Define the set X = {(x,y)|x > 0,y ≤ √x}.
(a) Sketch the set X in a graph.
(b) Is the set X convex? Explain why or why not.
(c) Is it closed? Explain why or why not. (d) Is it bounded? Explain why or why not. (e) Is it compact? Explain why or why not.

Answers

Answer 1

The set X is convex.

In geometry, a subset of an affine space over the real numbers, or more broadly a subset of a Euclidean space, is said to be convex if it contains the entire line segment connecting any two points in the subset. A solid cube is an example of a convex set, whereas anything hollow or with an indent, such as a crescent shape, is not. Alternatively, a convex region is a subset that crosses every line into a single line segment.

b)The set X is convex as any two points on the set X is included in the whole set as x>0. So a line joining any two points on the set X is completely inside the set x.

c)set X is not a closed set as the compliment of the set is not an open set.

d)Set X is not bounded. If a set S contains both upper and lower bounds, it is said to be bounded. A set of real numbers is therefore said to be bounded if it fits inside a defined range. hence set x is not bounded.

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Define The Set X = {(x,y)|x > 0,y X}.(a) Sketch The Set X In A Graph.(b) Is The Set X Convex? Explain

Related Questions

Select the action you would use to solve x-4=16 then select property that justifies the action

Answers

The value of x is 64 and the property that justifies that action is the multiplication property of equality.

What is an expression?

It is defined as the combination of constants and variables with mathematical operators.

Mathematical statements are called expressions if they contain at least two terms that are connected by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.

As an illustration, the expression x + y is one where x and y are terms with an addition operator in between. There are two types of expressions in mathematics: numerical expressions, which only contain numbers, and algebraic expressions, which also include variables.

We have an expression:

x/4 = 16

Apply Multiplication property of equality:

Multiply by 4 on both sides:

(x/4)4 = 16×4

x = 64

Thus, the value of x is 64 and the property that justifies that action is the multiplication property of equality option (1) is correct.

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Rewrite the expression [tex]\sqrt (4x)}[/tex] using rational exponents

Answers

The expression √4x using rational exponents ( 4x )^{\frac{1}{2} } .

What is rational exponents?

Expressions having exponents that are rational values are known as rational exponents (also known as fractional exponents) (as opposed to integers ). It is beneficial to give rational exponents serious consideration even though all the standard exponent criteria still apply.

What is Integer Exponents?

In mathematics, exponents that should be integers are known as integer exponents. It may be an integer that is either positive or negative. It specifies how many times the base number should be multiplied by itself using positive integer exponents.

√4x

use [tex]\sqrt[n]{a^{x} } = a^{x/n}[/tex]

to rewrite

√4x = [tex]( 4x )^{\frac{1}{2} }[/tex]

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Algebra (4224_EOZ1)
HW Score: 88.89%, 16 of 18 points
O Points: 0 of 1
By air, the distance from city A to city B is 3003 miles less than the distance from city C to city D. If the total of these two distances is 7827 miles, find the distance from city C to city D
ework 2: 3.3 & 3.4
Brooke Conti
Question 14, 3.4.35
09/06/22 7:12

Answers

The Distance between city C and city D is 5405 miles.

Given that Distance from city a to city b is 3003 miles less than the Distance fron city c to city d, the total of these two Distance is 7807 miles and asked to find Distance between city C and city D.

Given that,

(d-c)-(b-a)=3,003 miles { (Distance between city D and city C)-(Distance between city A and city B)} Let's assume it as equation A

(d-c)+(b-a)=7,807 miles { (Distance between city D and city C)+(Distance between city A and city B)} Let's assume it as equation B

Add equation A and B

2(d-c)=10,810

(d-c)=5,405

Hence,Distance between city D and city C is 5,405

Therefore,The Distance between city C and city D is 5405 miles.

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Describe the features of a Cartesian Plane in terms of its axes, the direction of the axes and its centre.

Answers

Answer:

A Cartesian Plane is a plane in Geometry which is an flat surface of infinite size. It has two number lines that intersect at right angles at their zeros. One number line is horizontal, and the other number line is vertical. The point of intersection is the zero of each line. In the horizontal line, the numbers increase to the right. In the vertical line, the numbers increase up. The horizontal line is called the x axis. The vertical line is called the y axis. The center of the Cartesian Plane is the intersection of the two axes, the two number lines, and is called the origin. Points on the Cartesian Plane are described with two numbers in parentheses separated by a comma. The position of the point in the Cartesian Plane is given by the first number, called the x-coordinate, telling us the number of units to the right (positive) or left (negative) of the origin and by the second number, called the y-coordinate, telling us the number of units up (positive) or down (negative) from the origin.

