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3 years ago

6x-y=-145 X=4-2y Applying systems of linear equations.

Mathematics

1 answer:

sdas [7]3 years ago

5 0

So you change the x

24-12y-y=-145
24-13y=-145
-13y=169
13y=169
y=13

x=4-2x13
x=-22

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Is the line through points P(–3, –2) and Q(2, 3) perpendicular to the line through points R(10, –1) and S(15, –6)? Explain.

Alexus [3.1K]

Answer:

B. Yes. Their slopes have product -1.

Step-by-step explanation:

Given:

Line passing through P(-3, -2) and Q(2, 3)

Line passing through R(10, -1) and S(15, -6)

Required:

To determine if both lines are perpendicular.

SOLUTION:

Two lines are considered perpendicular if the product of their slopes equal -1.

To determine if both lines given in the question are perpendicular, first, calculate their slope using: $m = \frac{y_2 - y_1}{x_2 - x_1}$

Slope of line passing through P(-3, -2) and Q(2, 3):

Let,

$P(-3, -2) = (x_1, y_1)$

$Q(2, 3) = (x_2, y_2)$

$m = \frac{3 -(-2)}{2 -(-3)}$

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

Slope of line passing through R(10, -1) and S(15, -6):

Let,

$R(10, -1) = (x_1, y_1)$

$S(15, -6) = (x_2, y_2)$

$m = \frac{-6 -(-1)}{15 - 10}$

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

The product of their slopes = 1 × -1 = -1

<u><em>Therefore, the lines are perpendicular.</em></u>

The answer is: <em><u>B. "Yes. Their slopes have product -1."</u></em>

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4 years ago

Select all the functions that show an inverse variation...

trapecia [35]

Function y=3/x, y= 2/x+4, and xy=-3 shows an inverse variation option (b), (e), and (f) are correct.

<h3>What is a function?</h3>

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

As we know, when x is not equal to zero and k is a nonzero real number constant, the equation of the form xy = k describes the nonlinear function known as inverse variation.

a) y=6x

The above function is a linear function

b) y=3/x

xy = 3

The above function shows an inverse variation.

c) y=1/3x

y = (1/3)x

The above function is a linear function

d) y= -.07x

The above function is a linear function

e) y= 2/x+4

y = (2+4x)/x

xy = 2 + 4x

The above function shows an inverse variation.

f) xy=-3

The above function shows an inverse variation.

Thus, function y=3/x, y= 2/x+4, and xy=-3 shows an inverse variation option (b), (e), and (f) are correct.

Learn more about the function here:

brainly.com/question/5245372

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5 0

2 years ago

What is the measure of angle ABC?

olya-2409 [2.1K]

Answer:

the answer is already in the question

D. 130°

D. 130

4 0

3 years ago

A deli sells 2 hot dogs for $2.50. What is the constant of proportionality of dollars per hot dog?

Alik [6]

Answer:

$1.25 per hot dog

Step-by-step explanation:

Since we have given that

A deli sells 2 hot dogs for $2.50

i.e.

Cost of 2 hot dogs = $2.50

And we need to find the constant of proportionality of dollars per hot dog, for which we'll use unitary method.

So,

Cost of 1 hot dog is given by

2.50/2=$1.25

So, Cost of per hot dog is $1.25.

Hope this helps :)

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3 years ago

Assume y varies directly as x. if y=8 when x=42; find y when x=126

Soloha48 [4]

Varies directly basically means a multiple of

y = kx

where "k" is the constant of variation. You must solve for this first using the given information.

8 = 42k
8/42 = k
0.19= k

Equation: y = 0.19x
when x = 126
y = 0.19(126)
y = 24

6 0

3 years ago