Show work to determine the value of x.

Answer:

There is a hole at x = 3 and an asymptote at x = –1.

Step-by-step explanation:

f(x) = (x-3)/(x²-2x-3)

f(x) = (x-3)/(x-3)(x+1) = 1 / x+1    (x=3 is a hole)

asymptote while x+1 --> 0 and f(x) -->∞

x = -1 is vertical asymptote

Answer:

There is a hole at x = 3 and an asymptote at x = –1.

Step-by-step explanation:

I got it on edge

Answer:

This is way out of my level sorry. Thanks me

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

math

Answer:

Step-by-step explanation:

The answer is 54.5 on edg

For the triangle shown on the right, the term cos is used to complete the statement and the value of x is 54.5 degree for the triangle.

In a right angle triangle ratio of adjacent side to the hypotenuse side is equal the cosine angle between them.

\(\rm \cos=\dfrac{ adjacent}{hypotenuse}\)

Here, (a) is the adjacent side, (c) is the hypotenuse side and θ is the angle made between them.

The traingle is not provided in the image. Let the triangle for the given problem is similar to the attached image below.

Here the hypontenuse side is AC and adjacent side of triangle is 14.1 units. Thus by the property of right angle triangle,

\(\cos75=\dfrac{AB}{AC}\\\cos75=\dfrac{14.1}{x}\)

Now if we compare the above equation with the given statement __(75*)=14.1/x. The term cos is filled in the blank.

For the second part, we need to find the value of x. Thus solve the above equation further as,

\(\cos75=\dfrac{14.1}{x}\\x=\dfrac{14.1}{\cos75}\\x=\dfrac{14.1}{0.25882}\\x\approx54.5^o\)

Hence, For the triangle shown on the right, the term cos is used to complete the statement and the value of x is 54.5 degree for the triangle.

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The 3 sets of data with the same median but different mean are given as follows:

The mean of a data-set is calculated as the sum of all values in the data-set divided by the number of values in the data-set.

The median of a data-set is the middle value of the data-set, the value which 50% of the data-set is less than and 50% of the data-set is more than.

Hence, for a data-set of five elements, which is an odd cardinality, the median is the third element of the ordered data-set.

Then the three data-sets can be constructed with five elements, in which the third element is the same but the sum of the five elements is different.

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The difference between the actual quotient and the estimated quotient of 54,114 ÷ 29 is approximately 66.3448275862068965517241379.

To find the difference between the actual quotient and the estimated quotient of 54,114 ÷ 29, we need to first calculate the actual quotient and then the estimated quotient.

Actual quotient:

Dividing 54,114 by 29, we get:

54,114 ÷ 29 = 1,866.3448275862068965517241379 (approximated to 28 decimal places)

Estimated quotient:

Rounding the dividend, 54,114, to the nearest thousand gives us 54,000. Rounding the divisor, 29, to the nearest ten gives us 30. Now, we can perform the division with the rounded values:

54,000 ÷ 30 = 1,800

Difference between actual and estimated quotient:

Actual quotient - Estimated quotient = 1,866.3448275862068965517241379 - 1,800 = 66.3448275862068965517241379

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Answer:

y= -4

Step-by-step explanation:

To find the value of y when x = 6, we can substitute x = 6 into the equation and solve for y:

4(6) + y = 20

24 + y = 20

y = 20 - 24

y = -4

Therefore, when x = 6, y is equal to -4.

All values of x that satisfy |x|<1/2, |cos x-(1-x^2/2)| is less than or equal to 1/4.

The Taylor series for the cosine function is given by:

cos x = 1 − x2/2! + x4/4! − x6/6! + x8/8! − x10/10! + . . .

For|x| < 1/2, we can ignore the higher order terms, and thus the series reduces to:

cos x = 1 − x2/2

Therefore,\(|cos x − (1 − x2/2)| = |x2/2| = |x|2/2\). Since |x| < 1/2, we have |x|2/2 < 1/4. Hence,

\(|cos x − (1 − x2/2)| < 1/4.\)

Therefore, for all values of x that satisfy \(|x| < 1/2, |cos x-(1-x^2/2)|\) is less than or equal to 1/4.

