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3 years ago

What is the equation of the line that is perpendicular to and has the same y-intercept as the given line?

Mathematics

2 answers:

Anastasy [175]3 years ago

8 0

ANSWER

The required equation is

$y = 5x + 1$

EXPLANATION

The given line passes through the point

$(5,0) \: and \: (0,1)$

The slope of this line is given by the formula,

$m=\frac{y_2-y_1}{x_2-x_1}$

This implies that,

$m = \frac{1 - 0}{0 - 5}$

$m = - \frac{1}{5}$

The product of the slope of the two perpendicular lines should be negative one.

Thus,

$m_1\times m_2=-1$
This implies that,

$- \frac{1}{5} \times m_2=-1$

We multiply through by
$- 5$
to obtain,

$m_2=-1 \times - 5$

$m_2=5$
Therefore the slope of the line perpendicular to the given line is
$5.$

We use the slope intercept formula
$y =m x + b$

where
$b = 1$
is the y-value of the y-intercept.

We therefore have,

$y = 5x + 1$

as the required equation.

The correct answer is C.

Anestetic [448]3 years ago

8 0

Answer:

C. 5x+1

Step-by-step explanation:

edge2020

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BabaBlast [244]

$\underline{\bf{Given \:equation:-}}$

$\\ \sf{:}\dashrightarrow ax^2+by+c=0$

$\sf Let\:roots\;of\:the\: equation\:be\:\alpha\:and\beta.$

$\sf We\:know,$

$\boxed{\sf sum\:of\:roots=\alpha+\beta=\dfrac{-b}{a}}$

$\boxed{\sf Product\:of\:roots=\alpha\beta=\dfrac{c}{a}}$

$\underline{\large{\bf Identities\:used:-}}$

$\boxed{\sf (a+b)^2=a^2+2ab+b^2}$

$\boxed{\sf (√a)^2=a}$

$\boxed{\sf \sqrt{a}\sqrt{b}=\sqrt{ab}}$

$\boxed{\sf \sqrt{\sqrt{a}}=a}$

$\underline{\bf Final\: Solution:-}$

$\\ \sf{:}\dashrightarrow \sqrt{\alpha}+\sqrt{\beta}$

$\bull\sf Apply\: Squares$

$\\ \sf{:}\dashrightarrow (\sqrt{\alpha}+\sqrt{\beta})^2= (\sqrt{\alpha})^2+2\sqrt{\alpha}\sqrt{\beta}+(\sqrt{\beta})^2$

$\\ \sf{:}\dashrightarrow (\sqrt{\alpha}+\sqrt{\beta})^2 \alpha+\beta+2\sqrt{\alpha\beta}$

$\bull\sf Put\:values$

$\\ \sf{:}\dashrightarrow (\sqrt{\alpha}+\sqrt{\beta})^2=\dfrac{-b}{a}+2\sqrt{\dfrac{c}{a}}$

$\\ \sf{:}\dashrightarrow \sqrt{\alpha}+\sqrt{\beta}=\sqrt{\dfrac{-b}{a}+2\sqrt{\dfrac{c}{a}}}$

$\bull\sf Simplify$

$\\ \sf{:}\dashrightarrow \underline{\boxed{\bf {\sqrt{\boldsymbol{\alpha}}+\sqrt{\boldsymbol{\beta}}=\sqrt{\dfrac{-b}{a}}+\sqrt{2}\dfrac{c}{a}}}}$

$\underline{\bf More\: simplification:-}$

$\\ \sf{:}\dashrightarrow \sqrt{\alpha}+\sqrt{\beta}=\dfrac{\sqrt{-b}}{\sqrt{a}}+\dfrac{c\sqrt{2}}{a}$

$\\ \sf{:}\dashrightarrow \sqrt{\alpha}+\sqrt{\beta}=\dfrac{\sqrt{a}\sqrt{-b}+c\sqrt{2}}{a}$

$\underline{\Large{\bf Simplified\: Answer:-}}$

$\\ \sf{:}\dashrightarrow\underline{\boxed{\bf{ \sqrt{\boldsymbol{\alpha}}+\sqrt{\boldsymbol{\beta}}=\dfrac{\sqrt{-ab}+c\sqrt{2}}{a}}}}$

5 0

2 years ago

Read 2 more answers

On a bicycle, Miranda rides for 4 hours and is 50 miles from her house. After riding for 6 hours, she is 74 miles away. What is

Vera_Pavlovna [14]

<h2> Miranda's rate is 12 hours per mies.</h2>

Step-by-step explanation:

Given by question,

Miranda began her ride from home merely that she was 50 miles away from home after 4 hours of riding.

To find, Miranda's rate = ?

2 hours later she was 974 miles from home.

∴ 2 hours she rode = 74 miles - 50 miles

Miranda rides 24 miles in 2 hours.

∴ Miranda rides in 1 hour = $\dfrac{24}{2}$ $\dfrac{miles}{hour}$

= $12$ $\dfrac{miles}{hour}$

Thus, Miranda's rate is 12 hours per mies.

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3 years ago

If f(x) = sort of x-3, which inequality can be used to fund the domain of f(x)

sergey [27]

Is it multiple choice?

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3 years ago

Work out x most dedicated not rushed gets brainiest

Softa [21]

Answer:54

Step-by-step explanation:

Pentagon has 5 sides

n=5

Sum of interior angles=180(n-2)

Sum of interior angles=180(5-2)

Sum of interior angles=180x3

Sum of interior angles=540

Size of each interior angle =540/n

Size of each interior angle =540/5

Size of each interior angle=108

x=108/2

x=54

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You have 12 coins of which you need to flip only 4 heads. If the probability of flipping heads is 35%, what is the probability t

mel-nik [20]

Answer:

33.3333333333

Step-by-step explanation:

One coin would equal over 11 more would be 8.3333333333 so time that by 4

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