Which two inequalities can be used to find the solution to this absolute value inequality?

Which Two Inequalities Can Be Used To Find The Solution To This Absolute Value Inequality?

Answers

Answer 1

The two inequalities that can be used to find the solution are x-1 < 3 and x-1 > -3.

The given inequality is 3 + 2|x-1| < 9.

The absolute value |x-1| can be (x-1) or -(x-1).

We need to solve this inequality for this two cases.

So first if |x-1| = (x-1), then,

3 + 2|x-1| < 9

⇒ 3 + 2(x-1) < 9

⇒ 2(x-1) < 6

x-1 < 3

⇒ x < 4 is the solution.

Now if |x-1| = -(x-1), then,

3 + 2|x-1| < 9

⇒ 3 - 2(x-1) < 9

⇒ -2(x-1) < 6

⇒ -(x-1) < 3  

x-1 > -3  [When multiplied with (-1), the inequality reverses]

⇒ x > -2 is the solution.

Going through these steps, we can conclude that the two inequalities that can be used to find the solution to the absolute value inequality,

3 + 2|x-1| < 9 are x-1 < 3 and x-1 > -3.

Learn more about absolute value inequality at https://brainly.com/question/26752212

#SPJ1


Related Questions

Find the missing number: 11, 29, 11, when average (mean) Is 17

Answers

The missing number (x) from the sequence → 11, 29, 11, x  is 17.

We have the mean of given set of numbers.

We have to identify the missing number.

What is mean of a given set of data ?

The mean in math and statistics summarizes an entire dataset with a single number representing the data's center point or typical value. It is calculated  using the formula -

Mean (M) = ∑a[i] / n

where -  

∑a[i] = sum of the elements in a data set

n = total number of elements

According to the question - assume that the missing number is x. Then, we have -

11, 29, 11, x

Now, using the formula of mean -

M = ∑a[i] / n

17 = (11 + 29 + 11 + x)/4

68 = 51 + x

x = 68 - 51

x = 17

Therefore, the missing number is 17.

To solve more questions on Mean, visit the link below-

https://brainly.com/question/15448310

#SPJ1

-4 1/2 + 3 1/4 I need help solving this question. And please show me the steps.

Answers

It should be noted the difference between - 4 1/2 and 3 1/4 is - 1/14.

How to illustrate the information?

It should be noted that fractions are not while numbers. The number at the top is the numerator and the number down is the denominator.

In this case:

- 4 1/2 + 3 1/4

= - 4 2/4 + 3 1/4

= - 1 1/4

Therefore, it should be noted the difference between - 4 1/2 and 3 1/4 is - 1/14.

Learn more about fractions on:

brainly.com/question/17220365

#SPJ1

Solve the inequality and express your answer in interval notation.
x^2+ 12x+7<0

Answers

The solution in interval form is given as (-∞, -6-√29

] or [-6+√29, ∞)

Inequality expression

Given the quadratic inequality below;

x^2+ 12x+7<0

Using the general formula

x = -12±√12²-4(1)(7)/2(1)

x = -12±√144-28/2

x = -6±√116/2

x = -6±√29

Hence the solution in interval form is given as (-∞, -6-√29

] or [-6+√29, ∞)

Learn more on inequality here; https://brainly.com/question/24372553

#SPJ1

Find the value of unknown​

Answers

The value of x is 52° and the value of y is 104 ° as calculated using the chord properties of a circle.

A circle is defined as the locus of a moving point such that the distance of the point from a fixed point is always same.

A chord is a straight line joining any two points on a circle.The diameter is the largest chord.The angle subtended by the diameter at the center is always 90° .

In the given figure AC is the diameter of the circle.

We know that the  angle subtended by the chord is always 90°.

∴∠CBA = 90°

Now in ΔABC

∠ABC+∠BCA+ ∠CAB =180° (sum of all angles of a triangle is always 180°)

or, 90° + 38° + x° = 180°

or, 128° + x° =180°

or, x = 52°

Again in ΔDBC ,

DB=DC (radius of the circle)

∴∠DCB = ∠DBC (base angles of an isosceles triangles are equal)

∴∠DBC = 38°

Again in ΔDBC

∠DBC+∠BCD+ ∠CDB = 180° (sum of all angles of a triangle is always 180°)

or, y =  180° - 76°

or, y = 104°

Therefore the value of x is 52° and the value of y is 104 ° .

