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dangina [55]
3 years ago
9

Question 1: Find the equation of the line through point (5,4) and perpendicular to y=−43x−2. Use a forward slash (i.e. "/") for

fractions (e.g. 1/2. Question 2:Find the equation of the line through point (−2,−1) and perpendicular to 5x+6y=−6. Use a forward slash (i.e. "/") for fractions (e.g. 1/2.
Mathematics
1 answer:
Mariulka [41]3 years ago
8 0

Answer:

Question 1: y = 3/4x + 1/4.

Question 2: y = 6/5x + 7/5.

Step-by-step explanation:

Question 1: A line perpendicular to another line would have a slope that is the negative reciprocal of the other line. If the slope of the first line is -4/3, the slope of a line perpendicular to the first would have a slope of 3/4.

Since the line goes through (5, 4), we can just put the points into the equation, y = 3/4x + b.

4 = 3/4(5) + b

b + 15/4 = 4

b = 16/4 - 15/4

b = 1/4

So, the equation of the line is y = 3/4x + 1/4.

Question 2: 5x + 6y = -6

6y = -5x - 6

y = -5/6x - 1

As stated before, a line perpendicular to another will have a slope that is the negative reciprocal of the other. So, the slope of the other line is 6/5.

The line goes through (-2, -1), so we can put the points into the equation, y = 6/5x + b.

-1 = 6/5(-2) + b

b - 12/5 = -5/5

b = -5/5 + 12/5

b = 7/5

So, the equation of the line is y = 6/5x + 7/5.

Hope this helps!

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alexira [117]

Answer:

x = 2, 1 + 3i, 1 − 3i

Step-by-step explanation:

Find the Roots (Zeros)

x^4 − 6x^3 + 22x^2 − 48x + 40

Set x^4 − 6x^3 + 22x^2 − 48x + 40 equal to 0. x^4 − 6x^3 + 22x^2 − 48x + 40 = 0

Solve for x.

Factor the left side of the equation.

Factor x^4 − 6x^3 + 22x^2 − 48x + 40 using the rational roots test.

(x − 2) (x^3 − 4x^2 + 14x − 20) = 0

 Factor x^3 − 4x^2 + 14x − 20 using the rational roots test.

(x − 2) (x − 2) (x2 − 2x + 10) = 0

 Combine like factors.

(x − 2)2 (x^2 − 2x + 10) = 0

If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.

(x − 2)^2 = 0

x^2 − 2x + 10 = 0

 Set (x − 2)^2 equal to 0 and solve for x.

Set (x − 2)^2 equal to 0.

 (x − 2)^2 = 0

Solve (x − 2)^2 = 0 for x.

x = 2

 Set x^2 − 2x + 10 equal to 0 and solve for x.

Set x^2 − 2x + 10 equal to 0. x^2 − 2x + 10 = 0

Solve x^2 − 2x + 10 = 0 for x.

Use the quadratic formula to find the solutions.

−b ± (√b^2 − 4 (ac) )/2a

Substitute the values a = 1, b = −2, and c = 10 into the quadratic formula and solve for x.

2 ± (√(−2)^2 − 4 ⋅ (1 ⋅ 10))/2 ⋅ 1

Simplify.

Simplify the numerator.

  x =    2 ± 6i/ 2.1

Multiply 2 by 1

 x =  2 ± 6i/2⋅1

 Simplify

  2 ± 6i/2  

   x = 1 ± 3i

The final answer is the combination of both solutions.

x = 1 + 3i, 1 − 3i

The final solution is all the values that make (x − 2)2 (x2 − 2x + 10) = 0 true.

x = 2, 1 + 3i, 1 − 3i

3 0
3 years ago
Jake went to a fair and spent $5 on admissions, $6.50 on games, and $7.21
asambeis [7]

Answer:

Jake has <em>$11.29 </em>dollars left.

Step-by-step explanation:

To find the answer, we will add up<em> $5 + $6.50 + $7.21</em> and we get<em> $18.71</em>.  Now <em>subtract $30 from 18.71</em>, which is <em>$11.29</em>.  Therefore, <em>Jake has $11.29 dollars left.</em>

8 0
3 years ago
How do I solve this?
Vikentia [17]

Answer:

need help too

Step-by-step explanation:

8 0
2 years ago
 Ill Mark Brainliest if you answer correctly. The figure below shows a shaded circular region inside a larger circle:
pogonyaev

First we have to find the areas of both circle using the formula

Area = \pi r^2

For larger circle,

Area=  \pi(5)^2 = 25 \pi

For smaller circle,

Area = \pi (4)^2 = 16 \pi

Required probability

= \frac{25 \pi -16 \pi}{25 \pi} *100 = \frac{9}{25}*100 = 36%

Correct option is the second option .

8 0
3 years ago
Find x<br><br> A. X = 23<br> B. X = 31<br> C. X = 62<br> D. X = 118
Scorpion4ik [409]

Answer:

A

Step-by-step explanation:

6x-20= 118

6x= 118 + 20

6x = 138

x = 138/6

x= 23

8 0
2 years ago
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