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3 years ago

Line with slope 2 passes through point (3, 8). What is the distance between this line and the point (8, 3)?

Mathematics

2 answers:

larisa [96]3 years ago

6 0

Answer:

The answer to your question is: 6.7 units or 15/√5

Step-by-step explanation:

Data

slope = 2 Point (3, 8)

Another point (8, 3)

Formula

(y - y1) = m (x - x1)

d = |Ax + By + C| / √(A² + B²)

Process

Find the equation of the line

(y - 8) = 2(x - 3)

y - 8 = 2x - 6

2x - y + 2 = 0

Find the distance between the line andt the point

d = |2(8) - 1(3) + 2| / √2² + (-1)²

d = | 16 - 3 + 2| / √ 4 + 1

d = | 15 | / √5

d = 15 / √5

d = 6.7 units

brilliants [131]3 years ago

4 0

The answer to your question is 6.7 units or 15/√5

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Answer:

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Step-by-step explanation:

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3 years ago

Given the function f(x)=-5x^2-2x+20 find f(3)

Deffense [45]

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3 years ago

Explain how to find the vertex of 2x^2+12x+16

Elina [12.6K]

The vertex form:

$y=a(x-h)^2+k\\\\(h,\ k)-vertex$

Use $(a+b)^2=a^2+2ab+b^2\qquad(*)$

$2x^2+12x+16=2(x^2+6x)+16=2(x^2+2(x)(3))+16\\\\=2(\underbrace{x^2+2(x)(3)+3^2}_{(*)}-3^2)+16=2((x+3)^2-9)+16\\\\=2(x+3)^2+(2)(-9)+16=2(x+3)^2-18+16\\\\=\boxed{2(x-(-3))^2-2}\to h=-3,\ k=-2$

<h3>Answer: (-3, -2).</h3>

Other method:

$f(x)=ax^2+bx+c\\\\vertex:(h,\ k)\\\\h=\dfrac{-b}{2a},\ k=f(h)$

We have

$f(x)=2x^2+12x+16\\\\a=2,\ b=12,\ c=16$

Substitute:

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4 years ago

Erica bought a car for $24,000. She had to add Pennsylvania's sales tax of 6% . The total price of the car is closest to?

mylen [45]

The answer would be $25,440.

Since 24,000 is the original price and 6% is being added,

24,000(1.06) = 25440.

1.06 equals 106% of the 24000.

Solution 2:

So 6% is added to the 24,000 car price.

6% of 24,000 = 24,000(.06)

So the total final price will be 24,000 + 24000(.06) = 25440

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3 years ago

Read 2 more answers