please show all work so i can better understand. Thank you!
- 2. Find all values of x where f '(x) = 0 for f(x) = arcsin(e2x – 2x).

The length of side x in simplest radical form with a rational denominator is x√3.

To find the length of side x in simplest radical form with a rational denominator given x√3, some steps need to be followed.

Steps are:
1. Identify the radical: In this case, it is √3.

2. Identify the denominator: To rationalize the denominator, we want to eliminate the radical from the denominator. Since the given expression has x√3, the denominator we need to rationalize is 1.

3. Rationalize the denominator: To do this, multiply the expression by a value that will cancel out the radical in the denominator without changing the value of the expression. Since our denominator is 1, we need to multiply the expression by √3/√3.

4. Multiply the expression: (x√3) * (√3/√3) = x√3 * √3 = x(√3)^2 = x(3).

5. Simplify the expression: x(3) = 3x.

So, the length of side x in simplest radical form with a rational denominator is 3x.

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Therefore , the solution of the given problem of unitary method  comes out to be space between Mars' and Jupiter's orbits contains rock-like objects.

To complete the work, the well-known straightforward strategy, actual variables, and any essential components from the very first and specialised inquiries can all be utilised. In response, customers might be given another opportunity to sample the product. Otherwise, important advancements in our comprehension of algorithms will be lost.

Here,

What makes up the majority of the sun?

hydrogen a

The names of the planets nearest to the sun are:

Inner planets, B

A. 2n² is the general formula for the main shell.

Except for one planet, all of them revolve in the same direction. What planet is that?

(1) Venus

Which of the following is the solar system's inner planet?

Mercury, a.

The region of space between Mars' and Jupiter's orbits contains rock-like objects, which are known as:

Asteroid C.

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Her profit when 0 people attend is -$50 and each person pays 10

From the question, we have the following parameters that can be used in our computation:

y = 10x - 50.

The graph is added as an attachment

This means that

x = 0

So, we have

y = 10(0) - 50.

y = -50

She made a loss of 5-

This represents her profit when 0 people attend

This represents the slope of the function

The slope of the function is 10

So, each person pays 10

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Answer:

Step-by-step explanation:

f(x) = ax² + bx + c      a= -8

f(x) = -8x² + bx + c     that a controls the direction and the stretch.

So the function will be stretched by 8.  The negative represents the direction because, it's negative, it will be facing down.  

Not sure how your class describes it but it could be facing down, concaved down, or expands downward.  

The volume of the cone with a radius of 8cm and height of 15 cm is V = 1005.3 cm³, so the correct option is C.

Remember that for a cone of radius R, and height H, the volume is given by the formula below:

V = (1/3)*pi*R²*H

Where pi = 3.1416

In this case, we know that the radius of the cone is 8cm and the height is 15cm, replacing that in the volume formula we will get:

V = (1/3)*3.1416*(8cm)²*15cm = 1,005.3 cm³

Then the correct option is c.

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Answer:

You are correct.
Hope this helps!

Step-by-step explanation:

The lines intersect at one point and that is the solution.

( The image shows a graph with infinite solutions. ( ignore the Byjus thing i was just trying to find an image that showed an example ... ) )

The total differential of the function z = 7x^4y^5 is dz is (28x^3y^5)dx + (35x^4y^4)dy.

To find the total differential of the function z = 7x^4y^5, we need to compute the partial derivatives with respect to x and y, and then express dz in terms of dx and dy.

Computing the partial derivative with respect to x,
∂z/∂x = 4 * 7x^3y^5 = 28x^3y^5

Computing the partial derivative with respect to y,
∂z/∂y = 5 * 7x^4y^4 = 35x^4y^4

Express dz in terms of dx and dy,
dz = (∂z/∂x)dx + (∂z/∂y)dy
dz = (28x^3y^5)dx + (35x^4y^4)dy

So, the total differential of the function z = 7x^4y^5 is dz = (28x^3y^5)dx + (35x^4y^4)dy.

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The approximate total amount Valerie will pay for her new car is $38,287.

How much will Valerie pay in total for her new car?

To calculate how much Valerie will pay in total for her new car, we need to consider several factors.

First, let's determine the trade-in value of her 2006 Hyundai Sonata. Since the car is in good condition, Valerie will receive 87.5% of the listed trade-in price for that year, which is $6,784. Therefore, the trade-in value is approximately $5,938.80 ($6,784 * 0.875).

Now, let's calculate the total cost of the new car. The list price is $32,495, and Valerie plans to make a down payment of $1,877. Thus, the remaining amount to be financed is $32,495 - $1,877 - $5,938.80 = $24,679.20.

Next, let's consider the interest on the financing. The interest rate is 8.64% per year, compounded monthly. Over five years, this amounts to 60 monthly payments. Using an amortization formula, we can determine that the monthly payment is approximately $516.27.

Additionally, Valerie will have to pay sales tax, vehicle registration fee, and documentation fee. The sales tax is 8.23% of the total cost, which is ($24,679.20 + $2,243) * 0.0823 = $2,329.48. The vehicle registration fee is $2,243, and the documentation fee is $314. The total additional fees amount to $2,329.48 + $2,243 + $314 = $4,886.48.

Finally, to calculate the total amount Valerie will pay, we add the down payment, monthly payments, trade-in value reduction, and additional fees: $1,877 + (60 * $516.27) + $5,938.80 + $4,886.48 = $38,285.88.

Rounding to the nearest cent, Valerie will pay approximately $38,286 for her new car. Thus, the correct answer is option c: $38,287.

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The ratios are 1. Current ratio = 2.90, 2. Acid-test ratio = 2.22, 3. Inventory turnover ratio = 3.57, 4. Debt to equity ratio = 0.77, 5. Return on equity ratio = 15%.

The ratios to be computed are:

1. Current ratio

2. Acid-test (quick) ratio

3. Inventory turnover ratio

4. Debt to equity ratio

5. Return on equity ratio

1. Current ratio = Current assets / Current liabilities

Current assets = Cash + Accounts receivable + Inventory = $17,205 + $80,290 + $68,820 = $166,315

Current liabilities = Accounts payable = $57,350

Current ratio = $166,315 / $57,350 = 2.90

2. Acid-test (quick) ratio = (Cash + Accounts receivable) / Current liabilities

Acid-test ratio = ($17,205 + $80,290) / $57,350 = 2.22

3. Inventory turnover ratio = Cost of goods sold / Average inventory

Average inventory = (Beginning inventory + Ending inventory) / 2

Beginning inventory = $57,350

Ending inventory = $68,820

Average inventory = ($57,350 + $68,820) / 2 = $63,085

Inventory turnover ratio = $225,600 / $63,085 = 3.57

4. Debt to equity ratio = Total liabilities / Total equity

Total liabilities = Accounts payable + Mortgage payable = $57,350 + $114,700 = $172,050

Total equity = Common stock + Retained earnings = $160,580 + $63,085 = $223,665

Debt to equity ratio = $172,050 / $223,665 = 0.77

5. Return on equity ratio = Net income / Average equity

Average equity = (Beginning equity + Ending equity) / 2

Beginning equity = Common stock + Retained earnings = $137,640 + $45,880 = $183,520

Ending equity = Common stock + Retained earnings + Net income - Dividends = $160,580 + $63,085 + $31,100 - $21,700 = $232,065

Average equity = ($183,520 + $232,065) / 2 = $207,793

Return on equity ratio = $31,100 / $207,793 = 0.15 or 15%

Therefore, the ratios are:

1. Current ratio = 2.90

2. Acid-test ratio = 2.22

3. Inventory turnover ratio = 3.57

4. Debt to equity ratio = 0.77

5. Return on equity ratio = 15%

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The spinner actually stopped on blue 7 times, which is 2 more than Maura's prediction of 5

Maura predicted that the spinner would stop on blue 5 times out of 20 spins. This is a predicted probability of 5/20 or 0.25.

However, the actual number of times the spinner stopped on blue was 37.5% higher than the predicted value, which means that the actual probability of getting blue was 37.5% higher than the predicted probability. We can express the actual probability as:

Actual probability of getting blue = 0.25 + 0.375*0.25

= 0.34375

This means that the spinner actually stopped on blue 0.34375 * 20 = 6.875 times.

Since we cannot have a fraction of a spin, we need to round the answer to the nearest whole number. Rounding up, we get:

The spinner actually stopped on blue 7 times.

