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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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A dog walker charges a flat rate of $6 per walk plus an hourly rate of $30. How much does the dog walkercharge for a 45 minute w
leonid [27]

hello

from the question given, the dog walker charges a flat rate of $6 and an extra $30 per hour.

we can write out an equation in function notation

let the number of hours be represented by x

f(x)=6+30x

now we can proceed to solve the cost of the walk for 45 minutes

\begin{gathered} 1hr=60\min s \\ \text{xhr}=45\min s \\ x=\frac{45}{60} \\ x=\frac{3}{4} \\ \text{therefore 45mins = 3/4 hours} \end{gathered}

now we can input the value into the equation and know the cost for 45 minutes walk

\begin{gathered} f(x)=6+30x \\ x=\frac{3}{4} \\ f(x)=6+30(\frac{3}{4}) \\ f(x)=6+22.5 \\ f(x)=28.5 \end{gathered}

from the calculation above, the cost of 45 minutes walk will cost $28.5

6 0
1 year ago
Name
kozerog [31]

2, 8, 32, 128,

Multiply by 4 for each number

8/2= 4

32/8= 4

128/32= 4

128*4=512

512*4= 2,048

Answer: D 512, 2,048

5 0
3 years ago
Toms banks baleances at the end of the months 1,2,3 are 1600 ,1664,1730.56 what will toms balance be at the end of month 5
Sergeeva-Olga [200]

Answer:

Tom's balance at the end of month 5 = 1,871.77

Step-by-step explanation:

a = 1600

ar = 1664

ar² = 1730.56

common ratio, r = ar/a

= 1664/1600

= 1.04

r = 1.04

what will toms balance be at the end of month 5

Month 5 = ar⁴

= 1600 * 1.04⁴

= 1600 * 1.16985856

= 1,871.773696

Approximately 1,871.77

Tom's balance at the end of month 5 = 1,871.77

5 0
3 years ago
The table shows the number of cell phone towers a
Olin [163]

Answer:

The correct option is;

B. Yes. The ratios of towers to customers (thousands) are all equivalent to a unit rate of 52 Towers/(Thousand customers)

Step-by-step explanation:

The given data can be presented as follows;

Cell Phone Towers

Customer (thousands)    {}   Towers

1) 5.25            {}                          273

2) 6.25            {}                         325

3) 7.25            {}                         377

4) 9.25            {}                         481

From the given data, we have the ratio Towers/Customer (thousands) given as follows;

For 1), we have;

273 Towers/(5.25 thousands customers) = 52 Towers/(Thousand customer)

For 2), we have;

325 Towers/(6.25 thousands customers) = 52 Towers/(Thousand customer)

For 3), we have;

377 Towers/(7.25 thousands customers) = 52 Towers/(Thousand customer)

For 4), we have;

481 Towers/(9.25 thousands customers) = 52 Towers/(Thousand customer)

Therefore, the ratios of towers to customers (thousands) all have the same equivalent unit rate of 52 Towers/(thousand customers).

6 0
3 years ago
Pls help me!!!! (question is in the picture)
Svetllana [295]
The fourth answer is correct. When dividing by x to the half (aka square root of x), divide every power of x by two.
7 0
3 years ago
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