The right triangle on the right is a scaled copy of the right triangle on the lef
Identify the scale factor. Express your answer as a whole number or fraction
in simplest form.
10
10
20
20

Tara invests $555 into a savings account that has an interest rate of 12.6% and is compounded quarterly. It will take 18.6 years for the account to reach a balance of $5,600.

The amount that the lender charges the client above and beyond the initial amount is referred to as the interest rate. Given the time worth of money, a person who deposits money in a bank or other financial organisation also gets extra revenue known as interest received by the depositor.

Using the quarter compound formula given below-

[tex]$ \rm A = P (1 + \frac{r}{4})^{4 \times t}[/tex]

Where,

Interest in a year (r)= 12.6% = 12.6/100= 0.126

Actual amount (P)= $555

Final amount (A)= $5,600

Lets solve:

[tex]5,600 = 555(1+0.126/4)^{4t[/tex]

Or, [tex](4.126/4)^{4t}= 5600/555[/tex]

Or, 4t ln(4.126/4)= ln 5600/555

Or, 4t =74.532

Or, t ≈ 18.6

Hence the correct answer is 18.6 years

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The probability of selecting a vowel first and then not a vowel second is 2/6 x 5/5 = 10/30 = 1/3.

Probability is a branch of mathematics that deals with the likelihood of something happening. It is used to quantify the chance of a certain event occurring and can help to predict the outcome of a given situation. Probability is based on the concept of randomness, which is the idea that an event's outcome is determined by chance and cannot be controlled or predicted.

The word "replacement" contains 2 vowels (e,a) and 4 consonants (r,p,l,c). Therefore, the probability of selecting a vowel first is 2/6 (2 out of 6 cards are vowels). Since there are 5 cards left after the first selection, the probability of selecting a non-vowel second is 5/5 (5 out of 5 cards are non-vowels).

Therefore, the probability of selecting a vowel first and then not a vowel second is 2/6 x 5/5 = 10/30 = 1/3.

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Complete questions as follows-
You select a card at random from the cards that make up the word “replacement”. Without replacing the card, you choose a second card.
Find the probability of choosing a vowel and then not a vowel.  There is 1 letter for each card.explain how you got the answer please?

Answer:

Step-by-step explanation:

(a) We can use the standard normal distribution to solve this problem. We first need to standardize the distribution by using the formula:

Z = (X - μ) / σ

where X is the transaction time, μ is the mean, σ is the standard deviation, and Z is the standard normal variable.

For 5 customers to finish the transaction within 20 seconds, we need to find the probability that 5 out of 6 customers have a transaction time less than or equal to 20 seconds. We can use the binomial distribution to find this probability:

P(X = 5) = 6C5 * (0.5)^5 * (0.5)^1 = 0.2344

where 6C5 is the number of ways to choose 5 customers out of 6.

(b) After the network upgrade, the transaction time will be reduced by 15%, so the new mean and standard deviation are:

μ' = 0.85 * μ = 17 seconds

σ' = 0.85 * σ = 4.25 seconds

(c) To find the 97th percentile of Y, we need to find the value of t such that P(Y ≤ t) = 0.97. Since Y is a normally distributed variable, we can standardize it using the formula:

Z = (Y - μ') / σ'

Then we can find the value of t using a standard normal distribution table or calculator:

Z = 1.88

t = μ' + Z * σ' = 17 + 1.88 * 4.25 = 25.99 seconds

(d) After the upgrade, a higher proportion of customers can finish the transaction within 20 seconds. This is because the mean transaction time has decreased from 20 seconds to 17 seconds, which means that more customers will have a transaction time less than or equal to 20 seconds.

Answer:

200ft²

Step-by-step explanation:

SA = 8(15) + (8+15+17) 20

= 120+ (4)(20)

= 120+80

= 200ft²

Rounding to the nearest unit, the average annual rate of change during this time period is 10,797.

An equation is a mathematical statement that shows that two expressions are equal. It typically contains variables, coefficients, and mathematical operations such as addition, subtraction, multiplication, and division. An equation can be solved to find the value of the variable that makes the statement true. Equations are used in many areas of mathematics and science, as well as in everyday life, to model relationships and solve problems.

