Solve the inequality n + 20 < -42, and write the solution in interval notation.

Answers

Answer 1

Answer:

(-∞, -62)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right  

Equality Properties

Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of Equality

Algebra I

Terms/CoefficientsInterval Notation - [Brackets] denote inclusion, (Parenthesis) denote exclusion

Step-by-step explanation:

Step 1: Define

n + 20 < -42

Step 2: Solve for n

[Subtraction Property of Equality] Subtract 20 on both sides:                      n < -62

∴ Any number n smaller than -62 would work as a solution to the inequality. Our solution set in interval notation would be (-∞, -62).


Related Questions

What is the endpoint formula given midpoint?

Answers

Answer:

  B = 2M -A

Step-by-step explanation:

For given endpoint A and midpoint M, the other endpoint B can be found using the definition of the midpoint:

  M = (A+B)/2

  2M = A+B . . . . . multiply by 2

  2M-A = B . . . . . subtract A

The second endpoint can be found by subtracting the given endpoint from twice the midpoint:

  B = 2M -A

A square has an area of 16 square millimeters. What is the length of each side of the square?

Answers

Answer:

The length of each side of the square is 4 mm

Step-by-step explanation:

AS we can see that , it is said that it is as square so all sides of a square are equal

Area(A)= 16 square millimetres

Length (L) = ?

or

[tex]L^{2}[/tex] = Area

[tex]L^{2}[/tex] = 16

L = [tex]\sqrt{16}[/tex]

L =[tex]\sqrt 4^{2}[/tex]

Therefore L = 4 mm

Hope it will help :)

Saige's spaceship traveled 588588588 kilometers (\text{km})(km)left parenthesis, start text, k, m, end text, right parenthesis in 606060 seconds (\text{s})(s)left parenthesis, start text, s, end text, right parenthesis.

Answers

Answer:

A is proportional

B and C are NOT proportional

Step-by-step explanation:

First, simplify 588 and 60:

588 divided by 6

60 divided by 6

= 98

  10

Simplify them again by dividing them both by 2

= 49

   5

Let's look at A:

441 and 45

Simplify by dividing by 9

= 49

   5

It's pretty obvious that A is proportional because the simplified values are exactly the same.

Next, let's check B:

215  and 25

Simplify by dividing by 5

= 43

   5

Now that its simplified you can compare

43   is smaller than 49

5                               5

B is not proportional

Finally, let's check C:

649 and 110

Simplify by dividing by 11

= 51

  10

Make 51 and 49 have the same denominator so we can compare them

          10         5

51 can stay the same because 5 times 2 equals 10

10

49 times 2

5 times 2

=  98

    10

Now that the denominators are the same we can compare

51 is much smaller than 98

10                                     10

Therefore, C is also not proportional.

Hope that helps :D

Final answer:

The velocity of Saige's spaceship is 9,809,809 km/s.

Explanation:

Given that Saige's spaceship traveled 588,588,588 kilometers in 60 seconds, we can calculate the velocity of the spaceship by dividing the distance traveled by the time taken. Velocity = Distance / Time. Velocity = 588,588,588 km / 60 s = 9,809,809 km/s. Therefore, the velocity of Saige's spaceship is 9,809,809 km/s.

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For breakfast Jamie can choose from cereal, eggs, or a muffin. She also can drink coffee, orange juice, or milk. How many total outcomes are possible?

Answers

Final answer:

Jamie has 9 possible combinations for breakfast based on her choices of 3 different foods and 3 different drinks.

Explanation:

The subject of the question is in the field of probability in mathematics. The question is asking for the total number of outcomes or combinations possible given Jamie's breakfast choices. Jamie can choose from 3 foods (cereal, eggs, muffin) and 3 drinks (coffee, orange juice, milk).

To find the total number of outcomes, you multiply the total number of options in each category. In this case, it would be 3 (food choices) multiplied by 3 (drink choices), which sets the total possible outcomes to be 9.

Therefore, Jamie has 9 possible combinations for her breakfast choice.

