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3 years ago

Determine the value of z in the figure answers: z = 50° z = 45° z = 10° z = 30°

Mathematics

1 answer:

ycow [4]3 years ago

3 0

Answer:

z = 10°

Step-by-step explanation:

Since the two sides are equal, the two base angles have to be equal

That means that 5z and 130 form a straight line and add to 180 degrees

5z+130 = 180

Subtract 130 from each side

5z = 50

Divide by 5

5z/5 = 50/5

z=10

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DiKsa [7]

Step-by-step explanation:

The area = (5 × 3) + (2 × 3) = 15 + 6 = 21

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3 years ago

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3 years ago

Simplify the left side of equation so it looks like the right side. cos(x) + sin(x) tan(x) = sec (x)

uranmaximum [27]

Step-by-step explanation:

Consider LHS

$\cos(x) + \sin(x) \tan(x) = \sec(x)$

Apply quotient identies

$\cos(x) + \sin(x) \times \frac{ \sin(x) }{ \cos(x) } = \sec(x)$

Multiply the fraction and sine.

$\cos(x) + \frac{ \sin {}^{2} (x) }{ \cos(x) } = \sec(x)$

Make cos x a fraction with cos x as it denominator.

$\cos(x) \times \cos(x) = \cos {}^{2} (x)$

$\frac{ \cos {}^{2} (x) }{ \cos(x) } + \frac{ \sin {}^{2} (x) }{ \cos(x) } = \sec(x)$

Pythagorean Identity tells us sin squared and cos squared equals 1 so

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Apply reciprocal identity.

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7 0

3 years ago

(X^4)-(45x^2)+324 what are the zeroes? And how many turning points?

dmitriy555 [2]

Zeroes:

We must solve

$x^4-45x^2+324=0$

To do so, we define the auxiliary variable $t=x^2$ . The equation becomes

$t^2-45t+324=0$

The quadratic formula yields the solutions

$t=9,\quad t=36$

Substituting back $t=x^2$ gives

$x^2=9 \iff x=\pm 3,\quad x^2=36 \iff x=\pm 6$

So, the zeroes are -6, -3, 3, 6.

Turning points:

Turning points are points where a function stops being increasing to become decreasing, or vice versa. Since functions are increasing when their first derivative is positive and decreasing when it's negative, turning points are points where the first derivative is zero.

We have

$f(x)=x^4-45x^2+324 \implies f'(x)=4x^3-90x$

If we set the derivative to be zero, we have

$4x^3-90x=0 \iff x(4x^2-90)=0$

So, the derivative is zero if x=0 or

$4x^2=90 \iff 2x^2=45 \iff x^2=\dfrac{45}{2}\iff x=\pm\sqrt{\dfrac{45}{2}}$

6 0

3 years ago

If the die were to be rolled 6000 times, would we expect to obtain exactly 1000 '2's? explain your answer.

ludmilkaskok [199]

The probability of that occurring is 0%. There are 6 sides in a typical dice, which means the probability of rolling a 2 is 1/6th. (1/6)^1000 will give you the probability of rolling a 2 exactly 1000 times. (1/6)^1000 equates to 0%.

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2 years ago