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3 years ago

Please help with this question!!

Mathematics

1 answer:

xxMikexx [17]3 years ago

8 0

$\text{Let}\ k:y=m_1x+b_1\ \text{and}\ l:y=m_2x+b_2\\\\l\perp k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\\text{We have the points J(-24, -4) and K(-4, 6)}.\\\\\text{The formula of a slope:}\\\\m=\dfrac{y_2-y_1}{x_2-x_1}\\\\\text{substitute:}\\\\m_1=\dfrac{6-(-4)}{-4-(-24)}=\dfrac{10}{20}=\dfrac{1}{2}\\\\\text{therefore}\ m_2=-\dfrac{1}{\frac{1}{2}}=-2\\\\\text{The formula of a midpoint:}\\\\\left(\dfrac{x_1+x_2}{2};\ \dfrac{y_1+y_2}{2}\right)\\\\\text{substitute the coordinates of the points J and K:}$

$x=\dfrac{-24+(-4)}{2}=\dfrac{-28}{2}=-14\\\\y=\dfrac{-4+6}{2}=\dfrac{2}{2}=1\\\\\text{midpoint}\ (-14,\ 1)\\\\\text{The point-slope form:}\\\\y-y_1=m(x-x_1)\\\\\text{substitute}\ m=-2,\ x_1=-14\ \text{and}\ y_1=1:\\\\y-1=-2(x-(-14))\\\\\boxed{y-1=-2(x+14)}$

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Can you rearrange it so T is the subject

OverLord2011 [107]

The formula after making t subject of the formula is:

$t = \frac{2-3q}{q+4}$

Step-by-step explanation:

Given formula is:

$q = \frac{2-4t}{t+3}$

To make t the subject of the formula we have to isolate t

So,

Cross-multiplying

$q(t+3) = 2-4t\\qt+3q = 2-4t$

Adding 4t on both sides

$qt+3q+4t = 2-4t+4t\\qt+3q+4t = 2$

Subtracting 3q from both sides

$qt+3q+4t-3q = 2-3q\\qt+4t = 2-3q$

Taking t common on left hand side

$t(q+4)=2-3q$

Dividing both sides by q+4

$\frac{t(q+4)}{q+4}=\frac{2-3q}{q+4}\\t = \frac{2-3q}{q+4}$

The formula after making t subject of the formula is:

$t = \frac{2-3q}{q+4}$

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3 years ago

Find the diameter of a sphere with a surface area of 196π square centimeters

aleksandr82 [10.1K]

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2 years ago

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bagirrra123 [75]

Answer:

A.Put each person's name on a separate piece of paper in a bag. Randomly draw the winning name; and D.Roll a number cube. If it lands on an even number, Roddy wins. If it lands on an odd number, Scott wins.

Step-by-step explanation:

In order for it to be a fair decision, both boys have to have an equal chance of being selected.

For choice A, drawing their names from a bag, both names are equally likely to be chosen; that makes this fair.

For choice B, there is 1 way to get both heads when flipping a coin. There are 2 ways to get heads and tails when flipping a coin. This gives Scott a greater chance, so this is not fair.

For choice C, there are 2 ways to get a 1 or a 2. There are 4 ways to get anything else. This gives Scott a greater chance, so this is not fair.

For choice D, there are 3 even numbers and 3 odd numbers. Both boys have an equal chance, so this is fair.

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4 years ago

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Leviafan [203]

Answer:

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Step-by-step explanation:

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3 years ago

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