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A rectangle sandbox has an area of 64 square yards. What might be the perimeter of the sandbox?

Answers

Answer:

32

Step-by-step explanation:

Answer:

32

Step-by-step explanation:

Given that the measure of ∠x is 30°, and the measure of ∠y is 60°, find the measure of ∠z.

Answers

Answer:

90°

Step-by-step explanation:

Since vertical angles are equal, ∠x is equal to its vertical angle. Since the total angles in a triangle are 180, and x + y = 90, then the angle supplementary to z = 180 - 90 = 90. To find z, it's just 180 - 90 = 90.

I need help with this I don’t understand this

Answers

D.1296 is the answer

Answer:

the answer would be A

Step-by-step explanation:

multiply 7 x 6 and that would get you to 42 and if you multiply 42 x 6 that would get you 252 and if you do that with the rest of the numbers you will see that it could work if you multiply them by 6 so basically the constant rate of the numbers would be 6.

6x+10>5x-12
Help needed

Answers

Answer:

x > -22

Step-by-step explanation:

6x+10>5x-12

Subtract 5x from each side

6x-5x+10>5x-5x-12

x+10 > -12

Subtract 10 from each side

x+10-10>-12-10

x > -22

A broker pays his salespeople 25 percent of the commission for listing a property and 40 percent of the

commission for selling it. If the commission rate is 6 percent and a salesperson received $3,265.28 on a

property that he sold, what was the sales price? (Round answer to nearest dollar.)

Answers

Answer: The sales price was $83,725

Step-by-step explanation: The commission rate for selling the property has been given as 6 percent of the sales price.

If the salesperson received a total of 3265.28, (which is 25% + 40% = 65% of the commission) then that means he has received the amount calculated  as follows;

(3265.28/x) = 65/100

(Where x is the commission earned)

By cross multiplication we now have

(3265.28 x 100)/65 = x

5023.5 = x

Having calculated the commission as $5023.5, we remember that the commission rate is 6%, and hence, to calculate the sales price (which is 100%) we take the following steps;

(5023.5/y) = 6/100

(Where y is the total sales figure)

By cross multiplication we now have

(5023.5 x 100)/6 = y

83725 = y

Therefore, the sales price was, $83,725

Final answer:

To find the sales price of a property based on the commission received, divide the commission earnings by the percentage commission for selling the property, then divide that total by the overall commission rate. Rounding to the nearest dollar, the sales price was $136,053.

Explanation:

The subject of this question is Mathematics, specifically pertaining to business and commission calculations. The problem involves determining the sales price of a property based on the commission received by a salesperson.

Understand that a salesperson received $3,265.28, which represents 40% of the commission for selling a property.Calculate the total commission by dividing the salesperson's earnings by the selling commission percentage: $3,265.28 ÷ 0.40 which equals $8,163.20 total commission.Find the sales price of the property by dividing the total commission by the commission rate: $8,163.20 ÷ 0.06.Calculate the sales price: $8,163.20 ÷ 0.06 = $136,053.33.Round the sales price to the nearest dollar, which gives us $136,053.

Hence, the sales price of the property was $136,053.

What is the radius of a hemisphere with a volume of 49037 ft", to the nearest tenth

of a foot?

Answers

Answer:

28.6 ft

Step-by-step explanation:

Given an hemisphere of volume [tex]49037 ft^3[/tex]

Volume of a Hemisphere of radius r [tex]=\frac{2}{3}\pi r^3[/tex]

Therefore:

[tex]\frac{2}{3}\pi r^3=49037 \\r^3=49037 X \frac{3}{2 \pi}\\r=\sqrt[3]{49037 X \frac{3}{2 \pi}} \\r=28.6\: foot[/tex]

The radius of the hemisphere is 28.6 foot to the nearest tenth.

