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2 years ago

What is an equation of the line that passes through the point (-2,-3) and is parallel to the line 4x-y=1

Mathematics

2 answers:

Agata [3.3K]2 years ago

4 0

Answer: y = 4x + 5

Step-by-step explanation:

Rearranging 4x-y = 1 we get y = 4x-1 as the equation of the line.

Since the new line is parallel to y=4x-1, that means the slopes are equal. Therefore, the slope of the line is 4.

So, the equation of the line is y = 4x+b

To figure out b, we can plug in the point (-2,-3) into the equation.

So -3 = -2*4 + b

-3 = -8 + b

And we get b = 5.

Therefore, the equation of the line is y = 4x + 5

SVEN [57.7K]2 years ago

4 0

Answer:

y = 4x + 5

Step-by-step explanation:

First, we need to find the slope of the given equation: 4x - y = 1

Subtract 4x from both sides

4x - y = 1

- 4x - 4x

-y = 1 - 4x

Divide both sides by -1 to make the y variable positive

-y/-1 = (1 - 4x)/-1

y = -1 + 4x

This means the slope of this equation is 4

Our parallel equation will be y = 4x + b

Plug in the given coordinates

-3 = 4(-2) + b

-3 = -8 + b

Add 8 to both sides

-3 = -8 + b

+ 8 + 8

b = 5

Plug in the new b into the original parallel equation

y = 4x + 5

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Help! ASAP!!!

solniwko [45]

Answer:

7.2 units

Step-by-step explanation:

Coordinates of city A = (0, 0)

Coordinates of city B = (6, 4)

Use the distance formula to find the distance between the two cities as follows:

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

Let,

$A(0, 0) = (x_1, y_1)$

$B(6, 4) = (x_2, y_2)$

Plug in the values into the formula

$AB = \sqrt{(6 - 0)^2 + (4 - 0)^2}$

$AB = \sqrt{(6)^2 + (4)^2}$

$AB = \sqrt{36 + 16} = \sqrt{52}$

$AB = 7.2$ (nearest tenth)

6 0

3 years ago

A group of individuals were surveyed about their plans for vacation. There were 21 individuals who said they were going to the d

Alexeev081 [22]

Answer:

140 individuals were surveyed

42 people are planning on going to the mountains

Step-by-step explanation:

The question is missing the information regarding the percentage of people who said that they were going to each of the possible destinations. After a quick google search I've found that, in the original question, 32% of individuals were going to the beach, 15% to the desert, 23% to major cities, and 30% to the mountains.

If 21 people said they were going to the desert, and that corresponds to 15% of the total number of people surveyed, the number of people surveyed is:

$21=n*0.15\\n=140\ individuals$

140 individuals were surveyed

Since 30% responded "the mountains", the number of people planning on going to the mountains is:

$m = 140*0.30\\m=42\ people$

42 people are planning on going to the mountains

3 0

3 years ago

The sum of the number is 103.the second number is 4 times the third.the third number is 5 more then the first .what are the numb

Zigmanuir [339]

Answer:

13, 18, 72

Step-by-step explanation:

let x-5 represent the first number, since the first number is 5 less than the third number. let x represent the third number. let 4x represent the third number, since it's four times greater than the third number.

set up an equation, and make it equal to 103:

x-5+x+4x=103

solve:

6x-5=103

6x=108

x=18

so, the third number is 18.

the first number is equal to x-5, so:

18-5=13

the second number is equal to 4x, so:

4(18)=72

so, the three numbers are 13, 18, and 72.

4 0

2 years ago

Can someone please help me find this answer.

Stels [109]

Answer:

-2x+4

Step-by-step explanation:

multiply all the components of the bracket by - 1.

then you arrive at the answer above

8 0

3 years ago

The quadratic function f (x) = - 45x2 + 350x + 1,590 models the population of a city where x represents the number of years sinc

kramer

Answer: 2,215,000

Step-by-step explanation:

Given: The quadratic function $f (x) = - 45x^2 + 350x + 1,590$ models the population of a city where x represents the number of years since 2005.

To Find: population of the city in 2010

We need to put x= 2010-2005 = 5

$f (5) = - 45(5)^2 + 350(5) + 1,590\\\\=-1125+1750+1590 =2215$

Hence, the estimated population of the city in 201 = 2215 thousands or 2,215,000 .

3 0

3 years ago