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2 years ago

A curve has equation y x = + 2 5 y and a line has equation 2 5 x y + = 1.

Mathematics

1 answer:

wlad13 [49]2 years ago

4 0

Answer:

Watch DIm

Step-by-step explanation:

Watch dim channel

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Help math look at pic

Sloan [31]

Answer: $\Large\boxed{(-4,~-3)~\text{and}~(-2,~1)}$

Step-by-step explanation:

Given the system of equation

$1)~y=-(x+2)^2+1$

$2)~y=2x+5$

Expand the parenthesis of the 1) equation

$y=-(x+2)^2+1$

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

$y=-x^2-4x-4+1$

$y=-x^2-4x-3$

Current System

$1)~y=-x^2-4x-3$

$2)~y=2x+5$

Substitute the y value of the 1) equation with the 2) equation

$2x+5=-x^2-4x-3$

Add ( x² + 4x + 3) on both sides

$2x+5+(x^2+4x+3)=-x^2-4x-3+(x^2+4x+3)$

$2x+5+x^2+4x+3=0$

Combine like terms

$x^2+2x+4x+5+3=0$

$x^2+6x+8=0$

Factorize the quadratic equation

$(x+4)(x+2)=0$

$x=-4~\text{or}~x=-2$

Substitute the x values into one of the equations to find the y value

$y=2x+5$

$y=2(-4)+5=-8+5=-3$

$y=2(-2)+5=-4+5=1$

Therefore, the two solutions are:

$\Large\boxed{(-4,~-3)~\text{and}~(-2,~1)}$

Hope this helps!! :)

Please let me know if you have any questions

8 0

2 years ago

A Walgreens purchase comes to $28. Find the total cost if a 2% sales tax is included.

OverLord2011 [107]

Answer:

The answer is $28.56

Step-by-step explanation:

To find the 2% sales tax, you need to multiply the 2% or 0.02 by 28.

Doing this will give you 0.56.

Then you add 0.56 to 28 to get 28.56, hence, $28.56 is the total cost.

Hope it helps!

4 0

3 years ago

The legth of a rectangle is the same as the legth of each side of a square. The legth rectangle is 4 cm more than 3 times the wi

ankoles [38]

Let, length and breadth of rectangle is L and B respectively.

It is given that :

The length rectangle is 4 cm more than 3 times the width of the rectangle.

L = 3B + 4 ......1 )

Also, area of square = area of the rectangle + 66

L² = LB + 66

Putting value of L from

L² = ( 3B + 4 )( B ) + 66

L² = 3B² + 4B + 66

( 3B + 4 )² = 3B² + 4B + 66

9B² + 16 + 24B = 3B² + 4B + 66

6B² + 20B - 50 = 0

3B² + 10B - 25 = 0

3B² + 15B - 5B -25 = 0

3B( B + 5 ) -5( B + 5 ) = 0

B = 5/3 units

L = 3( 5/3 ) + 4

L = 5 + 4 = 9 units

Hence, this is the required solution.

6 0

3 years ago

the utilities bill for the Miller's' house in April was $132. forty two percent of the bill was for gas, and the rest was for el

Lynna [10]

Hey You!

132*42% = 55.44

132 - 55.44 = 76.56

So, the Millers paid $55.44 for gas and $76.56 for electricity.

4 0

3 years ago

Read 2 more answers

How do I solve this problem

bija089 [108]

Attach a photo so we can see the problem

4 0

3 years ago