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MA_775_DIABLO [31]
2 years ago
11

the line y=ax-1 is parallel to the line by-(a+1)x=2. These two lines have the same distance to the origin. find a and b

Mathematics
1 answer:
Levart [38]2 years ago
6 0

By using the parallel condition and the fact that the distance to the origin is the same, we will see that a = 1 and b = 2.

<h3>How to find the values of a and b?</h3>

First, remember that two lines are parallel if have the same slope and different y-intercept.

In this case, we know that

y = a*x - 1

b*y - (a + 1)*x = 2

Are parallel, if we write both of them in the slope-intercept form, we get:

y = a*x - 1

y = (a + 1)*x/b + 2/b

Note that because both of the lines are parallel, the slopes must be equal, then we have that:

(a + 1)/b = a

Then if we know that the distance of both lines to the origin is the same, we have that:

|-1/(√(a^2 + 1))| = | (2/b)/(√(((a + 1)/b)^2 + 1))|

Because the slopes are equal the denominators are equal, this means that:

|-1| = |2/b|

And the y-intercepts must be different, this means that:

b = 2

now we can solve:

(a + 1)/b = a

(a + 1)/2 = a

a + 1 = 2a

1 = 2a - a = a

a = 1 and b = 2.

If you want to learn more about linear equations, you can read:

brainly.com/question/1884491

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Suppose h(x)=3x-2 and j(x) = ax +b. Find a relationship between a and b such that h(j(x)) = j(h(x))
sergejj [24]

Answer:

\displaystyle a = \frac{1}{3} \text{ and } b = \frac{2}{3}

Step-by-step explanation:

We can use the definition of inverse functions. Recall that if two functions, <em>f</em> and <em>g</em> are inverses, then:

\displaystyle f(g(x)) = g(f(x)) = x

So, we can let <em>j</em> be the inverse function of <em>h</em>.

Function <em>h</em> is given by:

\displaystyle h(x) = y = 3x-2

Find its inverse. Flip variables:

x = 3y - 2

Solve for <em>y. </em>Add:

\displaystyle x + 2 = 3y

Hence:

\displaystyle h^{-1}(x) = j(x) = \frac{x+2}{3} = \frac{1}{3} x + \frac{2}{3}

Therefore, <em>a</em> = 1/3 and <em>b</em> = 2/3.

We can verify our solution:

\displaystyle \begin{aligned} h(j(x)) &= h\left( \frac{1}{3} x + \frac{2}{3}\right) \\ \\ &= 3\left(\frac{1}{3}x + \frac{2}{3}\right) -2 \\ \\ &= (x + 2) -2 \\ \\ &= x \end{aligned}

And:

\displaystyle \begin{aligned} j(h(x)) &= j\left(3x-2\right) \\ \\ &= \frac{1}{3}\left( 3x-2\right)+\frac{2}{3} \\ \\ &=\left( x- \frac{2}{3}\right) + \frac{2}{3} \\ \\ &= x  \stackrel{\checkmark}{=} x\end{aligned}

3 0
2 years ago
Step by step please and thank you.
cupoosta [38]

Answer:

  the probability is 2/9

Step-by-step explanation:

Assuming the coins are randomly selected, the probability of pulling a dime first is the number of dimes (4) divided by the total number of coins (10).

  p(dime first) = 4/10 = 2/5

Then, having drawn a dime, there are 9 coins left, of which 5 are nickels. The probability of randomly choosing a nickel is 5/9.

The joint probability of these two events occurring sequentially is the product of their probabilities:

  p(dime then nickel) = (2/5)×(5/9) = 2/9

_____

<em>Alternate solution</em>

You can go at this another way. You can list all the pairs of coins that can be drawn. There are 90 of them: 10 first coins and, for each of those, 9 coins that can be chosen second. Of these 90 possibilities, there are 4 dimes that can be chosen first, and 5 nickels that can be chosen second, for a total of 20 possible dime-nickel choices out of the 90 total possible outcomes.

  p(dime/nickel) = 20/90 = 2/9

8 0
3 years ago
-2(p - 1) = 15 anserwwwww plssssss
adelina 88 [10]

Answer:

-6.5

Step-by-step explanation:

-2(p - 1) = 15

-2p + 2 = 15

-2p = 13

p = -6.5

6 0
3 years ago
Select the correct answer​
White raven [17]

Answer:

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Step-by-step explanation:

5 0
3 years ago
Alesha has $25. She spent $4 on lunch and $3 for a book everyday. How many days could Alesha use the money for?
Xelga [282]
4+3 = 7
This is the amount of dollars spent each day
25/7 = 3 4/7
This means the money will last for 3 days.
3 0
2 years ago
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