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My name is Ann [436]

3 years ago

8

What is the midpoint of the vertical line segment graphed below? (2, 4), (2, -9) A. (4, -5). B. (2, -5/2). C. (2, -5). D. (4, 5/

2)

1 answer:

omeli [17]3 years ago

8 0

Answer:

B. $(2, -\frac{5}{2})$

Step-by-step explanation:

Given:

(2, 4) and (2, -9)

Required:

Midpoint of the vertical line with the above endpoints

Solution:

Apply the midpoint formula, which is:

$M(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})$

Where,

(2, 4) = (x_1, y_1)

(2, -9) = (x_2, y_2)

Plug in the values into the equation:

$M(\frac{2 + 2}{2}, \frac{4 + (-9)}{2})$

$M(\frac{4}{2}, \frac{-5}{2})$

$M(2, -\frac{5}{2})$

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Step-by-step explanation:

Let $f(A) = \sin A + \csc A$ , we proceed to transform the expression into an equivalent form of sines and cosines by means of the following trigonometrical identity:

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By the quadratic formula, we find the following solutions:

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Since sine is a bounded function between -1 and 1, the only solution that is mathematically reasonable is:

$\sin A \approx 0.382$

By means of inverse trigonometrical function, we get the value associate of the function in sexagesimal degrees:

$A \approx 22.457^{\circ}$

Then, the values of the cosine associated with that angle is:

$\cos A \approx 0.924$

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$f(A) = \frac{\sin^{2} 2A+1}{\sin 2A}$

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If we know that $\sin A \approx 0.382$ and $\cos A \approx 0.924$ , then the value of the function is:

$f(A) = \frac{4\cdot (0.382)^{2}\cdot (0.924)^{2}+1}{2\cdot (0.382)\cdot (0.924)}$

$f(A) = 2.122$

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When solving negative one over eight (x + 35) = −7, what is the correct sequence of operations?

Maksim231197 [3]

<span>The answer is: [C]:
__________________________________________________________
Multiply each side by −8, subtract 35 from each side.
___________________________________________________________
Explanation:
___________________________
Given: You have (-1/8)*(x + 35) = -7
________________________________________
Note that all the answer choices given start with: "Multiply each side by....";
</span>____________________
Given the choices, multiplying EACH SIDE of the equation by "(-8)" would make sense, since doing would cancel the "(-1/8)" on the "right-hand side" of the equation above to a "1" (i.e "cancel out" that ("-1/8") value); and would result in making the "right side" of the equation above ("-7") a positive integer number.
Then you would be left with: x + 35 = 56 ; so the next step would be to:
__________
Subtract: "(35)" from each side of the question [hence the answer choice] to isolate "x" on one side of the equation; and to solve for "x".
_______________________________________________________

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