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2 years ago

Find the simultaneous equation x-2y=1,y^2-3xy+8=0

Mathematics

1 answer:

Hitman42 [59]2 years ago

5 0

Answer:

(-2.2, -1.6), (3, 1)

Step-by-step explanation:

You don't have to go far to find the equations. They are right there in your problem statement. Perhaps you want to find the solutions to the equations.

Use the first equation to write an expression for x, then substitute that into the second equation:

x = 2y +1

y^2 -3(2y+1)(y) +8 = 0

-5y^2 -3y +8 = 0

-(5y +8)(y -1) = 0

y = -8/5 or y = 1

The corresponding values of x are ...

x = 2(-8/5)+1 = -11/5

x = 2(1) +1 = 3

The solutions are (x, y) = (-2.2, -1.6) and (3, 1).

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You need 660 mL of a 40% alcohol solution. On hand, you have 35% alcohol mixture. You also have a 95% alcohol mixture. How much

ozzi

Answer:

A. 605 mL of the 35% solution

B. 55 mL of the 95% solution

Step-by-step explanation:

It is given that, you need 660 mL of a 40% alcohol solution. On hand, you have 35% alcohol mixture. You also have a 95% alcohol mixture.

Let x and y be the amount of 35% alcohol solution and 95% alcohol solution (in mL) respectively.

So,

Amount equation: $x+y=660$ ...(1)

Alcohol equation : $0.35x+0.95y=0.40(660)\Rightarrow 0.35x+0.95y=264$ ...(2)

On solving (1) and (2), we get

$0.35(660-y)+0.95y=264$

$231-0.35y+0.95y=264$

$0.6y=264-231$

$y=\dfrac{33}{0.6}$

$y=55$

Now, substitute y=55 in (1).

$x+55=660$

$x=660-55$

$x=605$

Therefore, we need 605 mL of the 35% solution and 55 mL of the 95% solution.

4 0

2 years ago

Please please help me out with this problem

Hatshy [7]

Answer:

y = 3x - 4

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, - 4) and (x₂, y₂ ) = (2, 2) ← 2 points on the line

m = $\frac{2+4}{2-0}$ = $\frac{6}{2}$ = 3

Note the line crosses the y- axis at (0, - 4) ⇒ c = - 4

y = 3x - 4 ← equation of line

6 0

3 years ago

maria bought 7 boxes. a week later half of all her boxes were destroyed in a fire. there are now only 22 boxes left. with how ma

VashaNatasha [74]

Answer:

Step-by-step explanation:

x=22+7

x=29

8 0

2 years ago

Read 2 more answers

Prove that the value of the expression does not depend on the variable x:

Leviafan [203]

Answer:

See below

Step-by-step explanation:

If an expression is not dependent on x, it simplified form must not contain x. To show that this is the case for (a) and (b) we need to simplify them and assess:

(a)

$(x-5)(x+8)-(x+4)(x-1)=\\=x^2-5x+8x-40-x^2-4x+x+4=-36$