All categories

3 years ago

what is the slope intercept form of the linear equation with a graph that passes through (-2,2) and is perpendicular to the grap

h of y=1/3x+9

Mathematics

1 answer:

gtnhenbr [62]3 years ago

6 0

$\text{The slope-intercept form}\ y=mx+b.\\\\Let\\k:y=m_1x+b_1\\l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\\------------------------\\\text{Let}\ k:y=\dfrac{1}{3}x+9\ \text{and}\ l:y=mx+b\\\\l\ \perp\ k\iff\dfrac{1}{3}m=-1\qquad|\cdot3\to m=-3\\\\l:y=-3x+b\\\\\text{Substitute the coordinates of the point (-2, 2) to the equation}\\\text{of the line}\ l:\\\\2=-3(-2)+b\\2=6+b\qquad|-6\\-4=b\to b=-4\\\\\boxed{Answer:\ y=-3x-4}$

You might be interested in

You are paid 3.50 for every case you deliver to a store. If you deliver fifty seven cases, what will you be paid for that delive

Stels [109]

Answer:

199.50

Step-by-step explanation:

Given the 3.50 payment for every case delivered to a store:

This means that you will earn 199.50 for delivering 57 cases, because:

57 cases × 3.50 each case = 199.50

Therefore, you will be paid 199.50 for that delivery.

3 0

2 years ago

Read 2 more answers

Determine whether each expression is equivalent to 49^2t – 0.5.

vampirchik [111]

Answer:

None of the expression are equivalent to $49^{(2t - 0.5)}$

Step-by-step explanation:

Given

$49^{(2t - 0.5)}$

Required

Find its equivalents

We start by expanding the given expression

$49^{(2t - 0.5)}$

Expand 49

$(7^2)^{(2t - 0.5)}$

$7^2^{(2t - 0.5)}$

Using laws of indices: $(a^m)^n = a^{mn}$

$7^{(2*2t - 2*0.5)}$

$7^{(4t - 1)}$

This implies that; each of the following options A,B and C must be equivalent to $49^{(2t - 0.5)}$ or alternatively, $7^{(4t - 1)}$

A. $\frac{7^{2t}}{49^{0.5}}$

Using law of indices which states;

$a^{mn} = (a^m)^n$

Applying this law to the numerator; we have

$\frac{(7^{2})^{t}}{49^{0.5}}$

Expand expression in bracket

$\frac{(7 * 7)^{t}}{49^{0.5}}$

$\frac{49^{t}}{49^{0.5}}$

Also; Using law of indices which states;

$\frac{a^{m}}{a^n} = a^{m-n}$

$\frac{49^{t}}{49^{0.5}}$ becomes

$49^{t-0.5}}$

This is not equivalent to $49^{(2t - 0.5)}$

B. $\frac{49^{2t}}{7^{0.5}}$

Expand numerator

$\frac{(7*7)^{2t}}{7^{0.5}}$

$\frac{(7^2)^{2t}}{7^{0.5}}$

Using law of indices which states;

$(a^m)^n = a^{mn}$

Applying this law to the numerator; we have

$\frac{7^{2*2t}}{7^{0.5}}$

$\frac{7^{4t}}{7^{0.5}}$

Also; Using law of indices which states;

$\frac{a^{m}}{a^n} = a^{m-n}$

$\frac{7^{4t}}{7^{0.5}}$ = $7^{4t - 0.5}$

This is also not equivalent to $49^{(2t - 0.5)}$

C. $7^{2t}\ *\ 49^{0.5}$

$7^{2t}\ *\ (7^2)^{0.5}$

$7^{2t}\ *\ 7^{2*0.5}$

$7^{2t}\ *\ 7^{1}$

Using law of indices which states;

$a^m*a^n = a^{m+n}$

$7^{2t+ 1}$

This is also not equivalent to $49^{(2t - 0.5)}$

6 0

3 years ago

How does one calculate the radius of a cone when given the total surface area

sergeinik [125]

Answer:

The surface area formula for a cone, given its diameter (or radius) and height, is π x (diameter / 2) 2 + π x (diameter / 2) x √ (diameter / 2) 2 + (height 2), where (diameter / 2) is the radius of the base (d = 2 x r), so another way to write it is π x radius 2 + π x radius x √ (radius 2 + (height 2)

3 0

2 years ago

GIVING ALL MY POINTS! GIVING BRAINLIEST! I have a plagiarism checker-

koban [17]

The reason fractions need a common denominator before adding or subtracting is so that the numbers of pieces you are adding/subtracting are all the same size. Note that the numerator of a fraction just tells you how many pieces you have of that size.

5 0

2 years ago

Find the unknown length of x

nlexa [21]

25 is the length of x, using the 30-60-90 special triangle method

8 0

2 years ago