Giovanna owns a farm. She is going to randomly select one animal to present at the state fair. She has 6 pigs, 7 chickens, and 10 cows. What is P (chicken)

Answers

Answer:

P(chicken) ≈ 0.3

Step-by-step explanation:

Giovanna will select one animal from 6 pigs or 7 chickens or 10 cows to present at the state fair. From the question, there are a total of 6 + 7 + 10 = 23 animals to choose from.

If she selects a chicken, then P(chicken) = 7/23 = 0.304

P(chicken) ≈ 0.3

Answer:

7/23 OR 0.304...826

Step-by-step explanation:

Please refer to the attached image for explanations

The radius of a circle is 3 km. what is the circle's area and what is the formula you have to use?

Answers

Answer:

Circle's area = 28,26 km

Formula = π r²

Step-by-step explanation:

[tex]circle's \: \: area = \pi \: {r}^{2} \\ circle's \: \: area = 3,14 \times {3}^{2} \\ circle's \: \: area = 28,26 \: km \\ circle's \: \: area = 28.260 \: m[/tex]

Find the difference.
(4m^2 - m+2) - (-3m^2+ 10m + 4) =(

Answers

Answer:

7m^2 - 11m - 2

Step-by-step explanation:

Distribute the negative.

4m^2 - m + 2 + 3m^2 - 10m - 4 = ?

Now, add the like terms.

4m^2 + 3m^2 = 7m^2

-m + (-10m) = -11m

2 + (-4) = -2

7m^2 - 11m - 2

Cindy asked to borrow Melinda's math book. Which sentence shows a correctly written response to Cindy's question?​

Answers

Answer:

C

Step-by-step explanation:

Please help me Factor x2 − 4x + 5

Answers

Step-by-step explanation:

Look it's so simple once you learn it's very easy you have to multiply the 1 and 3rd digit so answer is 5 now you have to find the factors of 5 so

x2 - 4x + 5

x2 - 5x + x + 5

x (x - 5) +1 (x + 5)

(x - 5) (x + 1) are the factors but please recheck the question maybe there is a mistake in sign because my factors x + 5 and x - 5 this should be one sign either positive or negative

Plzzz help thank you!!

Answers

Answer:

i think is 240 or it could be 64

I think the answer is 64

Use any method to solve the equation. If necessary, round to the nearest hundredth. 9x^2 = 17

Answers

Answer:

1.37

Step-by-step explanation:

First, we want to isolate the variable x. Do this by dividing both sides by 9:

[tex]\frac{9x^2}{9} =17/9[/tex]

[tex]x^{2} =17/9[/tex]

Now, square root both sides:

[tex]\sqrt{x^2}= \sqrt{17/9}[/tex]

x = [tex]\sqrt{17/9} =\sqrt{17}/3[/tex]

Finally, we can use a calculator to finish off the problem:

x = [tex]\sqrt{17}/3[/tex] ≈ 1.37

Hope this helps!

9x^2 = 17

Divide both sides by 9

X^2 = 17/9

Take the square root of both sides

X = sqrt(17/9) and -sqrt(17/9)

Simplify:

X = sqrt(17)/3 and -sqrt(17)/3

A scenic overlook which extends over a ravine is shaped like a kite.
Find mZX
O a. 104°
Ob.40°
O c. 112°
O d. 208

Answers

A quadrilateral is a polygon with 4 number of sides and 4 vertices. The measure of the ∠X is 104°.

What is a quadrilateral?

A quadrilateral is a polygon with 4 number of sides and 4 vertices. A few examples of a quadrilateral are square, rectangle, rhombus, parallelogram, etc.

Given a scenic overlook which extends over a ravine is shaped like a kite. Since in a kite the measure of all the angles is 360°, also, the measure of the angle formed by the two non-equal sides is equal. Therefore, the measure of the two angles that will be equal is ∠X and ∠Z.

Further, the sum of the measure of all the angles can be written as,

∠X + ∠Y + ∠Z + ∠W = 360°

∠X + 40° + ∠X + 112° = 360°

2∠X = 360° - 112° - 40°

2∠X = 208°

∠X = 208°/2

∠X = 104°

Hence, the measure of the ∠X is 104°.

