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The value of k for which the quadratic equation 4s² - 4s + (k - 2) has one real solution is:

k = 16.

A quadratic equation is modeled by the rule presented as follows:

y = ax² + bx + c

The discriminant of the quadratic function is given as follows:

Δ = b² - 4ac.

The numeric value of the coefficient and the number of solutions of the quadratic equation is defined as follows:

In this problem, the equation is given as follows:

4x² - 4s + (k - 2) = 0.

Hence the coefficients are given as follows:

a = 4, b = -4, c = k - 2.

Hence the discriminant is:

Δ = (-4)² - 4(4)(k - 2)

Δ = 16 - 16k + 32

Δ = 48 - 3k

It has one real solution if Δ = 0, hence:

48 - 3k = 0

3k = 48

k = 48/3

k = 16.

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Answer:

9/34

Step-by-step explanation:

I find when multiplying fractions, its easier to separate them into the numerator and denominator.

So we have 12 x 3, and 17 x 8

12 x 3 = 36

17 x 8 = 136

So we have 36/136

Simplified, that is 9/34

We use the Serial Autocorrelation in the classical linear regression model.

In the classical linear regression model the serial autocorrelation is assumed to solve the problem.

Hence, we use the Serial Autocorrelation in the classical linear regression model.

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The time it takes to paint the whole bookcase is 50 minutes.

From the information, Wilson paints 40% of a bookcase in 20 minutes.

Let the time taken to paint the whole bookcase be x. This will be illustrated as:

20/x = 40/100

Cross multiply

40x = 100 × 20

40x = 2000.

Divide

x = 2000 / 40

x = 50

The time taken is 50 minutes.

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Answer:

The answer is 18 hours

Step-by-step explanation:

3 hours x 6 days

3x6 = 18

The distance yet to be covered by Ashlee is 6.8 miles.

Ashlee is riding her bike to the beach. The beach is 17 miles from her home. She has already travelled 3/5 of the total distance. We need to find out how much farther she has to cycle.

Let the distance left to be covered by Ashlee be represented by the variable "D". The distance already covered by Ashlee on her cycle is calculated below.

d = (3/5)×17

d = 10.2

So she has already covered a distance of 10.2 miles. The distance yet to be covered is the difference between the total distance and the distance covered.

D = 17 - 10.2

D = 6.8

Hence, the distance yet to be covered by Ashlee is 6.8 miles.

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Answer:

[tex]f(x)=-|2x|[/tex]

Step-by-step explanation:

First, find the slope of the right side of the graph. It is -2. But because an absolute value always makes the value inside positive, we put the negative sign outside the absolute value.

The rule of thumb for absolute value graphs is: if it opens upwards, the absolute value is positive; if it opens downwards, the absolute value is negative.

So, the equation we can construct from this information is:

[tex]f(x)=-|2x|[/tex]

Step-by-step explanation:

we have a basic fee of $40 just for renting the car.

and we rent it for 2 days for $30 per day.

so, this costs

40 × 2×30 = 40 + 60 = $100

Answer:

x-intercept (88/7,0), y-intercept (0,11)

Answers:

x intercept = 88/7

y intercept = 11

===============================================

Explanation:

To find the y intercept, we replace f(x) with 0 and solve for x.

f(x) = (-7/8)x + 11

0 = (-7/8)x + 11

(7/8)x = 11

7x = 8*11

7x = 88

x = 88/7 is the x intercept

It is located at (x,y) = (88/7, 0)

The x intercept always occurs when y = 0.

88/7 = 12.5714 approximately, but I would stick to the fraction form since it's most exact.

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

The y intercept always occurs when x = 0.

f(x) = (-7/8)x + 11

f(0) = (-7/8)*0 + 11

f(0) = 0 + 11

f(0) = 11 is the y intercept

It is located at (0,11)

The y intercept is much easier to find since we just need to read off the last value of the function (aka the constant value).

There are two lakes that have crocodiles and alligators in the same proportion.The two lakes are Lake Winnipeg and Lake Champlain.

This is the only lakes where this is the case, making them the only lakes with a proportional relationship between the number of crocodiles and the number of alligators. crocodiles and alligators have been known to live in the same body of water, but they are usually not found in the same proportion. In these two lakes, however, they are found in equal numbers.

Crocodiles and alligators are both reptiles that belong to the same order, which is why they can live in the same environment and in the same proportion.It is most likely because these lakes have a warm climate which is suitable for these reptiles.

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After solving the equation made for a triangle, the value of angle A will be equal to 21.

Simple polygons with three sides and three internal corners make up triangles. Being one of the fundamental geometric shapes, it is symbolized by the symbol and consists of three connected vertices.

As per the given data in the question,

Angle A is 13 less than angle C.

Let angle C is x then angle A is equal to (x - 13) and,

Angle B is 11 less than 4 times of angle C then,

B = 4x - 11

Add all the angles and equate them with 180.

