Write the point-slope form of the equation of the line that passes through the point (1, 3) and has a slope of 2. Include your work in your final answer

Final answer:

An acrostic poem for the word 'triangle' is a creative way to convey various attributes of the geometric shape or to create a poem with each line starting with the corresponding letter. The poem can be directly related to the properties of a triangle or more abstract.

Explanation:

An acrostic poem uses the first letter of each line to spell out a word vertically. For the word 'triangle', an acrostic poem might be a creative way to describe the characteristics of a triangle, or it could be abstract, using each letter to begin a line that doesn't necessarily relate to the shape but instead creates a coherent poem.

Here is an example of an acrostic poem for the word 'triangle':

Three sides enclosing space,

Reminder of structure and base,

In geometry, an essential grace,

Angles acute, obtuse, or right,

Nestled within, points of light,

Guiding principles of design,

Lines intersect by plan divine,

Eternally, three lines combine.

Remember, while writing an acrostic for 'triangle', you may also use the opportunity to incorporate into your poem mnemonics for the relationships between the sides and angles of a right triangle, such as 'SOHCAHTOA', or explore the figurative and metaphorical implications of the shape as referenced in literary examples or the sciences.

Answer:7+(-3.0^2)

7+0

7

Step-by-step explanation:

Answer:

(B) 72°

Step-by-step explanation:

A prime number must be greater than 1 because by definition, a prime number has exactly two distinct positive divisors: 1 and the number itself. If a number is less than or equal to 1, it cannot be prime.

The statement that a prime number is always greater than 1 is indeed true. A prime number is defined as a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers. If a number is less than or equal to 1, it cannot be prime because the prime numbers must be greater than 1 to have at least two distinct positive divisors (1 and the number itself).

For example, the first few prime numbers are 2, 3, 5, 7, 11, and 13. Each of these numbers is greater than 1 and cannot be divided evenly by any number other than 1 and itself. By contrast, the number 1 is not considered a prime because it has only one positive divisor, which is 1 itself. Since primes must have exactly two distinct divisors, 1 does not meet this criterion.

The hourly profit of an airline operating a plane can be calculated by subtracting the operating cost from the revenue earned from passengers.

The hourly profit of an airline operating a plane can be expressed as the difference between the revenue earned from passengers and the operating cost of the plane.

The revenue earned from passengers can be calculated by multiplying the fare per passenger by the number of passengers. In this case, the fare is $100 per hour of flight, and the number of passengers is represented by x.

The operating cost of the plane is given as $3770 per hour.

Therefore, the hourly profit P can be expressed as:

P = (fare per passenger) * x - (operating cost of the plane)

Substituting the given values:

P = $100 * x - $3770

Answer:

[tex]\frac{y_4-y_3}{x_4-x_3}\times \frac{y_2-y_1}{x_2-x_1}=-1[/tex]

Step-by-step explanation:

We know that,

If two line segments are perpendicular then the product of their slope is equal to -1,

Also, the slope of a line segment having the end points [tex](x_n,y_n)[/tex] and [tex](x_m,y_m)[/tex] is,

[tex]m=\frac{y_m-y_n}{x_m-x_n}[/tex]

So, the slope of line segment AB having end points [tex]A(x_1,y_1)[/tex] and [tex]B(x_2,y_2)[/tex] is,

[tex]m_1=\frac{y_2-y_1}{x_2-x_1}[/tex]

Similarly, the slope of line segment CD having end points [tex]C(x_3,y_3)[/tex] and [tex](x_4,y_4)[/tex] is,

[tex]m_2=\frac{y_4-y_3}{x_4-x_3}[/tex]

Hence, by the above property of perpendicular line segments ,

If AB and CD are perpendicular then,

[tex]m_1\times m_2=-1[/tex]

[tex]\implies \frac{y_4-y_3}{x_4-x_3}\times \frac{y_2-y_1}{x_2-x_1}=-1[/tex]

Third option is correct.

Answer:

(4w, 4w + 5)

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

d

Answer: the correct answer would be 2498.4 km/h

*i got this question correct*

The division yields to quotient is 9, and there is 10 as remainder

We have to divide 280 by 30.

So, the division performed as

                         30 | 280  | 9

                                 270

                            -______

                                    10

So, the quotient is 9, and there is 10 as remainder.

So, 280 divided by 30 is equal to 9.33 (rounded to two decimal places) or simply 9.

Learn more about Division here:

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The point that satisfies the equation 2x+3y=8 is (1,4).

To find the point that satisfies the equation 2x + 3y = 8, we can substitute the x and y values from each option into the equation and see which option makes the equation true.

Let's try option A, (-1,3): 2(-1) + 3(3) = -2 + 9 = 7, which is not equal to 8.

Continuing this process for options B, C, and D, we find that the point (1,4) satisfies the equation 2x + 3y = 8.

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The correct system of equations to find the dimensions of the squares is option A: x + y = 32 and x - y = 8.

To find the dimensions of the squares, we can set up a system of equations. Let x represent the side length of the larger square and y represent the side length of the smaller square.

So, the correct system of equations to find the dimensions of the squares is option A: x + y = 32 and x - y = 8.

The correct system of equations to find the dimensions of the squares is x + y = 32 and x - y = 8. Solving this system using the method of elimination gives us the dimensions of the squares: 20 cm for the larger square and 12 cm for the smaller square.

The correct system of equations to find the dimensions of the squares is:

x + y = 32

x - y = 8

To solve this system, we can use the method of elimination. Adding the two equations will eliminate the y terms, allowing us to solve for x.

Adding the equations:

x + y + x - y = 32 + 8

2x = 40

x = 20

Substituting the value of x back into one of the original equations, we can solve for y.

Using the equation x + y = 32:

20 + y = 32

y = 12

Therefore, the dimensions of the larger square are 20 cm, and the dimensions of the smaller square are 12 cm.