.88 + $10.50

g(12) = $208.38

Answer:

g(x)=16.49x+10.50

$208.38

Step-by-step explanation:

let the cost of x bags = g(x)

cost of one bag = $16.49

cost of x bags = $16.49x

shipping and handling charges = $10.50

total cost of x bags = 16.49x + 10.50

g(x) = 16.49x + 10.50

To determine the cost of 12 bags, substitute x with 12 and simplify:

g(12) = 16.49(12) + 10.50

= 208.38

Mark bought groceries two days during the week.
.
Mark purchased $15.00 worth of groceries and paid $17.10 after taxes on Monday.

Mark paid $51.30 after taxes on a purchase of groceries that cost $ 45.00 on Friday

Which equation models the relationship between y, the cost of the groceries after taxes,
and x, the cost of the groceries before taxes?

A. y=0.15x
B. y=1.14x + 0.15
C. y=1.14x
D. y=.015x + 17.10

Answers

Answer:

Its either A or C

Step-by-step explanation: times the 45.00 x 0.15 and then try 45.00 x 1.14 it will give you the answer :D

If the scale factor of figure A to figure B is 3:8 find the value of x

Answers

If the scale factor of figure A to figure B is 3:8, the value of x is 9.

We are given Figure A and Figure B, along with their respective scale factors. To solve the problem, we must utilize the proportion rule. The ratio of the two figures is 3:8, so we can write the equation for proportion as follows -

3/8 = x/24

Applying the cross-multiplication rule, we get,

3 * 24 = 8 * x

Further solving for the value of x, we get,

x = (3 * 24) / 8

x = 9

Hence, the value of x is 9.

Answers

The expression which is equivalent to 8x²√375x + 2³√3x^7 if x = 0 is; 0.

Which expression is equivalent to the expression given?

According to the task content, the expression given is; 8x²√375x + 2³√3x^7.

On this note, it follows that when x=0 is substituted into the expression; the evaluation amounts to zero, 0.

Answers

To approximate the integral ∫[0,2] ln(x^3+2) dx using Romberg integration with an O(h^4) approximation, we can construct a Romberg integration table and perform the necessary calculations.

Romberg integration is a numerical method that uses a combination of Richardson extrapolation and the trapezoidal rule to estimate definite integrals. The method involves creating a table of approximations with progressively smaller step sizes (h) and refining the estimates using a recursive formula.

To find an O(h^4) approximation, we can start by setting up the Romberg integration table with different step sizes. The table will contain different approximations at each level, and the final result will be in the last column.

Using the Romberg integration method, the O(h^4) approximation for the given integral is 3.01389.

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Help me with this please.

Answers

yeskcpowp kecksowofi h wncksorigud meocosuebd wkxos

In the figure below, O is between Mand P, and N is the midpoint of MO. IF NO = 3 and MP=10, find OP.
show work please and you will get brainliest✌

Answers

Answer:

Step-by-step explanation:

Since N to O is 3 and N is the midpoint of MO then M to N would be 3 as well. So that means M to O is 6 leaving 4 left.

im very lost amd i just want a quick answer.

Answers

An angle bisector is a line that divides an angle into two equal parts

From the figure attached, we will observe that Line RU bisects Angle TRP into two parts (TRU & PRU)

Hence, the corect answer is a. (RU)

Gravel is being dumped from a conveyor belt at a rate of 25 ft3/min, and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast (in ft/min) is the height of the pile increasing when the pile is 11 ft high

Answers

When the pile of gravel, in the shape of a cone with equal base diameter and height, reaches a height of 11 feet, the height of the pile is increasing at a rate of 60/121π feet per minute. This rate indicates how fast the height of the pile is increasing at that specific height.

Let the height and radius of the cone be h and r respectively. Then the volume V of the cone is given by; V = 1/3 πr²h. Also given, the coarseness is such that the base diameter and height are always equal. Therefore, r = h/2. Also, given that gravel is being dumped at a rate of 25 ft³/min. The rate of change of volume with respect to time is given by; dV/dt = 25 ft³/min.

We need to find the rate at which the height of the pile is increasing when the height of the pile is 11 feet. Now we will find the relation between V and h;

V = 1/3 πr²hV = 1/3 π(h/2)²hV = 1/12 πh³.

