The sum of two consecutive integers is 85. Find the integers.
(Enter your answers as a comma-separated list.)

Step-by-step explanation:

a = 55° because angles on a straight line (around a single point on one side of the line) add up to 180°.

b = 75° because alternate angles (with parallel lines) are equal.

c = 50°, because alternate angles (with parallel lines) are equal.

d = 50°, because corresponding angles (with parallel lines) are equal.

Answer:

0.00265251989

Hope this helped.

1. 1-cos²x / sinx = sin²x / sinx = sinx
2. Cos X – Cos x = 0
3. (sin^2 + tan^2 u + cos^2 u) / (sec u) = (1 + tan^2 u) / (sec u) = sec^2 u / sec u = sec u
4. (sec^2 x – tan^2 c) / (cos^2 x + sin^2 x) = (1/cos^2 x - sin^2 x / cos^2 x) / 1 = (1 - sin^2 x) / cos^2 x = cos^2 x / cos^2 x = 1
5. (sec^2 + csc^2 x) - (tan^2 x + cot^2 x) = (1/cos^2 x + 1/sin^2 x) - (sin^2 x / cos^2 x + cos^2 x / sin^2 x) = (sin^4 x + cos^4 x) / (sin^2 x cos^2 x) = 1 / (sin x cos x)
6. tan x cot x = (sin x / cos x) * (cos x / sin x) = 1
7. cot u sin u = (cos u / sin u) * sin u = cos u
8. sec (-x) cos (-x) = (1 / cos (-x)) * cos (-x) = 1
9. cot (-θ) tan (-θ) = (cos (-θ) / sin (-θ)) * (sin (-θ) / cos (-θ)) = 1
10. sec^2 (-x) – tan^2 (-x) = (1/cos^2 (-x)) - (sin^2 (-x) / cos^2 (-x)) = (1 - sin^2 (-x)) / cos^2 (-x) = cos^2 (-x) / cos^2 (-x) = 1
11. sec u sin u = (1 / cos u) * sin u = sin u / cos u = tan u

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The difference in area between a circle with a radius of 10 centimeters and a square inscribed in it is  114 cm².

The difference in area between a circle with a radius of 10 centimeters and a square inscribed in it can be found by calculating the area of the circle and the area of the square and then subtracting the two.

First, calculate the area of the circle using the formula

A = πr²,

where A is the area and r is the radius.

A = π(10)² = 100π ≈ 314.16 square centimeters

Next, calculate the area of the square. Since the square is inscribed in the circle, the diameter of the circle is equal to the diagonal of the square. The diameter of the circle is 2r, or 20 centimeters.

Using the Pythagorean theorem, we can find the side length of the square:

s² + s² = (20)²

2s² = 400

s² = 200

s ≈ 14.14 centimeters

The area of the square is s² or (14.14)² ≈ 199.97 square centimeters.

Finally, subtract the area of the square from the area of the circle to find the difference:

314.16 - 199.97 ≈ 114.19 square centimeters

To the nearest whole, the difference in area is 114 square centimeters.

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The answer to this question is as follows The plaque measures 14 inches equation tall as a result.

A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.  

Because we are aware that the plaque has a parallelogram shape, we may determine its height using the formula for a parallelogram's area. The formula for a parallelogram's area is:

Base area x height

In this instance, we are aware that the area is 126 square inches, and the base (the bottom border) is 9 inches. Thus, we can enter those values into the formula to find the height:

126 = 9h

h = 126/9

h = 14

The plaque measures 14 inches tall as a result.

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Answer:

12/18, 2/3, and 18/27.

Step-by-step explanation:

In order to find ratios that are equivalent to a certain fraction they must have common divisibles.

In this case...
[tex]\frac{6}{9}[/tex]
If the common divisible is two....
[tex]6\times2=12[/tex]
[tex]9\times2=18[/tex]
[tex]=\frac{12}{18}[/tex]

You could also simplify the ratio:
[tex]\frac{6}{9} \div3=\frac{2}{3}[/tex]
[tex]=\frac{2}{3}[/tex]

If the common divisible is three:
[tex]6\times3=18[/tex]
[tex]9\times3=27[/tex]
[tex]=\frac{18}{27}[/tex]

The final velocity of the jet flying in the north direction after accelerating for 15s is 473 m/s.

When observed from a specific point of view and as measured by a specific unit of time, velocity is the direction at which an item is moving and serves as a measure of the pace at which its position is changing. How quickly or slowly an object is travelling can be determined by its velocity and speed. Being a vector quantity, we need to define velocity in terms of both magnitude (speed) and direction. A body is considered to be accelerating if the magnitude or direction of its velocity changes.

Given,

The initial velocity u = 200 m/s

Acceleration of jet a = 18.2 m/s²

Time taken t = 15s

We are asked to find the final velocity v of the jet.

W can use the following formula to find the final velocity.

v = u+ at

  = 200 + (18.2) × 15

 = 473 m/s (north)

Therefore the final velocity of the jet flying in the north direction after accelerating for 15s is 473 m/s.

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The solution to the equation is x = 12.

The equation for "twice the difference of some number and 8 amounts to the quotient of 112 and 14" can be written as:

2(x - 8) = 112/14

Where x is the unknown number.

First, simplify the right side of the equation by dividing 112 by 14 to get:

2(x - 8) = 8

Next, distribute the 2 on the left side of the equation:

2x - 16 = 8

Finally, solve for x by isolating the variable on one side of the equation:

2x = 8 + 16

2x = 24

x = 24/2

x = 12

Therefore, the solution to the equation is x = 12.

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The solutions are x ≈ -2.744 and x ≈ -17.106.

To solve this equation, we need to get rid of the fractions by multiplying each term by the least common multiple (LCM) of the denominators. The LCM of x+6 and 5x+30 is (x+6)(5x+30).

Multiplying each term by the LCM gives us:
(5)(x+6)(5x+30)/(x+6) = (7)(x+6)(5x+30)/(5x+30) - 2(x+6)(5x+30)

Simplifying the fractions and distributing the terms gives us:
5(5x+30) = 7(x+6) - 2(x+6)(5x+30)

Expanding and simplifying the terms gives us:
25x + 150 = 7x + 42 - 10x^2 - 180x - 360

Combining like terms and rearranging gives us:
10x^2 + 198x + 468 = 0

Using the quadratic formula, we can find the values of x:
x = (-198 ± √(198^2 - 4(10)(468)))/(2(10))

Simplifying gives us:
x = (-198 ± √(39204 - 18720))/(20)

x = (-198 ± √20484)/(20)

x = (-198 ± 143.126)/(20)

The two solutions for x are:
x = (-198 + 143.126)/(20) ≈ -2.744
x = (-198 - 143.126)/(20) ≈ -17.106

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To find the new coordinates of the points after Louis multiplied each x-coordinate and y-coordinate of triangle ABC by -2, we can use the following formulas:

New x-coordinate = -2 * old x-coordinate

New y-coordinate = -2 * old y-coordinate

Let's apply these formulas to each point in triangle ABC:

Point A: (-3, 4)

New x-coordinate of A = -2 * (-3) = 6

New y-coordinate of A = -2 * 4 = -8

New coordinates of A: (6, -8)

Point B: (1, 1)

New x-coordinate of B = -2 * 1 = -2

New y-coordinate of B = -2 * 1 = -2

New coordinates of B: (-2, -2)

Point C: (5, -2)

New x-coordinate of C = -2 * 5 = -10

New y-coordinate of C = -2 * (-2) = 4

New coordinates of C: (-10, 4)

Therefore, the new coordinates of the points after Louis multiplied each x-coordinate and y-coordinate of triangle ABC by -2 are:

A: (6, -8)

B: (-2, -2)

C: (-10, 4)

Answer: B -_-

Step-by-step explanation:

0 0=2

The correct statement regarding the monthly payments is given as follows:

D. Yes, because $320 is greater than the amount of interest he is

charged per year.

The monthly payment formula is defined by the equation as follows:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

In which the parameters are listed as follows:

The parameter values for this problem are given as follows:

P = 2700, r = 0.12, n = 12.

Hence:

r/12 = 0.12/12 = 0.01.

Hence the monthly payment is calculated as follows:

A = 2700 x 0.01 x (1.01)^12/(1.01^12 - 1)

A = $240.

The interest is less than $320, hence he will manage to pay off the loan.

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The multiplicative property of equality states that the same number can be added to or multiplied by both sides of an equation to obtain an equivalent equation. In this case, dividing both sides by 6 gives us u = 78/6 = 13.

The multiplicative property of equality states that if two numbers are equal, then multiplying both sides of the equation by the same number will also result in an equation that is still equal. In other words, if a=b, then ac=bc. We can use this property to solve for the variable u in the equation 78=6u.

To isolate the variable on one side of the equation, we can divide both sides by 6. This will give us:

78/6 = 6u/6

Simplifying the equation gives us:

13 = u

So the solution for u is 13.

In conclusion, the multiplicative property of equality with whole numbers was used to solve for the variable u in the equation 78=6u. The solution is u=13.

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Answer:

AB = 6.71

Step-by-step explanation:

The vertical leg of the right triangle

= absolute value of difference in y-coordinates between A(-1, 6) and B(5, 3)

= |6  - 3| = |3|
= 3

The horizontal leg of the right triangle
= absolute value of difference in x-coordinates between A(-1, 6) and B(5, 3)
= |- 1 - 5|
=|- 6|

= 6

By the Pythagorean theorem, the hypotenuse AB is related to each of these two legs by the formula

AB² = 3² + 6²
AB² = 9 + 36

AB² = 45

AB = √45

or

AB = 6.7082039324

= 6.71 significant to 3 significant figures

Significant figures means number of digits excluding leading and trailing zeros

Answer:

32 cubic feet

Step-by-step explanation:

The formula for a cylinder is [tex]\pi r^{2} h[/tex].

The radius of the cylinder is equal to 1.5 feet, since it is [tex]\frac{diameter}{2}[/tex].

Plugging in, the cylinder's full volume is  [tex]6\pi 1.5^2[/tex] which is approximately 42.4 cubic feet.

To find the amount of water when it is 3/4 full, multiply 42.4 x .75, to get around 31.8, and 32 when rounded

Answer:

9/7 is smallerrrr

This expression will generate all angles coterminal with 240 degrees.

To convert an angle from degrees to degrees, minutes, and seconds, we need to use the following formulas:
1 degree = 60 minutes
1 minute = 60 seconds

First, we need to convert the decimal part of the angle to minutes:
0.32 degrees * 60 minutes/degree = 19.2 minutes

Next, we need to convert the decimal part of the minutes to seconds:
0.2 minutes * 60 seconds/minute = 12 seconds

So, the angle 124.32 degrees is equal to 124 degrees, 19 minutes, and 12 seconds:
124.32 ∘ = 124 ∘ 19 ′ 12 ′′

To convert an angle from degrees, minutes, and seconds to decimal degrees, we need to use the following formulas:
1 degree = 60 minutes
1 minute = 60 seconds

First, we need to convert the minutes to degrees:
36 minutes / 60 minutes/degree = 0.6 degrees

Next, we need to convert the seconds to degrees:
36 seconds / 3600 seconds/degree = 0.01 degrees

So, the angle 48 degrees, 36 minutes, and 36 seconds is equal to 48.61 degrees:
48 ∘ 36 ′ 36 ′′ = 48.61 ∘

To find the angle of least positive measure that is coterminal with a given angle, we need to use the formula:
A = A + 360n

Where A is the given angle, and n is an integer. We need to find the smallest positive value of n that makes the expression equal to a positive angle less than 360 degrees.

For the given angle A = 725 degrees, we can use n = -2:
A = 725 + 360(-2) = 725 - 720 = 5 degrees

So, the angle of least positive measure that is coterminal with 725 degrees is 5 degrees.

To find an expression that generates all angles coterminal with a given angle, we can use the formula:
A = A + 360n

Where A is the given angle, and n is an integer. For the given angle A = 240 degrees, the expression is:
240 ∘ + 360n

This expression will generate all angles coterminal with 240 degrees.

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The average rate of change of g(x) over the interval [2, 5] is -2.1.

The formula to calculate the slope of a line passing through two points (x₁, y₁) and (x₂, y₂) is:

slope = (y₂ - y₁) / (x₂ - x₁)

Using this formula, we can calculate the slopes of the two secant lines for f(x) and g(x) over the interval [2, 5]. Let's start with f(x):

slope_f = (f(5) - f(2)) / (5 - 2)

= (-0.1(5)² - (-0.1(2)²)) / (5 - 2)

= (-0.1(25) + 0.1(4)) / 3

= (-2.5 + 0.4) / 3

= -2.1 / 3

= -0.7

Therefore, the average rate of change of f(x) over the interval [2, 5] is -0.7.

Now, let's calculate the average rate of change of g(x):

slope_g = (g(5) - g(2)) / (5 - 2)

= (-0.3(5)² - (-0.3(2)²)) / (5 - 2)

= (-0.3(25) + 0.3(4)) / 3

= (-7.5 + 1.2) / 3

= -6.3 / 3

= -2.1

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Complete Question:

how do the average rates of change for the pair of functions compare over the given interval

f(x)= -0.1x²

g(x)= -0.3x²

2≤x≤5

In the triangle ABC, the value of AC is obtained as 5 units.

What are triangles?

Triangles are a particular sort of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here. An example of a 3-sided polygon is a triangle. The total of a triangle's three angles equals 180 degrees. One plane completely encloses the triangle.

A triangle ABC is given.

The measure of AB is given as 10 units.

The measure of KB is given as 2 units.

The measure of KM is given as 1 unit.

According to the indirect measurement -

AB / AC = KB / KM

Substitute the values in the equation -

10 / AC = 2 / 1

2 AC = 10

AC = 5  

Therefore, the value of AC is obtained as 5 units.

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The equation x^(4)+6x^(3)-3x^(2)-24x-4=0 has possible rational roots ± 1, 2, 4, ± 1/2, 1/4.

Given the equation: $x^4+6x^3-3x^2-24x-4=0$

To identify possible rational roots we use Rational Root Theorem which states that:

If a polynomial function with integer coefficients has any rational roots then the numerator must divide the constant term and the denominator must divide the leading coefficient. Let's identify possible rational roots. The constant term is -4 and the leading coefficient is 1. Therefore, the possible rational roots are as follows:± 1, 2, 4± 1/2, 1/4

We use synthetic division to test several possible rational roots in order to identify the roots of the equation.

x−40−3−2−4−4−4−4−2+2-2+2-2+2+2-1+1-1+1-1+1+1+4-2+4-2+4-2+4+0-4+0-4+0-4±1 is the root of the equation since the remainder is zero. Therefore, divide the polynomial by x − 1.x^4+6x^3-3x^2-24x-4 = (x-1)(x^3+7x^2+4x+4x+4) = (x-1)(x^3+7x^2+8x+4)

The roots of the equation are x = 1, -2 ± i, where i = √(-1).

Hence, we have completed the following:

Possible rational roots: ± 1, 2, 4, ± 1/2, 1/4

Synthetic division to test possible rational roots: x−40−3−2−4−4−4−4−2+2-2+2-2+2+2-1+1-1+1-1+1+1+4-2+4-2+4-2+4+0-4+0-4+0-4

Possible rational root: ±1

Divide polynomial by (x-1): x^4+6x^3-3x^2-24x-4 = (x-1)(x^3+7x^2+4x+4x+4) = (x-1)(x^3+7x^2+8x+4)

Roots of the equation: x = 1, -2 ± i, where i = √(-1).

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The standard form to this equation is x=2/3.

This equation is in the form of a linear equation in one variable, where the variable is x.

The equation is written as x=2/3, meaning that the value of x is equal to 2/3.

The equation can be interpreted as the ratio of two numbers, 2 and 3. The numerator, 2, represents the number of parts, and the denominator, 3, represents the total number of parts.

This equation can be used to solve for the fraction of the total number of parts represented by the numerator. In this case, the fraction is 2/3, or 2 parts out of a total of 3 parts.

The equation can also be interpreted as a proportion. If we make the numerator the unknown value, x, then the equation becomes x/3 = 2/3. This equation can be solved using the cross-multiplication method.

By multiplying the denominators together and setting them equal to each other, then solving for x, we get x = 2/3. This equation shows that the value of x is equal to 2/3 of the total number of parts.

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To find out how many points Ava had at the end of round one, we need to work backwards from the end of the game using probability. Here are the steps to do so:

Step 1: At the end of the game, Ava had 50 points. This was after she lost 2/7 of her total points in the fifth round. Let's call the number of points she had before the fifth round X. So:

50 = X - (2/7)X

Step 2: Solve for X by combining like terms:

50 = (5/7)X

Step 3: Multiply both sides of the equation by 7/5 to isolate X:

X = 70

Step 4: Now we know that Ava had 70 points before the fifth round. This was after she increased her total points by 75% in the fourth round. Let's call the number of points she had before the fourth round Y using probability. So:

70 = Y + (75/100)Y

Step 5: Solve for Y by combining like terms:

70 = (175/100)Y

Step 6: Multiply both sides of the equation by 100/175 to isolate Y:

Y = 40

Step 7: Now we know that Ava had 40 points before the fourth round. This was after she decreased her point total by 3/5 in the third round. Let's call the number of points she had before the third round Z. So:

40 = Z - (3/5)Z

Step 8: Solve for Z by combining like terms:

40 = (2/5)Z

Step 9: Multiply both sides of the equation by 5/2 to isolate Z:

Z = 100

Step 10: Now we know that Ava had 100 points before the third round. This was after she increased her point total by 25% in the second round. Let's call the number of points she had before the second round A using probability. So:

100 = A + (25/100)A

Step 11: Solve for A by combining like terms:

100 = (125/100)A

Step 12: Multiply both sides of the equation by 100/125 to isolate A:

A = 80

Step 13: Now we know that Ava had 80 points before the second round, which means she had 80 points at the end of the first round.

Therefore, the answer is 80 points using probability.

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If both a and b are positive numbers and (b)/(a) is greater than 1, then a-b will be negative.

This is because when (b)/(a) is greater than 1, it means that b is greater than a. So when you subtract a from b, you will get a negative number.

For example, let's say a = 2 and b = 5.

(b)/(a) = (5)/(2) = 2.5, which is greater than 1.

So when we subtract a from b, we get:

b - a = 5 - 2 = 3, which is a positive number.

But when we subtract b from a, we get:

a - b = 2 - 5 = -3, which is a negative number.

Therefore, if both a and b are positive numbers and (b)/(a) is greater than 1, then a-b will be negative.

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Answer:

,15

Step-by-step explanation:

ez

The linear functions of the scenario are y = 12x and y = 24/2x

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

(1, 12) and (2,24)

From the question, we understand that the function is a linear function

A linear function is represented as

y = mx + c

Using the above as a guide, we have the following equations

m + c = 12

2m + c = 24

Subtract the equations

m = 12

Substitute 12 for m in m + c = 12

12 + c = 12

Evaluate

c =0

So, the equation is y = 12x

An equivalent equation is y = 24x/2

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In order for the system of equations to be consistent, k must not be equal to 31.6087.

In order for the system of equations to be consistent, the determinant of the coefficient matrix must not be equal to zero. The coefficient matrix is:

| -3  4  7 |
| -11 24 k |
| 2  -5 -8 |

The determinant of this matrix is:

(-3)(24)(-8) + (4)(k)(2) + (7)(-11)(-5) - (7)(24)(2) - (4)(-11)(-8) - (-3)(k)(-5)

Simplifying this expression gives:

576 + 8k + 385 - 336 - 352 + 15k = 0

Solving for k gives:

23k = 727

k = 727/23

k ≈ 31.6087

Therefore, in order for the system of equations to be consistent, k must not be equal to 31.6087.

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The two linear equations are y = 6x + 14 and y = x/4 + 1. Then the correct options are A and B.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Let's check all the options, then we have

A) y = 6x + 14, the equation is a linear equation because the degree is one.

B) y = x/4 + 1, the equation is a linear equation because the degree is one.

C) y = x³, the equation is a cubic equation because the degree is three.

D) y = 3/x  +2, the equation is a non-linear equation because the degree is negative one.

The two linear equations are y = 6x + 14 and y = x/4 + 1. Then the correct options are A and B.

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Answer:

See explanation

Step-by-step explanation:

50 is 5*10, so multiply 3 by 5 also to get 5 and 15/50. First answer is 15

5 and 15/50 is also equal to 4 and 65/50. second answer is 65

carry the numerator on the second line to get 30 for the third answer.

finally, subtract 3 from 4 to get 1, and subtract 30 from 65 to get 35/50.

last two answers are 1, and 35.

Answer:

hope this helps.

Step-by-step explanation:

This construction is also known as the "perpendicular bisector" construction.

To construct a line through a given point that is perpendicular to a given line using a ruler and compass, you will need to follow these steps:

By following these steps, you have used the ruler and compass to construct a line through a given point that is perpendicular to a given line. This construction is also known as the "perpendicular bisector" construction.

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