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2 years ago

What is the equation in slope-intercept form of a line that is perpendicular to y=1/4x−1 and passes through the point (4, 1)?

Mathematics

2 answers:

wolverine [178]2 years ago

7 0

Y=4x-15

This line passes through (4,1) and is perpendicular to y=1/4x-1

Harlamova29_29 [7]2 years ago

4 0

Answer:

y = -4x + 17

Step-by-step explanation:

Slope of the perpendicular line: -4

(4,1)

y-intercept: 1 - (-4)(4)

= 1+16 = 17

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Solve the equation for all values of x in simplest form (x + 3)^2 = -16

Arlecino [84]

Answer:

x = -7 or x = 1

Step-by-step explanation:

Given expression:

(x + 3)² = -16

Problem;

Solve for x;

Solution:

To solve for x; we use the factorization method;

Take -16 to the left of the equation;

(x + 3)² = -16

(x + 3)² + 16 = 0

(x+ 3)² + 4² = 0

if x² + y² = (x + y)(x - y)

So;

(x + 3 + 4) (x + 3 - 4) = 0

(x + 7)(x - 1) = 0

x + 7 = 0 or x - 1 = 0

x = -7 or x = 1

6 0

2 years ago

Find the complex fourth roots of 81(cos(3pi/8) + i sin(3pi/8))

BartSMP [9]

By using De Moivre's theorem:

If we have the complex number ⇒ z = a ( cos θ + i sin θ)
∴ $\sqrt[n]{z} = \sqrt[n]{a} \ (cos \ \frac{\theta + 360K}{n} + i \ sin \ \frac{\theta +360k}{n} )$
k= 0, 1 , 2, ..... , (n-1)

For The given complex number ⇒ z = 81(cos(3π/8) + i sin(3π/8))


Part (A) find the modulus for all of the fourth roots

∴ The modulus of the given complex number = l z l = 81

∴ The modulus of the fourth root = $\sqrt[4]{z} = \sqrt[4]{81} = 3$

Part (b) find the angle for each of the four roots

The angle of the given complex number = $\frac{3 \pi}{8}$
There is four roots and the angle between each root = $\frac{2 \pi}{4} = \frac{\pi}{2}$
The angle of the first root = $\frac{ \frac{3 \pi}{8} }{4} = \frac{3 \pi}{32}$
The angle of the second root = $\frac{3\pi}{32} + \frac{\pi}{2} = \frac{19\pi}{32}$
The angle of the third root = $\frac{19\pi}{32} + \frac{\pi}{2} = \frac{35\pi}{32}$
The angle of the fourth root = $\frac{35\pi}{32} + \frac{\pi}{2} = \frac{51\pi}{32}$

Part (C): find all of the fourth roots of this

The first root = $z_{1} = 3 ( cos \ \frac{3\pi}{32} + i \ sin \ \frac{3\pi}{32})$
The second root = $z_{2} = 3 ( cos \ \frac{19\pi}{32} + i \ sin \ \frac{19\pi}{32})$

The third root = $z_{3} = 3 ( cos \ \frac{35\pi}{32} + i \ sin \ \frac{35\pi}{32})$
The fourth root = $z_{4} = 3 ( cos \ \frac{51\pi}{32} + i \ sin \ \frac{51\pi}{32})$

7 0

3 years ago

Find the value of x.

tatiyna

Answer:

x = 19

Step-by-step explanation:

(5x+4)+(x-2)+(3x+7) = 180

5x+4+x-2+3x+7 = 180

9x+9 = 180

9x = 171

x = 171/9