Here,

To find the average annual rate of change, we need to calculate the total change in subscribers over the 6-year period and divide by the number of years. The total change is the final value minus the initial value, or:

335,244 - 270,461 = 64,783

The number of years is 6.

So the average annual rate of change is:

64,783/6 = 10,797.17

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The numbers "1⁄2, 3⁄4, 60%, .56, 85% " are represented on number line such as given below in figure.

A number line is a pictorial representation of numbers on a straight line. It’s a reference for comparing and ordering numbers. It can be used to represent any real number that includes every whole number and natural number. Just to recollect, the whole number is a set of numbers that include all counting numbers (1, 2, 3,4,5,6 …….) and zero (0), whereas the natural number is the set of all counting numbers i.e. 1, 2, 3, 4, 5, 6……..

Writing numbers on a number line make it easier to compare the numbers. From the above figure, we can see that the integers on the left side are smaller than the integers on the right side. For example, 0 is less than 1, -1 is less than 0, -2 is less than -1, and so on.

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Answer:f(2)=27
             g(-4)=3
             h(3)=28/9

Step-by-step explanation:
f(x)=-3I x- 11 I, when f(2)

f(2)= -3 I 2-11 I
f(2)= -3 I -9 I
f(2)= -3*-9
f(2)=27

g(x)=1 + the square root of x+8, when g(-4)

g(-4)=1+the square root of -4+8
g(-4)=1 + the sqaure root of 4( 2= the sqaure root of 4 )
g(-4)=1+ 2
g(-4)=3



h(x)=3x^2 +1/ x^2, when h(3)
h(3)=3(3)^2 +1/ 3^2
h(3)=3(9)+1/9
h(3)=28/9


HOPE IT HELPS :)

The inverse function of f, what is the value of (ƒ-¹)' (-4) -1/16 ∓ i/(8√3)

We know that the point (1,-4) is on the graph of f, so we can use this information to find the value of x for which f(x) = -4:

-4 = -x³ + 3x² + (6x)

-x³ + 3x² + 6x + 4 = 0

We can solve this equation using various methods, such as graphing, factoring, or using the cubic formula. One possible method is to use synthetic division to test factors of the constant term (4) and find one that gives a remainder of zero. By testing -1 as a factor, we get:

-1 | 1 -3 6 4

-1 4 -10

1 -4 10 -6

Therefore, the equation can be factored as:

-(x + 1)(x² - 4x + 6) = 0

Using the quadratic formula or completing the square, we can find the roots of the quadratic factor:

x = 2 ± √2i

Since the function f is not one-to-one, we must restrict its domain to make it invertible. One possible domain is x ≤ 2, so the inverse function f⁻¹(x) is:

f⁻¹(x) = 1 ± √(1 - 2x)/x

Note that there are two possible values for f⁻¹(-4), one for each branch of the inverse function. To find the value of (f⁻¹)'(-4), we need to take the derivative of the inverse function at x = -4:

(f⁻¹)'(x) = -1/x² ∓ √(1 - 2x)/2x³

(f⁻¹)'(-4) = -1/16 ∓ i/(8√3)

Therefore, the value of (f⁻¹)'(-4) is either -1/16 - i/(8√3) or -1/16 + i/(8√3), depending on which branch of the inverse function we choose.

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Answer: 6 + 18j

Step-by-step explanation: you distribute the 3

Toy Cost Percentage

Aditya Kashyap

ohn spent 20% of his money on food. He spent 2/5 of the remainder on a toy. The toy cost $12.

(a) What percentage of his money did he spend on the toy?

b) How much money did he have at first?

(a) To find the percentage of his money that John spent on the toy, we need to first find the total amount of money he had left after spending 20% on food.

Let's say John had x amount of money initially.

Then, he spent 20% of x on food, which is 0.2x.

So, he had (x - 0.2x) = 0.8x amount of money left.

Next, he spent 2/5 of this remaining amount on a toy, which cost $12.

Therefore, 2/5 of 0.8x = $12

Simplifying this, we get:

0.32x = $12

x = $37.50

So, John had $37.50 initially.

