5 points
26. The equation x^2 + 8x - k(x + 8) = 0 has equal roots. Find the value of k.
please help
will mark it BRAINLIEST.
I really need help :(
​

Major findings of the role by Iran in the early cold war :

Iran did not bothered about superpower rather tried to gain economic advantages from NATO and soviet troops.

Given,

Role of Iran in cold war.

As mentioned in history,

The parties that were involved in the war were the USA and soviet union. During the war the allies of the USA and soviet union joined them to provide their support to the USA and soviet union  .

Iran did not bothered much about the superpowers , rather they tried to get all they could using the war by gaining advantages.

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Sarah's company started out with a $350 value and is currently changing at a rate of $100 annually.

The annual fee is expressed as an equation in slope-intercept form:

y = 100x + 350.

y = mx + b, where m is the line's slope and b is its y-intercept, is the formula for a straight line.

Given details:

The table displays the prices that Sarah charged each client during the course of her business's first two years:

Year                            Annual Dog-walking Fee

2010                            $350

2014                            $750

A.

Sarah has so increased the cost by $400 over the past four years.

For Sarah's company, its rate of change called slope will be,

m = 750 - 350 / 4

m = 100

Therefore, Sarah is raising the cost by $100 yearly.

Due to the payment she received for the first year, the calculated values of a business is $350.

B. Define x as the period of time that has passed since she began her business in 2010.

Consequently, the annual fee equation can be expressed in slope-intercept form as,

y = mx + c

where y stands for the cost she must pay after x years.

Her company's baseline value is therefore $350, and its rate of change is $100 annually.

The annual fee is expressed as an equation in slope-intercept form.: y = 100x + 350.

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The probability that, in an hour, at least 4 cars will enter the car wash is 0.94.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

It is given that:

Cars enter a car wash according to a Poisson process at a mean rate of 2 cars per half an hour.

Here the value of λ is:

λ = 2 cars/half an hour

λ = 4 cars/hour

The probability that, in an hour, at least 4 cars will enter the car wash:

P(x = 4) = 4⁴e⁻⁴/5

After solving:

P(x = 5) = 0.937 ≈ 0.94

Thus, the probability that, in an hour, at least 4 cars will enter the car wash is 0.94.

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The synergy from the merger is $4,125,000.

To calculate the synergy from the merger, we need to compare the value of Fly-By-Night before and after the acquisition of Flash-in-the-Pan Restaurants. The synergy represents the additional value created through the combination of the two firms.

Given that the purchase of Flash-in-the-Pan Restaurants is expected to increase Fly-By-Night's annual after-tax cash flow by $330,000 indefinitely, we can calculate the present value of this incremental cash flow using the appropriate discount rate of 8 percent.

Present Value of Incremental Cash Flow = Incremental Cash Flow / Discount Rate

Present Value of Incremental Cash Flow = $330,000 / 0.08

Present Value of Incremental Cash Flow = $4,125,000

Now, we can determine the value of Fly-By-Night after the merger by adding the present value of the incremental cash flow to its current market value:

Value of Fly-By-Night after Merger = Current Market Value of Fly-By-Night + Present Value of Incremental Cash Flow

Value of Fly-By-Night after Merger = $23 million + $4,125,000

Value of Fly-By-Night after Merger = $27,125,000

The synergy from the merger can be calculated by subtracting the market value of Fly-By-Night before the merger ($23 million) from the value of Fly-By-Night after the merger ($27,125,000):

Synergy = Value of Fly-By-Night after Merger - Current Market Value of Fly-By-Night

Synergy = $27,125,000 - $23 million

Synergy = $4,125,000

Therefore, the synergy from the merger is $4,125,000. This represents the additional value that would be created through the acquisition of Flash-in-the-Pan Restaurants by Fly-By-Night.

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Answer:

The answer is 4 1/3

Step-by-step explanation:

\(m=\frac{10-(-3)}{7-4} =\frac{13}{3} =(simplify)= 4\frac{1}{3}\)

The 10%-90% rise time of the response is approximately 0.3 seconds, to the nearest third decimal place.

To determine the 10%-90% rise time of a response, we need to find the time it takes for the response to go from 10% of its steady-state value to 90% of its steady-state value.

Looking at the graph or response data provided, we can estimate that the steady-state value of the response is approximately 1.4.

10% of 1.4 is 0.14, and 90% of 1.4 is 1.26.

So we need to find the time it takes for the response to go from 0.14 to 1.26.

By examining the graph or data, we can see that this occurs between t = 0.9 seconds and t = 1.2 seconds.

The difference between these two times is:

1.2 - 0.9 = 0.3 seconds

Therefore, the 10%-90% rise time of the response is approximately 0.3 seconds, to the nearest third decimal place.

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Answer:

∴ m∠KIJ = 18°  and   m∠HIJ = 50°

Thus, option a is correct.

Step-by-step explanation:

From the figure, it is clear that:

m∠KIH = m∠HIJ + m∠KIJ

Given

now substituting m∠KIH = 68°, m∠KIJ = (2x + 6)° and m∠HIJ = (9x - 4)° in the equation

m∠KIH = m∠HIJ + m∠KIJ

68° = (2x + 6)° + (9x - 4)°

switch sides

\(\left(2x+6\right)+\left(9x-4\right)=68\)

Group like terms

\(2x+9x+6-4=68\)

\(11x+2=68\)

Subtract 2 from both sides

\(11x+2-2=68-2\)

Simplify

\(11x=66\)

Divide both sides by 11

\(\frac{11x}{11}=\frac{66}{11}\)

Simplify

\(x=6\)

Hence, the value of x = 6

Therefore,

m∠KIJ = (2x + 6)° = 2(6) + 6 = 12 + 6 = 18°

m∠HIJ = (9x - 4)° = 9(6) - 4 = 54 - 4 = 50°

∴ m∠KIJ = 18°  and   m∠HIJ = 50°

Thus, option a is correct.

The probability that the mean weight of the 17 fruits will be between 489 grams and 500 grams is approximately 0.0322 - 0.0322 = 0.0000 (rounded to four decimal places).

The probability that the mean weight of 17 randomly picked fruits falls between 489 grams and 500 grams can be calculated using the Central Limit Theorem.

The mean weight of the 17 fruits will follow a normal distribution with a mean equal to the population mean (494 grams) and a standard deviation equal to the population standard deviation divided by the square root of the sample size (√17).

First, we calculate the z-scores for the lower and upper bounds:

Lower z-score:

z_lower = (489 - 494) / (8 / √17)

Upper z-score:

z_upper = (500 - 494) / (8 / √17)

Then, we use a standard normal distribution table or a calculator to find the probabilities associated with these z-scores. The probability that the mean weight falls between 489 grams and 500 grams is equal to the difference between these two probabilities.

Let's calculate the probabilities:

z_lower = (489 - 494) / (8 / √17) ≈ -1.8409

z_upper = (500 - 494) / (8 / √17) ≈ 1.8409

Using a standard normal distribution table or a calculator, we find that the probability corresponding to z_lower is approximately 0.0322 and the probability corresponding to z_upper is also approximately 0.0322.

The problem presents a normal distribution of fruit weights, with a given mean of 494 grams and a standard deviation of 8 grams. When we randomly select a sample of 17 fruits, the mean weight of this sample will also follow a normal distribution. According to the Central Limit Theorem, as the sample size increases, the distribution of the sample mean approaches a normal distribution, regardless of the shape of the population distribution.

In this case, since the range is relatively narrow and the sample size is moderate, the probability of the mean weight falling between 489 grams and 500 grams is quite low, approximately 0.0000.

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Think of a mirror, something that produces your reflection. The Y axis is the line that is vertical on the graph.

D) Is not the answer because it does not reflect over the y-axis.

B) Is not the answer because the figure is not reflected, even though it went across the y-axis.

C) Is not the answer because it reflected over the x-axis, not the y-axis.

Therefore, your answer is A)

The figure is reflected across the y-axis and each figure faces one another.

The corresponding differential element, rewrite the integral in terms of the new variable, integrate with respect to the new variable, replace the new variable with the original variable, and simplify the expression to find the solution.

To perform u-substitution with indefinite integrals, follow these steps:

Identify a suitable substitution: Look for a part of the integrand that resembles the derivative of a function. Choose a variable u to substitute for that part.

Calculate du: Take the derivative of u with respect to the original variable. This will help us express du in terms of the original variable.

Rewrite the integral: Substitute the chosen variable and du in the original integral, replacing the part to be substituted with u and the corresponding differential element du.

Integrate with respect to u: Treat the integral as a new integral with respect to u. Evaluate the integral using the rules of integration.

Replace u with the original variable: Rewrite the result of the integration in terms of the original variable.

Simplify and solve: If necessary, simplify the expression further or perform additional algebraic manipulations to obtain the final result.

Let's illustrate these steps with an example:

Consider the integral ∫(2x + 3)² dx.

Identify a suitable substitution: Let u = 2x + 3.

Calculate du: Take the derivative of u with respect to x: du/dx = 2. Rearrange the equation to solve for du: du = 2 dx.

Rewrite the integral: In terms of u and du, the integral becomes ∫u² (du/2).

Integrate with respect to u: Treat the integral as a new integral with respect to u: (1/2) ∫u² du = (1/2) * (u³/3) + C, where C is the constant of integration.

Replace u with the original variable: Substitute back u = 2x + 3 in the result: (1/2) * ((2x + 3)³/3) + C.

Simplify and solve: Further simplify the expression if necessary to obtain the final result.

In summary, to perform u-substitution with indefinite integrals, identify a suitable substitution, calculate the corresponding differential element, rewrite the integral in terms of the new variable, integrate with respect to the new variable, replace the new variable with the original variable, and simplify the expression to find the solution.

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Step-by-step explanation:

age of lilly=8

age of brother=8-5=3

age of sister=2×8

=16

Therefore lilly age is 8

her brother's age is 3 (Tommy)

and her sister's age is 16 (Claire)

hope this helps

Answer

Tommy is 3 and Claire is 16

Step-by-step explanation:

8-5=3 (Tommy's age)

8x2=16 (Clarie's age)

Answer:

4, 5 and 27.

Step-by-step explanation:

There are 2 cube numbers between 0 and 36 .

They are 8 and 27.

36 - 27 = 9 so the other 2 numbers could be 4 and 5 because they are both factors of 20.

36 - 8 = 28  whose factors are 2 * 2 * 7 which are not factors of 20.

Let `z = (-a + bi)` be a complex number where `a > 0` and `b > 0`.To determine arg(z), we have;$$\theta = \tan^{-1}\frac{b}{-a}$$Therefore,

$$\theta = -\tan^{-1}\frac{b}{a}$$Since both `a` and `b` are positive, $\theta$ lies in the fourth quadrant.Thus, $\theta = -\tan^{-1}\frac{b}{a} = -\tan^{-1}\frac{1}{3} = -\frac{\pi}{3}$.Therefore, $\arg z = \theta = \boxed{-\frac{\pi}{3}}$.Cube roots of `32 + 32√3i`:Let `z = 32 + 32√3i` be a complex number.To find the cube roots of `z`, we have;$$z^{\frac{1}{3}} = \sqrt[3]{r}\left(\cos\frac{\theta + 2n\pi}{3} + i\sin\frac{\theta + 2n\pi}{3}\right)$$where `r` is the magnitude of `z` and `n` is an integer.Let's calculate `r` and `θ`.We have;$$r = |z| = \sqrt{32^2 + (32\sqrt{3})^2} = 64$$and$$\tan\theta = \frac{32\sqrt{3}}{32} = \sqrt{3} \implies \theta = \frac{\pi}{3}$$Thus, we have;$$z^{\frac{1}{3}} = 4\left[\cos\left(\frac{\frac{\pi}{3} + 2n\pi}{3}\right) + i\sin\left(\frac{\frac{\pi}{3} + 2n\pi}{3}\right)\right]$$$$\implies z^{\frac{1}{3}} = 4\left[\cos\frac{\pi}{9} + i\sin\frac{\pi}{9}, \cos\frac{7\pi}{9} + i\sin\frac{7\pi}{9}, \cos\frac{13\pi}{9} + i\sin\frac{13\pi}{9}\right]$$Sketch in the complex plane:In the Argand diagram below, the points represent the three cube roots of `z`. The first cube root is plotted in green, the second in purple, and the third in blue.

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The Argument = atan(32√3 / 32) = π/3 The cube roots of 32+32√3i will have a magnitude of cube root of 64, which is 4. Also, their arguments will be π/9, 7π/9 and 13π/9.

Given that z = (-a + √3i) where a is a positive real number.

We have to determine the arg(z).Arg(z) refers to the angle that z makes with the positive real axis in the complex plane.

We know that tan(arg(z)) = (imaginary part of z) / (real part of z)Here, the real part of z is -a and the imaginary part of z is √3i.

So,tan(arg(z)) = √3i / (-a)arg(z) = atan(√3i / -a)Now, we need to find the cube roots of 32+32√3i and sketch them in the complex plane.

Let's find the magnitude and argument of 32+32√3i.

Magnitude = √(32² + (32√3)²) = 64

Argument = atan(32√3 / 32) = π/3

The cube roots of 32+32√3i will have a magnitude of cube root of 64, which is 4. Also, their arguments will be π/9, 7π/9 and 13π/9.

To sketch these roots in the complex plane, we draw a circle of radius 4 centered at the origin and then mark the points that are at angles π/9, 7π/9 and 13π/9 from the positive real axis.

The sketch will look like this:

Thus, the cube roots of 32+32√3i have been determined and sketched in the complex plane.

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Answer: The first two

Step-by-step explanation:

Sharon needs to score at least 99 in her fourth game to have an average score of 114 for all four games.

We can start by using the formula for the average (arithmetic mean):

average = sum of scores/number of scores

We know the average she wants to achieve is 114, and she has already bowled 3 games with scores of 108, 97, and 152. Therefore, the sum of her scores so far is:

sum of scores = 108 + 97 + 152 = 357

We also know that she wants to have an average of 114 after bowling four games, so we can write:

114 = (357 + x) / 4.

where x is the score she needs to achieve in her fourth game.

Multiplying both sides by 4, we get:

456 = 357 + x

Subtracting 357 from both sides, we get:

x = 99.

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Answer: He has 4 apples left.

Step-by-step explanation:

5-1=4

(hope this helps)

Answer:4

Step-by-step explanation: James had 5 apples which later he gave one to aliya so 5-1 is 4

Answer:

150 because he bought them

Step-by-step explanation:

The required number of pounds in 64 kilograms is approximately 141.09 pounds.

The word "pounds" comes from the name of an old Roman measurement called the Libra pondo. The translation of this Latin phrase is "a pound by weight." The origin of our term "pound" is pondo, and the origin of its unrelated abbreviation, "lb," is the libra portion.

64 kilograms is equal to approximately 141.09 pounds. To convert 64 kilograms to pounds, you can use the conversion factor of 2.20462, which states that one kilogram is equal to 2.20462 pounds.

Therefore, to convert 64 kilograms to pounds, you can simply multiply 64 by 2.20462. The resulting value will give you the weight in pounds. It's important to note that the kilogram is the base unit of mass in the International System of Units (SI) and the pound is a unit of weight commonly used in the United States and other countries that use the imperial system.

Therefore, when converting from kilograms to pounds, it's not just a matter of converting the units but also considering the difference between mass and weight.

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Answer:

(x + 6)(x + 7)

Step-by-step explanation:

To factor the trinomial x^2 + 13x + 42, we need to find two numbers that multiply to 42 and add up to 13.

One way to do this is to list all the pairs of factors of 42 and see which pair adds up to 13:

1, 42 -> 1 + 42 = 43

2, 21 -> 2 + 21 = 23

3, 14 -> 3 + 14 = 17

6, 7 -> 6 + 7 = 13

So the pair of factors that we want is 6 and 7. We can use these numbers to rewrite the middle term of the trinomial:

x^2 + 13x + 42 = x^2 + 6x + 7x + 42

Next, we can group the first two terms and the last two terms:

x^2 + 6x + 7x + 42 = (x^2 + 6x) + (7x + 42)

Now, we can factor out the greatest common factor from each group:

x(x + 6) + 7(x + 6)

Notice that we have a common factor of (x + 6) in both terms. We can factor this out:

(x + 6)(x + 7)

The algebraic expression that models the situation when Jenny had $105, but she is spending $13 per week is 105 - 13w.

Let the number of weeks be represented by x

Therefore, since Jenny had $105, but she is spending $13 per week, the appropriate expression will be:

= 105 - (13 × w)

= 105 - 13w

The expression is 105 - 13w.

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Answer:

x= 2/3

Step-by-step explanation:

if they are equating,

10x +38 = 40+7x

10x-7x = 40-38

3x = 2

x= 2/3

Answer:

x = 0.6666666667

Step-by-step explanation:

Simplifying

10x + 38 = 40 + 7x

Reorder the terms:

38 + 10x = 40 + 7x

Solving

38 + 10x = 40 + 7x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-7x' to each side of the equation.