To learn more about circle visit:

https://brainly.com/question/23247585

#SPJ9

Write the slope, intercept form of the equation of the line describe

Through (3,-2) and parallel to y=-x+5

Answers

Answer:

y = - x + 1

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - x + 5 ← is in slope- intercept form

with slope m = - 1

• Parallel lines have equal slopes , then

y = - x + c ← is the partial equation of the parallel line

to find c substitute (3, - 2 ) into the partial equation

- 2 = - 3 + c ⇒ c = - 2 + 3 = 1

y = - x + 1 ← equation of parallel line

COMPLETE
You can verify that your answer is a solution to the original equation by checking -1/2(-14)-3=4 is a
true statement. Which property of equality allows you to do this?
Oreflexive
Otransitive
substitution

Answers

Answer:  Substitution

Explanation:

Think of a substitute teacher. They temporarily replace your original teacher. The same idea applies with replacing the variable with a number.

For example, the equation x+2 = 7 has the solution x = 5. We can check this by substituting or replacing x with 5 to say 5+2 = 7, which is indeed a true mathematical statement. This confirms the solution.

Drag the purple points to show the location of G, H, and I after a 90° clockwise rotation around (0, 0) Then enter the coordinates of G', H, and I' in the table.

Answers

Answer:The value of coordinates G', H', and F' are (1,6) , ( 7,3) and (4 , 0) respectively.What are coordinates?A pair of numbers that employ the horizontal and vertical distinctions from the two reference axes to represent a point's placement on a coordinate plane. typically expressed by the x-value and y-value pairs (x,y).Coordinates are always written in the form of small brackets the first term will be x and the second term will be y.For example (5,3) here 5 will be for the x and 3 will be for the y.Another example is (9,0) here 9 is for x and 0 is for y.

Step-by-step explanation:

what is (2.49 x 10^4)\(3.0x 10^2) written in scientific notation?
a. 8.3 x 10^1 b. 0.83x 10^2 c. 83x 10^2 d. 830x 10^1

Answers

A.) 8.3 x 10^1

The rules of scientific notation are similar to the laws of exponents (if u know them) in the sense that: 10^a / 10^b is equal to 10^(a-b)

So, 10^4 / 10^2 = 10^(4-2) = 10^2.

Then, you divide 2.49 by 3.0 and you get 0.83. But correct scientific notation requires the decimal to be one digit right of the first significant digit, so 0.83 becomes 8.3 and when you change the decimal place you also have to change the scientific notation. So 0.83 x 10^2 becomes 8.3 x 10^1 because we are moving the decimal place to the right. When the decimal moves to the right the power of ten decreases and when the decimal moves to the left it increases.

Hope this helped!

Find the equation the line with a slope of 2 and that passes
through the point (1, 6).
Enter your answer in slope-intercept form, y = mx + b

Answers

Answer:

y = 2x +4

Step-by-step explanation:

Equation of a line in slope-intercept form is

y = mx + b

where m is the slope and b is the y-intercept, the point at which the line crosses the y axis (at x = 0)

Given slope is 2 we get the equation as

y = 2x + b

We have to solve for b by plugging in the x and y values for point(1,6)

Thus we get y = 6 = 2(1) + b

Or 6 = 2 + b

b= 6-2 = 4

Equation in slope-intercept form is

y = 2x +4

Hi!

Apply the Point-Slope formula:

[tex]\textsl{y-y1=m(x-x1)}[/tex]

◈Where:

y₁ -> the y-coordinate of the pointm -> slopex₁ -> x-coordinate

◈We know that:

y₁ -> 6m -> 2x₁ -> 1

◈Plug in the values:

[tex]\boldsymbol{y-6=2(x-1)}[/tex](simplify) [tex]\boldsymbol{y-6=2x-2}[/tex](add 6 to both sides) [tex]\boldsymbol{y=2x+4}[/tex]

[tex]\bigstar\textsf{\textbf{Solution: \boxed{\textsf{\textbf{2x+4}}}}}[/tex]

Have a great day!

I hope this helped!

-stargazing

Find the distance of the line segment below.