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Final answer:

Without additional details it is not possible to solve for the measure of angle Z (mZX) in a kite. Kite properties and given angle measures are typically used to solve for unknown angles.

Explanation:

The question asks to find the measure of angle Z (mZX) in a kite. A property of a kite is that it has two pairs of adjacent sides that are equal. Another property is that the diagonals intersect at right angles. Furthermore, kites have one pair of opposite angles that are equal, known as the non-vertex angles.

If the kite diagram was provided with certain angles or relationships between the angles, we could use that information to calculate mZX. Typically, we would use the properties of the kite's angles and sides to form equations and solve for the unknown angle.

Without additional information provided, we cannot definitively solve for mZX. Usually, in the context of a geometry problem like this, one would apply the knowledge of geometric shapes, their properties, and other given information to solve for the unknown angle.

What’s the square root of 6

Answers

Answer:

2.44948974

Hope I could help.

Brainliest plz ;)

Which prism is similar to a right rectangular prism with a length of 5.2 units, a width of 2 units, and a height of 3 units?

Answers

Answer:

The second rectangle on edg

Step-by-step explanation:

Answer: B.) (2nd choice)

h=1.5

w=1

l=2.6

Step-by-step explanation:

the meaning of logarithm

Answers

Answer:

the meaning of logarithm is a quantity representing the power to which a fixed number (the base) must be raised to produce a given number.

Step-by-step explanation:

: )

I REALLY NEED HELP PLS ANSWER!!!!!

Answers

Negative I’m on khan academy doing something else though

Which equation represents the relationship of the measure of m∠X and m∠Y?

Answers

Answer:

The measure of f m∠X and m∠Y =180 i.e they are supplementary angles.

Step-by-step explanation:

Given:

Two angles

To Find:

Relationship between them

Solution:

For two angles to have relationship ,we need to know what represents in the figure

Here no terms are used to represent the angles

So two angles can be represented in sum of angles of triangles ,

as Consider a triangle XYZ then

X +Y=180 -Z

This will be representation

Otherwise,

Then could be linear ,interior alternate angle or supplementary angles

Which they adds up to 180 degree.

Depending upon the Condition representation will be establish.

Now,

m∠X and m∠Y=180............Supplementary angles. will be most effective .

Answer:

m∠X + m∠Y = 180°

Step-by-step explanation:

To make a glass sphere, 3,052.08 cm3 of molten glass is poured into a mold. Using 3.14 for π, Eduardo finds the circumference of the sphere using the steps below.







Which statement about Eduardo’s calculations is true?

Eduardo did not use the correct formula for the circumference.
Eduardo incorrectly used the length of the diameter to find the circumference.
Eduardo incorrectly calculated the radius.
Eduardo did not square the radius correctly in the second formula.

Answers

Answer:

Eduardo did not use the correct formula for the circumference.

Step-by-step explanation:

I was on the same question as you and guessed the assignment said this was the correct answer.

Which statement describes what these four powers have in common? 4 Superscript 0 (negative 2) Superscript 0 (one-third) Superscript 0 9 Superscript 0 All the powers have a value of 0 because the exponent is zero. All the powers have a value of 1 because the exponent is zero. All the powers have a value of –1 because the exponent is zero. All the powers have a fractional value because the exponent is zero.

Answers

Answer:

The answer would be that All the powers have a value if 1 because the exponent is zero.

Step-by-step explanation:

Use the exponent rule to help you

Answer:

it is 1

Step-by-step explanation:

i took this test on brainly

Please answer this correctly

Answers

Answer:

approximately 18 or [tex]\sqrt{324}[/tex]

Step-by-step explanation:

please give me brainliest

A triangle has vertices at R(1, 1), S(-2,-4), and T-3, -3). The triangle is transformed according to the rule Ro. 270". What
are the coordinates of S?


(-4,2)
(-2, 4)
(2,4)
(4,-2)

Answers

The coordinate of S if the triangle is transformed according to the rule Ro. 270 is (-4, 2)

Transformation of coordinates

Transformation is the process of changing the position of an object in a xy-plane.

