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SCORPION-xisa [38]
3 years ago
5

Write the equation of a line that passes through (2,6) and (-2,2)

Mathematics
1 answer:
Viktor [21]3 years ago
5 0

Answer:

y = x + 4

Step-by-step explanation:

The equation of the line is

y = mx + c

Step 1: find the slope

m = y2 - y1 / x2 - x1

Give points

( 2 , 6) ( -2 ,2)

x1 = 2

y1 = 6

x2 = -2

y2 = 2

m = 2 - 6 / -2 - 2

m = -4 / -4

m = 1

y = mx + c

y = 1x + c

y = x + c

Step 2: sub any of the two points given into the equation

( 2 , 6)

x = 2

y = 6

y = x + c

6 = 2 + c

6 - 2 = c

c = 4

Step 3: sub c into the equation

y = x + 4

The equation of the line is

y = x + 4

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You are constructing a cardboard box from a piece of cardboard with the dimensions 2 m by 4 m. You then cut equal-size squares f
postnew [5]

Answer:

Dimensions:

l =3,15 m

w=1,15 m

x= 0,42 m   (height)

V(max) = 1,52 m³

Step-by-step explanation:

The cardboard is L = 4 m   and   W = 2 m

Let call x the length of the square to cut in each corner, then, volume of open box is:

For the side L       is  L - 2*x               l =  4 - 2*x

For the side W      is  W - 2*x             w=  2 - 2*x

The height              is  x

Volume of the open box, as function of x is:

V(x) = ( 4 -2x) * ( 2 - 2x) *x    ⇒  V(x) = ( 8 - 8x -4x + 4x²) *x

V(x) = ( 8 -12x + 4x² )*x     V(x) = 8x - 12x² + 4x³

V(x) = 8x - 12x² + 4x³

Taking derivatives on both sides of the equation

V´(x) = 8 - 24x + 12x²

V´(x) = 0       8  - 24x + 12x² = 0     reordering    12x² - 24x + 8  = 0

or    3x² - 6x + 2 = 0

A second degree equation. Solving for x

x₁,₂  = ( 6 ± √36 - 24 ) /6

x₁,₂  = ( 6 ± 3.46) /6

x₁  =  6 + 3,46 /6     x₁  = 1.58  we dismiss such solution because 1,58 * 2 = 3,15 and is bigger than 2 one of the side of the cardboard

x₂  =( 6 - 3,46 ) / 6

x₂  = 0,42 m

Dimensions of the open box

l  = 4 - 2*x     l  = 4 - 0,85      l  =  3,15 m

w = 2 -2*x    w  = 2 - 0,85     w = 1,15 m

x = 0,42 m

V(max) =3,15*1,15*0,42

V(max) = 1,52 m³

8 0
3 years ago
QUESTION 14
Mice21 [21]

Answer: I think It's D

Step-by-step explanation: Comment if im right or wrong please

7 0
3 years ago
The following box plot shows the number of books sold each day at a store for 80 days. How many days did the bookstore sell 2 to
ddd [48]

Answer:

882

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
How many solutions?<br><br> y = 5(x – 4)<br> 4x + 12 = -y
kakasveta [241]

Answer:

One solution, x = 8/9

Step-by-step explanation:

One way to solve this is to take one equation and substitute into the other and then solve. So, take y=5(x-4) and put that into the other equation.

4x + 12 = -y

4x + 12 = -(5(x-4))       <--- substitution here

4x + 12 = -5(x-4)

4x + 12 = -5x + 20     <-- simplifying

4x + 5x = 20 - 12

9x = 8

x = 8/9

4 0
2 years ago
Some people believe that second born subjects are more intelligent (higher IQ test). Given the data, your job is to perform the
nexus9112 [7]

Answer:

C

Step-by-step explanation:

When to use regression test?

  • This is done to find the relationship between 2 variables. One dependent and one independent.

When to use Multiple regression test?

  • Extension of regression test. It is used to predict value of 1 variable when it depends on 2-3 other variables. Multivariable, basically.

When to use 1-sided t-test?

  • We check for possibility of relationship of something from one side. 1 side effect. With a hypothesis and its alternate.

When to use 2-sided t-test?

  • This is same as 1-tailed but it looks for possibility from 2sides. A hypothesis and alternate, whether less or more.

Now, Options A and B are not right since we aren't comparing 2 variables here. People believe second born subjects are more intelligent. We have to perform a test to see whether this is true or not. One sided answer. So, we will use One-sided t-test.

6 0
3 years ago
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