Line A and Line B are parallel. Line P is a transversal. If the measure of angle 8 is 140°, find the measures of the rest of the angles in the diagram. Then tell what the angle relationship is to angle 8.

Answers

The angle measures are;

Angle 7 is 40° = Angles 8 : supplementary

Angle 3 is 40° = Angles 8: supplementary angles

Angle 5 = 140° = Angle 8; corresponding angles

Angle 1 = 140° = Angle 8; corresponding angles

Angle 6 = 40° = Angle 8; supplementary angles

Angle 2 = 140° = Angle 8; corresponding angles

Angle 4 = 140° Angle 8; corresponding angles

How to determine the angles

Given that angle 8 measures 140 degrees

It is important to note that angles on a straight line equals 180 degrees

Then,

angle 7 + angle 8 = 180°

Substitute the values of angle 8

Angle 7 + 140 = 180

Angle 7 = 180 - 140

Angle 7 = 40°

Thus, If angle 7 is 40° then angle 3 is 40°, corresponding angles

Angle 5 = Angle 8; corresponding angles

Angle 1 = Angle 8; corresponding angles

Angle 6 = Angle 7; corresponding angles

Angle 2 = Angle 8; corresponding angles

Angle 4 = Angle 8; corresponding angles

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the difference of a number and eight is four. Find the number.

Answers

I think it might be two if you take 8 and divide it by 4 then it should equal two or 1/2 if we are doing relationships between numbers hope this helps

=
Find the exact value of the expression. Do not use a calculator.
sin 26° - cos 64°
sin 26° - cos 64° =
=
(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)

Answers

The value of the expression is 0 without calculation.

We have to find the exact value of

sin 26° - cos 26°

From the trigonometric function we know that:

cos (90°-Ф) = sinФ and,

sin(90° -Ф) = cosФ

By this, we have an expression that,

=sin 26° - cos 64°

=sin 26° - cos (90° - 26)

=sin 26° - sin 26°

Therefore the value of sin 26° - cos 64° =0.

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What proportion of people surveyed would be willing to pay more than $6.75 for a sandwich?

Answers

The proportion of people surveyed would be willing to pay more than $6.75 for a sandwich is 94.4%.

What is termed as normal distribution?

The normal distribution, also recognized as the Gaussian distribution, is a symmetric probability distribution about the mean, indicating that data near the mean occur more frequently than data far from the mean.

Early statisticians started to notice the same shape recurring in different distributions and designated it the normal distribution. Normal distributions are distinguished by their symmetric bell shape. The mean and median are the same; they are both in the middle of the distribution.

As, for the given value in the question;

The formula for finding the z-score is;

z = (x - μ)/s

where,

n = sample size ( = 528)

σ = standard deviation ( = 1.19)

μ = mean of the sample (= 6.56)

Put the values and fine z-score.

z = (x - μ)/s

z = (6.75 - 6.56)/1.19

z = 0.19/1.19

z = 0.159

For the probability; see the p-value from the positive z-score table.

p(z > 0.159) = 0.944

p(z > 0.159) = 94.4%

Thus, the probability that the people would be willing to pay more than $6.75 for a sandwich is calculated as 94.4%.

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The complete question is -

A sample of 528 people were asked how much they would be willing to pay for a sandwich. Their responses were approximately normal with a mean of $6.56 and a standard deviation of $ 1.19.

What proportion of people surveyed would be willing to pay more than $6.75 for a sandwich?

A rectangular garden is 6 ft longer than it is wide. Its area is 667 ft2. What are its dimensions?

Answers

The dimensions of the rectangular garden are 29 feet by 23 feet .

A rectangle is a quadrilateral with parallel opposite sides and equal angles. There are a lot of rectangular objects all around us. Any rectangular form's two defining characteristics are its length and width. A rectangle's longer and shorter sides are its width and length, respectively.

The area of a rectangle is given by length × width

Now the given area of the rectangle is 667 ft² .

Let the width of the rectangle is x ft. Therefore length = x + 6

Now area of the rectangle is x (x+6) = x² + 6 x

Therefore x² + 6 x = 667

or, x² + 6 x - 667 = 0

or, (x-23)(x+29) = 0

Either x = 23 or x = -29(not possible)

Hence the width is 23 feet.