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Answer:

B, C, F

Step-by-step explanation:

For the first part, this is the negative angle identity of the sine and cosine function. These identities are:

\(\cos(-\theta)=\cos(\theta)\)

\(\sin(-\theta)=-\sin(\theta)\)

Then (I believe I am reading this right), B is true. I am unsure because of the repeated value in the middle. The next piece is that sine is odd. By definition, an odd function is one such that:

\(f(-x)=-f(x)\)

As we just demonstrated with the identities, sine obeys this and therefore is odd. Cosine, on the other hand, is even because it follows:

\(f(-x)=f(x)\)

Last, the period of sine, or the distance on the x-axis it takes to complete one full wavelength, and the answer is \(2\pi\). If you look at a graph of the sine function, you will find that the wave repeats itself at the \(2\pi\) mark and it does this with cosine as well.

Solve for x.

2x + 9 = 33

2x = 24

x = 12

A. x = 7.5

B. x = 12

C. x = 21

D. x = 84

Answer:

\(2x + 9 = 33 \\ 2x = 33 - 9 \\ 2x = 24 \\ x = \frac{24}{2} \\ x = 12\)

Answer:

The fourth term of the expansion is -220 * x^9 * y^3

Step-by-step explanation:

Question:

Find the fourth term in (x-y)^12

Solution:

Notation: "n choose k", or combination of k objects from n objects,

C(n,k) = n! / ( k! (n-k)! )

For example, C(12,4) = 12! / (4! 8!) = 495

Using the binomial expansion formula

(a+b)^n

= C(n,0)a^n + C(n,1)a^(n-1)b + C(n,2)a^(n-2)b^2 + C(n,3)a^(n-3)b^3 + C(n,4)a^(n-4)b^4 +....+C(n,n)b^n

For (x-y)^12, n=12, k=3, a=x, b=-y, and the fourth term is

C(n,3)a^(n-3)b^3

=C(12,3) * x^(12-3) * (-y)^(3)

= 220*x^9*(-y)^3

= -220 * x^9 * y^3

The fourth term in the binomial expansion of ( x - y )¹² is given by the equation A₄ = -220 x⁹y³

The general term of the binomial expansion is Tr+1 = nCr x^n-r y^r . Here the coefficient values are found from the pascals triangle or using the combinations formula, and the sum of the exponents of both the terms in the general term is equal to n.

( x + y )ⁿ = ⁿCₐ ( x )ⁿ⁻ᵃ ( y )ᵃ

Given data ,

Let the binomial expansion be represented as A

Now , the value of A is

A = ( x - y )¹²   be equation (1)

On simplifying the equation , we get

The fourth term of the binomial expansion is calculated by

A₄ = ⁿC₃ a⁽ⁿ⁻³⁾ b³

Substituting the values in the equation , we get

A₄ = ¹²C₃ x⁽¹²⁻³⁾ ( -y )³

On further simplification , we get

A₄ = ( 12 )! / ( 9 )! 3! x⁹ ( -y )³

A₄ = 12 x 11 x 10 / 2 x 3 x⁹ ( -y) ³

A₄ =  -220 x⁹y³

Hence , the fourth term of binomial expansion is  -220 x⁹y³

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Answer:

x is the first mile marker

then, x+%2B+1 the second mile marker

given:

x%2Bx+%2B+1=655

2x+=655-1

2x+=654

x+=654%2F2

x+=327->the first mile marker

and

x+%2B+1=328 the second mile marker

Answer:

The correct equation that initially models the value of Rob's boat is option A, y = 40,000(0.93)*.

Since the value of the boat decreased by 7% each year, the value of the boat after three years can be represented by:

y = 40,000(0.93)^3

where y is the value of the boat after three years, and 40,000 is the initial value of the boat.

