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3 years ago

A line passes through the point (-8,7) and has a

Mathematics

1 answer:

zaharov [31]3 years ago

6 0

Answer:

y = (-5/2)x + 27

Step-by-step explanation:

Use the point slope formula y = mx + b.

Replace m with -5/2, x with -8 and y with 7:

7 = (-5/2)(8) + b. Find the y-intercept, b:

7 = -20 = b, or b = 27

The equation of this line is y = (-5/2)x + 27.

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ruslelena [56]

Answer:

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Step-by-step explanation:

3 0

3 years ago

Find the equation of locus of a point which moves such that its distance from (0,2) is one third distance from (-2,3). ( I WILL

scoray [572]

Answer:

$8(x^2+y^2)-4x-30y+23=0$

Step-by-step explanation:

Distance formula

$\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Let P(x, y) = any point on the locus

Let A = (0, 2)

Let B = (-2, 3)

If a point moves such that its distance from (0, 2) is one third distance from (-2, 3):

$PA=\dfrac{1}{3}PB$

Therefore, using the distance formula:

$\implies \sqrt{(x-0)^2+(y-2)^2}=\dfrac{1}{3}\sqrt{(x-(-2))^2+(y-3)^2}$

Square both sides:

$\implies x^2+(y-2)^2=\dfrac{1}{9}[(x+2)^2+(y-3)^2]$

$\implies x^2+y^2-4y+4=\dfrac{1}{9}(x^2+4x+4+y^2-6y+9)$

Multiply both sides by 9:

$\implies 9x^2+9y^2-36y+36=x^2+4x+4+y^2-6y+9$

$\implies 8x^2+8y^2-4x-30y+23=0$

$\implies 8(x^2+y^2)-4x-30y+23=0$

3 0

2 years ago

Simplify:(2x+y-z)^2-(2x+y+z)^2

storchak [24]

Q: "Simplify the following expression (2x+y-z)^2-(2x+y+z)^2"

As a simplified expression is

A: -8xz - 4yz

Hopefully this helps you ^0^

5 0

3 years ago

Simplify 14 to the 15th power over 14 to the 5th power . (4 points)

slega [8]

An expression is defined as a set of numbers, variables, and mathematical operations. The given expression when simplified will be equal to 14¹⁰. The correct option is A.

<h3>What is an Expression?</h3>

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The given expression can be simplified as shown below.

14¹⁵ / 14⁵

= 14¹⁵ × (1 / 14⁵)

Using the exponential property 1/aˣ = a⁻ˣ, we can write,

= 14¹⁵ x 14⁻⁵

Using the exponential property aˣ × aᵇ = a⁽ˣ⁺ᵇ⁾, we can write,

= 14⁽¹⁵⁻⁵⁾

= 14¹⁰

Hence, the given expression when simplified will be equal to 14¹⁰.

Learn more about Expression here:

brainly.com/question/13947055

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