Write the absolute value inequality in the form |xb| < c or |xb|>c that has the solution set x<7 or x>5.

The abslute frm f the given inequality is |x+1|>6.What is inequality?In mathematics, inequality is a statement f an rder relatinship that is a relatinship between tw values that are nt equal,greater than, greater than r equal t, less than, r less than r equal tbetween tw numbers r algebraic expressins. Such as 7<9 r 5>3 etc.Given inequality isx<7 r x>5The distance between -7 and 5 is5- (-7) = 5+7= 12Dividing that by 2 we get,12/2 =6It is the c valueWe use the greater than since we have an r|xb|>6 ----------------- (1)Substituting a value x=5 in equatin (1) with an equals sign t determine b we get5-b =6b= -1The abslute frm f the given inequality is |x+1|>6To know more about inequality https://brainly.com/question/30238989#SPJ1

Mathematics College

Write the absolute value inequality in the form |x−b| < c or |x−b|>c that has the solution set x<−7 or x>5.

Answers

Answer 1

The absοlute fοrm οf the given inequality is |x+1|>6.

What is inequality?

In mathematics, inequality is a statement οf an οrder relatiοnship that is a relatiοnship between twο values that are nοt equal,—greater than, greater than οr equal tο, less than, οr less than οr equal tο—between twο numbers οr algebraic expressiοns. Such as 7<9 οr 5>3 etc.

Given inequality is

x<−7 οr x>5

The distance between -7 and 5 is

5- (-7) = 5+7= 12

Dividing that by 2 we get,

12/2 =6

It is the c value

We use the greater than since we have an οr

|x−b|>6 ----------------- (1)

Substituting a value x=5 in equatiοn (1) with an equals sign tο determine b we get

5-b =6

b= -1

The absοlute fοrm οf the given inequality is |x+1|>6

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Related Questions

A rectangle is drawn so the width is 7 inches longer than the height . If the rectangle’s diagonal measurement is 34 inches, find the height

Answers

Answer:

To solve this problem, we can use the Pythagorean theorem, which relates the sides of a right triangle. Let's call the height "h" and the width "w". Then we have: w = h + 7 (since the width is 7 inches longer than the height) We also know that the diagonal measurement is 34 inches, so we can use the Pythagorean theorem to relate the height, width, and diagonal: h^2 + w^2 = d^2 Substituting the values we have: h^2 + (h+7)^2 = 34^2 Expanding and simplifying: 2h^2 + 14h - 795 = 0 Now we can solve for h using the quadratic formula: h = (-14 ± sqrt(14^2 - 4(2)(-795))) / (

Solve the simultaneous equations

X-Y=-1
2X-Y=0

Answers

Answer: X = 1, Y = 2

Step-by-step explanation:

X - Y = -1

X = Y - 1

2(Y - 1) - Y = 0

2Y - 2 - Y = 0

Y - 2 = 0

Y = 2

X - (2) = -1

X - 2 = -1

X = 2 - 1

X = 1

The mean weight of an adult is 79 kilograms with a standard deviation of 10 kilograms. If 188 adults are randomly selected, what is the probability that the sample mean would be greater than 80.5 kilograms? Round your answer to four decimal places.

Answers

The average adult weight is 79 kilοgrammes, with a standard deviatiοn οf 10 kilοgrammes.

We want tο find the prοbability that the sample mean οf 188 adults wοuld be greater than 80.5 kilοgrams.

An n-sample sample mean is given by: x = xi / n

where xi is the tοtal οf the sample's individual weights.

The sample mean distributiοn is apprοximately nοrmal, with mean = 79 and standard deviatiοn [tex]= 10 /\sqrt{(n)} = 10 / \sqrt{(188)0.727.}[/tex]

We can standardise the sample mean tο find the prοbability that it is greater than 80.5 kilοgrammes using the fοrmula: [tex]z = (x - ) / ( / \sqrt{(n)})[/tex]

where z is the standard nοrmal variable.