Length = 23 + 6 = 29 feet

Therefore the dimensions of the rectangle are 29 feet by 23 feet .

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3. What is one question you can ask yourself if you find you are making an irrational
decision because of the endowment effect?

Answers

Answer:

Asking yourself how much you'd be willing to spend if someone else offered you a similar product.

What is x in this equation .3=.5x-.7

Answers

By solving the linear equation it can be obtained that

The value of x is 2

What is a linear equation?

At first it is important to know about equation

Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.

A one degree equation is known as linear equation.

The given linear equation is

0.3 = 0.5x - 0.7

0.5x = 0.3 + 0.7

0.5x = 1

x = [tex]\frac{1}{0.5}[/tex]

x = 2

The solution of this linear equation is x = 2

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If f(x) = -2x² + 4 and g(x) = 3x - 3, find f (4) + g(-6).

Answers

Answer:

(-2[tex]x^{2}[/tex]+3x+1)

Step-by-step explanation:

f(x) = -2x² + 4 g(x) = 3x - 3 find f (4) + g(-6).

f(x)+g(x)

(-2[tex]x^{2}[/tex]+4) +(3x-3)

(-2[tex]x^{2}[/tex]+3x+4-3)

(-2[tex]x^{2}[/tex]+3x+1)

3-11-(-6) subtract this and thank youuuuuu

Answers

Answer:

3-11-(-6)

the answer will be

-2

Which of the following could be the rectangle's length and width?
(Area = length x width)
Choose all answers that apply:

A) 1 cm and 15 cm
B) 2 cm and 7 cm
C) 3 cm and 5 cm
D) 4 cm and 4 cm

Answers

The possible rectangle's length and width are A) 1 cm and 15 cm and C) 3 cm and 5 cm

How to determine the possible rectangle's length and width?

The given parameters are

Area = 15 square cm

The area is given as

Area = 15 square cm

The formula of area is

Area = Length x Width

Using the above formula, we have:

A) 1 cm and 15 cm ⇒ 15 square cm

B) 2 cm and 7 cm ⇒ 14 square cm

C) 3 cm and 5 cm ⇒ 15 square cm

D) 4 cm and 4 cm ⇒ 16 square cm

Hence, the possible rectangle's length and width are A) 1 cm and 15 cm and C) 3 cm and 5 cm

Answers

APY for Kevin's account = 1.67%

The interest on a loan or deposit that is computed based on both the original principle and the accumulated interest from prior periods is known as compound interest (also known as compounding interest). Compared to simple interest, which is computed just on the principal amount, it will cause a sum to increase more quickly.

The frequency of compounding determines the pace at which compound interest accumulates. The compound interest increases with the number of compounding periods.

APY = [tex](1 + \frac{r}{n})^{n} - 1[/tex] = [tex](1 + \frac{1.667}{365})^{365} - 1[/tex] = 1.0167 - 1 = 0.0167

APY = 1.67%

Therefore, APY for Kevin's account = 1.67%

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Anna and Julia are at point P. Point Q is due North of point P. They disagree about the shortest route from P to Q. Anna walks on a bearing of 330°, and then changes to a bearing of 040°, which takes her straight to Q. Julia walks 3 km on a bearing of 0200, after which she walks on a bearing of 300°, which then takes her straight to Q. Who took the shorter route?

Answers

The Shorter route as per the bearing calculations is taken up by Julia.

What is a bearing?

The angle from the north line, expressed in degrees, is the correct bearing to a given point. The real bearing will simply be referred to as the bearing.A point's bearing is the number of degrees inside the angle measured counterclockwise from the north line towards the line connecting the point and the compass's center.When describing the direction from one point in relation to another, a bearing is utilized.

Bearing calculations are illustrated below:

Route Taken up by Anna

360-330= 30°

First angle =90-30= 60°

Second angle= 60+(90-40) =110°

Third angle= 180-(110+30)= 40°

Route taken up by Julia:

First angle =20°

Second angle= 300-(180+20)=100°

Third angle=180-(20+100)=60°

Hence, the Shorter route as per the bearing calculations is taken up by Julia and bearing diagram is attached with the solution as an image.

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√₂
You invested $7000 between two accounts paying 5% and 8% annual interest, respectively. If the total interest
earned for the year was $500, how much was invested at each rate?
was invested at 5% and $ was invested at 8%.
Save
>

Answers

Answer:

$2000 was invested at 5% and $5000 was invested at 8%.

Step-by-step explanation:

Assuming the interest is simple interest.

Simple Interest Formula

I = Prt

where:

I = interest earned.P = principal invested.r = interest rate (in decimal form).t = time (in years).

Given:

Total P = $7000P₁ = principal invested at 5%P₂ = principal invested at 8%Total interest = $500r₁ = 5% = 0.05r₂ = 8% = 0.08t = 1 year

Create two equations from the given information:

[tex]\textsf{Equation 1}: \quad \sf P_1+P_2=7000[/tex]

[tex]\textsf{Equation 2}: \quad \sf P_1r_1t+P_2r_2t=I\implies 0.05P_1+0.08P_2=500[/tex]

Rewrite Equation 1 to make P₁ the subject:

[tex]\implies \sf P_1=7000-P_2[/tex]

Substitute this into Equation 2 and solve for P₂:

[tex]\implies \sf 0.05(7000-P_2)+0.08P_2=500[/tex]

[tex]\implies \sf 350-0.05P_2+0.08P_2=500[/tex]

[tex]\implies \sf 0.03P_2=150[/tex]

[tex]\implies \sf P_2=\dfrac{150}{0.03}[/tex]

[tex]\implies \sf P_2=5000[/tex]

Substitute the found value of P₂ into Equation 1 and solve for P₁:

[tex]\implies \sf P_1+5000=7000[/tex]

[tex]\implies \sf P_1=7000-5000[/tex]

[tex]\implies \sf P_1 = 2000[/tex]

$2000 was invested at 5% and $5000 was invested at 8%.

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The equation 2x2−6x−9=0 has two solutions.

Answers

The solution to the given equation is 3±3√3/2

Solving quadratic equation

Given the quadratic equation below

2x^2−6x−9=0

Solve using the general formula to have:

a = 2

b = -6

c = -9

Substitute

x = -b±√b²-4ac/2a

x = -(-6)±√(-6)²-4(2)(-9)/2(2)

x = 6±√36+72/4

x = 6±√108/4

x = 6±6√3/4

x = 3±3√3/2

Hence the solution to the given equation is 3±3√3/2

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Liam wants to buy raspberries and pears to make a fruit tart. Raspberries cost $2.50
per pound and pears cost $2.25 per pound. How much does he spend if he buys 3
ppunds of raspberries and 2 pounds of pears? How much does he spend if he buys a
pounds of raspberries and y pounds of pears?

Answers

He spends x pounds of Raspberries and y pounds of pears, then the equation can be 2.5x + 2.25 y

What is algebra?

Algebra is the part of mathematics that helps represent problems or situations in the form of mathematical expressions.

Given:

Raspberries cost $2.50 per pound

pears cost $2.25 per pound

so, she spends

=2.5 * 3 + 2.25 *2

=7.5+4.5

=$12

If he spends x pounds of Raspberries and y pounds of pears.

then the equation can be

2.5x + 2.25 y

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determine the range of the following graph, help me please!!

Answers

Answer: Range: -9<=y<=-4

Step-by-step explanation:

Starts at (-5,-4), ends at (3, -9). Look at the y-coordinates

Range starts at y=-4, ends at y=-9. In the graph, there are no y-coordinates that are greater than -4 and less than -9.

Range: -9<=y<=-4

Answer:

-9 ≤ y ≤ -4

Step-by-step explanation:

Hello!

The range is the set of y-values that the graph goes through.

The minimum y-value of this graph is -9, and the maximum y-value is -4. Since the endpoints are filled in, we use the ≥ or ≤ symbols to write the inequality.

The inequality is -9 ≤ y ≤ -4.

Suppose there are 17 jelly beans in a box—2 red, 4 blue, 4 white, and 7 green.

What part of the jelly beans is blue? Express your answer in each of the forms requested.

As a fraction ____

Hint: To enter a fraction, use the forward slash button on the keyboard.

As a decimal rounded to the nearest ten-thousandth (four decimal places). _______

As a percentage rounded to the nearest hundredth (two decimal places) ______

Answers

Answer: 4/17

0.2353

0.24

Step-by-step explanation:

4 blue jelly beans. 17 total jelly beans.

4/17=0.235294

0.235294=0.2353

0.2353=0.24

if 3 equal 8 what will equal 600

Answers

Answer:

if 3 equal 8 , then 600 will be 1600.

2 times 300 equals 600

help asap question in picture

Answers

[tex] \: \Large \mathbb{SOLUTION:}[/tex]

[tex] \: \: \rm{ \bigg( - \frac{5}{3} \bigg) {}^{2} } \\ [/tex]

[tex] \: \: \text{Determine the sign for exponential or radical expreasions}[/tex]

[tex] \: \: \rm{ \bigg( \frac{5}{3} \bigg) {}^{2} } \\ [/tex]

[tex] \: \: \text{Calculate the power}[/tex]

[tex] \: \: \rm \boxed{ \frac{25}{9} } \\ [/tex]

Answer:

[tex] \frac{25}{9} \\ [/tex]

Solution:

Determine the sign

[tex]( -\frac{5}{3} ) {}^{2} [/tex]

[tex]( \frac{5}{3} ) {}^{2} [/tex]

[tex] \frac{5 {}^{2} }{3 {}^{2} } \\ [/tex]

[tex] \frac{25}{3 {}^{2} } \\ [/tex]

[tex] \frac{25}{9} \\ [/tex]

Please help, I don’t know how to solve this!

Answers

Carry the 4 and to the exponent of 2

Whats 1,250 - 250 x 2?

Answers

Answer:750

Step-by-step explanation:

multiply the numbers

1250-250x2

1250-500

subract the two numbers and you will get

750

1250 - 250 • 2

1250 - 500

750

Green Sun has net working capital of $400, current assets of $2,315, and inventory of $1,100. �What is the Quick ratio?

Answers

Answer:

3:5.7

Step-by-step explanation:

please Mark me as

Answer:

its not a accurate questions

cant be answered

Step-by-step explanation:

-4 + (-19) = ? I need a answer

Answers

Answer: - 23

Step-by-step explanation:

Hope this helps!

????????????????????

Answers

Answer: 120 minutes, 105 km, proportional

Step-by-step explanation:

90 km/hr

180 km * 1 hr/90 km=

180 km/90 km * 1 hr=

2 hours=120 minutes

1 hour=60 minutes

70/60=x/90

7/6=x/90

7*90/6=x

x=7*15

x=105 km

Adult tickets to the museum cost $4, while student tickets
cost $3. If 105 tickets were sold for a total of $380, how
many of each were sold?

Answers

65 adult tickets were sold whereas 40 student tickets were sold as well

What approach is appropriate to solve the word problem?

The most suitable approach to determine the number of each type of tickets sold is by simultaneous equation such the word problems are modelled into equations which are solved together to ascertain the number of adult and student tickets sold altogether

let x be adult tickets sold

let y be student tickets sold

x+y=105........ equation 1

4x+3y=380........ equation 2

from equation 1, x=105-y

substitute for x in equation 2

4(105-y)+3y=380

420-4y+3y=380

420-y=380

420-380=y

40=y

y=40

x=105-40

x=65

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Which of the following equations are equivalent to -2m - 5m - 8 = 3 + (-7) + m?

m - 4 = -7m - 8
-8 - 3m = 4 - m
-3m - 8 = 4 - m
-15m = -4m
-7m - 8 = m - 4
-8 - 7m = -4 + m
You can have multiple answers

Answers

The equation equivalent to -2m - 5m - 8 = 3 + (-7) + m is

-7m - 8 = m - 4. Option E

This is further explained below.

Which of the following equations are equivalent to -2m - 5m - 8 = 3 + (-7) + m?

Generally, the equations equivalence is mathematically given as

-2m - 5m - 8 = 3 + (-7) + m

Therefore

-7m - 8 = 3 + (-7) + m

When we write the equation such that the variable appears on the right-hand side first, we get the following:

-7m - 8 = m - 4

In conclusion, The equation equivalent to -2m - 5m - 8 = 3 + (-7) + m is

-7m - 8 = m - 4.

Define the set X = {(x,y)|x > 0,y ≤ √x}. (a) Sketch the set X in a graph. (b) Is the set X convex? Explain why or why not. (c) Is it closed? Explain why or why not. (d) Is it bounded? Explain why or why not. (e) Is it compact? Explain why or why not.

Answers

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Define the set X = {(x,y)|x > 0,y ≤ √x}.
(a) Sketch the set X in a graph.
(b) Is the set X convex? Explain why or why not.
(c) Is it closed? Explain why or why not. (d) Is it bounded? Explain why or why not. (e) Is it compact? Explain why or why not.