Now differentiate both sides of the equation with respect to time;

dV/dt = d/dt (1/12 πh³)

dV/dt = 1/4 πh² dh/dt

From equation (1); dV/dt = 25 ft³/min

dV/dt = 1/4 πh²

dh/dt25 = 1/4 π(11/2)² dh/dt

dh/dt = 60/121π feet per minute.

Therefore, the height of the pile is increasing at a rate of 60/121π feet per minute when the height of the pile is 11 feet.

The concept used to solve this problem is related rates.

In related rates problems, we are given the rates at which certain variables are changing and we are asked to find the rate at which another variable is changing. To solve such problems, we typically set up an equation that relates the variables and then differentiate both sides of the equation with respect to time.

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What is the measure of each angle?

plz hurry and this will be 40 points :D

Answers

Answer:

27 and 63 degrees

Step-by-step explanation:

What additional information would be necessary to determine sin a without using the Pythagorean theorem explain brainly?

Answers

The Pythagorean Theorem, often known as Pythagoras Theorem, is a crucial concept in mathematics that describes how the sides of a right-angled triangle relate to one another. Pythagorean triples are another name for the sides of the right triangle. Here, examples help to demonstrate the formula and proof of this theorem.

In essence, the Pythagorean theorem is used to determine a triangle's angle and length of an unknown side. This theorem allows us to obtain the hypotenuse, perpendicular, and base formulae.

In order to determine sin a without using the Pythagorean theorem, we will need to have the value of the opposite side and angle. Sin (a) = opposite / hypotenuseHere, the hypotenuse is not given, so we will need to have the value of the opposite side and angle (a) in order to determine sin a without using the Pythagorean theorem.

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Can you please help me

Answers

Answer:

it would be the first one because it has a value of 1,966. and the second one has a value of 983 so the first one would be the one with the greater value

A chocolatier makes chocolate bon-bons in the shape of a sphere with a radius of 0.8 cm. the chocolate used in the bon-bons has a density of 1.3 g/cm 3 3 . if the chocolate used costs $0.03 per gram, how much would the chocolate for 110 bon-bons cost, to the nearest cent?

Answers

The cost of the chocolate for 110 bon-bons as per given radius , density and cost is equal to $8.80 to the nearest cent.

Volume of a sphere with radius r is ,

V = ( 4/3 )πr³

Radius 'r' of each chocolate bon-bon is 0.8 cm,

Volume of each bon-bon is equals to,

V = ( 4/3 )π (0.8)³

= 2.144 cm³

Density 'ρ' of the chocolate is 1.3 g/cm^3,

Mass 'm' of each bon-bon is equals to,

m = ρV

= ( 1.3 ) ( 2.144 )

= 2.78grams

The cost of the chocolate used in each bon-bon is $0.03 per gram,

This implies,

Cost of the chocolate used in one bon-bon is ,

= ( 0.03 ) × 2.78

= 0.0834

Rounding to the nearest cent, the cost of the chocolate for one bon-bon is $0.08.

Cost of the chocolate for 110 bon-bons,

= 110 × 0.08

= 8.8

Therefore, the chocolate for 110 bon-bons would cost $8.80 to the nearest cent.

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What equation represents a population of 300 animals at the crease and an annual rate of 23%

Answers

the population of the animals would increase by 69 annually (23% of 300= 69)

The absolute maximum value of f(x) = x3 - 3x2 + 12 on the closed interval (-2,4) occurs at what point?

Answers

The absolute maximum value of the function f(x) = x^3 - 3x^2 + 12 on the closed interval (-2, 4) occurs at x = 4.

To find the absolute maximum value of the function f(x) = x^3 - 3x^2 + 12 on the closed interval (-2, 4), we can find the critical points of the function within the interval and check the endpoints of the interval. A critical point is a value of x where the first derivative of the function is equal to zero or is undefined.

First we will find the first derivative of the function:

f'(x) = 3x^2 - 6x

The critical points occur when the first derivative is equal to zero:

3x^2 - 6x = 0

x(3x - 6) = 0

x = 0, x = 2

We now need to check if these critical points are maximum or minimum points. For this we need to calculate the second derivative of the function:

f''(x) = 6x - 6

If the second derivative at a critical point is positive, the critical point is a local minimum. If the second derivative at a critical point is negative, the critical point is a local maximum.

f''(0) = 60 - 6 = -6

f''(2) = 62 - 6 = 6

We can see that the second derivative at x = 2 is positive and the second derivative at x = 0 is negative, therefore x = 2 is a local minimum and x = 0 is a local maximum.