Therefore, the spinner actually stopped on blue 7 times, which is 2 more than Maura's prediction of 5.

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The geometric term best describes Marci's description of the sun's light is ray

A ray is a line that extends eternally in one direction from a point in geometry, in this case the sun.

It symbolizes a straight journey without any turning points.

As the sun's light propagates in a straight line throughout space without end, Marci's description fits the definition of a ray.

To explain Marci's depiction of the sun's light as a line that originates at the sun and never ends is to use the geometric term "ray."

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Answer: Ray

Step-by-step explanation:

A ray continues but may have a segment near the stopping point

The measures of angle T and S in a right angles triangle STU with side Lengths ST = 10 units and UT = 4 units are equals to

We have a triangle STU has a right angle at U so, we can call it a right angled triangle STU. Length of side ST = 10 units

Length of side TU = 4 units

We have to determine the measure of angle T and measure of angle S.

As we know that sum of inner angles of a triangle = 180°

So, m∠S + m∠T + m∠U = 180°

=> m∠S + m∠T = 180° - 90°

= 90°

Using the trigonometry formula, in right angles triangle STU,

tan (m∠T ) = US/UT

=> m∠T = √86/4

=>

Hence, required value are

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Complete question:

The above figure completes the question.

In the figure shown, what are ∠ and ∠? Triangle S T U has right angle U and is labeled as follows: S T, 10; T U, 4; and the long leg, unlabeled

Check the picture below.

The first four nonzero terms of the Taylor series for f(y) about 0 are:

[tex]-2y^2 + 48y^4/2![/tex] + ... = -[tex]2y^2 + 24y^4[/tex] + ...

To find the Taylor series for the function f(y) = ln(1 - 2y^4) about 0, we need to compute its derivatives at 0 and evaluate them at each term. Let's start by finding the first four derivatives:

f(y) = ln(1 - 2[tex]y^4)[/tex]

f'(y) = [tex]-8y^3 / (1 - 2y^4)[/tex]

f''(y) =[tex](24y^6 - 32y^2) / (1 - 2y^4)^2[/tex]

f'''(y) =[tex](-144y^9 + 384y^5) / (1 - 2y^4)^3[/tex]

f''''(y) =[tex](1920y^12 - 7680y^8 + 3456y^4) / (1 - 2y^4)^4[/tex]

Now we can evaluate each derivative at 0 to get the first four nonzero terms of the Taylor series:

f(0) = ln(1) = 0

f'(0) = 0

f''(0) = -2

f'''(0) = 0

f''''(0) = 48

Therefore, the first four nonzero terms of the Taylor series for f(y) about 0 are: -2y^2 + 48y^4/2! + ... = -2y^2 + 24y^4 + ...

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The given infinite series diverges.

Let f(x) = -5/x. Then, we can see that f(x) is a continuous, positive, and decreasing function for x ≥ 1. Now, we can apply the integral test to determine whether the series converges or diverges.

∫₅^∞ -5/x dx = -5 ln(x) |₅^∞ = -∞

Since the improper integral diverges, by the integral test, the infinite series also diverges.

To apply the integral test, we need to verify the following conditions:

f(x) is a continuous, positive, and decreasing function for x ≥ 1.

The series Σ aₙ and the integral ∫₁^∞ f(x) dx have the same convergence behavior.

Let f(x) = -5/x. Then, f(x) is a continuous function for x ≥ 1. Furthermore, f(x) is positive and decreasing because its derivative is f'(x) = 5/x² > 0 for x ≥ 1.

We can evaluate the integral ∫₁^∞ f(x) dx as follows:

∫₁^∞ -5/x dx = -5 ln(x) |₁^∞ = -∞

Since the improper integral diverges, the series Σ -5/n also diverges by the integral test.

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Answer: 1. Multiplying Powers with same Base

For example: x² × x³, 2³ × 2⁵, (-3)² × (-3)⁴

In multiplication of exponents if the bases are same then we need to add the exponents.

Consider the following:

1. 2³ × 2² = (2 × 2 × 2) × (2 × 2) = 23+2

= 2⁵

2. 3⁴ × 3² = (3 × 3 × 3 × 3) × (3 × 3) = 34+2

= 3⁶

3. (-3)³ × (-3)⁴ = [(-3) × (-3) × (-3)] × [(-3) × (-3) × (-3) × (-3)]

                       = (-3)3+4

                       = (-3)⁷

4. m⁵ × m³ = (m × m × m × m × m) × (m × m × m)

                 = m5+3

                 = m⁸

From the above examples, we can generalize that during multiplication when the bases are same then the exponents are added.

aᵐ × aⁿ = am+n

In other words, if ‘a’ is a non-zero integer or a non-zero rational number and m and n are positive integers, then

aᵐ × aⁿ = am+n

Similarly, (ab

)ᵐ × (ab

)ⁿ = (ab

)m+n

(ab)m×(ab)n=(ab)m+n

Note:

(i) Exponents can be added only when the bases are same.

(ii) Exponents cannot be added if the bases are not same like

m⁵ × n⁷, 2³ × 3⁴

Step-by-step explanation:

Answer:

2^4

Step-by-step explanation:

doing this type of division is like subtracting the powers, 9-5=4, 2^4.

the opposite applies for multiplaction, it's like addition for the powers,

2^9*2^5=2^14.

The sample space for the number solid is {1, 2, 3, 4, 5, 6} and the probability of rolling 1 is 1/6.

The sample space refers to the set of all possible outcomes of an experiment, while a sample value is a specific outcome in the sample space.

For the given 8-sided solid, the sample space would be {1, 2, 3, 4, 5, 6}, as the faces labeled "skip" are not counted as sample values.

Now, let's calculate the probability of rolling a 1. Probability is the likelihood of a particular outcome occurring, which can be calculated by dividing the number of successful outcomes (in this case, rolling a 1) by the total number of possible outcomes.

The total number of possible outcomes is 6 (1, 2, 3, 4, 5, and 6). There is only one successful outcome: rolling a 1.

So, the probability of rolling a 1 is:

P(1) = (Number of successful outcomes) / (Total number of possible outcomes)
P(1) = 1 / 6

Thus, the probability of rolling a 1 on this 8-sided solid is 1/6 or approximately 0.1667, or 16.67%.\

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The expression 148 + 19x³ represents the sum of 148 and the product of a number raised to the third power and 19.

To write the phrase "the sum of 148 and the product of a number raised to the third power and 19" in symbols using the variable x, we can write it as:

148 + 19x³

Here, we are adding 148 to the product of 19 and x raised to the third power. This expression represents the sum of 148 and the product of a number raised to the third power and 19. We can substitute any value for x to get the result of the expression. For example, if x is 2, then the expression becomes:

148 + 19(2³) = 148 + 19(8) = 300

Therefore, the sum of 148 and the product of a number raised to the third power and 19 is represented by the expression 148 + 19x³.

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El área de papel utilizada para cada CD es aproximadamente 20.41 cm².

How much paper area is used for each CD?

Para calcular el área de papel utilizado para cada CD, necesitamos determinar el área de la región entre dos círculos concéntricos.

El área de un círculo se calcula utilizando la fórmula A = πr², donde r es el radio. En este caso, tenemos dos círculos con radios diferentes: el radio mayor de 5.8 cm y el radio menor de 0.7 cm.

El área del papel utilizado será la diferencia de áreas entre los dos círculos. Entonces, podemos calcularlo de la siguiente manera:

Área utilizada = Área del círculo mayor - Área del círculo menor

= π(5.8²) - π(0.7²)

= π(33.64) - π(0.49)

≈ 105.72 - 1.54

≈ 104.18 cm²

Por lo tanto, aproximadamente se utilizan 104.18 cm² de papel para cada CD.

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Step-by-step explanation:

I have provided answer in attachment... this is solution of brainly tutor..

Sneha's current age is 16 years old. Sneha's mother is 44 years old.

Let's assume Sneha's current age is x.

Sneha's mother's current age = 2x + 12

After 8 years, Sneha's age = x + 8

After 8 years, Sneha's mother's age = 2x + 12 + 8 = 2x + 20

After 8 years, Sneha's mother's age will be 20 less than three times Sneha's age: 2x + 20 = 3(x + 8) - 20

Now we can solve for x:

2x + 20 = 3(x + 8) - 20

2x + 20 = 3x + 24 - 20

2x + 20 = 3x + 4

x = 16

Therefore, Sneha's current age is 16 years old.

Sneha's mother's current age = 2x + 12

= 2(16) + 12 = 44

So, Sneha's mother is 44 years old.

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The 85% confidence interval for the population proportion of people who are captured after appearing on the 10 Most Wanted list falls between 0.194 and 0.286.

To construct the 85% confidence interval for the population proportion of people who are captured after appearing on the 10 Most Wanted list, we can use the following formula:

[tex]\hat{p} \pm z^* \sqrt{\frac{\hat{p} (1 - \hat{p})}{n}}[/tex]

where [tex]$\hat{p}$[/tex] is the sample proportion, [tex]$n$[/tex] is the sample size, and [tex]$z^*$[/tex] is the z-score corresponding to the desired level of confidence. Since we are looking for an 85% confidence interval, the z-score is 1.440.

First, we can calculate the sample proportion:

[tex]\hat{p} = \frac{109}{455} = 0.240[/tex]

Next, we can plug in the values into the formula:

[tex]$$ 0.240 \pm 1.440 \sqrt{\frac{0.240 (1 - 0.240)}{455}} $$[/tex]

Simplifying this expression, we get:

[tex]$$ 0.240 \pm 0.046 $$[/tex]

Therefore, the 85% confidence interval for the population proportion of people who are captured after appearing on the 10 Most Wanted list is [tex]$(0.194, 0.286)$[/tex].

We can interpret this interval as follows: if we were to draw many samples of size 455 from the population of people who appear on the 10 Most Wanted list, and construct a 85% confidence interval for the proportion of people who are captured based on each sample, about 85% of these intervals would contain the true population proportion.

Furthermore, we are 85% confident that the true population proportion of people who are captured after appearing on the 10 Most Wanted list falls between 0.194 and 0.286.

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m > 8 is an inequality used to calculate the number of articles Mustafa could have written.

Let's assume that Mustafa has written m articles for the school newspaper.

Then, according to the given information:

Heloise has written 1/4 as many articles as Mustafa has, which means she has written 1/4 × m = m/4 articles.

Gia has written 3/2 as many articles as Mustafa has, which means she has written 3/2 × m = 3m/2 articles.

The combined total of articles written by all three is more than 22, so we can write:

m/4 + 3m/2 + m > 22

Simplifying and solving for m:

11m/4 > 22

m > 22 × 4/11

m > 8

Therefore, m > 8 is an inequality used to calculate the number of articles Mustafa could have written.

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Answer:

Step-by-step explanation:

The latus rectum of an ellipse is 288/13 when the ellipse equation is given as [tex]x^2/169 + y^2/144 = 1[/tex]. Option A is correct.

The standard form of an ellipse equation is given as  

[tex](x2/a2) + (y2/b2) = 1[/tex]

where :

a = lengths of the semi-major axes

b = length of semi-minor axes

The length of the chord through one of the foci that are perpendicular to the major axis is defined as the latus rectum of an ellipse.

From the given data the equation of the ellipse is given as :

x² / 169 + y² / 144 = 1

By comparing the standard equation and the given equation of the ellipse we get :

a² = 169

a = √169

[tex]a = 13[/tex]

b² = 144

b = √144

[tex]b = 12[/tex]

The distance between the center and one of the foci is given by

c = √(a² - b²)

= √(13² - 12²)

= 5

We can find the latus rectum by substuting a and b values in the latus rectum of an ellipse formula,

= 2×b²/a

= 2 × 12² / 13

= 288/13

Therefore, the latus rectum of an ellipse is 288/13.

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The MAD for this set of data is 0.8.

To find the MAD (Mean Absolute Deviation) for this set of data, we first need to find the mean of the ages:

Mean = (13 + 10 + 9 + 10 + 10 + 9 + 10 + 10 + 11 + 9) / 10 = 10.1

Next, we find the absolute deviation of each age from the mean:

|13 - 10.1| = 2.9

|10 - 10.1| = 0.1

|9 - 10.1| = 1.1

|10 - 10.1| = 0.1

|10 - 10.1| = 0.1

|9 - 10.1| = 1.1

|10 - 10.1| = 0.1

|10 - 10.1| = 0.1

|11 - 10.1| = 0.9

|9 - 10.1| = 1.1

Then, we find the average of these absolute deviations:

MAD = (2.9 + 0.1 + 1.1 + 0.1 + 0.1 + 1.1 + 0.1 + 0.1 + 0.9 + 1.1) / 10 = 0.8

Therefore,To find the MAD (Mean Absolute Deviation) for this set of data, we first need to find the mean of the ages:

Mean = (13 + 10 + 9 + 10 + 10 + 9 + 10 + 10 + 11 + 9) / 10 = 10.1

Next, we find the absolute deviation of each age from the mean:

|13 - 10.1| = 2.9

|10 - 10.1| = 0.1

|9 - 10.1| = 1.1

|10 - 10.1| = 0.1

|10 - 10.1| = 0.1

|9 - 10.1| = 1.1

|10 - 10.1| = 0.1

|10 - 10.1| = 0.1

|11 - 10.1| = 0.9

|9 - 10.1| = 1.1

Then, we find the average of these absolute deviations:

MAD = (2.9 + 0.1 + 1.1 + 0.1 + 0.1 + 1.1 + 0.1 + 0.1 + 0.9 + 1.1) / 10 = 0.8

Therefore, the MAD for this set of data is 0.8.

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each of Jennifer's five kids received 1/40 of the total pan of macaroni and cheese.

What is equivalent ratio?

The concept of a ratio in mathematics is the divisional comparison of two quantities, the antecedent and consequent. As an illustration, each ingredient must be added according to a ratio during cooking. So, we may argue that a ratio is employed to represent one quantity as a portion of another. The ratio can be written as a fraction as well. If the ratio a:b is a fraction, its form is a/b. As a result, it is simple to compare two or more equivalent ratios expressed as equivalent fractions.

If Jennifer had 7/8 of her pan of macaroni and cheese left after supper, this means she had 1 - 7/8 = 1/8 of the pan remaining.

To split the remaining macaroni and cheese evenly between her five kids, we need to divide 1/8 by 5.

1/8 divided by 5 can be written as (1/8) ÷ 5 = (1/8) x (1/5) = 1/40.

Therefore, each of Jennifer's five kids received 1/40 of the total pan of macaroni and cheese.

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By using concept of interior angle we find the value of X is -7.14 degrees.

The above problem involves finding the value of x in a triangle with two known angles measuring 78° and 152°.

The sum of the interior angles of any triangle is always 180°, so we can use this fact to set up an equation involving the third angle, which is given as 7x +3 degrees.

To solve for x, we first simplify the equation by combining the known angles:

78° + 152° + (7x + 3)° = 180°

Next, we can simplify by adding the two known angles:

230° + 7x° = 180°

This simplifies to:

7x° = -50°

Finally, we can solve for x by dividing both sides by 7:

x =  [tex]\frac{-50^\circ}{7}$$[/tex]

Therefore, x is approximately -7.14 degrees.

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The cross-product of u and v:
w = u × v = (5, -4, 8) × (-8, -4, 5) = (-20, -60, 32)

Thus, w is orthogonal to u. Since we need two vectors in opposite directions, we can negate w:
-w = (20, 60, -32)
Therefore, the two orthogonal vectors in opposite directions are w = (-20, -60, 32) and -w = (20, 60, -32).

To find two vectors that are orthogonal to u, we can use the cross-product. Let v = (4,5,0) and w = (-8,0,5). Then v x u = (40,40,45) and w x u = (20,-40,20). So two vectors orthogonal to u are (40,40,45) and (20,-40,20).

To determine whether two planes are orthogonal, parallel, or neither, we can look at the normal vectors of each plane. Let the first plane be defined by the equation 2x + 3y - z = 4 and the second plane being defined by the equation :

4x + 6y - 2z = 8.

The normal vector of the first plane is (2,3,-1) and the normal vector of the second plane is (4,6,-2).

Since the dot product of these two normal vectors is -2(3) + 3(6) - 1(2) = 14, which is not equal to 0, the planes are not orthogonal.

To determine if they are parallel, we can check if the ratio of their normal vectors is constant. Dividing the second normal vector by the first, we get (4/2, 6/3, -2/-1) = (2,2,2). Since this is a constant ratio, the planes are parallel.

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