Substituting the values, we get:

[tex]z = (80.5 - 79) / (10 / \sqrt{(188)}) \approx2.14[/tex]

Using a standard nοrmal table οr calculatοr, we can find the prοbability that z is greater than 2.14:

P(z > 2.14) ≈ 0.0161

Therefοre, the prοbability that the sample mean οf 188 adults wοuld be greater than 80.5 kilοgrams is apprοximately 0.0161, rοunded tο fοur decimal places.

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A rectangular prism has a base area of 54 m square, and a volume of 702 m. What is its height?

Answers

Answer:

Therefore, the height of the rectangular prism is approximately 13 meters.

Step-by-step explanation:

Let's call the height of the rectangular prism "h". We know that the base area is 54 m², which means that the product of the length "l" and the width "w" is 54. In other words:

l × w = 54

We also know that the volume of the rectangular prism is 702 m³, which means:

l × w × h = 702

We can use the first equation to solve for one of the variables, for example:

w = 54 / l

Substituting this expression for "w" into the second equation, we get:

l × (54 / l) × h = 702

Simplifying and canceling the "l" terms, we get:

54h = 702

Dividing both sides by 54, we get:

h = 702 / 54

Simplifying this expression, we get:

h ≈ 13

Therefore, the height of the rectangular prism is approximately 13 meters.

Vary the plane of intersection, and note all the types of cross sections you observe. In the table, describe the shape of the cross section formed when a particular plane passes through the pyramid.

Answers

Answer:

Cross Sections

In this task, you will use cross section flyer, an online tool, to investigate the cross sections of cones, cylinders, pyramids, and prisms by passing different planes through such objects.

For each part of this task, you will select a three-dimensional object from the list of shapes in the bottom-left corner of the screen. A three-dimensional view of the object appears on the left, and the two-dimensional cross section formed by the intersection of the object with the chosen plane appears on the right. The bottom-right controls allow you to rotate and move the plane of intersection. By varying the intersecting plane, you can change the resulting cross section.

You can also adjust the view of the three-dimensional object by clicking and dragging anywhere inside the object window. Use the coordinate X-Y-Z axes to guide you through the views. You can verify the name of a cross section by using the Click to show identification of cross section checkbox.

Aldrin bought 5 pencils and 7 notebooks. A notebook cost 10. 80 more than a pencil write an algebraic equation showing that the total amount of the school supplies bought is210. 00

Answers

Answer:

5x + 7(x + 10.80) = 210.00

Step-by-step explanation:

Let x be the cost of a pencil in dollars. Then, the cost of a notebook is 10.80 dollars more, which is x + 10.80 dollars.

Aldrin bought 5 pencils and 7 notebooks, so the total cost is:

5x + 7(x + 10.80) = 210.00

Simplifying and solving for x, we have:

5x + 7x + 75.60 = 210.00

12x = 134.40

x = 11.20

Therefore, a pencil costs 11.20 dollars and a notebook costs 10.80 dollars more, which is 22.00 dollars.

We can check that the total cost of 5 pencils and 7 notebooks at these prices is indeed 210.00 dollars:

5 pencils * 11.20 dollars/pencil + 7 notebooks * 22.00 dollars/notebook = 56.00 dollars + 154.00 dollars = 210.00 dollars

Fill in table using this function rule y= -4x - 2. I'm confused on on the table of function on what they y is when x is -10

Answers

When x is -10, the value of y is 38. This means that the point (-10, 38) is on the graph of the function y = -4x - 2.

We must determine the values of x and solve for the matching value of y in order to fill in the table using the function rule y = -4x - 2. The table can then be populated with the resulting values for x and y.

An illustration table with x values ranging from -3 to 3 is shown below:

x y

-3 10

-2 6

-1 2

0 -2

1 -6

2 -10

3 -14

We may easily change x in the function rule y = -4x - 2 to -10 to find the value of y when x is -10:

y = -4(-10) (-10) - 2 \sy = 40 - 2 \sy = 38

As a result, y equals 38 when x is -10. This indicates that the point (-10, 38) is located on the y = -4x - 2 function graph.

It's vital to remember that the numbers in the table are produced by inserting various x values into the function rule, and the resulting y-values represent the corresponding locations on the function's graph. The line passing through the point on the graph of the function y = -4x - 2 has a slope of -4 and a y-intercept of -2. (-10, 38).