___ units

Answers

Answer:

let (5,4)=(x1,y1)

(-3,-2)=(x2,y2)

now, by using distance formula

we get distance between line segment =10 unit

therefore distance =10 units ans

Solution,

As the formula...

[tex] = \sqrt{( - 3 - 5 {)}^{2} + ( - 2 - 4 {)}^{2} } [/tex]

[tex] = \sqrt{( - 8 {)}^{2} + ( - 6 {)}^{2} } [/tex]

[tex] = \sqrt{64 + 36} [/tex]

[tex] = \sqrt{100} [/tex]

= 10 units...

☘☘☘....

How many solutions does 2b - 5 = 9 have

Answers

Answer:

1 solution

b=7

Step-by-step explanation:

https://brainly.com/question/13774149

2b - 5 = 9

2b=14

b=7

1 solution

Line L intersecting plane M at Q

Answers

What? Not enough information

I’m not sure what to do

Answers

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here we go ~

First of all, it's a graph of mod function, which is transformed.

So, let's proceed with taking graph of modulus initially ~

[tex]\qquad \sf  \dashrightarrow \: y = |x| [/tex]

The required can be tranformed by moving it three units left and four units down.

so, we need to add 3 to x within the function to move it left by units.

i.e

[tex]\qquad \sf  \dashrightarrow \: y = |x + 3| [/tex]

Now, to move it down by 4 units we need to subtract 4 from the whole function.

[tex]\qquad \sf  \dashrightarrow \: y = |x + 3| - 4[/tex]

So, the correct choice is : C

the required can be transformed by moving at 3 units left and 4 units down do you understand ? after that are 3 and x

y = x + 3

now to move it down by 4 units we need to subtract for from the whole function which is y is equal to x + 3 - 4

y = |x+3| - 4

the answer is c

please help asap no one has been able to solve it :(
I need help

Answers

Answer:

givenMultiplication property of equalityMultiplicative inverse propertyMultiplicative identity propertyAddition property of equalityAdditive inverse propertyAdditive identity property

Step-by-step explanation:

You are given the solution to a 2-step linear equation and asked to identify the properties of equality and operations that support the steps of the solution.

Steps

5(x -3) = 20 . . . . This is the Given equation we're solving.

(1/5)(5(x -3)) = (1/5)(20) . . . . Both sides are multiplied by 1/5. The Multiplication property of equality says you can do this without changing the value of the variable.

1(x -3) = 4 . . . . (1/5)(5) is replaced by 1. The Multiplicative inverse property tells you the product of a number and its multiplicative inverse is 1.

x -3 = 4 . . . . 1(x -3) is replaced by (x -3). The Multiplicative identity property tells you multiplication by 1 changes nothing. These properties of multiplication are what allow you to remove the factor of 5 from the equation.

Now, we're about to do the same thing with addition: use its properties to remove the unwanted -3.

x -3 +3 = 4 +3 . . . . 3 is added to both sides. The Addition property of equality says you can do this without changing the value of the variable.

x +0 = 7 . . . . -3+3 is replaced by 0. The Additive inverse property tells you the sum of a number and its additive inverse is zero.

x = 7 . . . . x+0 is replaced by x. The Additive identity property tells you addition of 0 changes nothing. These properties of addition are what allow you to remove the added -3 from the equation.

__

Additional comment

Clearly, for exercises like this, it is essential to know the names of these properties and what they mean. Once you understand cancelling multiplication using multiplicative inverses, and cancelling addition using additive inverses, you are on your way to solving most algebra problems.

You must always keep in mind the properties of equality that tell you the same operation must be performed on both sides of the equal sign.

Understanding these properties can also help you understand the relation between multiplication and division, addition and subtraction. Division is multiplication by the multiplicative inverse; subtraction is addition of the additive inverse.

For a total accumulated amount of $3688.86, a principal of $2000, and a time period of 5 years, use the compound interest formula to find r, if interest is compounded
monthly.
r=

Answers

The interest rate required to get a total amount of $3,688.86 from compound interest on a principal of $2,000.00 compounded 12 times per year over 5 years is 12.306% per year.

