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3 years ago

Which equation represents the line that passes through the point (4, -5) and is perpendicular to the line x + 2y = 5?

Mathematics

1 answer:

Lerok [7]3 years ago

7 0

Answer:

y = 2x - 13

Step-by-step explanation:

Equation of a line is y = mx + c, m is the gradient and c is the intercept

The line passes through points 4 and -5, x is 4 and y is -5

-5 = 4m + c

When two lines are perpendicular, the products of their gradients are equal to -1, m1 * m2 = -1

x + 2y = 5

2y = -x + 5

y = (-1/2 * x) + 5

therefore m = -1/2

m1 * m2 = -1

m * -1/2 = -1

-m = -2 , therefore m = 2

-5 = 4 * 2 + c

c = -5 - 8, which is -13

Therefore the equation for the line is

y = 2x - 13

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Lucia is making invisibility potions. Each potion requires 22 eyes of newt. How many invisibility potion Lucia is making invisib

ira [324]

Answer:

Step-by-step explanation:

8 0

3 years ago

Which ordered pair is in the solution set of the system of linear inequalities? y >3/2 x – 1 y <3/2 x – 1 (–5, 2) (2, 2) (

Vikentia [17]

Answer:

No solution

Option 4 is correct

Step-by-step explanation:

Given: The system of inequality

$y>\dfrac{3}{2}x-1$

$y$

We need to choose correct option.

Option 1: (-5,2)

Put x=-5 and y=2

Equation 1 Equation 2

$2>\dfrac{3}{2}(-5)-1$ $2$

$2>-8.5$ $2$

TRUE FALSE

Option 2: (2,2)

Put x=2 and y=2

Equation 1 Equation 2

$2>\dfrac{3}{2}(2)-1$ $2$

$2>2$ $2$

FALSE FALSE

Option 3: (5,2)

Put x=-5 and y=2

Equation 1 Equation 2

$2>\dfrac{3}{2}(5)-1$ $2$

$2>6.5$ $2$

FALSE TRUE

Option 1, 2 and 3 are incorrect because both equation must be true for solution.

Hence, Option 4 is correct no solution.

6 0

3 years ago

Read 2 more answers

A cylinder has a height that is twice the length of the diameter. The diameter of the cylinder is 10 centimeters. What is the su

siniylev [52]

Answer:

Step-by-step explanation:

Givens

pi = 3.14

d = 10 cm

h = 2*d

Formula

The top of the cylinder is a solid circle. So the area of the circle is pi r^2
There is both a top and bottom to the circle so the fomula is 2*pi*r^2

The surrounding area of the cylinder is the circumference of the circle times the height. The circumference of the circle is 2*pi*r.
Then you just multiply by the height.
formula = 2*pi * r * h

The combined formula is given below.

SA = 2*pi*r^2 + 2*pi*r * h

Conversions

d = 10 cm

h = 2*10

h = 20 cm

r = d/2

r = 10 / 2

r = 5cm

Solution

SA = 2*pi*r^2 + 2*pi*r * h

SA = 2*3.14*5^2 + 2*3.14*5*20

SA = 157 + 628

SA = 785 cm^2

Answer: The surface area is 785 cm^2

5 0

2 years ago

Complete the equation of the line through ( 4 , -8 ) and ( 8 , 5 )

irinina [24]

Answer:

Therefore the equation of the line through ( 4 , -8 ) and ( 8 , 5 ) is

13x - 4y = 84.

Step-by-step explanation:

Given:

Let,

point A( x₁ , y₁) ≡ ( 4 ,-8)

point B( x₂ , y₂) ≡ (8 , 5)

To Find:

Equation of Line AB =?

Solution:

Equation of a line passing through Two points A( x₁ , y₁) and B( x₂ , y₂)is given by the formula

$(y - y_{1} )=(\frac{y_{2}-y_{1} }{x_{2}-x_{1} })\times(x-x_{1}) \\$

Substituting the given values in a above equation we get

$(y-(-8))=(\frac{5-(8)}{8-4})\times (x-4)\\ \\(y+8)=\frac{13}{4}(x-4)\\\\4(y+8)=13(x-4)\\4y+32=13x-52\\13x-4y=84...............\textrm{which is the required equation of the line AB}$

Therefore the equation of the line through ( 4 , -8 ) and ( 8 , 5 ) is

13x - 4y = 84.

4 0

3 years ago

Please answer !!!!!!!!!!!!!!!!

Stella [2.4K]

12 ft is your answer hope that helps

8 0

3 years ago