Given the coordinate of the triangles as R(1, 1), S(-2,-4), and (T-3, -3). If the triangle is transformed according to the rule Ro. 270", the resulting coordinate points are (x,y)→(y,−x)

The coordinate of S using the rule is (-4, 2)

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The coordinate of S if the triangle is transformed according to the rule Ro. 270 is (-4, 2)

What is transformation?

A transformation is a dramatic change in form or appearance. An important event like getting your driver's license, going to college, or getting married can cause a transformation in your life. A transformation is an extreme, radical change.

here, we have,

Transformation of coordinates

Transformation is the process of changing the position of an object in a xy-plane.

Given,

the coordinate of the triangles as R(1, 1), S(-2,-4), and (T-3, -3). If the triangle is transformed according to the rule Ro. 270", the resulting coordinate points are (x,y)→(y,−x)

The coordinate of S using the rule is (-4, 2)

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Find the volume of the composite figure to the nearest whole number. The cylinder in the middle of the prism is hollow and should not be included in the volume.

Answers

The nearest whole number, the volume of the composite figure is 1140 in^3.

The composite figure consists of two rectangular prisms. The first prism has dimensions 8 in. x 4 in. x 18 in., and the second prism has dimensions 10 in. x 4 in. x 18 in.

To find the volume of the composite figure, we need to subtract the volume of the hollow cylinder from the volume of the two rectangular prisms.

The volume of a rectangular prism is calculated as follows:

Volume = length x width x height

The volume of the first rectangular prism is therefore:

Volume = 8 in. x 4 in. x 18 in. = 576 in^3

The volume of the second rectangular prism is therefore:

Volume = 10 in. x 4 in. x 18 in. = 720 in^3

The volume of a cylinder is calculated as follows:

Volume = π * radius^2 * height

Since the cylinder in the middle of the prism is hollow, we only need to consider the volume of the cylinder wall. The radius of the cylinder is 1 in., and the height of the cylinder is 18 in. Therefore, the volume of the cylinder wall is:

Volume = π * 1 in.^2 * 18 in. = 56.52 in^3

The total volume of the composite figure is therefore:

Volume = (576 in^3 + 720 in^3) - 56.52 in^3 = 1140.48 in^3

To the nearest whole number, the volume of the composite figure is 1140 in^3.


27,965 is divisible by
A) 2
B) 3
C) 5
D) 8

Answers

Answer:

C) 5

Step-by-step explanation:

27,965/5 = 5593

Technically 27,965 can be divisible by any of these numbers but 5 i the only one that equals a whole number.

n a newspaper, it was reported that yearly robberies in Springfield were down 20% to 176 in 2011 from 2010. How many robberies were there in Springfield in 2010?

Answers

Answer: There were 220 robberies in Springfield in 2010

Step-by-step explanation: If the robberies were reported to be down 20% and the new figure is 176, it simply means the figure 176 depicts 80% (or 0.8) of the figure from year 2010.

We shall take the figure in year 2010 as x, which is 100% (or 1.0) and year 2011 is 176 which is 80% (or 0.8). What we now have is;

176/x = 0.8

176/x = 4/5

By cross multiplication we now have;

(176 x 5)/4 = x

880/4 = x

220 = x

Therefore, there were 220 robberies in Springfield in 2010

Answer: There were 220 robberies in Springfield in 2010.

Step-by-step explanation:

Hi, to answer this question we have to write an equation with the information given.

Since the robberies decreased 20%, it means that 2011 are robberies are the 80% (100%-20%) of the 2010 robberies (x).

So if we multiply the yearly robberies in 2010 (x) by 0.8 (decimal form, 80/100=0.8) , we obtain the number of yearly robberies in 2011 (176).

x (0.80) = 176

Solving for x

x = 176/0.8

x = 220  robberies (2010)

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Phil wrote down that he sold 0.44 of the eggs hecollected. Did Phil write the decimal correctly? Explain.