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r-ruslan [8.4K]
3 years ago
8

What is the equation perpendicular to y= -1/5x +3 and goes through the point (7,4)?

Mathematics
1 answer:
Sphinxa [80]3 years ago
7 0

Answer:

y - 4 = 5(x - 7) or y = 5x - 31

Step-by-step explanation:

Slope-intercept form: <em>y = mx + b</em> (m = slope, b = y-intercept)

Point-slope form: <em>y - y₁ = m(x - x₁)</em> ((x₁, y₁) = known point, m = slope)

1. Slope: perpendicular to -1/5 --> 5 (negative reciprocal)

2. Insert knowns into equation: y - 4 = 5(x - 7)

3. Turn into point-slope form (assuming that is what we are looking for):

Multiply: <em>y - 4 = 5x - 35</em>

Subtract: y = 5x - 31

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A= (4,5) B= (7,-9) what is AB ?
VMariaS [17]
If you are needing to find the distance between the two points, you must use a simple formula, cleverly named, the distance formula. Since I can't input special characters into the answer box, I'll explain it the best I can.

( The square root of (  (x - x)^2 + (y - y)^2 )  )

First, we need to find the first x subtracted from the second x, as so:
(4,5) and (7,-9)

4 - 7 = -3

Now, we square the -3.

-3^2 = 
-3 * -3 = 9

Next, we have to find the first y subtracted from the second y.
(4,5) and (7,-9)

5 - (-9) = 14

Now, we square the 14.

14^2 =
14 * 14 = 196

Let's see how the numbers fit in the formula:

sqrt((x - x)^2 + (y - y)^2)

sqrt((4 - 7)^2 + (7 - (-9))^2)

sqrt((-3)^2 + (14)^2)

sqrt( 9 + 196 )

This is where we currently are in the formula, all we have to do now is square root the total of 9 + 196.

sqrt( 9 + 196 )
sqrt( 205 )

The square root of 205 = 14.31782106...

There are a few answers you can consider:

1) sqrt(205)
2) 14.32 units
or
3) 14.31782106

Depending on the answer you desire, use the one that sounds the most correct to you. Although all three are correct, it may not be the answer you require. 

Hope I could help! If my math is incorrect, or I provided answers you were not looking for, please let know! However, if my answer is correct and well explained, please consider marking my answer as <em>Brainliest</em>! :)

Have a good one.
God bless!
4 0
3 years ago
A company has budgeted 5 1/4 hours to complete a project, with 1/3 of the time spent on research. How much time does the company
elena-s [515]

Given that a company budgeted 5 1/4 hours to complete a project, determine how much time they spent on research if they spent 1/3 of the total budget.

First, convert the budget from hours into minutes.

5 1/4 hours = 315 minutes

1 hour = 60 min

1/4 hour = 15 min

60 x 5 = 300

300 + 15 = 315

Then, divide the minutes by 3 or multiply it by 1/3.

315 / 3 = 105

315 x 1/3 = 105

Lastly convert to a mixed number.

1 3/4 hour

Thus, the company plans to spend 1 3/4 hours or 1 hour and 45 minutes on research.

7 0
3 years ago
What is the recursive rule for the sequence 2, -1, 1/2 , -1/4
Helga [31]

Answer:

a_n=\frac{-1}{2}a_{n-1}

a_1=2

Step-by-step explanation:

The recursive rule is a term defined in terms of other terms in the sequence.

The is a geometric sequence because it has a common ratio.

The common ratio can be found by dividing a term by previous term.

For example, all of these are equal:

\frac{-1}{2}

\frac{\frac{1}{2}}{-1}

\frac{\frac{-1}{4}}{\frac{1}{2}}

They are all equal to \frac{-1}{2}.

So we are saying:

\frac{\text{term}}{\text{previous term}}}=\frac{-1}{2}

More formally:

\frac{a_n}{a_{n-1}}=\frac{-1}{2}.

Multiply both sides by a_{n-1}:

a_n=\frac{-1}{2}a_{n-1}

When doing recursive form, you need to state a term of the sequence (or more depending on the recursive form you have).

So the first term is 2.

So the full thing for the answer is:

a_n=\frac{-1}{2}a_{n-1}

a_1=2

8 0
3 years ago
Solve for b. <br>4/3b+2=4-1/3b​
Maksim231197 [3]

Answer:

b = \frac{6}{5}

Step-by-step explanation:

Multiply through by 3 to clear the fractions.

4b + 6 = 12 - b ( add b to both sides )

5b + 6 = 12 ( subtract 6 from both sides )

5b = 6 ( divide both sides by 5 )

b = \frac{6}{5}

4 0
3 years ago
Point m is the midpoint of AB. if the coordinates of m (2,8) in the coordinates of A (10, 12) are the coordinates of B
vivado [14]
Point m is the midpoint of AB. if the coordinates of m (2,8) in the coordinates of A (10, 12) are the coordinates of B this is your answer 4/8
8 0
3 years ago
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