Now we need to check the endpoints of the interval to see if they are the absolute maximum or minimum

(-2)^3 - 3(-2)^2 + 12 = -2 - 12 + 12 = -2

(4)^3 - 3(4)^2 + 12 = 64 - 48 + 12 = 28

We can see that the maximum value of the function is 28 at x = 4 and the minimum value of the function is -2 at x = -2, so the absolute maximum value of the function f(x) = x^3 - 3x^2 + 12 on the closed interval (-2, 4) occurs at x = 4.

Therefore, The absolute maximum value of the function f(x) = x^3 - 3x^2 + 12 on the closed interval (-2, 4) occurs at x = 4.

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Round the decimal 7.16 ?

Answers

Answer:

7(nearest whole number)

7.2(1 decimal place)

URGENT PLS HELP

What is the result when 8.06 is subtracted from 22.92

Answers

Answer:

14.86 is the answer..............

Answer:

-14.86

hope this helps :)

A number more than 12
#1. N+12
#2. 12N
#3. 12+N
#4. 12-N

Answers

Answer:

#3: 12 + N

Step-by-step explanation:

Adding a number n to 12 results in "a number more than 12."

Thus, the correct answer is #3.

Suppose you brought 8 oranges and 1 grapefruit for a total price of $4.60. Later that day, you brought 6 oranges and 3 grapefruits for a total price of $4.80.What's the price of each type of fruit.

Answers

Answer:

assuming the prices did not change during the day,

8o+g=460

6o+3g=480

18o=900

o=50

g=60

so, oranges cost $0.50, grapefruit cost $0.60

Step-by-step explanation:

do good !

Answer:

oranges $0.5 grapefruit 0.6

Step-by-step explanation:

o = oranges

g= grapefruit

8o +1 g = 4.60

6o+3g= 4.80

Multiply the first by -3

-24o -3g = -13.80

6o +3g = 4.80

ADD BOTH (3g will be cancelled)

-18o = -9.00

o = 9/18 = 0.5

8(0.5) +1g= 4.60

4.00 +g = 4.60

g = 0.60

(-3,3) and m = 4
what is this in slope intercept form?

Answers

Answer:

y=4x

Step-by-step explanation:

I hope this answers your question.

If the circumference
of a circle is
62.8 feet, what is the radius of the
circle?
Use 3.14 for I.
Hint: C = 2Tr
radius-12] foot
Please explain how you got the answer for future problems

Answers

Answer:

Hope you like my answer

Answer:

radius = 10 feet

Step-by-step explanation:

C represents the circumference.

C = 2πr ,where r is the radius.

We are given C = 62.8 ft

Equating the two expressions of C :

2πr = 62.8

Then

2 × 3.14 × r = 62.8

Then

6.28 × r = 62.8

Then

$r = \frac{62.8}{6.28} = 10$

Given the following LP model, which is the correct standard form? Max(Z)=2X1+X2 Restrictions / Constrains 11×1+3×2≥33
8×1+5×2≤40
7×1+10×2≤70
7×1+10×2≤70 X1,X2≥0 Use this problem's information to answer questions 19 to 21. a. Max(Z)=3×1+2X2
11×1+3×2−51≤33
8×1+5×2+52≥40
7×1+10×2+53≥70
b. Max(Z)=3×1+2×2 11×1+3×2+51=33 8×1+5×2−52=40 7×1+10×2−53=70
c. Max(Z)=3×1+2×2 11×1+3×2−51=33 8×1+5×2+52=40 7×1+10×2+53=70
d. Max(Z)=3×1+2×2 11X1+3×2+$1=33 8×1+5×2+52=40 7×1+10×2+53=70

Answers

The correct standard form for the given LP model is option C: Max(Z) = 3x1 + 2x2, subject to the constraints 11x1 + 3x2 - 5 <= 33, 8x1 + 5x2 + 5 >= 40, and 7x1 + 10x2 + 5 >= 70, with x1, x2 >= 0. This option aligns with the original objective function and constraints of the LP model.

To convert the LP model into standard form, we need to rewrite the constraints with the variables on the left-hand side and constants on the right-hand side, with inequality signs (<= or >=) consistent throughout. Additionally, we introduce slack or surplus variables to transform any non-standard constraints.

In option C, the constraints are correctly transformed as 11x1 + 3x2 - 5 = 33, 8x1 + 5x2 + 5 >= 40, and 7x1 + 10x2 + 5 >= 70. These constraints are consistent with the original model. The objective function remains the same, Max(Z) = 3x1 + 2x2.

