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4 years ago

Find the equation of a line that is parallel to y = 2x + 3 and passes through (-1, -1).

Mathematics

1 answer:

drek231 [11]4 years ago

4 0

Answer:

y = 2x +1

Step-by-step explanation:

The given line is in "slope-intercept" form, where the slope is the coefficient of x, 2, and the intercept is the added constant, 3. The parallel line will have the same slope, but its constant will be different. We can find the constant by putting the given point into an equation with the constant as the unknown:

y = 2x + b

-1 = 2(-1) +b . . . substitute for x and y

2 -1 = b . . . . . . add 2

1 = b

So the equation for the parallel line is ...

y = 2x + 1

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What is the slope of line that passes through the points -2,4 and 1,-1

GalinKa [24]

Answer:

-5/3

Step-by-step explanation:

-2 to 1 =3 x=3

4 to -1=5 y=-5

y/x slope=-5/3 or -1 2/3

4 0

3 years ago

The sum of two numbers is 24.The difference of their square is 144.what are the two numbers?

dimulka [17.4K]

Answer:

9 and 16

Step-by-step explanation:

let the two numbers are X and Y

X+Y=24

X^2-Y^2=144

solve simultaneously

4 0

3 years ago

A. Do some research and find a city that has experienced population growth.

horrorfan [7]

A. The city we will use is Orlando, Florida, and we are going to examine its population growth from 2000 to 2010. According to the census the population of Orlando was 192,157 in 2000 and 238,300 in 2010. To examine this population growth period, we will use the standard population growth equation $N_{t} =N _{0}e^{rt}$
where:
$N(t)$ is the population after $t$ years
$N_{0}$ is the initial population
$t$ is the time in years
$r$ is the growth rate in decimal form
$e$ is the Euler's constant
We now for our investigation that $N(t)=238300$ , $N_{0} =192157$ , and $t=10$ ; lets replace those values in our equation to find $r$ :
$238300=192157e^{10r}$
$e^{10r} = \frac{238300}{192157}$
$ln(e^{10r} )=ln( \frac{238300}{192157} )$
$r= \frac{ln( \frac{238300}{192157}) }{10}$
$r=0.022$
Now lets multiply $r$ by 100% to obtain our growth rate as a percentage:
$(0.022)(100)$ =2.2%
We just show that Orlando's population has been growing at a rate of 2.2% from 2000 to 2010. Its population increased from 192,157 to 238,300 in ten years.

B. Here we will examine the population decline of Detroit, Michigan over a period of ten years: 2000 to 2010.
Population in 2000: 951,307
Population in 2010: 713,777
We know from our investigation that $N(t)=713777$ , $N_{0} =951307$ , and $t=10$ . Just like before, lets replace those values into our equation to find $r$ :
$713777=951307e^{10r}$
$e^{10r} = \frac{713777}{951307}$
$ln(e^{10r} )=ln( \frac{713777}{951307} )$
$r= \frac{ln( \frac{713777}{951307}) }{10}$
$r=-0.029$
$(-0.029)(100)$ = -2.9%.
We just show that Detroit's population has been declining at a rate of 2.2% from 2000 to 2010. Its population increased from 192,157 to 238,300 in ten years.

C. Final equation from point A: $N(t)=192157e^{0.022t}$ .
Final equation from point B: $N(t)=951307e^{-0.029t}$
Similarities: Both have an initial population and use the same Euler's constant.
Differences: In the equation from point A the exponent is positive, which means that the function is growing; whereas, in equation from point B the exponent is negative, which means that the functions is decaying.

D. To find the year in which the population of Orlando will exceed the population of Detroit, we are going equate both equations $N(t)=192157e^{0.022t}$ and $N(t)=951307e^{-0.029t}$ and solve for t:
$192157e^{0.022t} =951307e^{-0.029t}$
$\frac{192157e^{0.022t} }{951307e^{-0.029t} } =1$
$e^{0.051t} = \frac{951307}{192157}$
$ln(e^{0.051t})=ln( \frac{951307}{192157})$
$t= \frac{ln( \frac{951307}{192157}) }{0.051}$
$t=31.36$
We can conclude that if Orlando's population keeps growing at the same rate and Detroit's keeps declining at the same rate, after 31.36 years in May of 2031 Orlando's population will surpass Detroit's population.

E. Since we know that the population of Detroit as 2000 is 951307, twice that population will be $2(951307)=1902614$ . Now we can rewrite our equation as: $N(t)=1902614e^{-0.029t}$ . The last thing we need to do is equate our Orlando's population growth equation with this new one and solve for t:
$192157e^{0.022t} =1902614e^{-0.029t}$
$\frac{192157e^{0.022t} }{1902614e^{-0.029t} } =1$
$e^{0.051t} = \frac{1902614}{192157}$
$ln(e^{0.051t} )=ln( \frac{1902614}{192157} )$
$t= \frac{ln( \frac{1902614}{192157}) }{0.051}$
$t=44.95$
We can conclude that after 45 years in 2045 the population of Orlando will exceed twice the population of Detroit.

8 0

4 years ago

Rksheet

VLD [36.1K]

See below for the terms, coefficients, and constants in the variable expressions

<h3>How to determine the terms, coefficients, and constants in the variable expressions?</h3>

To determine the terms, coefficients, and constants, we use the following instance:

ax + by + c

Where the variables are x and y

Then the terms are ax, by and c
The coefficients are a and b
The constant is c

Using the above as guide, we have:

A) 2b + 2ac+5

Terms: 2b, 2ac, 5
Coefficient: 2, 2 and 5
Constant 5

B) 34abx + 16y +1

Terms: 34abx, 16y, 1
Coefficient: 34ab, 16
Constant: 1

C) st +4u + v

Terms: st, 4u, v
Coefficient: 4

D) 14xy + 6

Terms: 14xy, 6
Coefficient: 14, 6
Constant 6

E) 14x + 12y

Terms: 14x, 12y
Coefficient: 14, 12

F) 3+ 6-7+a

Terms: 3, 6, -7, a
Coefficient: 1
Constant: 3, 6, -7

Read more about terms, coefficients, and constants at:

brainly.com/question/14625487

#SPJ1

5 0

1 year ago

Two 6-sided dice are rolled. what is the probability that the sum of the two numbers on the dice will be greater than 8?

Serhud [2]

Answer: 5/18

Step-by-step explanation:

The sample space when two 6- sided dice are rolled is given below:

(+) 1 2 3 4 5 6

1 2 3 4 5 6 7

2 3 4 5 6 7 8

3 4 5 6 7 8 9

4 5 6 7 8 9 10

5 6 7 8 9 10 11

6 7 8 9 10 11 12

The total sample space is 36.

Sum greater than 8 are : {9,10,11,12}

which are 10 in number:

Therefore : the probability that the sum of the two numbers on the dice will be greater than 8 will be :

number of the sum greater than 8 / Total sample space

That is ;

P(sum greater than 8) = 10/36

P(sum greater than 8) = 5/18

6 0

3 years ago