Ask question

Ask question

All categories

3 years ago

11

Complete the equation of the line through (1,4)(1,4)left parenthesis, 1, comma, 4, right parenthesis and (2,2)(2,2)left parenthe

sis, 2, comma, 2, right parenthesis.

2 answers:

PolarNik [594]3 years ago

6 0

Answer:

The answer is y = -2x + 6

Step-by-step explanation:

Complete Question:

Complete the equation of the line through (1,4) and (2,2)

Answer: y = -2x + 6

Hope this helps! :)

Ivahew [28]3 years ago

5 0

Answer:

$y = -2x + 6$

Step-by-step explanation:

Given

$(x_1,y_1) = (1,4)$

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

Required

Determine the line equation

First, we calculate the slope (m) using

$m = \frac{y_2 - y_1}{x_2 - x_1}$

$m = \frac{2-4}{2-1}\\$

$m = \frac{-2}{1}$

$m = -2$

The equation is then calculated using:

$y - y_1 = m(x - x_1)$

$y - 4 = -2(x - 1)$

Open bracket

$y - 4 = -2x + 2$

$y = -2x + 2 + 4$

$y = -2x + 6$

You might be interested in

The coordinates of polygon ABCD are A(-4,-1), B(-2,3), C(2,2), and D(4,-3). Use these coordinates to complete the sentences belo

oee [108]

Answer:

The perimeter of polygon ABCD, to the nearest thousandth units is

22.227 units

The perimeter of polygon ABCD', to the nearest thousandth, would be 20.980 units

The area of polygon ABCD' is 19.5 units²

Step-by-step explanation:

The coordinates forming the polygon are

A (-4,-1), B(-2,3), C(2,2), and D(4,-3)

The perimeter then is given by the sum of the length of the sides as follows;

Length of line between two X and Y points distance, xi and yj apart is

length XY = $\sqrt{x^2+y^2}$

Therefore, the length between points AB is

length AB = $\sqrt{(-4 - (-2))^2+(-1-3)^2}$

= $\sqrt{(-4 +2)^2+(-4)^2} = \sqrt{-2^2+-4^2} = \sqrt{20}$ = 4.472 units

Similarly, length BC is given by

Length BC = $\sqrt{(-4)^2+1^2} = \sqrt{17}$ = 4.123 units

Length CD = $\sqrt{(-2)^2+5^2} = \sqrt{29}$ = 5.385 units

Length DA = $\sqrt{(8)^2+(-2)^2} = \sqrt{68}$ = 8.246 units

The perimeter is equal to;

length AB + Length BC + Length CD + Length DA

= 4.472 + 4.123 + 5.385 + 8.246 = 22.227 units

If the point D is moved up 2 units and left 1 unit we have

D' = x-1, y+2 where x and y are the coordinates of point D

D(4, -3) → D'((4-1), (-3+2)) = D'(3, -1)

The length D'A = $\sqrt{(7)^2+(0)^2} = \sqrt{49}$ =7 units

The perimeter of polygon ABCD'

length AB + Length BC + Length CD + Length D'A

= 4.472 + 4.123 + 5.385 + 7 = 20.980 units.

The area is given by the determinant of the 3 by 3 matrix using Cramer's Rule as follows

$S_{\bigtriangleup}$ = $(\frac{1}{2})|x_1y_2+x_2y_3+x_3y_1-x_1y_3-x_2y_1-x_3y_2|$

= $(\frac{1}{2})|x_1(y_2-y_3)+x_2(y_3-y_1) +x_3(y_1-y_2)|$

Triangle ABC we have

A(-4,-1)

B(-2,3)

C(2,2)

$S_{{\bigtriangleup}ABC}$ = $(\frac{1}{2})|x_1(y_2-y_3)+x_2(y_3-y_1) +x_3(y_1-y_2)|$

$=(\frac{1}{2})|(-4)(3-2)+(-2)(2-(-1)) +2((-1)-3)|$

= $=(\frac{1}{2})|-4-6 -8|= 9 units^2$

Triangle ACD'

A(-4,-1)

C(2,2)

D'(3, -1)

$S_{{\bigtriangleup}ACD'}$ = $(\frac{1}{2})|x_1(y_2-y_3)+x_2(y_3-y_1) +x_3(y_1-y_2)|$

$=(\frac{1}{2})|(-4)(2+1)+(2)(-1+1) +3((-1)-2)| = \frac{21}{2}$ = 10.5 units²

Area of polygon = $S_{{\bigtriangleup}ABCD'}$ = $S_{{\bigtriangleup}ABC}$ + $S_{{\bigtriangleup}ACD'}$ = (9 + 10.5) units²

Area of polygon ABCD' = 19.5 units².

7 0

3 years ago

WILL MARK BRAINLIEST!!!!PLZ HELP!!!! An expression is shown below: 3pf2 − 21p2f + 6pf − 42p2 Part A: Rewrite the expression by f

Lesechka [4]

Answer:

See below.

Step-by-step explanation:

So, we have:

$3pf^2-21p^2f+6pf-42p^2$

PART A:

Find the GCF. Notice that we have a 3 in every term and a p in every term. Thus, the GCF is 3p:

$3p(f^2-7pf+2f-14p)$

This is the most we can do.

PART B:

Continue from where we left off. Factor the entire expression:

$3p(f^2-7pf+2f-14p)\\3p(f(f-7p)+2(f-7p))\\3p((f+2)(f-7p))$

7 0

3 years ago

For f (x) = 4 x +1 and g(x) = x^2- 5, find (g/f)(x)

Lady bird [3.3K]

Answer:

The answer is: $\frac{x^2-5}{4x+1}$

Step-by-step explanation:

We are given: $f(x)=4x+1$ and $g(x) = x^2-5$

We need to find $(g/f)(x)$ .

Simply divide $g(x)$ and $f(x)\\$ .

Which equates to:

$(g/f)(x)= \frac{g(x)}{f(x)} =\frac{x^2-5}{4x+1}$

This cannot be simplified further, so it is the answer.

3 0

3 years ago

Caroline is going to the state fair with a group of friends. It costs her $12 for admission, and once she is inside the fair she

ioda

Answer:

a) y=0.75x+12 (y=ax+b)

b)a=0.75

c)b=12 (b=y-intercept, the place where the graph hits the Y axis). It's the starting cost, the cost that will be paid only one time

d) starts at (0,12) and goes up +0.75 each time

4 0

3 years ago

Read 2 more answers

Help me solve this algebra 1 question number 10

Anna [14]

Answer:

x=4/7

Step-by-step explanation:

You can write 36^4x-1=6^x+2 to 6^2(4x-1)=6^x+2. Then you can write

2(4x-1)=x+2, 8x-2=x+2, 7x=4, x=4/7

6 0

3 years ago