Option A has incorrect signs in the transformed constraints, and option B introduces surplus variables (+5) instead of slack variables (-5), resulting in an incorrect standard form. Option D includes a non-standard term with a dollar sign, which is inconsistent with linear programming conventions.

Therefore, option C is the correct standard form, adhering to the original LP model's objective function and constraints.

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Define the domain of the following:

{-2, -1, 0, 2, 5}

{-2, -1, 0, 1, 2, 3, 4, 5}

All Real Numbers

{3, -1, 3, 1, 2}

Answers

The domain of the relation in the graph is:

{-2, -1, 0, 2, 5}

How to define the domain for the graph?

A relation maps elements from one set (the domain) into elements from another set (the range).

Such that the domain is represented in the horizontal axis.

In the graph, we can see the points:

{(-2, -3), (-1, -1), (0, 3), (2, 1), (5, 2)}

The domain is the set of the first values of these points, then the domain is:

{-2, -1, 0, 2, 5}

The correct option is the first one.

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m∠2 = 4x + 4 and m∠1 = 5x − 2. Find x.

SHOW WORK

I ONLY NEED THE WORK!!!!!

Answers

Answer:

x = 6

Step-by-step explanation:

angles 1 and 2 are equal because the entire angle is bisected

so, 5x - 2 = 4x + 4

x - 2 = 4

x = 6

If you substitute 6 into each expression, they should be equal:

4(6) + 4 = 5(6) - 2

24 + 4 = 30 - 2

28 = 28

help needed. with show work

Answers

Check out the attached photo

Mrs jack bought 150 t-shirts for $18,712.50 from a factory she then sold each t-shirt for $199.9.How much for one t - shirt

Answers

5 binders
Step-by-step explanation:
(244.94 -199.99) / 8.99

please help i am confused

Answers

Answer:

The last answer.

Step-by-step explanation:

Regular means all the side lenghts are the same and all the interior angle measures are the same. Think a stop sign.

Irregular polygons have different side lengths and different interior angle measures.

All interior angles and sides are congruent

(Laws of Exponents with Integer Exponents MC)

Create an equivalent expression for five sevenths raised to the negative first power times eighteen hundredths raised to the second power.

(1.4)(0.18)2
(0.714)(0.18)2
seven fifths raised to the first power times the quantity one over eighteen hundredths raised to the second power
0.02

Answers

The equivalent expression of the expression given as five sevenths raised to the negative first power times eighteen hundredths raised to the second power is (a) (1.4) * (0.18)^2

How to determine the equivalent expression?

The expression is given as:

five sevenths raised to the negative first power times eighteen hundredths raised to the second power.

Mathematically, the expression is:

(5/7)^-1 * (18/100)^2

Apply the law of exponent

(7/5)^1 * (18/100)^2

Divide 7 by 5

(1.4)^1 * (18/100)^2

Evaluate the exponent

(1.4) * (18/100)^2

Divide 18 by 100

(1.4) * (0.18)^2

Hence, the equivalent expression of the expression given as five sevenths raised to the negative first power times eighteen hundredths raised to the second power is (a) (1.4) * (0.18)^2

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if 20m2 square of carpet cost 36, find the cost of 35m square and 15m square

Answers

Answer: 63 and 27.

Step-by-step explanation:

1 m² of carpet will cost:

$\displaystyle\\\frac{36}{20} =1,8.\\\\Hence,\\$

35 m² of carpet will cost:

$1,8*35=63.\\$

15 m² of carpet will cost:

$1,8*15=27.$

What are 2 properties of cheese that make it addictive?

Answers

The presence of casomorphins and the stimulation of dopamine release, contribute to the addictive nature of cheese, making it difficult to resist for many individuals.

Cheese possesses two properties that contribute to its addictive nature. Firstly, cheese contains casein, a protein found in milk, which breaks down during digestion to produce casomorphins. Casomorphins are opioid-like substances that can bind to the brain's opioid receptors, leading to feelings of relaxation and pleasure. This mechanism is similar to the effects of addictive drugs, reinforcing the craving for cheese.

Secondly, cheese is rich in fat, particularly saturated fats. These fats have been shown to stimulate the release of dopamine, a neurotransmitter associated with pleasure and reward, in the brain. The combination of the creamy texture and the release of dopamine creates a pleasurable sensory experience, further enhancing the appeal of cheese.

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