Given that the points (-32,-10) and (-74,11) lie on a line, what is the equation of the line

Answer:

x = 240/9

Step-by-step explanation:

Mathematically, when two triangles are similar, the ratio of their corresponding sides are equal

Thus, we have it that;

GH/IH = JL/KL

x/20 = 12/9

9 * x = 20 * 12

x = (20 * 12)/9

x = 240/9

N is equal to 119.

In a right triangle, the Pythagorean theorem states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the two legs.

Given:

Hypotenuse = 12

Leg 1 = 5

Leg 2 = √N

According to the Pythagorean theorem, we have the equation:

(Length of Hypotenuse)² = (Length of Leg 1)² + (Length of Leg 2)²

Substituting the given values, we get:

12² = 5² + (√N)²

144 = 25 + N

Rearranging the equation, we have:

N = 144 - 25

N = 119

Therefore, N is equal to 119.

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Answer:

Miguel

Step-by-step explanation:

What we know:

Miguel ate 3/4 of his sandwich.

Annie ate 5/8 of her sandwich.

First we have to make the denominators equal.

3/4×2=6/8

6 is bigger than 5 so it would be 6/8 or 3/4 and Miguel ate 3/4.

Can I please have brainliest?

Answer:

The slope is -9/4 or -2.25.

Step-by-step explanation:

To find the slope (S) we need to use the following equation:

\( S = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} \)

Where:

y₂: is the final height = 11 feet

y₁: is the initial heoght = 20 feet

x₂: is the final position is the horizontal direction = 4 feet

x₁: is the initial position = 0 (origin)

\( S = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} = \frac{11 - 20}{4} = -\frac{9}{4} = -2.25 \)            

Therefore, the slope is -9/4 or -2.25.

I hope it helps you!

Answer:

the answer is the third answer on the picture

Step-by-step explanation:

Answer:

3 times the difference of x and 8

Step-by-step explanation:

3 is being multiplied by (x-8)

The values of n that either player has a winning strategy is when the number of points are odd such as 3:-

The game is begun by A and then its chance of B to play the game alternatively, then all the possible moves are 1,2; 2,3; 1,3 in which all possible pairs are selected.

If the game end on an even number of moves then the game is won by A. For B to win, these points should be connected at the very end of the game.

Similarly, for even number of moves B wins the game when number of points is odd.

If the number of points is even the opposite of this happens that is, for even moves B wins and for odd number of moves A wins.

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Answer:

she's wrong

Step-by-step explanation:

4 - 2 < 5

Answer:

Ariyonne is wrong

Step-by-step explanation:

PLug 3 in to both equations. They should output 6 if she is right:

y = 4(3) - 2 = 10

y = 3 + 5 = 8

She is wrong. The correct intersection is: (2+1/3, 7+1/3)

Answer:

= 40g -24

Step-by-step explanation:

you would multiply everything in the bracket by 8 to expand this

e.g.

(8x5g )+ (8x5 )+ (8 x -2)

= 40g + 40 - 16

now simplify by subtracting the like terms

= 40g -24

Answer:

A rectangle doesn't have equal sides

Both sides are not equal

Answer:

25

Step-by-step explanation:

two sides on a triangle are always identical so the biggest could possible be 25 hope this helps

Answer:

2:1

1:2

x=16

y=4

p=46

p=23

Step-by-step explanation:

Zero divided by any real number is equal to zero.

By graphing the system of equations, we can see that the solution is (4, -2)

Here we want to solve the system of equations:

y = (-3/2)*x + 4

y = (1/2)*x - 4

To solve this graphically, we just need to graph both equations on the same coordinate axis and find the point where the lines intersect.

The graph can be seen on the image at the end.

We can see that the solution is (4, -2)

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Answer:

6 weeks :)

Step-by-step explanation:

it will take her 6 weeks

45-15 is 30.

30/5 is 6

Answer:

It will take her 6 weeks.

Step-by-step explanation:

$45-$15=$30

$30 ÷ $5 = 6

Answer:

Below.

Step-by-step explanation:

15y + 12x = 18

5y + 4x = 6

The  second equations is the first times 3 so they are basically the same.

Infinite Solutions.

2x+ 3y= 12

-6y= 4x-24          Rearranging the second equation:

-4x - 6y = -24      Multiplying the first equation by 2:

4x + 6y = 24      

- we see that the last equation is -1 * previous equation.

So there are infinite solutions.

I AGREE WITH THE COMMENT ABOVE, THAT'S THE RIGHT ANSWER, I'VE GOT 100% OUT OF 100% JUST BCS I INSERT THAT ANSWER, VERY HELPFUL!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

The first part of the integral evaluates to:

[(-1/ln(2)) * (1/2^∞) * (3∞ + 1)] - [(-1/ln(2)) * \((1/2^1)\) * (3(1) + 1)] = 0 - (-2/ln(2)) = 2/ln(2).

The second part of the integral is:

∫[1 to ∞] (-1/ln(2)) * \((3/2^x)\) dx = (-3/ln(2)) ∫[1 to ∞] \((1/2^x)\)dx.

To determine the convergence of the series ∑(3n+1)/(2^n), we can use the Integral Test.

Let's consider the function f(x) = (3x + 1)/(2^x). Taking the integral of f(x) from 1 to infinity, we have:

∫[1 to ∞] (3x + 1)/(\(2^x) dx.\)

To evaluate this integral, we can use integration by parts. Let u = (3x + 1) and dv = (1/2^x) dx. Then, we have du = 3 dx and v = (-1/ln(2)) * (1/2^x).

Applying the integration by parts formula, the integral becomes:

∫[1 to ∞] \((3x + 1)/(2^x) dx = [(-1/ln(2)) * (1/2^x) * (3x + 1)] [1 to ∞] - ∫[1 to ∞] (-1/ln(2)) * (3/2^x) dx.\)

The integral ∫(1/2^x) dx from 1 to infinity is a convergent geometric series with a common ratio less than 1. Therefore, its integral converges.

Since the integral of f(x) converges, the series ∑(3n+1)/(2^n) also converges by the Integral Test.

To approximate the sum of the series within an accuracy of 0.001, we can use the formula for the sum of a convergent geometric series:

S = a / (1 - r),

where a is the first term and r is the common ratio.

For this series, the first term is \((3(1) + 1)/(2^1) = 4/2 = 2,\) and the common ratio is\((3(2) + 1)/(2^2) = 7/4.\)

To determine the number of terms needed to approximate the sum within 0.001, we can set up the following inequality:

|S - Sn| < 0.001,

where S is the exact sum and Sn is the sum of the first n terms.

Substituting the values into the inequality, we have:

|2/(1 - 7/4) - Sn| < 0.001,

|8 - 7Sn/4| < 0.001,

|32 - 7Sn| < 0.004.

Solving this inequality, we find:

32 - 0.004 < 7Sn,

Sn > (32 - 0.004)/7.

Therefore, we need n terms such that Sn > (32 - 0.004)/7.

Calculating the right side of the inequality, we have:

Sn > (32 - 0.004)/7 ≈ 4.570.

So, we need at least 5 terms to approximate the sum within an accuracy of 0.001.

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Answer:

B.

choosing any marble

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

because it really does depend on the number of bricks

Answer:

It depends on the number of bricks.

Step-by-step explanation:

As b is the number of bricks in the equation then we wouldn't be able to identify the fee per load unless specified with a number.

Answer: The answer is 1.30

Step-by-step explanation: Because if you add the whole itt equal 1 and 3/10 is .30 which equals 1.30

Answer:

  1.3

Step-by-step explanation:

We assume that each square in the model represents 1 unit. Each square is divided into 10 parts, so each of those strips represents 1/10 unit, or 0.1 when written in decimal.

There are 3 of the 0.1-unit strips colored in the second square, representing 0.3 units. The number represented by the shaded portion of the model is ...

  1 + 0.3 = 1.3

The value of R(x) term is 36.

We are given that;

The equation x³ + 2x² - 72x - 28

Now,

We divide the first term, 8x, by the first term of d(x), which is x. This gives us 8, which is the third term of Q(x). We write 8 above the division bar and multiply it by d(x), which gives us 8x - 64. We subtract this from the new dividend, which gives us 36.

Since we cannot divide 36 by x-8 any further, we stop here and write 36 as the remainder R(x).

   x² + 10x + 8

  _______________

x-8 | x³ + 2x² - 72x - 28

    - (x³ - 8x²)

    -------------

        10x² - 72x

      - (10x² -80x)

      -------------

             8x -28

           - (8x -64)

           ----------

                36

Q(x) = x² + 10x + 8 and R(x) = 36.

Therefore, by the equation the answer will be R(x) = 36.

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Answer:

200%

Step-by-step explanation:

No, the probability be found by using the binomial probability formula with x counting the number who are left-handed. The correct option is (c) No, because the 100 adults were selected without replacement, the selections are dependent.

The binomial distribution assumes that the trials are independent, meaning that the outcome of one trial does not affect the outcome of any other trial. However, in this case, the 100 adults were selected without replacement, which means that the outcome of one selection affects the probability of the next selection. Therefore, the trials are dependent, and the binomial probability formula cannot be used.

Instead, we can use the hypergeometric distribution to calculate the probability of at least 30 left-handed adults in a sample of 100 adults selected without replacement from the U.S. population. The hypergeometric distribution takes into account the fact that the selections are dependent and is appropriate for this type of problem.

Therefore, the correct option is (c) No, because the 100 adults were selected without replacement, the selections are dependent.

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To determine the values of x for which both f(x) and g(x) are decreasing, we need to find the intervals where the derivatives f'(x) and g'(x) are negative.  Given that f'(x) = (x-1)(x-2)(x+1) and g'(x) = (x+2)(x-3)(x+3), we can identify the critical points where f'(x) and g'(x) change signs. These critical points occur at x = 1, x = 2, x = -1 for f'(x), and x = -2, x = 3, x = -3 for g'(x).

We can create a sign chart to analyze the intervals of increase and decrease for f(x) and g(x) based on the signs of their derivatives.

Considering the intervals between the critical points, we have:

For f(x):

- When x < -1, f'(x) < 0, indicating that f(x) is decreasing.

- Between -1 < x < 1, f'(x) > 0, meaning that f(x) is increasing.

- When x > 1, f'(x) < 0, indicating that f(x) is decreasing.

For g(x):

- When x < -3, g'(x) > 0, indicating that g(x) is increasing.

- Between -3 < x < -2, g'(x) < 0, meaning that g(x) is decreasing.

- When -2 < x < 3, g'(x) > 0, indicating that g(x) is increasing.

- When x > 3, g'(x) < 0, meaning that g(x) is decreasing.

Combining the intervals, we find that both f(x) and g(x) are decreasing for x < -1 and x > 3. Therefore, the values of x for which both f(x) and g(x) are decreasing are x < -1 and x > 3.

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Answer:

E(m) = 2,000 + 0.15(m + 20,000)

Step-by-step explanation:

The function calculates his monthly earnings E(m) = 2,000 + 15(m - 20,000). Therefore, option C is the correct answer.

Given that, Anthony sells cars. Each month, he is paid $2,000, plus a 15% commission on monthly sales above $20,000.

We need to calculate his monthly earnings (E) as a function of m, his monthly sales.

The composition of a function is an operation in which two functions say f and g generate a new function say h in the sort of manner that h(x) = g(f(x)). It method right here characteristic g is carried out to the characteristic of x. So, basically, a feature is implemented to the end result of another feature.

Now, the function for the given situation is E(m) = 2,000 + 15(m - 20,000).

The function is E(m) = 2,000 + 15(m - 20,000). Therefore, option C is the correct answer.

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The domain of the graph is 2 ≤ x ≤ 5.

Domain refers to the specific space of a website, including a domain name, associated IP address and a set of web pages that are hosted by a web server. Domain names are used to identify websites, and they are often used as a way to easily access a website. Domain names are assigned to each web server, allowing users to access the website by typing in the domain name instead of the IP address.

This means that all x-values must be greater than or equal to 2 and less than or equal to 5 in order for them to be part of the domain. This can also be written in interval notation as [2,5].

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The Domain is (0, ∞) or {x | x > 0} and Range is  (-∞, ∞) or {y | y ∈ ℝ} with inequality notation.

To graph the function, we can plot the given points on a coordinate plane. The x-values in the table represent the input values (x), and the y-values represent the corresponding output values (f(x)).

Let's plot the points (x, y) from the table:

(1/125, -3)

(1/25, -2)

(1/5, -1)

(1, 0)

(5, 1)

(25, 2)

(125, 3)

Now, let's connect the points to create the graph of the function.

     |

     |

     |

     |

   3 |                   *

     |

     |

   2 |             *

     |

     |

   1 |       *

     |

     |

     | *

   0 |________________________

     -3  -2  -1   0   1   2   3

Based on the graph, we can observe that the function represents a logarithmic curve. As the x-values increase, the corresponding y-values increase logarithmically.

Domain:

The domain of a logarithmic function is the set of all positive real numbers (x > 0), since the logarithm of a negative number or zero is undefined. In this case, since all the x-values in the table are positive, the domain of f(x) is x > 0.

Domain notation:

Interval notation: (0, ∞)

Set-builder notation: {x | x > 0}

Range:

The range of a logarithmic function depends on its base. Since the base is not specified in the given information, we assume the common logarithm (base 10) as the default. The range of a common logarithmic function is all real numbers.

Range notation:

Interval notation: (-∞, ∞)

Set-builder notation: {y | y ∈ ℝ}

In summary: Domain: (0, ∞) or {x | x > 0} and Range: (-∞, ∞) or {y | y ∈ ℝ}

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The area of the triangular piece of property is approximately 63,121.75 square feet.

The area is the entire amount of space occupied by a flat (2-D) surface or an object's form. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a form on paper is the area that it occupies.

Starting at the first corner, the surveyor walks 480 ft in the direction N36°W. We can break this down into its northward and westward components:

Northward component = 480 cos(36°)

≈ 388.75 ft

Westward component = 480 sin(36°)

≈ 295.42 ft

This takes the surveyor to the second corner of the property.

From the second corner, the surveyor walks S21°W to get to the third corner. We can again break this down into its southward and westward components:

Southward component = 480 cos(21°)

≈ 435.89 ft

Westward component = 480 sin(21°)

≈ 168.75 ft

Finally, the surveyor walks N82°E to get back to the starting point.

We can break this down into its northward and eastward components:

Northward component = 388.75 ft

Eastward component = 435.89 sin(82°)

≈ 426.04 ft

Now we have the lengths of all three sides of the triangular property:

Side 1 = 480 ft

Side 2 = √[(295.42 - (-168.75))^2 + (388.75 - 435.89)^2]

≈ 421.66 ft

Side 3 = √[(426.04 - 295.42)^2 + (388.75 - 0)^2]

≈ 296.13 ft

calculate the area of the triangular property, we can use Heron's formula:

Area = √[s(s - a)(s - b)(s - c)]

where s is the semiperimeter (half the perimeter) of the triangle,

and a, b, and c are the lengths of its sides.

s = (480 + 421.66 + 296.13)/2 ≈ 598.40

Area = √[598.40(598.40 - 480)(598.40 - 421.66)(598.40 - 296.13)]

Area ≈ 63,121.75 sq ft

Therefore, the area of the triangular piece of property is approximately 63,121.75 square feet.

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