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Naddik [55]
11 months ago
12

What is the slope of a line perpendicular to the line whose equation is x - y = 6. Fully reduce your answer. Answer: Submit Answ

er
Mathematics
1 answer:
NikAS [45]11 months ago
5 0

Answer:

Explanation:

The standard form of an equation is expressed as y = mx+b

m is the slope

Given the equation x - y = 6

Rewrite in standard form;

-y = -x + 6

Multiply through by -1

-(-y) = -(-x) - 6

y = x - 6

Compare with the standard equation

mx = 1x

mx+b

m is the slope

Given

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Find the equation of the lines, that is parallel to the line 9x-8y=1, and tangent to the elipses 9x^2+16y^2=52.
lara31 [8.8K]

Answer:

The equations of the lines that satisfy these conditions are

y = (9/8)x + (13/4)

And

y = (9/8)x - (13/4)

They can be written further as

8y = 9x + 26

and

8y = 9x - 26

Step-by-step explanation:

The line parallel to the line 9x - 8y = 1 has the same slope as 9x - 8y = 1

Writing the equation of the line in the (y = mx + c) form

8y = 9x - 1

y = (9/8)x - 1

So, the line(s) we are looking for has/have slope(s) of (9/8).

Its equation is then

y = (9/8)x + k

This line is then said to be tangent to the ellipses

9x² + 16y² = 52

So, since the line is a tangent to the ellipses, it will have the same coordinates as the ellipses at the point of contact.

9x² + 16y² = 52

y = (9/8)x + k

y² = (81/64)x² + (18k/8)x + k²

y² = (81/64)x² + (9k/4)x + k²

Substituting this into the ellipses equation,

9x² + 16y² = 52

9x² + 16[(81/64)x² + (9k/4)x + k²] = 52

9x² + (81/4)x² + 36kx + 16k² = 52

29.25x² + 36kx + 16k² - 52 = 0

Taking note that the two lines that will be tangent to the ellipses and parallel to the line given, to establish tangency, we make the discriminant of this equation 0. Hence, the roots of that equation will have equal roots.

So, the discriminant, b² - 4ac = 0

29.25x² + 36kx + 16k² - 52 = 0

a = 29.25

b = 36k

c = 16k² - 52

(36k)² - (4)×(29.25)×(16k² - 52) = 0

1296k² - 1872k² + 6084 = 0

576k² = 6084

k = ±(13/4)

So, the equation(s) of the line(s) required is

y = (9/8)x ± (13/4)

So, the equations include

y = (9/8)x + (13/4)

And

y = (9/8)x - (13/4)

Multiplying by 8, we obtain

8y = 9x + 26

8y = 9x - 26

Hope this Helps!!!

6 0
3 years ago
Here are two points (-3,4),(1,7) What is the slope of the line between them?
valentina_108 [34]

Answer:

3/4

Step-by-step explanation:

3 0
3 years ago
Which expression is equivalent to 1/2(2x-8)<br> A) 4x− 16<br> B) x− 4<br> C) 2x− 4<br> D) x− 8
inn [45]

Answer:

B) x - 4

Step-by-step explanation:

In this question, you have to simplify the expression to get your answer.

Solve:

1/2(2x - 8)

Use the distributive property.

1/2(2x) + 1/2(-8)

x + 1/2(-8)

x - 4

Your answer would be B) x - 4

5 0
2 years ago
Read 2 more answers
Can someone plz help me with this
Levart [38]
D.
None of the above. Because your expression would be, 2 + 0.75 x 6.
Hope it helps. ;)
7 0
3 years ago
A line is drawn through (-7, 11) and (8.-9). The equation
gavmur [86]

Answer:

this answer has to be A because the libra of the pole goes west

Step-by-step explanation:

this answer has to be A because the libra of the pole goes west

8 0
3 years ago
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