What is the reference angle for -150 degrees

suter [353]

Adding a negative is the same as subtracting, so here we have 5/8-5/6. Let's find our least common denominator to use as our common denominator for both fractions. That would be 24. So, we multiply 5/8 by 3/3 because to get an equivalent fraction, you multiply by a version of 1- then you multiply 5/6 by 4/4. So, you get 15/24-20/24 equals -5/24. Hope this helps!

3 0

3 years ago

You tell your dad that you want ₹800 as pocket-money every month. He can deposit some money in the bank such that the interest h

mr_godi [17]

160,000 because you need to first multiply 800 by 12 since it is from a year (annum) to months you should get 9,600 then rather than multiplying by 0.06 to find 6% we divide to find what it is 6% of.

8 0

3 years ago

#13. A lighthouse casts a 128-foot shadow. A nearby lamppost that measures 5 feet 3

Ad libitum [116K]

Answer:84

Step-by-step explanation:Using proportions, it is found that the height of the lighthouse is of 84 ft.

This question is solved by proportions, using a rule of three.

For a height of 5.25 feet, the shadow is of 8 feet. What is the height when the shadow is of 128 feet?

The rule of three is:

5.25 feet - 8 feet

x feet - 128 feet

Applying cross multiplication:

The height of the lighthouse is of 84 ft.

credit:joaobezerra

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7 0

3 years ago

Find the values that make this a parallelogram (please show work)

Dmitry [639]

Answer:

Correct answer is: 7. y = 28° and x = 29° 8. y = 7 and x = 5

Step-by-step explanation:

7.

In the parallelogram, adjacent angles are supplementary and the opposite angles are the same.

According to this:

(3 y - 20) + (4 y + 4) = 180 => 7 y - 16 = 180 => 7 y = 180 + 16 => 7 y = 196

y = 196/7 = 28° => y = 28°

4 x + (2 x + 6) = 180 => 6 x + 6 = 180 => 6 x = 180 - 6 => 6 x = 174

x = 174/6 = 29° => x = 29°

8.

At the parallelogram, the diagonal is split into two equal parts.

According to this:

3 y - 3 = 2 y + 4 => 3 y - 2 y = 4 + 3 => y = 7

x - 1 = 2 x - 6 => 2 x - x = 6 - 1 => x = 5

God with you!!!

7 0

4 years ago

Please help me with this 2 Calc questions

r-ruslan [8.4K]

20. A rational function $\frac{p(x)}{q(x)}$ (where $p,q$ are polynomials in $x$ ) has a removable discontinuity at $x=a$ if for some positive integer $n$ we can factorize

$p(x) = (x-a)^n p^*(x)$

$q(x) = (x-a)^n q^*(x)$

$\implies \dfrac{p(x)}{q(x)} = \dfrac{(x-a)^n p^*(x)}{(x-a)^n q^*(x)} = \dfrac{p^*(x)}{q^*(x)}$

That is, we "remove" the discontinuity at $x=a$ because while $x\neq a$ , we have $\frac{x-a}{x-a}=1$ . The discontinuity is still there, since $\frac{p(a)}{q(a)}$ is undefined, but in the limit sense we can essentially ignore the factors of $x-a$ . The graph of $\frac{p(x)}{q(x)}$ will have all the features of $\frac{p^*(x)}{q^*(x)}$ aside from a hole at $x=a$ .

In this case, we have

$f(x) = \dfrac{x+4}{x^2-x-20} = \dfrac{x+4}{(x+4)(x-5)}$

and when $x\neq-4$ , we can cancel the factor of $x+4$ so that

$f(x) = \begin{cases}\dfrac1{x-5} & \text{if }x \neq -4 \\\\ \text{DNE} & \text{if }x = -4\end{cases}$

("DNE" = "does not exist", i.e. is undefined. For some reason "undefined" wouldn't render...)

This means $x=-4$ is a removable discontinuity.

We cannot do the same with the factor of $x-5$ , so in contrast $x=5$ is a non-removable discontinuity.

21. The pieces of $f(x)$ defined on $x$ and $x>2$ are themselves continuous since they are polynomials. Then the continuity of $f(x)$ over the entire real line depends on the point where the pieces meet.