Given,

The total amount (A)= $3688.86

Principal (P) = $2000

time period (t) = 5 years.

compounded monthly (n) = 12

rate of interest per year = ?

we know that r=n[(A/P)¹/ⁿt  -1]

substitute the above values.

r = 12 × [(3688.86/2000)¹/⁽¹²⁾⁽⁵⁾ - 1]

r = 12 × [(1.84443)¹/⁶⁰ - 1]

r = 12 × 0.0102

r = 0.12306

Now convert r to R as a percentage.

R = r × 100

R = 0.12306 × 100

R = 12.306%

Hence the rate of interest compounded monthly is 12.306%

Learn more about Compound Interest here:

brainly.com/question/24924853

#SPJ9

Find the sum. 2 3/8 + 4 4/8

Answers

6 and 7/8ths is the answer

Question 8, 1.2.35-PS
Part 1 of 5
iew an example
HW Score: 44.44%, 4
O Points: 0 of 1
- Scatterplots and Graphs
K
If a ball is thrown into the air at 96 feet per second from the top of a 109-foot-tall building, its height can be modeled by the function S=109+961-162, where S is in feet and t is in seconds.
Complete parts a through e below.
a. Graph this function for t representing 0 to 8 seconds and S representing 0 to 300 feet. Choose the correct graph below.

Answers

The quadratic function in this problem is represented by Graph C.

What is the quadratic function for this problem?

The quadratic function for the projectile height after t seconds is given by:

S(t) = 109 + 96t - 16t²

From this, we have that:

Due to the negative coefficient of t², it is a concave down parabola, which remoces option d.The initial height is of 109 feet, which removes option b.The initial velocity is positive, which means that the parabola has increasing height for a while before decaying, which removes option A.

Thus, the quadratic function in this problem is represented by Graph C.

More can be learned about quadratic functions at https://brainly.com/question/24808124

#SPJ1

Sally is running laps around a track. She runs 12 laps to warm up. Then she runs 13² laps.
How many laps does Sally run in all? Move numbers to the boxes to show the answer.

Answers

Answer:

181

Step-by-step explanation:

Sally is running laps around a track. She runs 12 laps to warm up. Then she runs 13² laps.

First write the equation. we know she alr ran 12 laps so its going to be +12

to 13^2. so the equation will be 12+13^2 then using PEMDAS we know that we have to do the exponents first so 13^2 is just 13 * 13 which is 169. so now the equation is 169+12 now just add. the answer is 181

For the following exercises, find functions
f(x) and g(x) so the given functions can be expressed as h(x)=f(g(x)). There are multiple possible answers. If the answers require exponents, enter the answer with an exponent in f(x) but not in g(x).
h(x)= 8/(x+4)^2

Answers

The functions f(x) and g(x) so the given function can be expressed as h(x) = f(g(x) are f(x) = 8/x^2 and g(x) = x + 4

How to find functions f(x) and g(x) so the given functions can be expressed as h(x) = f(g(x))?

The function h(x) is given as:

h(x) = 8/(x + 4)^2

The definition of the function h(x) is

h(x) = f(g(x))

So, we have:

f(g(x)) = 8/(x + 4)^2

Let g(x) = x + 4

So, we have:

f(g(x)) = 8/(g(x))^2

Express g(x) as x

So, we have:

f(x) = 8/x^2

Hence, the functions f(x) and g(x) so the given function can be expressed as h(x) = f(g(x) are f(x) = 8/x^2 and g(x) = x + 4

Read more about composite functions at:

https://brainly.com/question/13502804

#SPJ1

In the triangle above, if BC = 21 and sin A = 0.7, what is the length of AB?

With explanation

Answers

Haahjahahahahahahahah this?

Question 2 If n = 22, + = 30, and s = 7, construct a confidence interval at a 98% confidence level. Assume the data came from a normally distributed population. Give your answers to three decimal places. ​

Answers

The confidence interval for n = 22, X bar = 30 and σ = 7 at a 98% confidence level is 30 ± 3.472 which means the value will range between [26.528 – 33.472] respectively.

In statistics, a confidence interval is a range of values that is determined through the use of observed data, calculated at a desired confidence level that may contain the true value of the parameter being studied.

The formula used for the calculation of confidence interval is given by

Confidence level = X bar ± Z×σ/√n

where, X bar is the sample mean, Z is the confidence level value, σ is the sample standard deviation and n is the sample size.