Now, to find the percentage of his money that he spent on the toy, we can use the formula:

Percentage = (Amount spent on toy / Total initial amount) x 100

Amount spent on toy = $12

Total initial amount = $37.50

Plugging these values into the formula, we get:

Percentage = (12 / 37.50) x 100

Percentage = 32%

Therefore, John spent 32% of his money on the toy.

(b) John had $37.50 at first.

We need to mix 3.2 units of the 25% orange juice with 0.8 Units of the 100% orange juice to get a 4-unit mixture with a 25% concentration of pure orange juice.

The first thing we need to do is figure out how much of each type of orange juice we need to mix together to get the desired 25% concentration. Let's call the amount of the 25% orange juice "x" and the amount of the 100% orange juice "y".

We know that the total amount of juice we want to end up with is "4" (since the function f(x) is equal to 4 + 2). So we can write an equation based on that:

x + y = 4

We also know that we want the final concentration to be 25%, which means that the amount of pure orange juice in the mixture should be 25% of the total volume. To calculate that, we can use the formula:

0.25 = (0.25x + y) / 4

Simplifying that equation, we get:

0.25x + y = 1

Now we have two equations with two unknowns (x and y), which we can solve using substitution or elimination. I'll use substitution here:

x = 4 - y (from the first equation)
0.25(4 - y) + y = 1 (substituting for x in the second equation)
1 - 0.25y + y = 1
0.75y = 0
y = 0

Uh-oh, that's not good. It looks like we can't use any of the 100% orange juice, or we'll end up with a concentration greater than 25%. Let's double-check our equations and see if there's a mistake.

x + y = 4
0.25x + y = 1

Hmm, it looks like we made a mistake in the second equation. The 0.25x term should be multiplied by the concentration of the 25% orange juice, which is 0.25 (or 25% as a fraction). So the correct equation should be:

0.25(0.25x) + y = 1

Now let's solve for y:

0.0625x + y = 1
y = 1 - 0.0625x

Substituting that into the first equation, we get:

x + (1 - 0.0625x) = 4
0.9375x = 3
x = 3.2

So we need to mix 3.2 units of the 25% orange juice with 0.8 units of the 100% orange juice to get a 4-unit mixture with a 25% concentration of pure orange juice.

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1. The solutions of the equation 6/(x+1)= x/(x-1) are x = 2 and x = 3.

2. The solutions of the equation x+ 4/x= -5 are x = -1 and x = -4.

What are the solutions ?

1. 6/(x+1) = x/(x-1)

To solve this equation, we first need to get rid of the fractions by multiplying both sides of the equation by the least common multiple of the denominators, which is (x+1)(x-1):

6(x-1) = x(x+1)

Expanding the left side, we get:

6x - 6 = x² + x

Moving all the terms to one side, we get:

x² - 5x + 6 = 0

This is a quadratic equation that can be factored as:

(x - 2)(x - 3) = 0

So, the solutions are x = 2 and x = 3. However, we need to check if these solutions are valid, because we cannot divide by zero.

Checking x = 2:

6/(2+1) = 2/(2-1)

2 = 2, which is true

Checking x = 3:

6/(3+1) = 3/(3-1)

3/2 = 3/2, which is true

Therefore, the solutions are x = 2 and x = 3.

2. x + 4/x = -5

To solve this equation, we first need to get rid of the fraction by multiplying both sides of the equation by x:

x² + 4 = -5x

Moving all the terms to one side, we get:

x² + 5x + 4 = 0

This is a quadratic equation that can be factored as:

(x + 1)(x + 4) = 0

So, the solutions are x = -1 and x = -4. However, we need to check if these solutions are valid, because we cannot divide by zero.

Checking x = -1:

-1 + 4/(-1) = -5

-1 - 4 = -5, which is true

Checking x = -4:

-4 + 4/(-4) = -5

-4 - 1 = -5, which is true

Therefore, the solutions are x = -1 and x = -4.

What is common multiple?

A common multiple is a number that is a multiple of two or more given numbers. For example, the common multiples of 2 and 3 are 6, 12, 18, 24, etc. These are all numbers that can be divided by both 2 and 3 without a remainder. A common multiple is "common" to the given numbers because it is a multiple of all of them.

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Complete question is:

1. The solutions of the equation 6/(x+1)= x/(x-1) are x = 2 and x = 3.

2. The solutions of the equation x+ 4/x= -5 are x = -1 and x = -4.

Answer:

Of course! The value of 3 log 4 is approximately 4.7712. Does that match your answer?

The trees in Aspen Grove Park are under 15 feet tall are 60%

the total number of trees in Aspen Grove Park, but we can find out that number by using the given percentage of trees that are over 15 feet tall.
To do this, we can use a proportion:
[tex]40/100 = 32/x [/tex]
Simplifying this, we can cross-multiply:
[tex]40x = 32 * 100 [/tex]
[tex]40x = 3200 [/tex]
[tex]x = 80[/tex]
So, there are a total of 80 trees in Aspen Grove Park.
Now, we can calculate the percentage of trees that are not over 15 feet tall by subtracting the percentage of trees that are over 15 feet tall from 100%:
[tex]100% - 40% = 60% [/tex]

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According to the given information, the equation that represents the proportional relationship is y = (1/4)x

What is proportion?

Proportion is a mathematical concept that describes the equality of two ratios. In other words, it is a statement that two ratios or fractions are equal.

For example, if we have two fractions, a/b, and c/d, we can say that they are in proportion if:

a/b = c/d

We can see that the ratio between X and Y is always 4:1, which means that Y is one-fourth of X. We can write this as:

Y = (1/4)X

Therefore, the equation that represents the proportional relationship is:

y = (1/4)x

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Answer: 24 problems done before dinner

Step-by-step explanation:

Take the 32 total math problems and divide it by 3/4 (the amount of problems done before dinner) getting you 24 problems done before dinner

The job would need to pay $500 to cover Cole's expenses.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

Let's define some variables to represent the unknowns in this problem:

Let x be the number of hours that the server will work at the next job.

Let y be the total amount of money that Cole will make from the next job.

With these variables, we can set up a system of equations:

The cost of the equipment and server hire is $100 plus the server's hourly wage multiplied by the number of hours worked:

100 + 16x = total cost

The amount that Cole will make from the next job is the base pay of $50 plus the server's hourly wage multiplied by the number of hours worked:

y = 50 + 18x

We want to find the value of y that will make up for the $100 expense. In other words, we want to find the value of x that satisfies the equation:

total cost = y

Substituting the second equation into the first equation, we get:

100 + 16x = 50 + 18x

Solving for x, we get:

x = 25

Substituting x = 25 into the second equation, we get:

y = 50 + 18(25) = 500

Therefore, the job would need to pay $500 to cover Cole's expenses.

We can graph the two equations to visualize the solution:
   y = 50 + 18x          y = 100 + 16x

   --------------------   --------------------

x = 0 |        50      |   |        100      |

    |               |   |               |

    |               |   |               |

    |               |   |               |

    |               |   |               |

    --------------------   --------------------

              25                      25

The point where the two lines intersect is (25, 500), which represents the solution to the system of equations.

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If you were to buy one of each bond today, you would have to spend b. ABC $1104.75 and XYZ $1100.50.

The following algorithm must be used to determine a bond's price:

[tex]Bond\ price=(\frac{coupon\ payment}{(1+yield)^{time}} )+(\frac{coupon\ payment}{(1+yield)^{time+1}} )+...+(\frac{coupon\ payment+face\ value}{(1+yield)^{Time+n}} )[/tex]

Where:

dividend Payment: The bond's yearly dividend payment (in dollars)

Yield: The bond's yield to expiration (as a decimal)

Time: the interval between the issuance of each coupon and the receipt of its monetary value. (in years)

Face worth: The bond's face worth (in dollars)

The price of each bond can be determined as follows using the data in the table:

a. For bond ABC:

Coupon Payment = $7.50 (7.5% of $1000 face value)

Yield = 3.04% (convert 3.04 to a decimal)

Time = 0.5 years (since the bond's maturity date is July 15 and today marks the midway point between those dates)

Face Value = $1000

[tex]Bond\ price=(\frac{7.5}{(1+0.0304)^{0.5}} )+(\frac{7.5}{(1+0.0304)^{1.5}} )+(\frac{1000}{(1+0.0304)^{2}} )[/tex]

