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2 years ago

Write the equation of a line with the given slope and y intercept. m = 4 b = -2

Mathematics

1 answer:

Westkost [7]2 years ago

7 0

Answer: y=4x-2

Step-by-step explanation:

Use the y=mx+b template to write the equation out. M is the slope which should be in front of x. This is why y=4x-2 is correct

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Simplify expressions 2a+3+a+4

Norma-Jean [14]

3a plus 7. you group the whole numbers together and than the a's. so 3+4 is 7. 2a + a is 3a.

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2 years ago

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brilliants [131]

Answer:

(a) x=2, y=-1

(b) x=2, y=2

(c) $\displaystyle x=\frac{5}{2}, y=\frac{5}{4}$

(d) x=-2, y=-7

Step-by-step explanation:

Cramer's Rule

It's a predetermined sequence of steps to solve a system of equations. It's a preferred technique to be implemented in automatic digital solutions because it's easy to structure and generalize.

It uses the concept of determinants, as explained below. Suppose we have a 2x2 system of equations like:

$\displaystyle \left \{ {{ax+by=p} \atop {cx+dy=q}} \right.$

We call the determinant of the system

$\Delta=\begin{vmatrix}a &b \\c &d \end{vmatrix}$

We also define:

$\Delta_x=\begin{vmatrix}p &b \\q &d \end{vmatrix}$

And

$\Delta_y=\begin{vmatrix}a &p \\c &q \end{vmatrix}$

The solution for x and y is

$\displaystyle x=\frac{\Delta_x}{\Delta}$

$\displaystyle y=\frac{\Delta_y}{\Delta}$

(a) The system to solve is

$\displaystyle \left \{ {{x+y=1} \atop {x-2y=4}} \right.$

Calculating:

$\Delta=\begin{vmatrix}1 &1 \\1 &-2 \end{vmatrix}=-2-1=-3$

$\Delta_x=\begin{vmatrix}1 &1 \\4 &-2 \end{vmatrix}=-2-4=-6$

$\Delta_y=\begin{vmatrix}1 &1 \\1 &4 \end{vmatrix}=4-3=3$

$\displaystyle x=\frac{\Delta_x}{\Delta}=\frac{-6}{-3}=2$

$\displaystyle y=\frac{\Delta_y}{\Delta}=\frac{3}{-3}=-1$

The solution is x=2, y=-1

(b) The system to solve is

$\displaystyle \left \{ {{4x-y=6} \atop {x-y=0}} \right.$

Calculating:

$\Delta=\begin{vmatrix}4 &-1 \\1 &-1 \end{vmatrix}=-4+1=-3$

$\Delta_x=\begin{vmatrix}6 &-1 \\0 &-1 \end{vmatrix}=-6-0=-6$

$\Delta_y=\begin{vmatrix}4 &6 \\1 &0 \end{vmatrix}=0-6=-6$

$\displaystyle x=\frac{\Delta_x}{\Delta}=\frac{-6}{-3}=2$

$\displaystyle y=\frac{\Delta_y}{\Delta}=\frac{-6}{-3}=2$

The solution is x=2, y=2

$\displaystyle \left \{ {{-x+2y=0} \atop {x+2y=5}} \right.$

Calculating:

$\Delta=\begin{vmatrix}-1 &2 \\1 &2 \end{vmatrix}=-2-2=-4$

$\Delta_x=\begin{vmatrix}0 &2 \\5 &2 \end{vmatrix}=0-10=-10$

$\Delta_y=\begin{vmatrix}-1 &0 \\1 &5 \end{vmatrix}=-5-0=-5$

$\displaystyle x=\frac{\Delta_x}{\Delta}=\frac{-10}{-4}=\frac{5}{2}$

$\displaystyle y=\frac{\Delta_y}{\Delta}=\frac{-5}{-4}=\frac{5}{4}$

The solution is

$\displaystyle x=\frac{5}{2}, y=\frac{5}{4}$

(d) The system to solve is

$\displaystyle \left \{ {{6x-y=-5} \atop {4x-2y=6}} \right.$

Calculating:

$\Delta=\begin{vmatrix}6 &-1 \\4 &-2 \end{vmatrix}=-12+4=-8$

$\Delta_x=\begin{vmatrix}-5 &-1 \\6 &-2 \end{vmatrix}=10+6=16$

$\Delta_y=\begin{vmatrix}6 &-5 \\4 &6 \end{vmatrix}=36+20=56$

$\displaystyle x=\frac{\Delta_x}{\Delta}=\frac{16}{-8}=-2$

$\displaystyle y=\frac{\Delta_y}{\Delta}=\frac{56}{-8}=-7$

The solution is x=-2, y=-7

4 0

2 years ago

3 2/5 + 9 1/10= Simplest form

Talja [164]

Change each mixed fraction to improper

3 2/5 = 15/5 + 2/5 = 17/5

9 1/10 = 90/10 + 1/10 = 91/10

Find a common denominator. Multiply 2 to both numerator and denominator of 17/5

17/5(2/2) = 34/10

34/10 + 91/10 = 125/10

125/10

Simplify. Divide

125/10 = 12.5

12.5 is your answer

hope this helps

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2 years ago

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There is 1/ 3 gallon of water in a 3-gallon container. What fraction of the container is filled?

kolbaska11 [484]

Step-by-step explanation:

2/3 gallons is empty

1/3 gallons is filled

3*1/3= 1

1 gallon filled

6 0

2 years ago

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-4+(5+6/-6×5)-2 extra stuff to ask question

natta225 [31]

Answer:

Step-by-step explanation:

-4 + (5+6/ -6 × 5) -2

Solve the brackets first!

-4 + (11/ -30) -2

Add the -4 and -2

-6 + (-11/30)

[If you meant -2 multiplied by (-11/30) then , something like this, If not then continue after the bracket!:

-4 + (11/15)

(-60+11)/15

-49/15 Answer ]

Now,

-6 -11/30

(-180-11)/30

-191/30

Hope this helps!

Please mark brainliest! Would really appreciate!

7 0

2 years ago

Write the equation of a line with the given slope and y intercept. m = 4 b = -2​

Write the equation of a line with the given slope and y intercept. m = 4 b = -2