Given that, n = 22, X bar = 30, σ = 7 and Z = 2.326 for 98%

= 30 ± 2.3263 × 7/√22

= 30 ± 3.472

= [26.528 – 33.472]

Therefore, The confidence interval for n = 22, X bar = 30 and σ = 7 at a 98% confidence level is 30 ± 3.472 which means the value will range between [26.528 – 33.472] respectively.

Hence, 30 ± 3.472 or [26.528 – 33.472] is the required answer.

Learn more in depth about confidence interval at https://brainly.com/question/14825274

#SPJ9

The perimeter of a rectangular field is surrounded by 96 meters of fencing. If the field is partitioned into two parts as shown, a total of 110 meters of fencing is required. Find the dimensions of the field.

Answers

The dimensions of the field is Length = 34 meters, width = 14 meters.

Let rectangle: x for width, y for length.

2 ( x + y ) = 96

x + y = 48

2 ( x + y ) + x = 110

x = 110 - 96

x = 14

x + y = 48

y = 48 - 14 = 34

Length = 34 meters, width = 14 meters.

A quadrilateral with equal angles and parallel opposing sides is referred to as a rectangle. Around us, there are a lot of rectangle items. The length and breadth of any rectangle form serve as its two distinguishing attributes. The width and length of a rectangle, respectively, are its longer and shorter sides.

A closed shape with four sides that forms a 90° angle is known as a rectangle. A rectangle can have many different characteristics. The following list includes some of a rectangle's key characteristics.

A quadrilateral is a rectangle.

A rectangle's opposing sides are equal and parallel to one another.

Each vertex of a rectangle has a 90° internal angle.

360° is the total of all interior angles.

The diagonals cut each other in half.

The diagonals are all the same length.

To learn more about rectangle visit:https://brainly.com/question/15019502

#SPJ4

Find the equation to the line below.
y=4/5x +?

Answers

Answer:

y =x - 1

Step-by-step explanation:

Slope intercept of a line: y =mx + b

Here, m is the slope and b is the y-intercept.

Plot any two points on the line. (5,4)  & (0,-1)

[tex]\sf \boxed{Slope =\dfrac{y_2-y_2}{x_2-x_1}}[/tex]

          [tex]\sf =\dfrac{-1-4}{0-5}\\\\=\dfrac{-5}{-5}\\\\=1[/tex]

m = 1

At y-intercept x = 0.  So, the -1 is the y-intercept.

m = 1 & b = -1

y = 1x + (-1)

A mile is 5,280 feet between which two integers is the elevation of the trench in miles-22,889 feet is between and miles

Answers

The elevation of the trench is between 4 miles and 5 miles.

Between which integers is the elevation of the trench in miles?

Herein we have the information of the elevation of the trench in feet and we need to determine between which integers in miles is that elevation, based on the unit conversion from feet to miles. The exact elevation in miles is found by simple rules of three:

x = 22,889 feet × (1 / 5,280 miles / feet)

x ≈ 4.335 miles

The elevation of the trench is between 4 miles and 5 miles.

To learn more on unit conversions: https://brainly.com/question/11543684

#SPJ1

Write 21 50 as a percent and as a decimal.

Answers

Hopefully you meant 21/50 it is 42% and 0.42

How tall is the flag pole (please give explanation too)

Answers

Answer:

  22 3/4 ft

Step-by-step explanation:

The diagram seems to show a 6 1/2 ft person casting a 9 ft shadow at the same time a flagpole is casting a 31 1/2 ft shadow. You want the height of the flagpole.

Proportion

Shadow lengths are presumed proportional to the height of the object making them. This means ...

  h/(31 1/2) = (6 1/2)/9 . . . . . all lengths in feet

Multiplying by 31 1/2, we get ...

  h = (31 1/2)(6 1/2)/9 = (819/4)/9 = 91/4

  h = 22 3/4 . . . . ft

The flagpole is 22 3/4 feet tall.