= 7.356 + 7.235 + 925.984

= $940.575

Since we are purchasing one bond and the face value is $1,000, we split this amount by 10 to get the price for one bond:

Price for one bond ABC = $940.575 / 10 = $94.058

b. For bond XYZ:

Coupon Payment = $84 (8.4% of $1000 face value)

Yield = 1.7% (convert 1.7 to a decimal)

Time = 0.5 years

Face Value = $1000

[tex]Bond\ Price = (84 / (1 + 0.017)^{0.5}) + (84 / (1 + 0.017)^{1.5}) + (1000 / (1 + 0.017)^2)[/tex]

= 83.379 + 81.838 + 968.661

= $1133.878

Since the face value of a bond is $1,000 and we are only purchasing one, we split this amount by 10 to get the price for one bond:

Price for one bond XYZ = $1133.878 / 10 = $113.388

Therefore, the correct answer is:b. ABC: $1104.75 XYZ: $1100.50

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Answer:

A 30 degree angle is an acute angle cause its less than 90 degrees

Answer:

A thirty degree angle is an acute angle.

A thirty degree angle is formed when two lines meet or intercept at a point .

A thirty degree angle is one in which the measure is less than 90 degrees

Answer:

There are no two numbers whose product is 52 and whose sum is 11.

Step-by-step explanation:

give the 1st number is x and the 2nd number is y, then

x + y = 11 and xy = 52

x + y = 11 => y = 11 - x

x(11 - x) = 52

11x - x^2 = 52

=> x^2 - 11x + 52 = 0

Using quadratic formula: ax^2 + bx + c = 0

with a = 1, b = -11, c = 52

=> x = [-b ± √(b^2 - 4ac)]/2a

=> x = [-(-11) ± √((-11)^2 - 4x1x52)]/2x1

=> x = [11 ± √(121 - 208)]/2

=> x = [11 ± √(-87)]/2

Since the square root of a negative number is not a real number, there are no real solutions to this equation. Therefore, there are no two numbers whose product is 52 and whose sum is 11.

The inverse probability of drawing either an 8 or a 9 from a deck of cards is 0.852.

What is probability?

The likelihood of an occurrence can be determined using probability. It can only be applied to determine how likely an event is to occur. a scale with 0 being impossible and 1 being a specific occurrence.

We know that there are 52 cards in a deck consisting of 4 cards of each number.

So,

⇒ Probability of drawing 8 = [tex]\frac{4}{52}[/tex]

⇒ Probability of drawing 8 = [tex]\frac{1}{13}[/tex]

Similarly,

⇒ Probability of drawing 9 = [tex]\frac{4}{52}[/tex]

⇒ Probability of drawing 9 = [tex]\frac{1}{13}[/tex]

Now,

Let event A be drawing a 8 and event B drawing a 9.

So,

⇒ P (A ∪ B) = [tex]\frac{1}{13}[/tex] + [tex]\frac{1}{13}[/tex]  - ([tex]\frac{1}{13}[/tex] * [tex]\frac{1}{13}[/tex] )

⇒ P (A ∪ B) = [tex]\frac{2}{13}[/tex] - [tex]\frac{1}{169}[/tex]

⇒ P (A ∪ B) = [tex]\frac{25}{169}[/tex]

⇒ P (A ∪ B) = 0.148

Inverse probability = 1 - 0.148

Inverse probability = 0.852

Hence, the inverse probability of drawing either an 8 or a 9 from a deck of cards is 0.852.

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Answer:

Step-by-step explanation:

Fill in the blanks using the available answer choices. The vertices of a quadrilateral are A(–3, 1) , B(4, 2) , C(9, –3) and D(2, –4) . Complete the statement to best classify what type of quadrilateral ABCD is. In quadrilateral ABCD , have equal length and there are right angles, so ABCD is best classified as a .

An expression to represent the shaded region shown in the Venn diagram is AuB.

A Venn diagram is a visual tool used to show the similarities and differences between two or more sets of items or concepts. It consists of one or more overlapping circles, with each circle representing a set and the area where the circles overlap representing the intersection of the sets.

In this context, the symbol u represents the union between two or more of the circles. Based on this, the correct expression to represent the Venn diagram is AuB.

