What are four ways an inequality can be written?

Answers

Answer 1

Answer:

There are four ways to represent an inequality: Equation notation, set notation, interval notation, and solution graph.


Related Questions

how many terms are there in the series. 201.208.215......319​

Answers

Answer:

222

Step-by-step explanation:

add 7 no. to each of like 201+7 = 208, 208+7=215 ,215+7=222

The height (in meters) of a shot cannonball follows a trajectory given by h(t) = -4.9t^2 + 14t - 0.4 at time t (in seconds). As an improper fraction, for how long is the cannonball above a height of 6 meters? Please show steps. Thank you!

Answers

Solve for 6 = -4.9t^2 + 14t - 0.4 and you will have 2 positive numbers. First one is when cannonball reach 6 meters and second is when after it starts to fall down to 6 meters. I estimate first number to be 0.5 and the second to be 2.5 so the duration is 2 seconds.

Solve the following equation for
a
a. Be sure to take into account whether a letter is capitalized or not.

Answers

Answer:

6/5 n = a

Step-by-step explanation:

n = 5/6a

Multiply each side by 6/5

6/5 n = 6/5 * 5/6a

6/5 n = a

3x-2=2(x-5)

find the value of x ​

Answers

Now we have to,

find the required value of x.

Let's begin,

→ 3x-2 = 2(x-5)

→ 3x-2 = 2x-10

→ 3x-2x = -10+2

→ x = -8

Hence, value of x is -8.

Answer:

x = -8

Step-by-step explanation:

3x - 2 = 2 ( x + 5

Solve for x.

Let's solve,

3x - 2 = 2 ( x + 5 )

Step 1:- Distribute 2.

3x - 2 = 2 × x + 2 × 5

3x - 2 = 2x - 10

Step 2 :- Move constant to the right-hand and change their sign.

3x = 2x - 10 + 2

Step 3:- Add -10 and 2.

3x = 2x - 8

Step 4 :- Move variable to the left-hand side and change their sign.

3x - 2x = -8

Step 5 :- Subtract 2x from 2x.

x = -8

Hence, value of x = -8.

(2 + i)-(4 - 6/)(-3 +3/)

Answers

Answer:

C

Step-by-step explanation:

(2+i)-(4-6i)(-3+3i)

=(2+i)-(-12+12i+18i-18i^2)

=(2+i)-[-12+30i-18(-1)]

=(2+i)-(-12+30i+18)

=(2+i)-(30i+6)

=2+i-30i-6

=-4-29i

The electric cooperative needs to know the mean household usage of electricity by its non-commercial customers in kWh per day. They would like the estimate to have a maximum error of 0.09 kWh. A previous study found that for an average family the variance is 5.76 kWh and the mean is 16.6 kWh per day. If they are using a 98% level of confidence, how large of a sample is required to estimate the mean usage of electricity

Answers

Answer:

A sample of 3851 is required.

Step-by-step explanation:

We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.98}{2} = 0.01[/tex]

Now, we have to find z in the Z-table as such z has a p-value of .

That is z with a pvalue of , so Z = 2.327.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

Variance is 5.76 kWh

This means that [tex]\sigma = \sqrt{5.76} = 2.4[/tex]

They would like the estimate to have a maximum error of 0.09 kWh. How large of a sample is required to estimate the mean usage of electricity?

This is n for which M = 0.09. So

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]0.09 = 2.327\frac{2.4}{\sqrt{n}}[/tex]

[tex]0.09\sqrt{n} = 2.327*2.4[/tex]

[tex]\sqrt{n} = \frac{2.327*2.4}{0.09}[/tex]

[tex](\sqrt{n})^2 = (\frac{2.327*2.4}{0.09})^2[/tex]

[tex]n = 3850.6[/tex]

Rounding up:

A sample of 3851 is required.

In 1995 the U.S. federal government debt totaled 5 trillion dollars. In 2008 the total debt reached 10 trillion dollars. Which of the following statements about the doubling time of the U.S. federal debt is true based on this information?

Answers

Where are the statements?

Jarvis invested some money at 6% interest. Jarvis also invested $58 more than 3 times that amount at 9%. How much is invested at each rate if Jarvis receives $1097.19 in interest after one year? (Round to two decimal places if necessary.)

Use the variables x and y to set up a system of equations to solve the given problem.

Answers

9514 1404 393

Answer:

$3309 at 6%$9985 at 9%

Step-by-step explanation:

Let x and y represent amounts invested at 6% and 9%, respectively.

  y = 3x +58 . . . . . . . the amount invested at 9%

  0.06x +0.09y = 1097.19 . . . . . . total interest earned

__

Substituting for y, we have ...