Simplifying this equation, we get:

y = 40,000(0.7951)

y = 31,804

However, we know that the actual value of the boat after three years was $32,174.28. This means that our initial assumption that the boat decreased by 7% each year is incorrect and we need to adjust the equation accordingly.

To find the correct equation, we can use the formula for exponential decay:

y = a(1 - r)^t

where y is the final value, a is the initial value, r is the rate of decay (expressed as a decimal), and t is the time in years.

In this case, we know that the final value of the boat is $32,174.28, and that the boat was owned for three years. We also know that the value of the boat decreased by 7% each year.

So we can set up an equation:

32,174.28 = 40,000(0.93)^3

Simplifying this equation, we get:

32,174.28 = 31,804.00

This equation is approximately true, which means that the initial value of the boat was $40,000 and the correct equation that initially models the value of Rob's boat is:

y = 40,000(0.93)^t

where t is the time in years.

Answer:

add me as a friend and give me thanks

Step-by-step explanation:

the answer is A for sure

Answer:

Step-by-step explanation:

25% percent of Amanda's day was spent on either meals or homework.

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The solution to the inequality f(x²-2) < f(7x-8) over D₁ = (-∞, 2) is:

-∞ < x < 1 or 1 < x < 6 or 6 < x < 2

Given the inequality,

    f(x²-2) < f(7x-8) over D₁ = (-∞, 2)

We need to find the values of x that satisfy this inequality.

Since we know that f is increasing over its domain, we can compare the values inside the function to determine the values of x that satisfy the inequality.

First, we can find the values of x that make the expressions inside the function equal:

x² - 2 = 7x - 8

Simplifying, we get:

x² - 7x + 6 = 0

Factoring, we get:

(x - 6)(x - 1) = 0

So the values of x that make the expressions inside the function equal are x = 6 and x = 1.

We can use these values to divide the domain (-∞, 2) into three intervals:

-∞ < x < 1, 1 < x < 6, and 6 < x < 2.

We can choose a test point in each interval and evaluate

f(x² - 2) and f(7x - 8) at that point. If f(x² - 2) < f(7x - 8) for that test point, then the inequality holds for that interval. Otherwise, it does not.

Let's choose -1, 3, and 7 as our test points.

When x = -1, we have:

f((-1)² - 2) = f(-1) < f(7(-1) - 8) = f(-15)

Since f is increasing, we know that f(-1) < f(-15), so the inequality holds for -∞ < x < 1.

When x = 3, we have:

f((3)² - 2) = f(7) < f(7(3) - 8) = f(13)

Since f is increasing, we know that f(7) < f(13), so the inequality holds for 1 < x < 6.

When x = 7, we have:

f((7)² - 2) = f(47) < f(7(7) - 8) = f(41)

Since f is increasing, we know that f(47) < f(41), so the inequality holds for 6 < x < 2.

Therefore, the solution to the inequality f(x²-2) < f(7x-8) over D₁ = (-∞, 2) is:

-∞ < x < 1 or 1 < x < 6 or 6 < x < 2

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The total cost of the pita bread and hummus dips will be $305.00.

To determine the cost of the pita bread and hummus dips, Toula can use the following expressions:

Cost of pita bread:

Number of crates needed = (150 bags) / (50 bags/crate) = 3 crates

Cost of each crate = $15.00

Total cost of pita bread = (Number of crates needed) × (Cost of each crate) = 3 crates × $15.00/crate = $45.00

Cost of hummus dips:

Number of boxes needed = (65 containers) / (5 containers/box) = 13 boxes

Cost of each box = $20.00

Total cost of hummus dips = (Number of boxes needed) × (Cost of each box) = 13 boxes × $20.00/box = $260.00

Therefore, the expressions Toula can use to determine the costs are:

Cost of pita bread = 3 crates × $15.00/crate

Cost of hummus dips = 13 boxes × $20.00/box

The total cost will be the sum of the costs of pita bread and hummus dips:

Total cost = Cost of pita bread + Cost of hummus dips

Total cost = $45.00 + $260.00

Total cost = $305.00

Therefore, the total cost of the pita bread and hummus dips will be $305.00.

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Answer:

Option A on edge

Step-by-step explanation:

Its point W.

Step-by-step explanation:

To calculate the future value of your account after 10 years, we can use the formula for compound interest:

FV = PV * (1 + r/n)^(n*t)

where:

FV is the future value of the account

PV is the present value of the account (in this case, $100,000)

r is the annual interest rate (in this case, 5%)

n is the number of times interest is compounded per year (assuming monthly compounding, n=12)

t is the number of years (in this case, 10)

Using this formula, we can calculate the future value of your account after 10 years:

FV = 100000 * (1 + 0.05/12)^(1210) + 80012*10

FV = $146,912.45

Therefore, after 10 years, with $100,000 initial investment, adding $800 per month and an annual interest rate of 5%, you will have approximately $146,912.45 in your account.

Answer:

28.86

Step-by-step explanation:

According to the scenario, computation of given data are as follows,

Exponential smoothing a = 0.1

we can calculate forecast for each week by using following formula,

Forecast for week = Forecast of last week + a × ( actual calls of last week - forecast of last week)

By using this method, forecast for all week are as follows

Week            Actual calls                Forecast                     Calculation

1                        28                               28

2                       34                               28                    [28 + 0.1 × ( 28 - 28)]

3                       38                               28.60              [28 + 0.1 × ( 34 - 28)]

4                       27                               29.54              [28.6 + 0.1 × ( 38 - 28.6)]

5                       25                              29.29               [29.54 + 0.1 × ( 29 - 29.54)]

6.                                                         28.86             [29.29 + 0.1 × ( 25 - 29.29)]

Answer: 90 different meal packages.

Step-by-step explanation:

Given data:

Types of drinks available = 5

Types of sandwiches available = 6

Types of chips available = 3.

Solution:

No of meal packages possible for this combination

= 6*5*3

= 90

A total of 90 different meal packages would be gotten:

The mistake that Katie made in the stem and leaf diagram, was that she D. Missed a length.

Looking at the stem and leaf diagram, we see that there are 14 leaves. This means that there are 14 lengths of caterpillars. However, there are 15 lengths shown on the table.

This means that there is a length missing that Katie failed to account for. Upon close inspection of the stem and leaf plot, we find that the missing length is a second value of 70 because there are two lengths that are 70 but this is shown only once on the stem and leaf plot.

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Answer:   Mean:4   Median:5    Mode:5,2

Step-by-step explanation:

Answer:

5 ≥ p

Step-by-step explanation:

Add 5 to both sides:

0 ≥ p - 5

+5      + 5

________

5 ≥ p

Answer:

p <= 5

Step-by-step explanation:

Let's solve your inequality step-by-step.

0≥p−5

Step 1: Flip the equation.

p−5≤0

Step 2: Add 5 to both sides.

p−5+5≤0+5

p≤5

Answer:

p≤5

Therefore, standard deviation problem solution is at least 90% of the​ trucks can be expected to travel 55,36 miles or less per year.

Statistics uses variance as a gauge of difference. The following equation of that number is used to determine the average variance in between data and the mean. It includes all data points in with its computations, in contrast to other numeric measures of variability, by comparing the value of each data point to the mean.

Here,

a.

z1 = (23 - 40) / 12 = -1.42

z2 = (40 - 40) / 12 = 0

P(-1.42 < z < 0) = 0.4199

So, approximately 0.4199 or 41.99% of trucks can be expected to travel between 23 and 40 thousand miles in a​ year.

b.

z1 = (30 - 40) / 12 = -0.83

z2 = (60 - 40) / 12 = 1.67

P(z < -0.83) + P(z > 1.67) = 0.2023 + 0.0475 = 0.2498

So, approximately 24.98% of trucks can be expected to travel either less than 30 or more than 60 thousand miles in a​ year.

c.  Thus:

x = 40 + 1.28(12) = 55.36

So, standard deviation problem solution is at least 90% of the​ trucks can be expected to travel 55,36 miles or less per year.

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Answer:

Its 4.58

Step-by-step explanation: