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2 years ago

3x - 3y = 9 and x + 3y = 12 Elimination

Mathematics

1 answer:

Firlakuza [10]2 years ago

8 0

Answer:

$x=5.25,y=2.25$

Step-by-step explanation:

We can add the two equations to eliminate the variable $y$ and solve for $x$ :

$3x-3y+x+3y=9+12$

$4x=21$

$x=5.25$

Now, we can use substitution to solve for $y$ :

$x+3y=12$ (given)

$5.25+3y=12$

$3y=12-5.25$

$=6.75$

$y=2.25$

Hope this helps :)

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First-order linear differential equations

kkurt [141]

Answer:

$(1)\ logy\ =\ -sint\ +\ c$

$(2)\ log(y+\dfrac{1}{2})\ =\ t^2\ +\ c$

Step-by-step explanation:

1. Given differential equation is

$\dfrac{dy}{dt}+ycost = 0$

$=>\ \dfrac{dy}{dt}\ =\ -ycost$

$=>\ \dfrac{dy}{y}\ =\ -cost dt$

On integrating both sides, we will have

$\int{\dfrac{dy}{y}}\ =\ \int{-cost\ dt}$

$=>\ logy\ =\ -sint\ +\ c$

Hence, the solution of given differential equation can be given by

$logy\ =\ -sint\ +\ c.$

2. Given differential equation,

$\dfrac{dy}{dt}\ -\ 2ty\ =\ t$

$=>\ \dfrac{dy}{dt}\ =\ t\ +\ 2ty$

$=>\ \dfrac{dy}{dt}\ =\ 2t(y+\dfrac{1}{2})$

$=>\ \dfrac{dy}{(y+\dfrac{1}{2})}\ =\ 2t dt$

On integrating both sides, we will have

$\int{\dfrac{dy}{(y+\dfrac{1}{2})}}\ =\ \int{2t dt}$

$=>\ log(y+\dfrac{1}{2})\ =\ 2.\dfrac{t^2}{2}\ + c$

$=>\ log(y+\dfrac{1}{2})\ =\ t^2\ +\ c$

Hence, the solution of given differential equation is

$log(y+\dfrac{1}{2})\ =\ t^2\ +\ c$

8 0

3 years ago

The mixed number -4 1/5 can be written as the improper fraction -19/15 True False

pshichka [43]

The mixed number -4 1/5 can be written as the improper fraction -19/15
It's false

- 4 1/5 = - (20/5 + 1/5) = -21/5

Hope it helps

8 0

2 years ago

Read 2 more answers

A face of a solid is

gtnhenbr [62]

Answer:

The Second Answer , a pattern of two-dimensional shapes that can be folded to form a solid figure . 

3 0

1 year ago

Read 2 more answers

The table below shows two equations:

CaHeK987 [17]

Answer:

The solutions to equation 1 are x = 3, −1.5, and equation 2 has no solution.

Step-by-step explanation:

Rearranging the two equations, you get ...

|4x -3| = 9 . . . . . has two solutions
|2x +3| = -5 . . . . has no solutions (an absolute value cannot be negative)

The above-listed answer is the only one that matches these solution counts.

_____

Testing the above values of x reveals they are, indeed, solutions to Equation 1.

4 0

3 years ago

Read 2 more answers

Please Help!

RUDIKE [14]

Answer:

1. this is the definition of a midpoint - bc the definition of a midpoint is: “If a point is a midpoint of a segment, then it divides that segment into two congruent parts” or “If a point divides a segment into two congruent parts, then it's the midpoint of that segment.”

2. this is the division property of equality -"The division property of equality states that when we divide both sides of an equation by the same non-zero number, the two sides remain equal". so, in this situation we want to isolate x which means dividing both sides by 20. This will keep both sides equal just more simplified ( before, it was 20 and 100, after dividing both sides by 20 it is 1 and 5 which is the same ratio therefore they are still equal)

3. this one's the subtraction property of equality- this property means you can subtract the same number from both sides of an equation and get an equivalent equation. in this situation, they subtracted 15 from both sides to get AB = 30 and it ends being still being equal to AB + 15= 45.

4. this is the symmetric property of equality - "This property states that if a = b, then b = a. That is, we can interchange the sides of an equation, and the equation is still a true statement." "it states that values are still equal no matter which side of the equal sign they're on." That's why its possible for XY=ST and ST=XY

5. this is definition of congruence - which basically states that if a value of one thing is equal to the value of another thing those two things can be called congruent.

6. this is substitution property- this is the property that allows you to substitute one value for another in an equation. the property states that if

x = y, then x can be substituted in for y in any equation, and y can be substituted for x in any equation, just like what they show here with 5AB substituting for CD in the equation.

i hope this helped! im not that good at explaining so if u have more questions lmk!

3 0

2 years ago