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Part B What is the recursive formula for the sequence 8, 10, 12.5, 15.625

Answers

Answer:

Step-by-step explanation:

The given sequence can be written as:

a_1 = 8

a_2 = 10

a_3 = 12.5

a_4 = 15.625

To find the recursive formula, we need to find the common ratio (r) between consecutive terms:

r = a_2 / a_1 = 10 / 8 = 1.25

r = a_3 / a_2 = 12.5 / 10 = 1.25

r = a_4 / a_3 = 15.625 / 12.5 = 1.25

Since the common ratio is constant, we can use the formula for a geometric sequence to find the recursive formula:

a_n = r * a_{n-1}

Substituting r = 1.25 and a_1 = 8, we get:

a_n = 1.25 * a_{n-1}

Therefore, the recursive formula for the given sequence is:

a_n = 1.25 * a_{n-1}, with a_1 = 8.

A portfolio has a value P(E, S), so that the value P is a function of E, the price of a Euro in Canadian dollars, and S, the level of the TSX stock index. Presently the portfolio is worth $207,000, while a Euro is $1.50 Canadian, and the index is S = 18,000. If the partial derivatives of P have values ∂P ∂E = 80,000, and ∂P ∂S = −20, what approximately will the portfolio value be if the price of a Euro goes down by 0.07 and the stock index goes down by 629?

Answers

Answer:

The new value of the portfolio would be $207,000 - $18,180 = $188,820

Step-by-step explanation:

Using the first-order partial derivatives, we can calculate the approximate change in the portfolio value due to changes in E and S using the formula:

ΔP ≈ ∂P/∂E * ΔE + ∂P/∂S * ΔS

where ΔE is the change in the price of a Euro and ΔS is the change in the TSX stock index.

Given that ∂P/∂E = 80,000 and ∂P/∂S = -20, and the changes ΔE = -0.07 and ΔS = -629, we can plug in the values and get:

ΔP ≈ 80,000 * (-0.07) + (-20) * (-629)

≈ -5,600 - 12,580

≈ -18,180

Therefore, the portfolio value is expected to decrease by approximately $18,180 if the price of a Euro goes down by $0.07 and the TSX stock index goes down by 629 points. The new value of the portfolio would be $207,000 - $18,180 = $188,820.

The average annual cost (in dollars) of tuition and fees at a 2 -year college for selected years is shown in the given table, where year 0 represents 2004. The data can be approximated by the equation y=83.66x+3915 . Predict the average annual cost in 2014 to the nearest dollar.

Answers

The average annual cοst in 2014 is $4751.6.

What is equatiοn?

The definitiοn οf an equatiοn in algebra is a mathematical statement that demοnstrates the equality οf twο mathematical expressiοns. Fοr instance, the equatiοn 3x + 5 = 14 cοnsists οf the twο equatiοns 3x + 5 and 14, which are separated by the 'equal' sign.

Here the given equatiοn that represent the annual cοst in dοllars.

=> y = 83.66x+3915

Where x= number οf years

In 2004 , t = 0 years

Sο , In 2014 , t = 2014-2004 = 10 years.

Then average annual cοst in 2014 is,

=> y=83.66(10)+3915

=> y=836.6+3915

=> y = $4751.6.

Hence the average annual cοst in 2014 is $4751.6.

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Let A ={1, 2, 3, 4, 5}, and let R be the relation on A given by
R= {(x, y): x y and x is prime)
i. List the elements of R
ii. Give matrix representation of R
iii. Give di-graph of R.
iv. Check whether R is reflexive, symmetric, transitive, equivalence, anti-symmetric,
asymmetric and irreflexive with reasons.

Answers

Asymmetric: Since, for instance, (2,3) is in R but (3,2) is not, R is not asymmetric. No element in A is connected to itself under R, making R irreflexive.

describe range.

The collection of output values that such a function of relation can produce is referred to as the range in mathematics. It is the distinction between the largest or smallest values within an ensemble of data or a collection of all conceivable function or relation output values.

In other terms, it is the range of possible values for a variable. For instance, the range is 21 - 3 = 18 if the integers are 3, 7, 12, 15, and 21. The set of all value of y which may be produced by a function f(x) for the given subject area of x values is known as the range.

given

We will now examine the many characteristics of the relation R:

As no element in A is connected to itself under R, R is not reflexive. For instance, R does not support (2,2).

R is not symmetric since, for instance, (3,2) is not in R yet (2,3) is.

R is transitive because, for instance, the existence of (2,3) and (3,5) in R entails the existence of (2,5) in R.

Equivalence: As R is not reflexive or symmetric, it is not an equivalence relation.

Asymmetric: Since, for instance, (2,3) is in R but (3,2) is not, R is not asymmetric. No element in A is connected to itself under R, making R irreflexive.

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RQPS is rotated 180° clockwise about the origin.
10
9
8
7
6
5
R
S
P
1 2 3 4 5 6 7 8 9 10
What are the coordinates of P'?
OA. (-7,2)
B. (-2,-7)
O, C. (-7,-2)
D. (7,-2)

Answers

Step-by-step explanation:

The answer is (-2, -7)

Before rotated, the coordinates of P is (7,2)

Imagine if P is rotated 360° clockwise, it will come back to the initial place (7,2).

Now it is just rotated 180° clockwise, halfway of 360° clockwise. So the coordinates should be(-7,-2) after rotated 180° clockwise.

I need help can someone help thxxxx

Answers

Answer:

I hope this helps :)

Step-by-step explanation:

its the correct answer

models the
A 25% orange juice drink is mixed with a 100% orange juice drink. The function f(x) (4)(1.0)+z(0.25)
=
concentration of orange juice in the drink after a gallons of the 25% drink are added to 4 gallons of pure juice.
4+z
What will be the concentration of orange juice in the drink if 2 gallons of 25% drink are added? Give the answer as a percent
but do not include the percent sign (%).

Answers

The amount of citrus juice in the combination is therefore 0.75, or 75%.

A volume basic meaning is what?

The area filled within an object's boundaries in three dimensions is referred to as its volume. It is also referred to as the object's potential.

If 2 gallons of 25% orange juice drink are added to 4 gallons of pure orange juice, then the total volume of the mixture will be 2 + 4 = 6 gallons.

Let's use the given function f(x) to calculate the concentration of orange juice in the mixture:

f(2) = (4 × 1.0 + 2 × 0.25) / (4 + 2)

= (4 + 0.5) / 6

= 4.5 / 6

= 0.75

Therefore, the concentration of orange juice in the mixture is 0.75 or 75%.

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Eleni rents a car on two separate occasions. The first time she pays $180 for 3 days and 150km

Answers

The average cost per day is $90 and the average cost per km is $0.655.

To calculate the average cost per day, we need to first calculate the total cost of renting the car for both occasions and divide it by the total number of days.

The total cost of renting the car for both occasions is $180 + $180 = $360. The total number of days is 4 (2 days for each occasion).

Therefore, the average cost per day is $360 ÷ 4 = $90.

To calculate the average cost per km, we need to first calculate the total cost of renting the car for both occasions and divide it by the total number of kilometers driven.

The total cost of renting the car for both occasions is $180 + $180 = $360. The total number of kilometers driven is 550km (150km for the first occasion + 400km for the second occasion).

Therefore, the average cost per km is $360 ÷ 550km ≈ $0.655.

Correct question is " Eleni rents a car on two separate occasions. The first time, she paid $180 for 2 days and 150km. The next time, she paid $180 for 2 days and 400km. What is the average cost per day? What is the average cost per km?"

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Can anyone help? Look at image below

Answers

Linear Scale Factor:

1) Enlargement. Scale Factor = 18/6 = 3

2) Reduction. Scale factor = 6/12 = 1/2

Kaira collects data on the costs of maracas: $12.50, $13.00, $13.25, $14.25,
$14.50, $14.50, $14.50, $14.75, $15.75, $16.00, $16.50. Explain why a stem-and-leaf
plot would be an appropriate display to use to analyze and interpret the data.

Answers

The stem and leaves display the image and distribute information continuously. These charts are similar to histograms, but instead of using lines, they show numbers. It is a useful tool, especially when searching for statistical information.

The stem and leaf diagram, also known as the stem and leaf diagram, is a method of organizing data in a way that makes it easy to observe the frequency of importance of different species. A chart that shows numerical data arranged in a series. Each data value or number is divided into stems and leaves.

Rows and sheets are represented in the form of a special table in which each first digit or digit of the document value is divided by the stem and the last digit of the document in sheets. The letter is used to represent the stem and leaf, called stem and leaf values.

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16. Find the difference 4/9 - ⅖

17. Find the quotient 2/9 / ⅚

18. Write each terminating decimal as a quotient of integers. (a) 0.437 (b) 8.2

19. Use the method below to decide whether each rational number would yield a repeating or a terminating decimal.
(Hint: Write in lowest terms before trying to decide.)

Terminating decimal - if the only prime factor of the denominator is 2 or 5 or both.
Repeating decimal - if a prime other than 2 or 5 appears in the prime factorization of the denominator.
Example: 24/75 can be simplified to 8/25 by dividing 3 into both the numerator and the denominator. Next, factor the denominator 25 using prime factors: 25 = 5x5, the only prime factor of the denominator is 5 in this case, so the original fraction is a Terminating decimal
(a) 8/15
Is the fraction simplified? (Yes/No) If not, simplify the fraction.
Does the simplified denominator contain factors other than 2 or 5? (Yes/No)
Is it a terminating or repeating decimal? (Terminating/Repeating)

(b) 8/35 Is the fraction simplified? (Yes/No) If not, simplify the fraction.
Does the simplified denominator contain factors other than 2 or 5? (Yes/No)
Is it a terminating or repeating decimal? (Terminating/Repeating)

(c) 13/125 Is the fraction simplified? (Yes/No) If not, simplify the fraction.
Does the simplified denominator contain factors other than 2 or 5? (Yes/No)
Is it a terminating or repeating decimal? (Terminating/Repeating)

(d) 3/24 Is the fraction simplified? (Yes/No) If not, simplify the fraction.
Does the simplified denominator contain factors other than 2 or 5? (Yes/No)
Is it a terminating or repeating decimal? (Terminating/Repeating)

(e) 22/55 Is the fraction simplified? (Yes/No) If not, simplify the fraction.
Does the simplified denominator contain factors other than 2 or 5? (Yes/No)
Is it a terminating or repeating decimal? (Terminating/Repeating)

(f)) 24/75 Is the fraction simplified? (Yes/No) If not, simplify the fraction.
Does the simplified denominator contain factors other than 2 or 5? (Yes/No)
Is it a terminating or repeating decimal? (Terminating/Repeating)

Answers

1 ) Finding the difference 4/9 - ⅖:

We require a common denominator to subtract fractions. The least frequent multiple of 9 and 5 in this example is 45. So we'll recast both fractions with 45 as the denominator:

[tex]\frac{4}{9} = \frac{20}{45} \\\frac{2}{5} = \frac{18}{45}[/tex]

Now we can subtract:

[tex]\frac{20}{45} - \frac{18}{45} = \frac{2}{45}[/tex]

Therefore, the difference between 4/9 and ⅖ is 2/45.

How will you find if the fraction is terminating or repeating?

Examine the prime factors of the denominator when the fraction is in its simplest elementary form to determine if it will have a terminating or repeating decimal. The decimal will end if they are made up of 2s and/or 5s.

2) calculating the quotient 2/9 / ⅚:

Fractions are divided by multiplying the first fraction by the reciprocal of the second fraction. So:

2/9 ÷ ⅚ = 2/9 x 6/5

Before multiplying, we can simplify:

2/9 x 6/5 = 12/45

And here's another example:

12/45 = 4/15

As a result, the quotient of 2/9 56 is 4/15.

3) Writing each terminating decimal as an integer quotient:

(a) 0.437 = 437/1000

(b) 8.2 = 82/10 = 41/5

4) Choosing whether each rational number will result in a repeated or terminating decimal:

(a) 8/15