Five more than the quotient of a number and 9 is equal to 3

Answers

Answer:

5+n/9=3

Step-by-step explanation:

help with 2,3,&4. pleaseee!! wil mark as brainly list

Answers

Answer:

brainly list not allowed macht

Find B if A=70° and a + b = 80°

Answers

Answer:

B=30°

Step-by-step explanation:

Recall that the sum of interior angles of a triangle equals to 180°. So basically

[tex]A+B+\alpha+\beta=180^{\circ}[/tex]

[tex] \implies B + {70}^{ \circ} + {80}^{ \circ} = {180}^{ \circ} \\ \implies B = {180}^{ \circ} - {150}^{ \circ} \\ \implies B = \boxed{{30}^{ \circ} }[/tex]

Country A produces about six times the amount of diamonds in carats produced in country B.If the total produced in both countries is 28,000,000 carats

Answers

The diamonds produced by country A and B are 24,000,000 and 4,000,000 carats respectively.

Here, we are given that Country A produces about six times the amount of diamonds in carats produced in country B.

Let the diamonds produced by country B be x

Then, the diamonds produced by country A will be 6x

The total diamonds produced by the two countries = 28,000,000

Thus, we can get the following equation-

x + 6x = 28,000,000

7x = 28,000,000

x = 28,000,000/ 7

x = 4,000,000

⇒ 6x = 24,000,000

Thus, the diamonds produced by country A and B are 24,000,000 and 4,000,000 carats respectively.

Learn more about linear equations here-

https://brainly.in/question/48534636

#SPJ9

Other Questions
consider the primary objectives of marketing: for effective marketing to occur, what must marketers do before they can satisfy the needs of their customers? Kenneth measured a hotel and made a scale drawing. The scale he used was 1 inch = 4 feet. The actual length of a room in the hotel is 20 feet. How long is the room in the drawing can someone help give me any short story ideas about the industrial revolution? A is a mark with length and direction, created by a point that moves across a surface which can vary in length, width, direction, curvature and color. Different types of these are horizontal, vertical, diagonal, curvy, and zigzag.Word Bank:texture shape elements of art value color segments form line implied lines The sum of three consecutive odd numbers is 177. Find the number. Step by step please after albemarle's heat wave, the rest of june was cooler. in fact, at the end of the month, meteorologists reported that the average high for all 30 days in june was just $80^\circ$. what was the average high (in degrees fahrenheit) from june 11 through june 30? (enter your answer as a number without units.) Who set out to finish the work of reform started with the Council of Trent?O Pope Paul IIO Pope Paul IIIO Pope Paul IVO Pope Leo IQuestion 1 12 3 (15 - 6) + 3 Graph the line with a slope of 1/3 passing through point (-1, -1) HELPPPIs the density of an object always the same as its mass?YesNoHow would you calculate the density of an object?mass/areamass/volumeAfter completing the liquids portion of the lab, which liquid was the least dense?oilwatersyrupIn a density column experiment (like the one explained in the lesson), the density of the liquids depends on the order in which they are added to the column.TrueFalseWould a golf ball or a ping pong ball (of the same volume) have more density?golf ballping pong ball significant influence over an investee may be indicated by material intercompany trans-actions and interchange of managerial personnel. what numbers are missing from the pattern? 11,22,?,?,?,?,77,88,99Please Answer ASAP!!! HURRY:) Kristen goes on a cave tour with her family. They climb down to 8 meters below ground level.Then they climb the opposite of -8 meters to return to ground level.How many meters did they climb in all? Enter your answer in the box social workers need to learn about and engage in research for all of the following reasons except quizley For the function f(x) = x + 10/6x + 4, consider the following.(a)Find the vertical and horizontal asymptotes for the graph of f.Vertical:Horizontal:b)Find f^ 1.f^ 1(x) = c)Find the vertical and horizontal asymptotes for the graph of f^ 1Vertical:Horizontal:Show all steps. y=-x+4x + 2y = -8How many solutions does this linear system have?a. one solution: (8,0)b. one solution: (0,8)c. no solutiond. infinite number of solutions when teachers organize their classes into groups for a spelling bee they are indirectly teaching students the value of competion really need an explanation Solve the system by back substitution.-2x - 4y - z - 3w = -5y + 6z + 2w = 84z + 4w = 8-4w = -12Solution should be set like {( _ , _ , _ , _ )} What is a group of lines that go together in a poem?stanzacoupletrhymeparagraph