  0.06x +0.09(3x +58) = 1097.19

  0.33x + 5.22 = 1097.19 . . . . . . . . . simplify

  0.33x = 1091.97 . . . . . . . . . . . . subtract 5.22

  x = 3309 . . . . . . . . . . . . . . . . divide by 0.33

  y = 3(3309) +58 = 9985

$3309 is invested at 6%; $9985 is invested at 9%.

Which answer choice correctly identifies the extraneous information in the problem?

Anna babysat 2 children on Saturday night. She charges $8 an hour to babysit. She wants to save the money she earns babysitting to buy a stereo system that cost $225. If Nina babysat for 5 hours, how much money did she earn?

Answers

Answer: $40 / $80

Step-by-step explanation: 40$ if it's $8 for BOTH per hour, or if it's $8 for ONE per hour it's $80

Use what you know about decomposing fractions to write 11/10 as a mixed number.

Help please :(

Answers

Answer:

11/10 is 1 1/10

Step-by-step explanation:

1 1/10

This is because is we divide 11 by 10 we get 1 1/10, the answer to this question.

Hope this helps! Please make me the brainliest, it’s not necessary but appreciated, I put a lot of effort and research into my answers. Have a good day, stay safe and stay healthy.

Multiply (8 + 3i)(3 + 5i).
39 + 491
9+ 491
24 + 152
24 + 491 + 15/2

Answers

24+491+15/2 is
=522.5

(8+3)(3+5)=88

88+(39+491)= 618.

88+(9+491)= 588

88+(24+152)= 264.

sorry could not find the last ansswer..

help me please pls this ur really hard help

Answers

c done it on the test

surface areas of two similar figures are given. the volume of the larger figure is given. find the volume of the smaller figure​

Answers

9514 1404 393

Answer:

  216 in³

Step-by-step explanation:

The ratio of volumes is the 3/2 power of the ratio of areas.

  small volume = ((small area)/(large area))^(3/2) × (large volume)

  = (212/1325)^(3/2) × 3375 in³ = (4/25)^(3/2) × 3375 in³ = (8/125)×3375 in³

  small volume = 216 in³

52 POINTS I need help!
Question 1

The vertex form of the equation of a vertical parabola is given by
, where (h, k) is the vertex of the parabola and the absolute value of p is the distance from the vertex to the focus, which is also the distance from the vertex to the directrix. You will use the GeoGebra geometry tool to create a vertical parabola and write the vertex form of its equation. Open GeoGebra, and complete each step below. If you need help, follow these instructions for using GeoGebra.

Part A

Mark the focus of the parabola you are going to create at F(6, 4). Draw a horizontal line that is 6 units below the focus. This line will be the directrix of your parabola. What is the equation of the line?
Part B

Construct the line that is perpendicular to the directrix and passes through the focus. This line will be the axis of symmetry of the parabola. What are the coordinates of the point of intersection, A, of the axis of symmetry and the directrix of the parabola?
Part C

Explain how you can locate the vertex, V, of the parabola with the given focus and directrix. Write the coordinates of the vertex.
Part D

Which way will the parabola open? Explain.
Part E

How can you find the value of p? Is the value of p for your parabola positive or negative? Explain.
Part F

What is the value of p for your parabola?
Part G

Based on your responses to parts C and E above, write the equation of the parabola in vertex form. Show your work.
Part H

Construct the parabola using the parabola tool in GeoGebra. Take a screenshot of your work, save it, and insert the image below.
Part I

Once you have constructed the parabola, use GeoGebra to display its equation. In the space below, rearrange the equation of the parabola shown in GeoGebra, and check whether it matches the equation in the vertex form that you wrote in part G. Show your work.
Part J

To practice writing the equations of vertical parabolas, write the equations of these parabolas in vertex form:

focus at (-5, -3), and directrix y = -6
focus at (10, -4), and directrix y = 6.

Answers

Answer:

Step-by-step explanation:

A. Directrix: y = 4-6 = -2

:::::

B. Axis of symmetry: x = 6

Axis of symmetry intersects directrix at (6,-2)

:::::

C . Vertex is halfway between focus and directrix, at (6,1)

:::::

D. The focus lies above the directrix, so the parabola opens upwards.

:::::

E. Focal length p = 1/(4×0.5)

:::::

F. p = 0.5

::::

G. y = 0.5(x-6)² + 1

Answer:

the one above is correct

Step-by-step explanation:

h.We start with a circle and a line that goes through the center of the circle (C) and one vertex of the triangle (E).

Using the point on the line opposite the vertex as a center (D), we draw an arc with the same radius the circle has.

The two points of intersection with the circle are the other two vertices of the inscribed triangle (F, G).

