Sequence pattern for 2,1,3,7,13,21

Write a system of linear equations.Write two-variable equations in slope-intercept form.

kolbaska11 [484]

Answer:

A linear relation can be written in the slope-intercept form as:

y = a*x + b

Where a is the slope, and b is the y-intercept.

And if a line passes through the points (x₁, y₁) and (x₂, y₂), the slope can be written as:

a = (y₂ - y₁)/(x₂ - x₁)

Now let's look at our lines.

The left one passes through the points (0, -3) and (-2, 0)

Then the slope of this line is:

a = (0 - (-3))/(-2 - 0) = 3/-2 = -(3/2)

Then the line will be something like:

y = -(3/2)*x + b

Knowing that this line passes through the point (0, -3), we know that when x = 0, we must have y = -3

Then:

-3 = (-3/2)*0 + b

-3 = b

So the first linear equation is:

y = -(3/2)*x - 3

Now let's look at the second line, this one passes through the points (0, 2) and (1, 0)

Then the slope of this line is:

a = (0 - 2)/(1 - 0) = -2

And we can write the line as:

y = -2*x + b

Knowing that this line passes through the point (0, 2), we know that when x = 0 we must have y = 0, replacing that we get:

2 = -2*0 + b

2 = b

Then the equation of this line is:

y = -2*x + 2

Now that we know both equations we can write our system as:

y = (-3/2)*x - 3

y = -2*x + 2

To solve it, we need to remember that y = y

then:

(-3/2)*x - 3 = y = -2*x + 2

(-3/2)*x - 3 = -2*x + 2

We can solve this for x.

2*x - (3/2)*x = 2 + 3

(1/2)*x = 5

x = 5((1/2) = 5*2 = 10

And to find the y-value, we need to input this x-value in one of the equations:

y = -2*10 + 2 = -20 + 2 = -18

Then the solution of the system is the point (10, -18)

4 0

3 years ago

△DEF has vertices D (2,2), E (-2,-1), and F (-3,5). Complete the following charts indicating the location of △D′E′F′ and △D″E″F″

blondinia [14]

Reflecting DEF on the y-axis gives the following coordinates of D'E'F' as follows

the coordinate of D' (-2, 2)
the coordinate of E' (2, -1)
the coordinate of F' (3, 5)

Translating D'E'F' by the vector (3, -5) gives the following coordinate of D''E''F'' as follows

the coordinate of D'' (-2+3, 2-5) = (1, -3)
the coordinate of E'' (2+3, -1-5) = (5, -6)
the coordinate of F'' (3+3, 5-5) = (6, 0)

The diagram below shows the transformation of triangle DEF

3 0

3 years ago

How many days are in 48 hours?

erica [24]

48h=2 days.....................

3 0

3 years ago

PLEASE HELP!!!

Ira Lisetskai [31]

Y = –x2 + 4x + 12
y = –3x + 24
so
–x2 + 4x + 12 = –3x + 24

x^2 -7x + 12 = 0
(x - 4)(x - 3) = 0
x - 4 =0; x =4
x - 3 = 0; x= 3

y = –3x + 24 = -3(3) + 24 = -9+24 = 15 (when x = 3)
y = –3x + 24 = -3(4) + 24 = -12+24 = 12 (when x = 4)

answer
(3, 15) and (4, 12)

4 0

4 years ago

Read 2 more answers

Zareena has 24 minutes to work on her math homework and each problem is taking g her 2/3 of a minute on average to complete whic

adelina 88 [10]

Answer:

16

Step-by-step explanation:

if it takes her 2/3 a minute then

24 divided by 2/3 is the answer

3 0

3 years ago