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3 years ago

The line 2x + 5y = 1 meets the curve x² + 5xy - 4y² + 10 = 0 at the points A and B

Mathematics

1 answer:

lys-0071 [83]3 years ago

7 0

Answer:

A(3,-1) and B( -2,1)

Step-by-step explanation:

2x+5y=1. , or. y=(1–2x)/5………….(1)

x^2+5xy-4y^2+10=0…………………..(2)

Putting y=(1–2x)/5 from eqn. (1)

x^2+5x.(1–2x)/5–4/25.(1–2x)^2 +10=0

or. 25x^2+25x.(1–2x)-4.(1+4x^2–4x)+250 = 0

or. 25x^2+25x-50x^2–4–16x^2+16x+250=0

or. 41x^2–41x-246=0

or x^2– x - 6=0

or. (x-3).(x+2)=0

=> x= 3 or -2

But y=(1–2x)/5

=> y= (1–6)/5 or. (1+4)/5

hence, y= -1. or. 1

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The length of a rectangle is 5 centimeters more than the width. The area of the rectangle is 36 centimeters. What is the length?

UNO [17]

We can represent the width as x and the length as x+5. Then we can make the area formula A=(x)*(x+5), plug in 36 for A, and solve for x

36=x^2+5x (distribute)
0=x^2+5x-36
0=(x+9)(x-4)
So x=-9 and 4 but dimensions can't be negative so x=4

So if the width is 4, then the length is 9 (4+5)

Hope this helps :)

3 0

3 years ago

Read 2 more answers

Please help what is it

Serggg [28]

Answer: $4\sqrt{2}$ , 5.6

Or rounded it would be 6.

I hope I did this right. :)

6 0

3 years ago

(2x+1)/2=(x+2)/5<br><br>if possible can you show me step by step how to get the answer <br>

katrin2010 [14]

Answer:

$\boxed{\bold{Decimal \ Form: \ x \ = \ -0.125}}$

$\boxed{\bold{Fraction \ Form:x=-\frac{1}{8}}}$

Step By Step Explanation:

Apply Fraction Cross Multiply: If $\bold{\frac{a}{b}=\frac{c}{d}:then\ a\cdot \:d=b\cdot \:c}$

$\bold{\left(2x+1\right)\cdot \:5=2\left(x+2\right)}$

$\bold{\left(2x+1\right)\cdot \:5: \ 10x+5}$

$\bold{2\left(x+2\right): \ 2x+4}$

$\bold{10x+5=2x+4}$

Subtract 4 From Both Sides

$\bold{10x+5-5=2x+4-5}$

Simplify

$\bold{10x=2x-1}$

Subtract 2x From Both Sides

$\bold{10x-2x=2x-1-2x}$

Simplify

$\bold{8x=-1}$

Divide Both Sides By 8

$\bold{\frac{8x}{8}=\frac{-1}{8}}$

Simplify

$\bold{x=-\frac{1}{8}}$

Turn Fraction Into Decimal

$\bold{-1 \ \div \ 8 \ = \ -0.125}$

$\bold{-0.125}$

Regards,

Mordancy

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3 years ago

Hue is arranging chairs. She can form 5 rows of a given length with 2 chairs left over, or 7 rows of that same length if she get

Andru [333]

I just took the 16 chairs and added 2 since thats how many are left over, then since adding these 16 chairs, you are creating 2 more rows, so (16+2)/2 =9 Therefore, each row must have nine chairs in it and Hue starts off with 5x9+2= 47 chairs

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3 years ago

The length of a rectangle is 4 units shorter than half the width. If the length of the rectangle is 18 units, which equation can

sergey [27]

Answer:

A or the top option

Step-by-step explanation:

I used process of elimination

B simply does not work because in order for 4 to be subtracted by another number to equal 18, that number (width) would have to be negative

C also isn't correct since if it was solved out, we would add four to both sides, making the left side equal to w/2 + 4 which isn't what we want because the length is 4 shorter, not longer

D can be dealt with in the same way, by adding w/2 on both sides, making the left side 4 + w/2, the same as the previous option.

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3 years ago