38 + 10x + -7x = 40 + 7x + -7x

Combine like terms: 10x + -7x = 3x

38 + 3x = 40 + 7x + -7x

Combine like terms: 7x + -7x = 0

38 + 3x = 40 + 0

38 + 3x = 40

Add '-38' to each side of the equation.

38 + -38 + 3x = 40 + -38

Combine like terms: 38 + -38 = 0

0 + 3x = 40 + -38

3x = 40 + -38

Combine like terms: 40 + -38 = 2

3x = 2

Divide each side by '3'.

x = 0.6666666667

Simplifying

x = 0.6666666667

Given:

Factor of (x-7) is:

so factor of (x-7) is:

The 90% confidence interval for the difference μ₁ - μ₂ is approximately (-21.662, -3.538).

We have,

The engineer wants to estimate the difference in average tomato plant yields between using Add1 and Add2.

They collected samples of tomato plants grown with each additive.

They found that the average yield for Add1 was 173.08 tomatoes, and the average yield for Add2 was 185.31 tomatoes.

To calculate a 90% confidence interval for the difference in mean yields, we consider the variability in the data.

The standard deviation for Add1 is approximately 7.12 tomatoes, and for Add2, it is approximately 22.15 tomatoes.

Using these values, we calculate the confidence interval and find that the lower limit is approximately -21.662, and the upper limit is approximately -3.538.

In simpler terms, we can say that we are 90% confident that the true difference in mean yields between Add1 and Add2 falls between -21.662 and -3.538 tomatoes.

This suggests that Add2 may have a higher average yield compared to Add1, but further analysis is needed to draw a definitive conclusion.

Thus,

The 90% confidence interval for the difference μ₁ - μ₂ is approximately (-21.662, -3.538).

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Answer:

113.04 (i used 3.14 for pi)

Step-by-step explanation:

area of circle formula = pi r^2

radius = 6

6^2 = 36

3.14 x 36 = 113.04

Answer:

a) The sinusoidal equation is;

The function is h = -24·cos[π(t )] + 24

The sketch of one full revolution is attached

b) The height of the nail at 0.8 seconds is 43.42 cm

Step-by-step explanation:

The sinusoidal equation that models the nails height can be given as follows;

y = A·cos[B(x - C)]+D

A = The amplitude = Half maximum height =  48/2 = 24 cm

The period = 2·π/B = Time to complete one oscillation = 2 seconds

∴ B = 2·π/2 = π

x = t  = Time

C = The horizontal shift

D = the vertical shift = 24 cm

y = The height of the nail = h

We have;

h = -24·cos[π(t - C)] + 24

At t = 0, h = 0, therefore, we have;

0 = -24·cos[π(0 - C)] + 24

24·cos[π(0 - C)] = 24

∴ cos[π(0 - C)] = 24/24 = 1

π(0 - C) = 0

C = 0

The function is h = -24·cos[π(t )] + 24

b) The height of the nail at 0.8 seconds is given as follows;

h = -24×cos[π(0.8)] + 24 =

h = 19.42 + 24 = 43.42 cm.

Answer:

Margarine = 210 gram

Sugar = 180 gram

Syrup = 150 ml

Oats = 360 gram

Raisins = 75 grams

Step-by-step explanation:

Given:

Recipe for 8 flapjacks

140 g margarine

120 g sugar

100 mL syrup

240 g oats

50 g raisins

Find:

Recipe for 12 flapjacks

Computation:

Margarine = [140/8]12

Margarine = 210 gram

Sugar = [120/8]12

Sugar = 180 gram

Syrup = [100/8]12

Syrup = 150 ml

Oats = [240/8]12

Oats = 360 gram

Raisins = [50/8]12

Raisins = 75 grams

Answer:

???

Step-by-step explanation:

inadequate info a pic is needed :)

Answer:

50%

Step-by-step explanation:

real answer

Answer:

Perimeter= 12y units

3y(4) = 12y

Step-by-step explanation:

3y + 3y + 3y + 3y= 12y

Answer:

0.89

Step-by-step explanation:

31.95 is about 32

36.05 is about 36

32/36 is 0.888...

rounded is 0.89

Answer:

.89

Step-by-step explanation: