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Pani-rosa [81]
3 years ago
12

What is the value of x?

Mathematics
1 answer:
Vladimir [108]3 years ago
5 0
We know that

angle F=180°-(40+87)°=53°
applying the law of sines
EF/sin G=EG/sin F
EF=x
EG=13 cm
G=87°
F=53°
so

x/sin 87°=13/sin 53°---------> x=sin 87*(13/sin 53°)-------> x=16.3 cm

The answer is
x=16.3 cm
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Discuss the continuity of the function on the closed interval.Function Intervalf(x) = 9 − x, x ≤ 09 + 12x, x > 0 [−4, 5]The f
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Answer:

It is continuous since \lim_{x\to 0^{-}} = f(0) = \lim_{x \to 0^{+} f(x)

Step-by-step explanation:

We are given that the function is defined as follows f(x) = 9-x, x\leq 0 and f(x) = 9+12x, x>0 and we want to check the continuity in the interval [-4,5]. Note that this a piecewise function whose only critical point (that might be a candidate of a discontinuity)  x=0 since at this point is where the function "changes" of definition. Note that 9-x and 9+12x are polynomials that are continous over all \mathbb{R}. So F is continous in the intervals [-4,0) and (0,5]. To check if f(x) is continuous at 0, we must check that

\lim_{x\to 0^{-}} = f(0) = \lim_{x \to 0^{+} f(x) (this is the definition of continuity at x=0)

Note that if x=0, then f(x) = 9-x. So, f(0)=9. On the same time, note that

\lim_{x\to 0^{-}} f(x) = \lim_{x\to 0^{-}} 9-x = 9. This result is because the function 9-x is continous at x=0, so the left-hand limit is equal to the value of the function at 0.

Note that when x>0, we have that f(x) = 9+12x. In this case, we have that

\lim_{x\to 0^{+}} f(x) = \lim_{x\to 0^{+}} 9+12x = 9. As before, this result is because the function 9+12x is continous at x=0, so the right-hand limit is equal to the value of the function at 0.

Thus, \lim_{x\to 0^{-}} = f(0) = \lim_{x \to 0^{+} f(x)=9, so by definition, f is continuous at x=0, hence continuous over the interval [-4,5].

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mama giraffe: x

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Find all solutions to the following system of equations x+2y=0 ; x²-2x+y²-2y-3=0. Illustrate with a graph.
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Answer:

The solutions to the system of equations are the points (2, -1) and (-1.2, 0.6)

Step-by-step explanation:

Hi there!

We have the following system of equations:

x + 2y = 0

x² - 2x + y²- 2y - 3 = 0

The solutions of the system are the pairs (x, y) that satisfy both equations.

Let´s take the first equation and solve it for x:

x + 2y = 0

x = -2y

And now let´s replace the x in the second equation:

x² - 2x + y²- 2y - 3 = 0

(-2y)² -2(-2y) + y² - 2y - 3 = 0

4y² +4y + y² - 2y - 3 = 0

5y² + 2y - 3 = 0

Let´s use the quadratic formula to solve this quadratic equation:

[-b ± √(b² - 4ac)]/2a

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The solutions to this equation are:

y = -1 and y = 0.6

The values of x will be:

x = -2y

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and

x =-2(0.6) = -1.2

The solutions to the system of equations are the points (2, -1) and (-1.2, 0.6)

Please, see the attached figure. The points where the curves intersect are the solutions of the system.

Have a nice day!

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