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3 years ago

Y=2x+6

1 answer:

6 0

2x+6 would have a linear graph and a y-intercept of 6

The other equation isn’t really an equation you would just plot the point at (0,9)

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Mrs. Cupps has 8 bags of candy and each bag weighs 2.3 pounds, how much do all 8 bags weigh?

maw [93]

Answer:18.4 pounds.

Step-by-step explanation: Multiply 8 by 2.3 ,which gives you 18.4 .

8 0

3 years ago

Find e^cos(2+3i) as a complex number expressed in Cartesian form.

ozzi

Answer:

The complex number $e^{\cos(2+31)} = \exp(\cos(2+3i))$ has Cartesian form

$\exp\left(\cosh 3\cos 2\right)\cos(\sinh 3\sin 2)-i\exp\left(\cosh 3\cos 2\right)\sin(\sinh 3\sin 2)$ .

Step-by-step explanation:

First, we need to recall the definition of $\cos z$ when $z$ is a complex number:

$\cos z = \cos(x+iy) = \frac{e^{iz}+e^{-iz}}{2}$ .

Then,

$\cos(2+3i) = \frac{e^{i(2+31)} + e^{-i(2+31)}}{2} = \frac{e^{2i-3}+e^{-2i+3}}{2}$ . (I)

Now, recall the definition of the complex exponential:

$e^{z}=e^{x+iy} = e^x(\cos y +i\sin y)$ .

So,

$e^{2i-3} = e^{-3}(\cos 2+i\sin 2)$

$e^{-2i+3} = e^{3}(\cos 2-i\sin 2)$ (we use that $\sin(-y)=-\sin y)$ .

Thus,

$e^{2i-3}+e^{-2i+3} = e^{-3}\cos 2+ie^{-3}\sin 2 + e^{3}\cos 2-ie^{3}\sin 2)$

Now we group conveniently in the above expression:

$e^{2i-3}+e^{-2i+3} = (e^{-3}+e^{3})\cos 2 + i(e^{-3}-e^{3})\sin 2$ .

Now, substituting this equality in (I) we get

$\cos(2+3i) = \frac{e^{-3}+e^{3}}{2}\cos 2 -i\frac{e^{3}-e^{-3}}{2}\sin 2 = \cosh 3\cos 2-i\sinh 3\sin 2$ .

Thus,

$\exp\left(\cos(2+3i)\right) = \exp\left(\cosh 3\cos 2-i\sinh 3\sin 2\right)$

$\exp\left(\cos(2+3i)\right) = \exp\left(\cosh 3\cos 2\right)\left[ \cos(\sinh 3\sin 2)-i\sin(\sinh 3\sin 2)\right]$ .

5 0

3 years ago

Marta is making a scale drawing of her apartment for a school project. The apartment is 28ft wide. On her drawing, the apartment

ivolga24 [154]

Answer:

<h2>The scale is 1 inch rep 4 feet or </h2><h2>1:4</h2>

Step-by-step explanation:

This problem is on ratios, the ratio of one quantity to another is a way to represent their relative size.

Moreso, the scale of a drawing tells us to what extent the drawing has been increased (maximized) or decresed (minimized)

now given that the actual dimention of the appartmentis 28ft wide

and on the drawing the apartment is 7 inches wide, we can see that the actual dimension has been reduced by a factor of 28/7= 4

hence the scale to represent this reduction is

1 inch to represent 4 feet

7 0

3 years ago

What is the value of the expression 6 3/4(-11.5)?

ANTONII [103]

Answer:

-8.635

Step-by-step explanation:

I used trigonometric identification

6 0

3 years ago

Can someone help me answer a few of these? Thank you! :)

sesenic [268]

I’m going to try to answer these to the best of my ability.

1. Plane D
2. Plane C
3. AB
4. No
5. I don’t believe so because it doesn’t look like C is on the same plane as a AB and D.
6. I think so, yes! Collinear means that they are on the same line, and it looks like if you put a line between those two to connect them, they would connect perfectly!
7. B possibly? Because it looks like B, C, and D are all collinear and that they would pass through a straight line. A doesn’t look like it’s collinear with the rest of them.
8. No
9. Yes
10. Yes

I’m sorry if any of those are wrong, but I did make sure to try and put some explanations for some of them so you saw why I gave the answer that I gave! I hope that helped and like I said, I’m sorry if any of them are wrong, I tried my best!

4 0

3 years ago