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Answer:

Step-by-step explanation:

Bold = $8 or more per week,    Underlined = less than 8 per week

$5 = 1 person

$0 = 3 people

$10 = 2 people

$1 = 1 person

$8 = 2 people

The total amount of people = 1+3+2+1+2 = 9

The total amount of people who earn less than $8/week = 1+3+1 = 5 people

The total amount of people who earn $8 or more/week = 2+2 = 4 people

Conclusion, 5/9 total people earned less than $8/week

4/9 people earn $8 or more/week

Mistake there were less than half people who earned $8 or more per week unlike Pete stated

Correction; more than half of Pete's friends earn less than 8 dollars per week

The vertex οf the parabοla is at the pοint (-3/2, -21/4) and the range οf the functiοn wοuld be (-21/4, infinity).

A quadratic functiοn is a functiοn οf the fοrm  where a, b, and c are cοnstants, and a is nοt equal tο 0. It is a type οf pοlynοmial functiοn that can be graphed as a parabοla, which is a symmetric curve that οpens either upwards οr dοwnwards.

Given the table οf pοints fοr the cοntinuοus quadratic functiοn h(x), we can find the vertex and range οf the functiοn. Since the functiοn is quadratic and cοntinuοus, it can be represented in the standard fοrm [tex]$f(x)=a(x-h)^{2}+k,$[/tex], where (h, k) is the vertex οf the parabοla.

Tο find the vertex, we can use the fact that the x-cοοrdinate οf the vertex is given by -b/2a, where a and b are the cοefficients οf the quadratic term and the linear term, respectively. In this case, a = 1 (since the functiοn is cοntinuοus and quadratic), and b can be fοund using any twο pοints οn the parabοla:

[tex]\rm b=(h(x_2)-h(x_1))/(x_2-x1)=(4-7)/(-2+1)=3$[/tex]

Therefοre, the x-cοοrdinate οf the vertex is x = -b/2a = -3/2. Tο find the y-cοοrdinate οf the vertex, we can evaluate the functiοn at this value οf x:

[tex]$\rm h(-3/2)=(1)(-3/2-h)^{2}+k$[/tex]

Tο sοlve fοr k, we can use οne οf the pοints οn the parabοla, say (-6, 12):

[tex]$12=(1)(-6-h)^{2}+k\,$[/tex]

Expanding and simplifying, we get:

[tex]$12=(h-6)^{2}+k$[/tex]

Substituting -3/2 fοr h, we get:

[tex]$\begin{array}{l}{{12=(-(3/2)-6)^{2}+k}}\\\\ {{12=81/4+k}}\\\\ {{k=-21/4}}\end{array}$[/tex]

Therefοre, the vertex οf the parabοla is at the pοint (-3/2, -21/4).

Tο find the range οf the functiοn, we can lοοk at the shape οf the parabοla. Since the cοefficient οf the quadratic term is pοsitive, the parabοla οpens upwards, and the vertex is the lοwest pοint οn the graph. Therefοre, the range οf the functiοn is all real numbers greater than οr equal tο the y-cοοrdinate οf the vertex, which is -21/4. In interval nοtatiοn, we can write the range as (-21/4, infinity).

Hence, the vertex οf the parabοla is at the pοint (-3/2, -21/4) and the range οf the functiοn wοuld be (-21/4, infinity).

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absolute value inequality |x - 2| <= 7 and (x <= 9 or x >= -5)

To create an absolute value inequality that has the solution set x < 9 or x >= -5, we first need to find the midpoint between -5 and 9, which is:

Midpoint = (-5 + 9) / 2 = 2

now, we need to find the distance between the midpoint and either endpoint.

Distance = |9 - 2| = 7

Now we can use the formula:

|x - b| <= c

where b is the midpoint and c is the distance.

putting the values we found,

|x - 2| <= 7

To get the solution set x < 9 or x >= -5, we can split this inequality into two parts:

x - 2 <= 7 or -(x - 2) <= 7

Simplifying each part, we get:

x <= 9 or x >= -5

Combining the two inequalities we get :

|x - 2| <= 7 and (x <= 9 or x >= -5)

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