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forsale [732]
3 years ago
9

Find the value of n so that the line perpendicular to the line with the equation -2y + 4 = 6x + 8 passes through the points at (

n, -4) and (2, -8).
Mathematics
1 answer:
kolezko [41]3 years ago
6 0
If the line must be perpendicular to the equation, that means the slope is the reciprocal of the one in the given equation. So first we find that, the slope of the given equation. 

- 2y + 4 = 6x + 8
- 2y = 6x + 4
 
y = - 3x - 2

So the slope of the given equation is - 3x. That means the slope of our perpendicular equation must be 1/3x 

Now to find the value of n, plug in our given information and perpendicular slope into the slope equation:

Slope = (Y₂ - Y₁ ) / (X₂ - X₁)

1/3 = (- 8 - (-4)) / (2 - n)
1/3 = (- 8 + 4) / (2 - n)
1/3 = ( - 4) / (2 - n)

Multiply both sides by (2 - n) to get the binomial out of the denominator

(1/3)(2 - n) = - 4

Multiply both sides by 3 to isolate the binomial

2 - n = - 4(3)
2 - n = - 12

Subtract 2 from both sides to isolate the variable

- n = - 14

Divide by - 1 to get rid of the negative.

n = 14. Your coordinate is ( 14, - 4)

Now to find the equation that is perpendicular. 

y = 1/3x + b

Plug in either of the coordinates. I'm going to use the ordered pair we just found. 

- 4 = 1/3(14) + b
- 4 = 14/3 + b
- 12/3 = 14/3 + b

Subtract 14/3 on both sides.

- 26/3 = b

Your equation is y = 1/3x - 26/3


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Erika worked 18 hours last week and 20 hours this week. If she earns $6 per hour, how much did she earn these two weeks?
Crank
Hi!

If she worked 18 hours last week and 20 hours this week, then she worked 38 hours in total, because 18 + 20 = 38.

If she earns $6 per hour, and she worked for 38 hours, then she got 38 sets of 6, which you can find the answer to by multiplying 38 and 6.

This is essentially 6 + 6 + 6 +...

38 * 6 = $228

So she earned $228 these two weeks.

Hope this helped!
6 0
3 years ago
Read 2 more answers
Pierre deposits $9,000 in a certificate of deposit that pays 1.4% interest, compounded semi-annually.
Elenna [48]

9514 1404 393

Answer:

  • interest: $63
  • balance: $9063

Step-by-step explanation:

After 6 months, the interest accrued is ...

  I = Prt

  I = $9000·0.014·(6/12) = $63

This is added to the principal to get the balance at that point in time.

  $9000 +63 = $9063

__

The interest earned in the first 6 months is $63. The balance after 6 months is $9063.

_____

The compound interest formula will give you the same result for one compounding period. It tells you the balance is ...

  A = P(1 +r/n)^(nt)

where n is the number of times interest is compounded in a year (2), and t is the number of years (1/2). For annual rate r = 1.4%, this is ...

  A = $9000(1 +0.007)^(2×1/2) = $9000·1.007 = $9063

5 0
2 years ago
Between which two square roots of integers could you find π
LUCKY_DIMON [66]
Hello.

Since 3 < pi < 4, 
√9 < pi √16 

In fact, since pi^2 = 9.86, 

<span>√9 < pi < √10. 

Which means the you</span><span> can find pi between square roots √9 and √10.
</span>
Have a nice day
5 0
2 years ago
Please help!
UkoKoshka [18]

The values of x in the triangles and the angles in the rhombus are illustrations of tangent ratios

  • The values of x in the triangles are 21.4 units, 58 degrees and 66 degrees
  • The angles in the rhombus are 44 and 46 degrees, respectively

<h3>How to determine the values of x?</h3>

<u>Triangle 1</u>

The value of x is calculated using the following tangent ratio

tan(25) = 10/x

Make x the subject

x = 10/tan(25)

Evaluate

x = 21.4

<u>Triangle 2</u>

The value of x is calculated using the following tangent ratio

tan(x) = 8/5

Evaluate the quotient

tan(x) = 1.6

Take the arc tan of both sides

x = arctan(1.6)

Evaluate

x = 58

<u>Triangle 3</u>

The value of x is calculated using the following tangent ratio

tan(x) = 0.34/0.15

Evaluate the quotient

tan(x) = 2.27

Take the arc tan of both sides

x = arctan(2.27)

Evaluate

x = 66

<h3>How to calculate the angles of the rhombus?</h3>

The lengths of the diagonals are:

L1 = 2 in

L2 = 5 in

Represent the angles with x and y.

The measures of the angles are calculated using the following tangent ratios

tan(0.5x) = 2/5 and y = 90 - x

Evaluate the quotient

tan(0.5x) = 0.4

Take the arc tan of both sides

0.5x = arctan(0.4)

Evaluate

0.5x = 22

Divide by 0.5

x = 44

Recall that:

y = 90 - x

This gives

y = 90 - 44

Evaluate

y = 46

Hence, the angles in the rhombus are 44 and 46 degrees, respectively

Read more about tangent ratio at:

brainly.com/question/13347349

5 0
2 years ago
Please help solve the equation above.
Paladinen [302]

Answer:

x=12

Step-by-step explanation:

(9x-4)+(5x+16)=180

14x+12=180

     -12    -12

14x=168

then devide both sides by 14

x=12

8 0
3 years ago
Read 2 more answers
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