(x -13) + (4x - 11 ) + x = 180

6x -24 = 180

6x = 180 + 24

x = 204/6

x = 34.

Substitute x = 34 in angle A

A = (x - 13)

A = 21.

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The estimate of the average decay rate of change is -0.6

From the question, we have the graph and the interval is given as

t = 5 to 15

This can also be represented and expressed as

(a, b) = [5, 15]

From the attached graph, we have

f(5) = 12

f(15) = 6

The estimate of the average decay rate of change is calculated as

Rate = [f(b) - f(a)]/[b - a]

This gives

Rate = [f(15) - f(5)]/[15 - 5]

So, we have

Rate = [6 - 12]/[15 - 5]

Evaluate

Rate = -0.6

Hence, the average decay rate of change is -0.6

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The following measure's values are based on the number of peas provided.

Peas in a Pod mode is not possible.

Peas in a pod's median number is equal to 6

the average number of peas in a pod is 6

What is the number?

The definition of a number is "the count of the specified quantity."

utilized formula

Mean = sum of number of observation / toatal number present there

The answer to the query is

Considering counts of peas,

How many peas are in a pod = 4,5,6,7,8

Quantity of pods = 2,10,18,6,14

The number that represents the highest frequency is called the mode.

All of the numbers in the list have a frequency of one.

For the provided data, mode is not feasible.

If all the numbers are odd, the middle value, after placing them in ascending or descending order, is the median.

The supplied numbers' median is.

To obtain the mean value, replace the values in the formula.

Mean = 4+5+6+7+8/5 = 30/5 = 6

Consequently, the following measure's values are as follows based on the number of peas given:

Peas in a Pod mode is not possible.

Peas in a pod's median number is equal to 6

the average number of peas in a pod is 6

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The angle which corresponds with angle 2 given that; lines m and n are parallel and are intersected by transversal p is; angle 6.

Corresponding angles by definition are any pair of angles each of which happens to be on the same side of one of two lines cut by a transversal and also on the same side of the transversal.

Therefore, it follows from the definition above that the angle which is corresponding to Angle 2 as required in the task content is; angle 6.

This follows from the fact that angles 2 and 6; each happens to be on the same side of one of two lines cut by a transversal and also on the same side of the transversal.

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If a polynomial is divisible by another then that will be a factor of the polynomial. The value of c such that the given polynomial p(x) = 4x³ + cx² + x + 2 is divisible by (x + 2) is 8.

An algebraic factor is the multiplication of two algebraic terms.

That term could be in the form of summation multiplication or in subtraction.

The root of the quadratic equation formed by the algebraic factor is always real.

As per the given polynomial,

p(x) = 4x³ + cx² + x + 2

Divide  4x³ + cx² + x + 2 by (x+2)

First quotient = 4x²

Then, (4x³ + cx² )- (4x³ + 8x²)

Now in order to become it zero c must be the same as 8.

c = 8

Then, the second quotient = 1

(x + 2) - (x + 2) = 0

So, 4x³ + cx² + x + 2 = (x + 2)(4x² + 1)

Hence "The value of c such that the given polynomial p(x) = 4x³ + cx² + x + 2 is divisible by (x + 2) is 8".

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Using the simplification, the solution of the given expression for x is 107.5.

In the given question we have to solve the given expression.

The given expression is x-12.5=95.

Now solving the expression.

x-12.5=95

To solve the expression we add 12.5 on both side

x-12.5+12.5=95+12.5

x=107.5

The solution of the given expression for x is 107.5.

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Answer:

  -4.697 in/s

Step-by-step explanation:

You want to know the rate of change of radius of a cone 11 inches high with a radius of 5 inches and a volume that is decreasing at the rate of 541 cubic inches per second.

The volume of a cone is given by ...

  V = π/3r²h

The rate of change is found by implicit differentiation:

  V' = (π/3)((2rr')h +r²h')

Here, the height is constant, so h' = 0. Solving for r', we find ...

  r' = 3V'/(2πrh)

Using the given values of V', r, and h, we find the rate of change of radius to be ...

  r' = 3(-541 in³/s)/(2π(5 in)(11 in)) = -1623/(110π) in/s ≈ -4.69652 in/s

The radius is decreasing at about -4.697 inches per second.

__

Additional comment

The initial radius of the cone is irrelevant to the problem, since we want to know the rate of change at a specific different radius. Whether the cone is inverted or not is also irrelevant to its volume.

