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3 years ago

8. Parallel to the line y = 2x + 5 and contains the

Mathematics

1 answer:

Shalnov [3]3 years ago

7 0

Answer:

$y=2x-3$

Step-by-step explanation:

So we want to find an equation in slope-intercept form that is parallel to:

$y=2x+5$

And contains the point (4,5).

So to create the equation, we will need to slope and the y-intercept.

First, recall that parallel lines have the same slope. Since we want our equation to be parallel to y=2x+5, this means that the slope of the new equation must be 2.

Now, we can use the point-slope form to solve for the y-intercept. The point slope form is:

$y-y_1=m(x-x_1)$

Let (4,5) be x₁ and y₁. m is 2 since it's parallel to y=2x+5. Thus:

$y-5=2(x-4)\\$

Distribute:

$y-5=2x-8$

Add 5 to both sides:

$y=2x-3$

And that's our equation :)

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When an article is sold for $132.00, a profit of 10% is made. The cost of the<br> article is?

Orlov [11]

Answer:

118.8

Step-by-step explanation:

Profit=10%

=10/100 × $132

=$13.2

Cost price=Selling price- Cost price

=$132-$13.2

=$118.8

3 0

2 years ago

Need help fast!!<br> What is the value of x

prohojiy [21]

Answer:

4.5

Step-by-step explanation:

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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

What are the odds in favor of choosing a person at random who chose juice a?

stealth61 [152]

37:53

Step-by-step explanation:

Step 1 :

Given

Number of people choosing Juice A = 37

Number of people choosing Juice B = 32

Number of people choosing Juice C = 21

We need to find the odds in favor of choosing a person who chooses juice A

Step 2 :

Here the number of success is the number of people choosing juice A = 37

Number of failures is the number of the people not choosing juice A = Number of people choosing juice B + Number of people choosing juice C = 32+21 = 53

Hence the odds in favor of choosing a person who chooses juice A is 37:53

3 0

3 years ago

This one number 4<br><br> What to do

Readme [11.4K]

Answer:

231/8 simplified is 28 7/8

Step-by-step explanation:

first you have to convert all mixed fractions into improper fractions so 8 1/4 will become 33/4 and 3 1/2 will become 7/2 and then just multiply and you get 231/8 which simplified is 28 7/8

5 0

2 years ago