The scores for a particular examination are normally distributed with a mean of 68.5% and a standard deviation of 8.2%. What is the probability that a student who wrote the examination had a mark between 80% and 100%? Give your answer to the nearest hundredth.

Answers

Answer:

[tex]P(80/100<x<100/100)=0.08[/tex]

Step-by-step explanation:

We are given that

Mean,[tex]\mu=68.5[/tex]%=68.5/100

Standard deviation, [tex]\sigma=8.2[/tex]%=8.2/100

We have to find the probability that a student who wrote the examination had a mark between 80% and 100%.

[tex]P(80/100<x<100/100)=P(\frac{80/100-68.5/100}{8.2/100}<\frac{x-\mu}{\sigma}<\frac{100/100-68.5/100}{8.2/100})[/tex]

[tex]P(80/100<x<100/100)=P(1.40<Z<3.84)[/tex]

We know that

[tex]P(a<Z<b)=P(Z<b)-P(Z<a)[/tex]

Using the formula

[tex]P(80/100<x<100/100)=P(Z<3.84)-P(Z<1.40)[/tex]

[tex]P(80/100<x<100/100)=0.99994-0.91924[/tex]

[tex]P(80/100<x<100/100)=0.0807\approx 0.08[/tex]

Module 8: Directions: Respond to this question to demonstrate your understanding of the topic/content. Be sure to provide adequate and relevant details learned in the module to support your response. Pay close attention to organizing your response so it makes sense and uses correct grammar. Your response should be at least 5-7 sentences at a minimum.



Question: Describe how to eliminate the parameter to change from parametric to rectangular form. How does this ability help us with graphing parametric equations?

Answers

Answer:

rectangular equation, or an equation in rectangular form is an equation composed of variables like xx and yy which can be graphed on a regular Cartesian plane. For example y=4x+3y=4x+3 is a rectangular equation.

A curve in the plane is said to be parameterized if the set of coordinates on the curve, (x,y)(x,y) , are represented as functions of a variable tt .

x=f(t)y=g(t)x=f(t)y=g(t)

These equations may or may not be graphed on Cartesian plane.

Step-by-step explanation:

I hope this helps

Find the area of the shaded regions: the green is the shaded area

PLS HELP ME!!!! I NEED THE ANSWER BY THIS EVENING CUZ I HAVE RSM TOMORROW. PLS HELP!!!!!

Answers

Answer:

the green area stands for the safe operation space

Step-by-step explanation:

u say b×h meaning say 80degrees ×9cm which is 720..

many ® Black pencils cost N75 each and coloured pencils cost N105 each. If 24 mixed pencils cost #2010, how of them were black? (Hint: Let there be x black pencils. Thus there are 24 - x) coloured pencils.)​

Answers

Answer:

85

Step-by-step explanation:

I hope my answer help you

[tex]\lim_{x \to \4} x^{2} -3x[/tex]

Answers

(4)^2-3(4)=4Answer:

Step-by-step explanation:

Which set of statements explains how to plot a point at the location (Negative 3 and one-half, negative 2)?

A: Start at the origin. Move 3 and one-half units right because the x-coordinate is Negative 3 and one-half. Negative 3 and one-half is between 3 and 4. Move 2 units down because the y-coordinate is -2.


B: Start at the origin. Move 3 and one-half units down because the x-coordinate is Negative 3 and one-half. Negative 3 and one-half is between -3 and -4. Move 2 units left because the y-coordinate is -2.


C: Start at the origin. Move 3 and one-half units down because the x-coordinate is Negative 3 and one-half. Negative 3 and one-half is between -3 and -4. Move 2 units right because the y-coordinate is -2.


D: Start at the origin. Move 3 and one-half units left because the x-coordinate is Negative 3 and one-half. Negative 3 and one-half is between -3 and -4. Move 2 units down because the y-coordinate is -2.

Answers

Answer:

D: Start at the origin. Move 3 and one-half units left because the x-coordinate is Negative 3 and one-half. Negative 3 and one-half is between -3 and -4. Move 2 units down because the y-coordinate is -2.

Find the sum of the series if possible, if not possible explain why:

1+(−2/5)+(−2/5)^2+(−2/5)^3+⋯

Answers

Answer:

Step-by-step explanation:

5/7

Sum of a geometric series is a/(1-r) = 1/(1-(-2/5)) = 5/7

An object is dropped from 24 feet below the tip of the pinnacle atop a 1468-ft tall building. The height h of the object after t seconds is given by the equatior h= - 16t2 + 1444. Find how many seconds pass before the object reaches the ground. seconds pass before the object reaches the ground. (Type an integer or a decimal.)​

Answers

Answer:

9.5 seconds pass before the object reaches the ground.

Step-by-step explanation:

Height of the ball:

The height of the ball after t seconds is given by the following equation:

[tex]h(t) = -16t^2 + 1444[/tex]

Find how many seconds pass before the object reaches the ground.

This is t for which h(t) = 0. So

[tex]h(t) = -16t^2 + 1444[/tex]

[tex]-16t^2 + 1444 = 0[/tex]

[tex]16t^2 = 1444[/tex]

[tex]t^2 = \frac{1444}{16}[/tex]

[tex]t^2 = 90.25[/tex]

[tex]t = \pm \sqrt{90.25}[/tex]

Since it is time, we only take the positive value.

[tex]t = 9.5[/tex]

9.5 seconds pass before the object reaches the ground.

Find the missing length Indicated

Answers

Answer:

60

Step-by-step explanation:

x² = 144×25

= 3600

x =√3600 =60

yannie read 24 pages of a book. one fourth of the book is unread.how many pages are there?

Answers

Answer:

32

Step-by-step explanation:

24/3=8, 24+8=32

that's how I think of it

Find the tangent line equations for the given functions at the given point(s): f(x) = tan x + 9 sin x at (π, 0)

Answers

Answer:

[tex]{ \bf{f(x) = \tan x + 9 \sin x }}[/tex]

For gradient, differentiate f(x):

[tex]{ \tt{ \frac{dy}{dx} = { \sec }^{2}x + 9 \cos x }}[/tex]

Substitute for x as π:

[tex]{ \tt{gradient = { \sec }^{2} \pi + 9 \cos(\pi ) }} \\ { \tt{gradient = - 8 }}[/tex]

Gradient of tangent = -8

[tex]{ \bf{y =mx + b }} \\ { \tt{0 = ( - 8\pi) + b}} \\ { \tt{b = 8\pi}} \\ y - intercept = 8\pi[/tex]

Equation of tangent:

[tex]{ \boxed{ \bf{y = - 8x + 8\pi}}}[/tex]

Given that f(x)=x^2 and g(x)=5x+2 ​, find (f-g)(2)​, if it exists.

Answers

Answer:

(f - g)(2) = -8

General Formulas and Concepts:

Pre-Algebra

Distributive Property

Algebra I

Terms/CoefficientsFunctionsFunction Notation

Step-by-step explanation:

Step 1: Define

Identify

f(x) = x²

g(x) = 5x + 2

Step 2: Find

Substitute in functions:                                                                                     (f - g)(x) = x² - (5x + 2)[Distributive Property] Distribute negative:                                                    (f - g)(x) = x² - 5x - 2Substitute in x [Function (f - g)(x)]:                                                                   (f - g)(2) = 2² - 5(2) - 2Evaluate:                                                                                                          (f - g)(2) = -8

Write an expression representing the unknown quantity.

There are 5,682,953 fewer men than women on a particular social media site. If x represents the number of women using that site, write an expression for the number of men using that site.

The expression for the number of men is
.

Answers

9514 1404 393

Answer:

  x - 5,682,953

Step-by-step explanation:

If x is the number of women, and the number of men is 5,682,953 less, then the number of men is x -5,682,953

Rachel and Hugo sorted 236 crayons into boxes for a local arts project. Each box had 10 crayons. How many crayons were left over?

Help please lol

Answers

Answer:

6

Step-by-step explanation:

236/10 = 23 remainder 6, so 6 crayons is the answer

The graph of the parent function f(x) = |x| is dashed and the graph of the transformed function g(x) = |x – h| is solid.

Use the slider to change the value of h. How does changing the value of h affect the vertex?

Positive values of h shift the graph .
Negative values of h shift the graph

Answers

9514 1404 393

Answer:

positive: rightnegative: left

Step-by-step explanation:

In the transformed function f(x-h), the value of h is the right shift of the parent function.

For h positive, shift is to the right.

For h negative, shift is to the left.

Changing the value of h shifts the graph horizontally. Positive values of h shift the graph to the right. Negative values shift left.

Note: there is a minus sign in front while the value of h is positive, i.e. |x - 5| is shifted 5 units to the right, and |x - (-5)| = |x + 5| is shifted 5 units to the left.

Suppose an airline policy states that all baggage must be​ box-shaped with a sum of​ length, width, and height not exceeding 144 in. What are the dimensions and volume of a​ square-based box with the greatest volume under these​ conditions?

Answers

Answer:

110592 in³

Step-by-step explanation:

Since baggage should take the shape of a box; with the sum of it's dimension not exceeding 144 ;

Dimensions of a box : length, width, height

If ; l + w + h = 144

Greatest volume is obtained when the dimension is equal : such that l = w = h

Hence, each dimension becomes ; 144 / 3 = 48 in

Volume of box = length * width * height

Volume = 48 * 48 * 48

Volume = 48³ = 110592

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