If x + y = L and [tex]x^2+y^2[/tex] = M and the vales of L and M are constants, then the value of [tex]x^3+y^3[/tex] in terms of L and M is [tex]x^3+y^3=L^3-3(\frac{L^2-M}{2} )(L)[/tex]

The given values are

x + y = L

[tex]x^2+y^2[/tex] = M

We know the value of

[tex](x+y)^3=x^3+y^3+3xy(x+y)[/tex]

Rearrange the terms and convert to the suitable form

[tex]x^3+y^3=(x+y)^3-3xy(x+y)[/tex]

The value of x + y = L

Substitute the value of x + y in the equation

[tex]x^3+y^3=L^3-3xy(L)[/tex]

Here we have to find the value of xy

We know

[tex](x+y)^2=x^2+y^2+2xy[/tex]

Rearrange the terms and convert to suitable form

[tex]2xy=(x+y)^2-(x^2+y^2)[/tex]

Substitute the values in the equation

2xy = [tex]L^2-M[/tex]

xy = [tex]\frac{L^2-M}{2}[/tex]

Substitute the value of xy in the equation

[tex]x^3+y^3=L^3-3(\frac{L^2-M}{2} )(L)[/tex]

Hence, if x + y = L and [tex]x^2+y^2[/tex] = M and the vales of L and M are constants, then the value of [tex]x^3+y^3[/tex] in terms of L and M is [tex]x^3+y^3=L^3-3(\frac{L^2-M}{2} )(L)[/tex]

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Finally, we have [tex]2\frac{11}{24}[/tex] lbs of mini shrimps.

Given that;

A catering company needs 8.75 lbs of shrimp for a small party. they buy [tex]3\frac{2}{3}[/tex] lbs of jumbo shrimps, [tex]2\frac{5}{8}[/tex] lbs of medium-sized shrimps, and some mini-shrimps.

The total of 8.75th is changed as [tex]8\frac{3}{4}th\\[/tex]

Sum of  [tex]3\frac{2}{3}[/tex] +  [tex]2\frac{5}{8}[/tex] this is bought by the company.

So, to purchase the remaining  [tex]8\frac{3}{4}th\\[/tex] - [tex]3\frac{2}{3}[/tex] - [tex]2\frac{5}{8}[/tex]

We use a common denominator of 24 for the fraction parts.

Change [tex]8\frac{3}{4}[/tex] as [tex]8\frac{18}{24}[/tex]

Similarly, convert;

[tex]3\frac{2}{3}[/tex] as [tex]3\frac{16}{24}[/tex]

[tex]2\frac{5}{8}[/tex] as [tex]2\frac{15}{24}[/tex]

By solving all the above conversions, we get;

[tex]\frac{42-16-15}{24}[/tex] = 11/24

Considering all the factors together we have [tex]2\frac{11}{24}[/tex] lbs of mini shrimps.

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The salary of Kayden after 4 years will be $ 221,952.00

The annual salary is $48000

Salary rise is $4500

The rate of the this salary can be found out by [tex]\frac{48,000- 4500}{48000}[/tex]

= [tex]\frac{43,500}{48,000}[/tex] × 100

= 90.6 %

The time interval is 4 years

thus the prinicipal amount is given as $48000.

thus simple interest is P × R × T/ 100

which when calculated will give us

simple interest = $221,952.00

$221,952.00 is the total amount accrued from simple interest on a principal of $48,000.00 at a rate of 90.6% per year for 4 years. This includes both principal and interest.

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Answer:1. 8

2. 16

Step-by-step explanation:

The third term in the sequence generated by 5n is 15.

According to the question,

We have the following information:

The sequence is given by the formula 5n.

In this case, n represents the number of the term.

(Note that the sequence generated by this formula can not be a geometric sequence because the common ratio of these terms is not the same.)

So, we have to find the 3rd term of this sequence. Then, we will find the value of this sequence by putting the value of n as 3.

So, we have the following expression:

5*3

15

Hence, the third term in the sequence generated by 5n is 15.

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Answer:

the other 2 sides equal 70.5 ...but I am not for sure because you did not give me enough information (like a picture)

Answer:

x = 650/7

Step-by-step explanation:

7/26 = 25/x

7*x = 25*26

7x = 650

x = 650/7

Check:

7/26 = 25/(650/7)

7/26 = 25*7/650

7/26 = 175/65

7*650 = 26*175 = 4550

Answer:

the price per once is $0.165

Step-by-step explanation:

[tex]8 \: jar \: of \: peanut \: cost \: 1.32 \\ 1jar \: cost \: what \: \\ now \: to \: get \: price \: of \: each \: jar\\ 1.32 \div 8 \\ = .0165[/tex]

The equation that models the total amount of money y you pay if you buy x yards of fabric is y = 9.50x - 6

Given,

You have a coupon for a $6 discount at a fabric shop. You purchase fabric for $9.50 per yard.

We have to find an equation that models the total amount of money y you pay if you buy x yards of fabric.

Here,

The equation for the situation be like;

y = 9.50x - 6

Where,

y is the total amount paid

x is the number of yards of fabric you bought

That is,

The equation that models the total amount of money y you pay if you buy x yards of fabric is y = 9.50x - 6

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Answer:

1256.64

Step-by-step explanation: