write a formula that expresses the first variable as a function of the second: 1.the area of a circle as a function of its diameter

The measures of angle ABC and DBC are 41 degrees and 43 degrees

The angles are given as

Angle ABC = (5x + 1) degrees

Angle DBC = (6x - 5) degrees

Angle ABD = 84 degrees

The angles add up to 84 degrees

So, we have:

ABC + DBC = 84

This gives

5x + 1 + 6x - 5 = 84

Evaluate the like terms

11x = 88

Divide both sides by 11

x = 8

Substitute x = 8 in Angle ABC = (5x + 1) degrees and Angle DBC = (6x - 5) degrees

Angle ABC = (5 x 8 + 1) degrees

Angle DBC = (6 x 8 - 5) degrees

Evaluate

Angle ABC = 41 degrees

Angle DBC = 43 degrees

Hence, the measures of angle ABC and DBC are 41 degrees and 43 degrees

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Using the Factor Theorem, Andrew's error was at the application of the minus signal to the complex roots, and the polynomial of degree 3 is of f(x) = x³ - 7x² + 20x - 24.

The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:

[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]

In which a is the leading coefficient.

For this problem, the roots are given as follows:

Hence the polynomial is given as follows, considering leading coefficient a = 1:

[tex]f(x) = (x - 3)(x - 2 - 2i)(x - 2 + 2i)[/tex]

His error was at the application of the minus signal to the complex roots.

Then:

f(x) = (x - 3)[(x - 2)² - (2i)²]

f(x) = (x - 3)(x² - 4x + 4 + 4)

f(x) = (x - 3)(x² - 4x + 8)

f(x) = x³ - 7x² + 20x - 24.

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The result of the operation is 30 > 3 and the result is true

The inequality expression is given as:

-15 < -6

The operation on the inequality expression is given as:

Multiply both sides of the inequality by -1/2

So, we start by multiplying both sides of the above inequality by -1/2

This is represented as

-15 * -1/2 < -6 * -1/2

Evaluate the products

So, we have

30 > 3

The above inequality is true because 30 is greater than 3

Hence, the result of the operation is 30 > 3 and the result is true

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The perimeter of the rectangle is P = (17.2x₊16.4).

Given that,

Length, l = 8.6x₊3

Width, b = 5.2

In the formula P=2l+2w, where l is the rectangle's length and w is its width, the perimeter P of a rectangle is determined. Using the formula A=l×w, where l is the length and w is the width, we can determine the area A of a rectangle.

We need to find the expression for the perimeter of the rectangle. The formula for the perimeter of the rectangle is given by :

P=2(l₊b)

Putting values of l and b in the above formula:

p = 2(8.6x ₊ 3 ₊ 5.2)

= 2(8.6x ₊ 8.2)

= 2(8.6x) ₊ 2(8.2)

= 17.2x ₊ 16.4

So, the required perimeter of the rectangle is 17.2x₊16.4.

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−8

 5

y-intercept:

(0,−4)

Step-by-step explanation:

Answer:

He will fill 37 boxes and 11 cards will be left over

Step-by-step explanation:

The probability that at least one of them is operational is 0.999

Probability:

Probability means the possibility of happening the particular event. So, it can be written as the fraction of possible event by the total number of event.

Given,

The probability a D-Link network server is down is 0.10.

Here we need to find if you have three independent servers, what is the probability that at least one of them is operational.

Let D be an event that a D-Link network server is down.

It is given that the probability that a D-Link network server is down is

=> P(D) = 0.10

The number of independent servers

=> (n) = 3

The probability that none of the servers is working is

=>P(None) = P(D) x P(D) x P(D)

=> P(None) = 0.10 x 0.10 x 0.10

=> P(None) = 0.001

The probability that at least one of them is operational is given as

=> 1 - P(None)

=> 1 - 0.001

=> 0.999

Therefore, the probability that at least one of them is operational is 0.999.

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Answer:

It's really hard to really solve cause I'm a student in learning.

Answer:

x = 200

Step-by-step explanation:

substitute y = 15 into the equation

[tex]\frac{1}{5}[/tex] x - ([tex]\frac{2}{3}[/tex] × 15) = 30

[tex]\frac{1}{5}[/tex] x - (2 × 5) = 30

[tex]\frac{1}{5}[/tex] x - 10 = 30 ( add 10 to both sides )

[tex]\frac{1}{5}[/tex] x = 40 ( multiply both sides by 5 to clear the fraction )

x = 5 × 40 = 200

Using the relation between velocity, distance and time, it is found that she traveled 15 seconds at 10 m/s and 7 seconds at 50 m/s.

Velocity is distance divided by time, that is:

v = d/t.

For the first part, we have that she cycled a distance of d m in t seconds, at a velocity of 10 m/s, hence:

10 = d/t

d = 10t.

For the second part, we have that she cycled a distance of 500 - d meters, in 22 - t seconds, at a velocity of 50 m/s, hence:

50 = (500 - d)/(22 - t).

Since d = 10t, and applying cross multiplication:

500 - 10t = 50(22 - t)

500 - 10t = 1100 - 50t

40t = 600

t = 600/40

t = 15.

22 - t = 22 - 15 = 7, hence:

She traveled 15 seconds at 10 m/s and 7 seconds at 50 m/s.

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It appears that from graph that the function is increasing in the interval (-∞,-1) and (1,∞). Also the function is decreasing in the interval (-1,1) and (0.0.5).The function is not constant anywhere.

To check if this is correct, we will find the relative extrema of the function,

f(x) = x³-x²-2x+3

Find it derivative f'(x) = 3x²-2x-2

f'(x) = 0

⇒ x = 2 ± √(4+24)/3

      = 3.77 , -1.1

Find the second derivative f''(x) = 6x -2

f''(3.77) = 20.62>0

So the function has a relative minimum at x = 3.77.

f''(-1.1) = -8.6<0

So the function has a relative maximum at x = -1.1

Now we can conclude with the intervals where the function is increasing is before the relative maximum and after the relative minimum.

i.e., the intervals (-∞,-1) and (3.5,∞) [rounding to the nearest 0.5 unit]

So the interval in which the function is decreasing is between the relative maximum and minimum. i.e.,  the interval (-1, 3.5)

The function is nowhere constant.

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The graph is plotted in the following figure .

To plot a graph we need 2 pts .

First eqn is of a circle ( [tex]x^{2}[/tex] ) + ( [tex]y^{2}[/tex] ) = 4

Second eqn is of a line x - y = 1

The center of circle is ( 0 , 0 )

The circle passes through ( 2 , 0 ) , ( 0 , 2 ) , ( - 2 , 0 ) , ( 0 , - 2 ) .

The line passes through ( 0 , 1 ) , ( 0 , - 1 ) .

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Answer:

i think b

Step-by-step explanation:

Answer:

B. y = 2x + 8

Step-by-step explanation:

14x - 7y = 1

7y = 14x - 1

y = 2x - 1/7

If two lines are parallel, their slopes are equal.

With m = 2, x = -2, y = 4

y = mx + b

4 = 2(-2) + b

4 = -4 + b

b = 8

so y = 2x + 8

The number 86,360,000 using the number word "million" and then round to one decimal place is Eighty-six million three hundred sixty thousand.

The writing style used to express numbers in India is known as the Indian numeral system. In this case, numbers are divided into several time periods or groupings. This numbering scheme uses ten distinct symbols, including the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.

The order of the digits when using the Indian number system is one, ten, hundreds, thousands, ten thousand, lakhs, lakhs, crores, and crores. The era and locations are shown in the table below according to the amount of digits in a number.

Given number: 86,360,000

Eighty-six million three hundred sixty thousand in numbers

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Answer:

0.0416¯

Step-by-step explanation:

after the 1 six is being repeated. Hope this helps! :)

The expression that could represent the distance, in meters, that Abiona dives will be:

5 - (-2.1)

5 + 2.1

From the information, Abiona dives from a platform that is 5 meters above water. Her dive takes her 2.1 meters below the surface of the water.

The appropriate expression will be:

= 5.1 - (-2.1)

= 5.1 + 2.1

= 7.2

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Answer:

c

Step-by-step explanation:

This was a question asked by someone else roughly a week ago, here's the answer to that question. It's the same as this question. I hope this helps.

The student did the subtraction step of PEMDAS out of order.

PEMDAS is a rule regarding precedence of operations, given as follows, from highest to lowest precedence.

In this problem, the expression is:

(6 - 2)² + 12  - 3².

The student reached an answer of 97 as follows:

(6 - 2)² + 9² = 4² + 9² = 16 + 81 = 97.

The student did the subtraction first, hence the student did the subtraction step of PEMDAS out of order.

The correct solution is:

(6 - 2)² + 12  - 3² -> Solve the Parenthesis.

4² + 12 - 3² -> Solve the Exponents.

16 + 12 - 9 -> Solve the Addition and Subtraction.

19.

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The point estimate of the population proportion defective will be 0.0945

The formula for calculating the point estimate is expressed as;

p = x/n,

where p is the proportion of successes in the sample

n is the total sample

Given the following

n = 550 items

x = 52

Substitute

p = 52/550

p = 0.0945

Hence the point estimate of the population proportion defective will be 0.0945

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Answer:

the numerator (the top number)/ Denominator (bottom number)

Step-by-step explanation:

you should know this

Answer:

Fractional mathematics have to do with dealing with certain amounts of a number and mathematical proportions. Fractions are amounts out of a whole number.

The mass of pyramid is 6 grams and the cube is 8 grams

Let's assume the mass of a pyramid is x gram and mass of a cube is y gram .

So, algebraic mass of 6 and 4 pyramids is 6x grams and 4x grams. and algebraic mass of 2 cubes and 4 cubes is 2y grams and 4y grams .

Total algebraic mass of 4 pyramids and 2 cubes are , 4x + 2y = 40 ;(equation 1)

and Total algebraic mass 6 pyramids and 4 cubes are , 6x + 4y = 68 ;(equation 2)

Now we have to use adoption method to solve this problem ,  

we have to multiply equation (1) with 4 and equation (2) with 2 , and we will get ,

16x + 8y = 160 ; ( equation 3 )

12x + 8y = 136 ; ( equation 4 )

Now , we will substract equation ( 3 ) from equation ( 4 )

4x = 24 and x = 24/4 = 6

Let's put the value of x in equation ( 1 )

24 + 2y = 40 or, 2y = 16 or, y = 8

Here we can conclude , mass of pyramid is 6 grams and the cube is 8 grams.  

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The coordinates of the point where the chain should attach to the triangle are (3, 4).

Given that, a triangle is on a coordinate plane with coordinates (0,4), (3,8), and (6,0).

We need to find the coordinates of the point where the chain should attach to the triangle.

The centroid is the centre point of the object. The point at which the three medians of the triangle intersect is known as the centroid of a triangle. It is also defined as the point of intersection of all three medians. The median is a line that joins the midpoint of a side and the opposite vertex of the triangle. The centroid of the triangle formula is G = ((x1+x2+x3)/3 , (y1+y2+y3)/3).

Now, centroid = ((0+3+6)/3, (4+8+0)/4)

=(3, 4)

Therefore, the coordinates of the point where the chain should attach to the triangle are (3, 4).

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The area of the circle is 64π square unit and the circumference is 16π units

From the question, we are to find the area and circumference of the circle

The area of a circle is given by the formula,

A = πr²

Where A is the area

and r is the radius

Using the parameter, radius = 8

Then,

A = π × 8²

A = 64π square unit

Calculating the circumference

The circumference of a circle is given by the formula

C = 2πr

Where C is the circumference

and r is the radius

Thus,

C = 2  × π × 8

C = 16π units

Hence, the area of the circle is 64π square unit and the circumference is 16π units

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The percentage of u.s. land is national park system land is approximately 41.8%

Convert acres to square miles

Percentage of u.s. land is national park system land = national park system land / Total U.S. land area × 100

= 1476562.5 square miles / 3,537,000 square miles × 100

= 0.417461832061068 × 100

= 41.74618320610687%

Approximately,

41.8%

Therefore, the percentage of u.s. land is national park system land is approximately 41.8%

Complete question:

Total U.S. land area is 3.537 million square miles. Total U.S. national park system land occupies 954 million acres. What percentage of U.S. national park system land?

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Using the distance formula, the distance, to the nearest whole mile, between the two airports is: B. 1,304 miles.

The distance formula is: d = [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex].

Given the following locations:

P(1,17) = (x1, y1)

Q(12,10) = (x2, y2)

Use the distance formula to find the PQ:

PQ = √[(12−1)² + (10−17)²]

PQ = √[(11)² + (−7)²]

PQ = √170

PQ ≈ 13.04 units

1 unit = 100 miles

PQ = 13.04 × 100

PQ = 1,304 mils

Thus, using the distance formula, the distance, to the nearest whole mile, between the two airports is: B. 1,304 miles.

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Answer: B. 1,304 miles.

Answer:

W4 - 18w2 + 81 =0 this is the answer

Final answer:

The estimated number of days the aqi was over 100 in the year 1995 is calculated as 135 days.

Simple linear regression is expanded upon in quadratic regression. While quadratic regression has the drawback of requiring more data points to ensure that your data falls into the "U" shape, linear regression can be carried out with as few as two points (i.e., enough points to draw a straight line).

In situations where the second differences are constant, a quadratic model is adequate. We can ascertain the degree of the model for the data by identifying variations between the dependent values. The model will be linear if the initial difference has the same value. The model will be quadratic if the second difference has the same value as the first.

Explanation:

The air quality index, or aqi, calculates a number depending on how clean or dirty the air. Then it is estimate n, the number of days the aqi exceeded 100 in a specific year is evaluated and calculated as it is actually as 135 days on edge.

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Answer:

Graph A shows the system and solution to the system. Option A is correct.

The sum of Sharon's and John's ages is 70. Sharon is times as old as John. The system of equations regarding the problem is determined.

What is the equation?

The equation is the values of two expressions that are equal.

Let the age of Sharon's be x and Jhon's be y.

The sum of Sharon's and John's ages is 70.

x + y = 70  - - - - (1)

Sharon is times as old as John.

x = 4 y

Now put x = 4y in equation 1

4y + y = 70

5y = 70

y = 70/5

y = 14

Now put y = 14 in x = 4y

x = 4*14

x = 56

The solution of a system of equations is (14, 56) shown in graph 1.

Thus, graph A shows the system and solution to the system. Option A is correct.

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Step-by-step explanation:

Sharon is 14 years old and John is 56 years old.

The graph of the system of equations is given below where the solution is (14, 56).

An equation contains one or more terms with variables connected by an equal sign.

Example:

2x + 4y = 9 is an equation.

2x = 8 is an equation.

We have,

Let x be Sharon's age and y be John's age.

From the first sentence, we know that:

x + y = 70

From the second sentence, we know that:

y = 4x

Substituting y = 4x into the first equation, we get:

x + 4x = 70

5x = 70

x = 14

Substituting x = 14 into y = 4x, we get:

y = 4(14) = 56

The graph of the system of equations is given below where the solution is (14, 56).

Therefore,

Sharon is 14 years old and John is 56 years old.

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i) 9⁻⁴=1/6561

ii1/2⁻⁶=64

Positive exponent: An exponent defines the number of times a number is multiplied by itself. For example, 32. It means that the number 3 has to be multiplied twice. Here, the number 3 is a base number and 2 is an exponent. The exponent can be positive or negative.

Nagative exponent: We know that the positive exponent tells us how many times a number is multiplied by itself. Whereas, the negative exponent tells us how many times we have to divide the base number. In other words, the negative exponent describes how many times we have to multiply the reciprocal of the base. An example of negative exponents is 3-2.

Thus, x-2 is written as (1/x²).

i)Rewrite expression using a positive exponent  9⁻⁴

We know that positive exponent.

9⁻⁴=1/94

9⁻⁴=1/6561.

ii)Rewrite expression using a positive exponent 1/2⁻⁶

1/2⁻⁶=26

⇒1/2⁻⁶=64.

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