Match the inequality to its representation on a number line.
2. Write an inequality statement whose solution is an empty set.
6. Write an inequality statement to represent the graph shown.
en inequality statement to represent the graph shown.
4. Write an inequality statement whose solution is all real numbers. Graph the solution on a number line.
3. Write an inequality statement whose solution is some but not all real numbers. Graph the solution on a number line
9
Write an inequality statement whose solution is exactly one number. Graph the solution on a number line.

Answer: $6,992

Step-by-step explanation:

First you add 205 and 232 then multiply your answer by 16

The statements that are true is A,C,D

The area of the circle is defined as the product of the pie and the square of the radius.

The area of the circle = [tex]\pi r^{2}[/tex]

[tex]\pi[/tex]= 3.14

Given;

The length of the circumferences of the 3 holes is 38m millimeters. The large hole has a diameter of 14 millimeters

2[tex]\pi[/tex]R+2[tex]\pi[/tex]r+2[tex]\pi[/tex]r=38

R+2r=19/3.14...1

Radius of large hole=14/2=7mm

Substituting the value of R in equation 1

7+2r=19/3.14

2r=19*7/3.14

r=21.178

Therefore;

The small holes each have a radius of 12 millimeters.- True

The large hole has an area of approximately 615.5 square millimeters.-false

The combined length of the circumferences of the small holes is 24m millimeters.-True

The diameter of the large hole is 2 millimeters longer than that of each small hole.- True

Learn more about area of a composite figure here:

https://brainly.com/question/10254615

#SPJ1

Based on the function f(x) = 9x - 27, the input value when f(x) = 18 is equal to 5.

In Mathematics, a function can be defined as a mathematical expression which is typically used for defining and representing the relationship that exists between two or more variables such as an ordered pair in tables or relations.

In Mathematics, a domain is sometimes referred to as input value and it can be defined as the set of all real numbers for which a particular function is defined.

When the range (output value) of the given function f(x) = 9x - 27, the input value (domain) can be calculated as follows;

f(x) = 9x - 27

18 = 9x - 27

9x = 18 + 27

9x = 45

Input value, x = 45/9

Input value, x = 5

Read more on function here: https://brainly.com/question/9795474

#SPJ1

Exact values of csc θ=10/[tex]\sqrt{51}[/tex] and tan θ=       [tex]-\sqrt{5}/7[/tex]

Let θ be an angle in quadrant II such that cos θ = −7/10.

[tex](sinx^)^2 +(cosx)^2=1[/tex]

sin θ =[tex]\sqrt{51/100}[/tex]

cscθ=1/sinθ

cscθ=10/[tex]\sqrt{51}[/tex]

tanθ=sinθ/cosθ

tanθ= [tex]-\sqrt{5}/7[/tex]

Exact values of csc θ=10/[tex]\sqrt{51}[/tex] and tan θ=       [tex]-\sqrt{5}/7[/tex].

Learn more about quadrant,

https://brainly.com/question/30196267

Answer:187

Step-by-step explanation:

Writing 4⁻⁴ to have a positive exponent should be of the form 1/4⁴

In math, the term exponent refers to the number of times a certain number multiplies it self.

The number that is being multiplies is referred to as the base number while the number of times it multiplies itself is the exponents.

In the law of exponents, numbers with negative exponents will have positive when written in reciprocal form.

Because of this law, the number as in the problem is 4⁻⁴ the reciprocal form of this number is 1/4⁴ and the negative exponent vanishes

The positive exponent of the number is 4⁻⁴

Learn more about exponents at :

brainly.com/question/13669161

#SPJ1

Answer:

1/(4^4)

Step-by-step explanation:

A. Use the reciprocal of the base, then change the exponent to a positive number and place it with the number in the denominator.

No, the segments connecting points A, B, and C does not to form a right-angled triangle.

Mathematically, Pythagorean's theorem is given by this mathematical expression:

a² + b² = c²

Where:

a, b, and c represents the length of sides of a right-angled triangle.

In order for the segments connecting points A, B, and C to form a right-angled triangle, its side lengths must satisfy the Pythagorean's theorem:

AB² = (xB - xA)² + (yB - yA)²

AB² = (6 - (-2))² + (2 - 2)²

AB² = 8² + 0²

AB² = 8²

AB = 8

AC² = (xC - xA)² + (yC - A)²

AC² = (0 - (-2))² + (6 - 2)²

AC² = 2² + 4²

AC² = 4 + 16

AC = √20

BC² = (0 - 6)² + (6 - 2)²

BC² = (-6)² + 4²

BC² = 36 + 16

BC = √52

From Pythagorean's theorem, we have:

a² + b² = c²

√20² + √52² = 8²

20 + 52 = 64

72 ≠ 64 (False, not a right-angled triangle).

Read more on Pythagoras theorem here: brainly.com/question/16376191

#SPJ1

The 3 things, I noticed about parabola is given below.

A parabola is a curve drawn in a plane.

Where any point is at an equal distance from a fixed point (the focus) and a fixed straight line (the directrix)

We have a parabola.

From the graph of parabola:

1). The vertex of the parabola = (2, -5)

2). And the y-intercept = (0, 7)

3). The curve passes through (1, 2) and (3, 2).

Therefore, all the three points are given above.

To learn more about parabola;

https://brainly.com/question/21685473

#SPJ1

If an alloy is a mixture of different kinds of metal a company is going to produce an alloy that is 80% nickel . The number of pounds of iron that should be added is 640 grams.

Since 80% of the alloy is made of Iron and 20% is Nickel so,

Let x represent the total weight

160 grams = 20% × x

x = 160 / 20%

x = 800 grams

Iron should be 80% of the full weight of the alloy:

Pounds of iron = 80% x weight of Alloy x

Pounds of iron = 80% x 800 grams

Pounds of iron = 640 grams

Therefore  640 grams of Iron should be added.

Learn more about number of pounds of iron here:https://brainly.com/question/28369130

#SPJ1

Answer:

y = 8

Step-by-step explanation:

5x + 2y = -6 .... 5x = -6 - 2y ...... x = -6/5 -2y/5

3 × ( -6/5 -2y/5 ) - 2y = 22

-18/5 - 6y/5 - 2y = 22 ... (×5)

-18 - 6y - 10y = 110

-16y = 128 .... (× -1)

16y = -128 .... (÷16)

y = 8

The Average Rate of Change on the table from 2 ≤ x ≤ 5 is 3

The average rate of change of a function is a measure of how the output value of the function (y) changes with respect to the input value (x) as x changes. Mathematically:

Average rate of change = Δy/Δx

To find the Average Rate of Change on the table from 2 ≤ x ≤ 5:

when x =2, h(x) = 0 and when x = 5, h(x) = 9

Average rate of change = Δh/Δx

Average rate of change =  (9 - 0) / (5 - 2)

Average rate of change =  9/3

Average rate of change =  3

Learn more about average rate of change on:

brainly.com/question/12363445

#SPJ1

40L of each solution should be used

percentage, a relative value indicating hundredth parts of any quantity.

Let x=amount of 32% insecticide needed

Then 100-x=amount of 55% insecticide needed

Now we know that the amount of pure insecticide in the 32% solution(0.32x) plus the amount of pure insecticide in the 55% solution(0.55(100-x)) has to equal the amount of pure insecticide in the final mixture (0.44×100).

So our equation to solve is:

0.32x+0.52(100-x)=0.44×100 get rid of parens

0.32x+52-0.52x=44

52-44-0.2x=0

8=0.2x

x=40L

Hence, 40L of each solution should be used

To learn more on Percentage click:

https://brainly.com/question/28269290

#SPJ1

Option B and option C are correct, RT is the altitude of triangle PQR and RS is the median of triangle PQR

A triangle is a three-sided polygon that consists of three edges and three vertices.

A median of a triangle is a line segment that joins a vertex to the mid-point of the side that is opposite to that vertex

The altitude of a triangle is the perpendicular drawn from the vertex of the triangle to the opposite side.

RT is the perpendicular to the triangle PQR

RT is the altitude of triangle PQR.

RS is the median of triangle PQR

Hence, option B and option C are correct, RT is the altitude of triangle PQR and RS is the median of triangle PQR

To learn more on Triangles click:

https://brainly.com/question/2773823

#SPJ1

Answer: 29.2!

Step-by-step explanation: You must subtract 15 from 44.2 which would get you to 29.2!

The measure of angle x and angle y is x = 75° and y = 135°, respectively.

We know that,

If the angles of a triangle are θ₁, θ₂ and θ₃, respectively. Then the sum of θ₁, θ₂ and θ₃ is equal to 180°.

In triangle ABC,

⇒ 45° + 60° + x = 180°

⇒x = 180° − 105°

⇒x = 75°

Now, If the exterior angle of a triangle is θ and the two opposite interior angles are θ₁ and θ₂, then the sum of θ₁ and θ₂ will be equal to the θ.

⇒y = 60° + x

⇒y = 60° + 75°

⇒y = 135°

Therefore, x =75° and y = 135°

--The given question is incorrect, the correct question is

"What are the measures of angle x and angle y?"--

To know more about exterior angle, here

https://brainly.com/question/28835566

#SPJ4

The marginal distribution of tenure in counts for those who own a home is 76, while for those who rent a home is 40.

The marginal distribution of a subset of a group of random variables is the probability distribution of the variables included in the subset. It shows the probabilities of various values of the variables in the subset without reference to the values of the other variables.

Marginal variables are those variables in the subset of variables being included. These concepts are "marginal" because they can be encountered by summing values in a table along rows or columns, and writing the sum in the margins of the table.

For the given data. The marginal distribution of tenure can be calculated as,

Owns home = 71 + 5 = 76

Rents home = 13 + 27 = 40

--The given question is incomplete, the complete question is

"Here is a table classifying 116 thousand US households (in thousands) in 2013 by tenure and insurance. Here is a table giving the number of US households (in thousands) in 2013 by tenure and insurance status:

Insurance status

Owns home

Rents home

Insured

71

13

Uninsured

5

27

Find the marginal distribution of tenure in counts.

Owns home:

Rents home:"

To know more about marginal distribution, here

https://brainly.com/question/14310262

#SPJ4

Let's take this problem in steps:

 --> original price of the dress

What does this question give us:

 --> a 20% discount of the original price is $550

That means:

   ==> (100 - 20)% of the original price is $550

      ==> 80% of the original price is $550

In equation form:

     [tex]\dfrac{80}{100} * \text{ original price}=550\\\\\\\dfrac{80* \text{ original price}}{100} =550\\\\\\80* \text{ original price}=550*100=55000\\\\\\\text{original price}=\dfrac{55000}{80} = 687.5[/tex]

Thus the original price is $687.50

Answer: $687.50

The original price of Meah bought a dress is $687.50.

The percent discount should be divided by 100% in order to be converted to a decimal. Create the equation P=(1d)x P = (1 d) x to determine the item's original price, where P is the sale price, d is the discount expressed as a decimal, and x is the item's original price.

Explanation:

To solve this issue, let's do it piecemeal:

the dress's initial purchase price

This inquiry provides us with:

--> The amount after a 20% reduction equals $550.

that implies:

(100 - 20)% of the purchase price is $550.

The amount is $550, or 80% of the purchase price.

written as an equation

Consequently, $687.50 is the starting price.

In response, $687.50.

To learn more about original price refer to:

https://brainly.com/question/26357091

#SPJ1

The ratio of students who want waffles to the total number of students is 7/8.

What is the ratio?

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

Out of 8 students, 1 student wants pancakes and 8 - 1 = 7 students want waffles.

To find the ratio of the number of students who want waffles to the total number of students, we can divide the number of students who want waffles by the total number of students and express the result as a fraction.

So the ratio is:

(Number of students who want waffles) / (Total number of students) = 7/8

This fraction can be simplified by dividing both the numerator and denominator by the greatest common factor, which in this case is 1, so it remains the same.

Hence, the ratio of students who want waffles to the total number of students is 7/8.

To learn more about the ratio visit,

https://brainly.com/question/12024093

#SPJ1

Answer:

x = 3 is 17

Step-by-step explanation:

Given the function y = 5x + 2, the y-value when x = 3 is calculated as follows:

y = 5x + 2

y = 5 * 3 + 2

y = 15 + 2

y = 17

So the y-value when x = 3 is 17.

The interest paid if you purchase this car is $4,860.

A monthly payment is a payment made every month to pay off loans or advances. It's similar to EMI.

The interest rate used can be found using the formula: Interest rate = (monthly payment x number of payments) / principal.

Interest rate = (450 x 36) / 10000 = 16.2%

The interest rate used is 16.2%

The interest paid can be calculated using the formula: Interest = Principal x Interest rate x Number of payments / 12

Interest = 10000 x 0.162 x 36/12

Apply the multiplication operation, and we get

Interest = 4,860

Thus, the interest paid if you buy this car is $4,860

Learn more about the monthly payments here:

https://brainly.com/question/20761642

#SPJ1

When two expressions are joined by an equal sign, a mathematical statement is called an equation.

Let h be the number of hours for which the two costs would be the same.

PP charges               $2220 + ($45/hr)*h

D&S charges        $1850 + ($65/hr)*h

Note that the    ($/hr)*hours  gives $, because hours cancel out

Set the expression equal and solve for h (this is called the "break even point"):

         2200 + 45h = 1850 + 65h

            370 = 20h              (subtract 1850 from both sides)

             18,5 = h

     At 18.5 hours, the companies would charge the same amount.

      18  1/2 hours is 18 hours 30 minutes.

The complete question is,

Write and solve an equation to determine the number of hours for which the two costs would be the same.

Ms. Silver wants to hire a painter to paint her house. Painters Plus charges $2,220 plus $45 per hours. Davis & Sons charges $1,850 plus $65 per hour. Write and solve an equation to determine the number of hours for which the two costs would be the same.

To learn more about equation refer to:

https://brainly.com/question/29174899

#SPJ1

It is possible to construct a triangle whose sides are 3 cm 4 cm and 5 cm because the sum of two sides are greater than three sides.

In the given question, we have to classify a triangle having the sides 3cm 4cm and 5cm.

The sum of the two sides must always be greater than the third side in order to determine whether or not the given sides may form a triangle.

To check this we firstly add the 10.2 and 5.8

3 + 4 > 5

7 > 5

Now we add 3 and 5

3 + 5 > 4

8 > 4

Now we add 4 and 5

4 + 5 > 3

9 > 3

It is possible to construct a triangle whose sides are 3 cm 4 cm and 5 cm because the sum of two sides are greater than three sides.

To learn more about construct a triangle link is here

brainly.com/question/17209323

#SPJ4

The equation of a horizontal line passing through the point (- 3 8) is y = 8

From the question, we have the following parameters that can be used in our computation:

Point = (-3, 8)

This means that

(x, y) = (-3, 8)

Horizontal lines that do not pass through the origin do not intersect with the x-axis

This means that

Line = y

So, we have

y = 8

Hence, the equation is y = 8

Read more about line equations at

https://brainly.com/question/18831322

#SPJ1

a) The fraction of tank filled with gasoline is given by the equation A = 3/8

b) The solution to the system of equations is

xz - y = 11/6

yz + x = 13

3yz = 29

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

Given data ,

a)

Let the fraction be represented as A

Now , After first journey the amount of fuel left was = 1 - ( 7/16 )

On simplifying the equation , we get

The amount of fuel left = 9/16

( 1/3 ) of the fuel was used , so 2/3 of the fuel is left in the tank

Substituting the values in the equation , we get

The amount of fuel left in the tank A = ( 2/3 ) of ( 9/16 )

The amount of fuel left in the tank A = 3/8

Hence , the fraction is A = 3/8

b)

The value of x = 3 1/3 = 10/3

The value of y = 4 5/6 = 29/6

The value of z = 2

Let the equation be B = xz - y

Substituting the values in the equation , we get

B = ( 10/3 ) 2 - ( 29/6 )

B = 20/3 - 29/6

B = ( 40 - 29 ) / 6

B = 11/6

Let the equation be C = yz + x

Substituting the values in the equation , we get

C = ( 29/6 ) 2 + ( 10/3 )

C = 58/6 + 10/3

C = ( 58 + 20 ) / 6

C = 13

Let the equation be D = 3yz

Substituting the values in the equation , we get

D = 3 ( 29/6 ) 2

D = ( 29/6 ) x 6

D = 29

Hence , the equations are solved

To learn more about fractions click :

https://brainly.com/question/29766013

#SPJ1

By following the above procedure and having done the calculations the following questions can be answered:

Learn more about Shadow cast :

https://brainly.com/question/26950457

#SPJ4

Acute angle triangle examples are Equilateral Acute Triangle, Isosceles Acute Triangle, and Scalene Acute Triangle.

The definition of an acute triangle states that it is a type of triangle in which all three interior angles are acute angles or less than 90°. The sides of an acute-angled triangle can be similar or unequal depending on whether the triangle is equilateral, isosceles, or scalene.

As we know that triangles can be categorised on the basis of sides and angles, an acute triangle can also be further categorised as:

Equilateral Acute Triangle: In an equilateral acute triangle, all three angles are equal to 60° and all sides are equal.

Isosceles Acute Triangle: In an isosceles acute triangle, two sides and two angles are equal, and all interior angles are less than 90°.

Scalene Acute Triangle: In a scalene acute triangle, all the 3 sides are of dissimilar lengths and the 3 interior angles are of dissimilar measures but all the interior angles measure less than 90°.

To know more about interior angles, here

https://brainly.com/question/2125016

#SPJ4

Value of (f+g)(x) = 7x² + 12x - 9

A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

Given function

f(x) = 6x² + 12x - 6

g(x) = x² - 3

(f+g)x = f(x) + g(x)

= 6x² + 12x - 6 + x² -3

adding like terms

= 7x² + 12x - 9

Hence, 7x² + 12x - 9 is the value of (f+g)(x) .

Learn more about function here:

https://brainly.com/question/12431044

#SPJ1

The piecewise function of the given function is

y= -x/2+4 if x ≥ -2

y=  x/2+6 if x < -2

The solution is obtained using the modulus function.

What is modulus function?

The magnitude of a given number is indicated by the modulus of the number. By definition, a modulus function is a real-valued function, such as f: R -> R, where y = |x| for any x R OR f(x) = |x|.

F(x) is equal to the positive value of x for every non-negative value of x. However, f(x) is equal to the negative value of x for negative x values.

We are given y=-1/2|x+2|+5

So, first we need to solve for x+2≥0

We get x≥-2

Now, we get two equations,

y=-1/2(x+2)+5 if x ≥ -2

y= 1/2(x+2)+5 if x < -2

On solving the equations, we get

y=-1/2(x+2)+5 if x ≥ -2

y= -x/2-1+5

y= -x/2+4

y= 1/2(x+2)+5 if x < -2

y= x/2+1+5

y=  x/2+6

Hence, the final answer as a piecewise function is

y= -x/2+4 if x ≥ -2

y=  x/2+6 if x < -2

Learn more about modulus function from the given link

https://brainly.com/question/30098547

#SPJ1

The closest answer to the actual length of the shortest side, in meters, is G. 333.

Length is a measurement of distance or size. It can refer to the physical size of an object, such as its height, width, or depth, or it can refer to the amount of time it takes to complete an activity. Length is measured in a variety of units including inches, feet, meters, and miles. Length is one of the three fundamental dimensions of physical space, along with width and height.

This is because the ratio of the actual length of the longest side (1,000 meters) to the longest side on the map (9 inches) is 111.11:1. Therefore, the ratio of the actual length of the shortest side to the shortest side on the map is 111.11:3, which is equal to 37.04:1. When we multiply 3 inches (the length of the shortest side on the map) by 37.04, we get 111.12, which is closest to 333 meters (G).

To know more about length click-
https://brainly.in/question/48573392
#SPJ1