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3 years ago

Write an equation of the line that is parallel to y = 1/2x + 3 and passes through the point (10, -5).

Mathematics

1 answer:

bearhunter [10]3 years ago

8 0

y = mx + b

"m" is the slope, "b" is the y-intercept (the y value when x = 0)

You need to find "m" and "b"

For lines to be parallel, the slopes have to be the same.

The given line's slope is 1/2, so the parallel line's slope is also 1/2.

y = 1/2x + b

To find "b", you can plug in the point (10, -5) into the equation.

y = 1/2x + b

-5 = 1/2(10) + b

-5 = 5 + b Subtract 5 on both sides to get "b" by itself

-10 = b

y = 1/2x - 10 Your answer is D (you could have just found the slope to get your answer, since all the slopes are different)

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Plugging this into the equation,
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3 years ago

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3 years ago

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A drawer contains 3 white shirts, 2 blue shirts, and 5 gray shirts. A shirt is randomly

shutvik [7]

Answer:

Probability that first shirt is white and second shirt is gray if first shirt selected is set aside = $\frac{1}{4}$

Step-by-step explanation:

Given that

3 white, 2 blue and 5 gray shirts are there.

To find:

Probability that first shirt is white and second shirt is gray if first shirt selected is set aside = ?

Solution:

Here, total number of shirts = 3+2+5 = 10

First of all, let us learn about the formula of an event E:

$P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}$

$P(First\ White) = \dfrac{\text{Number of white shirts}}{\text {Total number of shirts left}}$

$P(First\ White) = \dfrac{3}{10}$

Now, this shirt is set aside.

So, total number of shirts left are 9 now.

$P(First\ White\ and\ second\ gray) = P(First White) \times P(Second\ Gray)\\\Rightarrow P(First\ White\ and\ second\ gray) = P(First White) \times \dfrac{\text{Number of gray shirts}}{\text{Total number of shirts left}}\\\\\Rightarrow P(First\ White\ and\ second\ gray) = \dfrac{3}{10} \times \dfrac{5}{9}\\\Rightarrow P(First\ White\ and\ second\ gray) = \dfrac{1}{2} \times \dfrac{1}{2}\\\Rightarrow P(First\ White\ and\ second\ gray) = \bold{\dfrac{1}{4} }$

So, the answer is:

Probability that first shirt is white and second shirt is gray if first shirt selected is set aside = $\frac{1}{4}$

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3 years ago