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3 years ago

What equation is parallel to y= -1/4+5 and passes through (2,-3)? HELPPPPP PLEASE!!!!

Mathematics

1 answer:

IrinaVladis [17]3 years ago

5 0

Answer:

y = -1/4x - 5/2.

Step-by-step explanation:

I am assuming you mean y = -1/4x + 5.

This has slope of -1/4 so the required equation has the same slope ( as they are parallel).

Using the point-slope form of the equation of a line:

y - (-3) = -1/4(x - 2)

y + 3 = -1/4(x - 2)

y = -1/4x + 1/2 - 3

y = -1/4x - 5/2

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4 years ago

What must be the value of n ?

jarptica [38.1K]

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3 years ago

Prove by mathematical induction that

postnew [5]

For $n=1$ , on the left we have $\cos\theta$ , and on the right,

$\dfrac{\sin2\theta}{2\sin\theta}=\dfrac{2\sin\theta\cos\theta}{2\sin\theta}=\cos\theta$

(where we use the double angle identity: $\sin2\theta=2\sin\theta\cos\theta$ )

Suppose the relation holds for $n=k$ :

$\displaystyle\sum_{n=1}^k\cos(2n-1)\theta=\dfrac{\sin2k\theta}{2\sin\theta}$

Then for $n=k+1$ , the left side is

$\displaystyle\sum_{n=1}^{k+1}\cos(2n-1)\theta=\sum_{n=1}^k\cos(2n-1)\theta+\cos(2k+1)\theta=\dfrac{\sin2k\theta}{2\sin\theta}+\cos(2k+1)\theta$

So we want to show that

$\dfrac{\sin2k\theta}{2\sin\theta}+\cos(2k+1)\theta=\dfrac{\sin(2k+2)\theta}{2\sin\theta}$

On the left side, we can combine the fractions:

$\dfrac{\sin2k\theta+2\sin\theta\cos(2k+1)\theta}{2\sin\theta}$

Recall that

$\cos(x+y)=\cos x\cos y-\sin x\sin y$

so that we can write

$\dfrac{\sin2k\theta+2\sin\theta(\cos2k\theta\cos\theta-\sin2k\theta\sin\theta)}{2\sin\theta}$

$=\dfrac{\sin2k\theta+\sin2\theta\cos2k\theta-2\sin2k\theta\sin^2\theta}{2\sin\theta}$

$=\dfrac{\sin2k\theta(1-2\sin^2\theta)+\sin2\theta\cos2k\theta}{2\sin\theta}$

$=\dfrac{\sin2k\theta\cos2\theta+\sin2\theta\cos2k\theta}{2\sin\theta}$

(another double angle identity: $\cos2\theta=\cos^2\theta-\sin^2\theta=1-2\sin^2\theta$ )

Then recall that

$\sin(x+y)=\sin x\cos y+\sin y\cos x$

which lets us consolidate the numerator to get what we wanted:

$=\dfrac{\sin(2k+2)\theta}{2\sin\theta}$

and the identity is established.

8 0

3 years ago

HEY GUYS I NEED HELP WITH THIS PLZZ! write down everything from the detail of how yall found ur answer plzz! 20 points or more..

aleksley [76]

Answer:

1/6+1/8+$13.50+$5=x

x=$18.79

Step-by-step explanation:

i add them

first i find the common denominator for 1/6 and 1/8

then i add 13.50 by 5

then add 18.50 by 7/24

i hope this explains how i got my answer

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4 years ago

Read 2 more answers

The answer to 1/6+3/4

Harman [31]

Answer:

$\frac{11}{12}$

Step-by-step explanation:

Least Common multiplier of 6 and 4 : 12

Adjust fractions based on the LCM:

$\frac{2}{12}+\frac{9}{12}=\frac{11}{12}$

8 0

3 years ago