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3 years ago

5√45 + √−27 − 3√20 − 2√−3

Mathematics

1 answer:

RSB [31]3 years ago

7 0

Answer:20.1246118 + 1.73205081 i

Step-by-step explanation:

21 31 25 1+ 24 5 25 3+ 35 s 38 1 42 3+ 41 5 39 24 31 22 26 27 19 25t ... 26n 31 31 1+ 32 2+ 35 2 40 s 45 2 49 7+ 52 14+ 49 21+ 41 22 36 27 29 31 ... 20 31 20 21 || 23 || 6 || 27 3 33 25 37 2 42 2 41 || 27 | 40 21+ 34 22 || 29 || 27 | 19 ... 29 14 22 20 21 24 _)+−−−|−-T-~~~T),(Nos;---f) ----·... --|·---- | | | | | 3|1-----° s√≠√∞13 ni.

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Find the equation of the line that is perpendicular to y = 2x + 8 and passes though the point (8, –8).

zloy xaker [14]

Option B: $y=-\frac{1}{2} x-4$ is the equation of the line.

Explanation:

Given that the equation of the line is perpendicular to $y = 2x + 8$ and passes through the point $(8,-8)$

We need to determine the equation of the line.

The equation of the line can be determined using the formula,

$y-y_1=m(x-x_1)$

First, we shall find the value of m.

From the equation $y = 2x + 8$ , the slope is 2.

Since, the lines are perpendicular, the slope is given by

$m=-\frac{1}{2}$

Thus, the slope is $m=-\frac{1}{2}$

Substituting the slope $m=-\frac{1}{2}$ and the point $(8,-8)$ in the formula $y-y_1=m(x-x_1)$ , we get,

$y+8=-\frac{1}{2} (x-8)$

Simplifying, we get,

$y+8=-\frac{1}{2} x+4$

Subtracting both sides by 8, we get,

$y=-\frac{1}{2} x-4$

Thus, the equation of the line is $y=-\frac{1}{2} x-4$

Therefore, Option B is the correct answer.

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3 years ago

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3 years ago

Find all solutions to the following system of equations -y²+6y+x-9=0 ; 6y=x+27.Illustrate with a graph.

Dimas [21]

Answer:

The solution to the system is the pair (9, 6)

Step-by-step explanation:

Hi!

First, let´s write the system of equations:

-y² + 6y + x -9 = 0

6y = x +27

The solutions of the system are the pairs (x, y) that satisfy both equations.

Let´s take the second equation and solve it for x:

6y = x +27

Subtract 27 from both sides of the equation

6y - 27 = x

Now, we can replace x in the first equation and solve it for y:

-y² + 6y + x -9 = 0

-y² + 6y + 6y - 27 -9 = 0

-y² + 12y - 36 = 0

Notice that -y² + 12y - 36 = -(y - 6)², then:

-(y - 6)² = 0

y - 6 = 0

y = 6

(alternatively you can solve the quadratic equation using the quadratic formula).

Now let´s find the value of x:

x = 6y -27

x = 6·6 -27

x = 9

The solution to the system is the pair (9, 6)

Please see the attached figure. The point where the curves intersect is the solution to the system.

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3 years ago

Which expressions are equivalent to x^4/5

Anni [7]

None of the above! The correct answer is 5 square root x^4 and it isn’t listed
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3 years ago

X^2-x-12 factor completely

steposvetlana [31]

Use the sum-product pattern

2
−

−
1
2
x
2
−
x
−
12
x2−x−12

2
+
3

−
4

−
1
2
x
2
+
3
x
−
4
x
−
12
x2+3x−4x−12
2
Common factor from the two pairs

2
+
3

−
4

−
1
2
x
2
+
3
x
−
4
x
−
12
x2+3x−4x−12

(

+
3
)
−
4
(

+
3
)
x
(
x
+
3
)
−
4
(
x
+
3
)
x(x+3)−4(x+3)
3
Rewrite in factored form

(

+
3
)
−
4(+3)x
(x+3)−4(x+3)
x(x+3)−4(x+3)
(−4)(+3)
(x−4)(x+3)
(x−4)(x+3)

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3 years ago