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2 years ago

Ruby frosted 8 cookies in 20 minutes. At this rate how many cookies could she frost in 2 hours?

1 answer:

3 0

We know that an hour has 60 minutes. She took 20 minutes to do one batch so we can see how many batches she makes with dividing 60 by 20. This would give us 3 batches per hour. Now we know she makes 8 frosted cookies per 20 minutes so we multiply 8 by 6 (2 hours as 20 min) and it would give us 48 frosted cookies

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What value of x satisfies the equation x + 3 = -(x + 1)? a. x = 8

ludmilkaskok [199]

Answer:

-2

Step-by-step explanation:

x + 3 = -(x + 1)

open the bracket

x + 3 = -x -1

x+x= -1-3

2x= -4

X = -4/2= -2

8 0

3 years ago

Write -3+4i in the form r(cosx+isinx)

Zanzabum

$-3+4i$ is a complex number that satisfies

$\begin{cases}r\cos x=-3\\[1ex]r\sin x=4\\[1ex]r=\sqrt{(-3)^2+4^2}\end{cases}$

The last equation immediately tells you that $r=5$ .

So you have

$\begin{cases}\cos x=-\dfrac35\\[1ex]\sin x=\dfrac45\end{cases}$

Dividing the second equation by the first, you end up with

$\dfrac{\sin x}{\cos x}=\tan x=\dfrac{\dfrac45}{-\dfrac35}=-\dfrac43$

Because the argument's cosine is negative and its sine is positive, you know that $\dfrac\pi2$ . This is important to know because it's only the case that $y=\tan x\implies \arctan y=x$ whenever $-\dfrac\pi2$ . The inverse doesn't exist otherwise.

However, you can restrict the domain of the tangent function so that an inverse can be defined. By shifting the argument of tangent by $\pi$ , we have

$\tan(x-\pi)=y\implies x=\pi+\arctan y$

All this to say

$\tan x=-\dfrac43\implies x=\pi+\arctan\left(-\dfrac43\right)\approx2.2143\text{ rad}\approx126.9^\circ$

So, $-3+4i=5(\cos126.9^\circ+i\sin126.9^\circ)$ .

5 0

3 years ago

ΔXLW ≅ΔXDG.

Svetach [21]

Answer:

16.4

Step-by-step

3 0

3 years ago

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Is 1234.... infinite or finite

nlexa [21]

Answer:

infinite set

Step-by-step explanation:

4 0

2 years ago

Read 2 more answers

When all seats are filled, a Ferris wheel can take 72 people for a rude. There are 313 people waiting to ride the wheel. Which d

LekaFEV [45]

Yes, the answer would be "b". There are a total of 313 people wanting to ride it. Only 72 people can ride it at a time. "x" in the drawing represents how much times is takes for all the people to ride it. You are correct, hope this helps! =)

7 0

3 years ago