All categories

2 years ago

What are the solutions of the following system? -2x^2 + y=-5 y=-3x^2+5

Mathematics

2 answers:

Ray Of Light [21]2 years ago

8 0

Answer:

Step-by-step explanation:

Doss [256]2 years ago

5 0

$\begin{cases}-2x^2+y=-5\\y=-3x^2+5\end{cases}\\\\\\
-2x^2+(-3x^2+5)=-5\\\\
-2x^2-3x^2+5=-5\quad|-5\\\\-5x^2=-10\quad|:(-5)\\\\x^2=2\\\\
\boxed{x=-\sqrt{2}\qquad\vee\qquad x=\sqrt{2}}\\\\\\
y=-3x^2+5\qquad\vee\qquad y=-3x^2+5\\\\
y=-3(-\sqrt{2})^2+5\qquad\vee\qquad y=-3(\sqrt{2})^2+5\\\\
y=-3\cdot2+5\qquad\vee\qquad y=-3\cdot 2+5\\\\
y=-6+5\qquad\vee\qquad y=-6+5\\\\
\boxed{y=-1\qquad\vee\qquad y=-1}\\\\\\
\begin{cases}x=-\sqrt{2}\\y=-1\end{cases}\qquad\vee\qquad\begin{cases}x=\sqrt{2}\\y=-1\end{cases}$

Answer C.

You might be interested in

Part 2: Solve the following word problem. Show all work to receive full credit..

lys-0071 [83]

The numerical representation and final elevation of the fish relative to sea level are :

Final position = -13.52 + 7.8
Final position = - 5.72

Given the Parameters :

Initial depth of fish = - 13.52

Change in elevation of fish = 7.8 feets

Positions below sea level are represented as negative values (-) ;

Hence, initial position of fish = - 13.52

Change in position = Rise in depth of 7.8 feets

The numerical representation of the final position of the fish can be written thus :

Final position = Initial position + change in position

Final position = - 13.52 + 7.8

Hence, the final position of the fish will be :

Final position of fish = -13.52 + 7.8 = - 5.72

Learn more : brainly.com/question/18109354

6 0

2 years ago

Read 2 more answers

One brother says of his younger brother: “Two years ago, I was three times as old as my brother was. In three years’ time, I wil

aleksklad [387]

Answer:

Step-by-step explanation:

Let us suppose two years ago my brother's age was x years

Then, my age was 3x

Three years from now, my brother's age will be (x +2+3) = (x+5) years

And my age will be (3x+2+3) = (3x+5) years

But it is given that i will be twice as old as my brother.

So, 2(x+5)= (3x+5)

or, x= 5 years

So my brother's present age is 5+2= 7 years

And my age is 5*3+2= 17 years

5 0

3 years ago

Read 2 more answers

What is the 6th term of the geometric sequence 4, −20, 100, ...?

shtirl [24]

Let's calculate r of this G.P: (-20)/(4) = - 5(100)/(-20) = - 5So r = -5
The formula to find the nth term of a GP is;
a(n) = a(r)ⁿ⁻¹
a₆ = a(r)⁶⁻¹
a₆ = 4(-5)⁵ = -12500

3 0

3 years ago

Read 2 more answers

Can someone please help i am very stuck :

Oliga [24]

The answer is
the first one is x= 18.98
a^2+b^2=c^2
8 cm^2+17 cm^2= x^2
64+289=x^2
√x^2= √353
x=18.89
the second one is x= 18.7
a^2+b^2=c^2
7 m^2+ x^2= 20 m^2
49 m+x^2=400 m
-49 -49
√x^2=√352
x= 18.7
Hope this helps!

5 0

2 years ago

Jake has a rectangular garden that measures 12 feet by 14 feet. He wants to increase the area by 50% and plans to increase each

emmasim [6.3K]

In order to increase the area of a rectangular garden that measures 12 feet by 14 feet by 50% Jake must increase each dimension by equal lengths, x:

$x\approx 2.9ft$

<h2>Explanation:</h2><h2 />

First of all, let's calculate the area of the original rectangular garden:

$A=b\times h \\ \\ b:base \\ \\ h:height \\ \\ \\ b=12ft \\ \\ h=14ft \\ \\ \\ A=12(14) \\ \\ A=168ft^2$

Jake wants to increase the area by 50%, so the new area would be:

$A'=168(1.5) \\ \\ A'=252ft^2$

He wants to increase the area by 50% and plans to increase each dimension by equal lengths, x, so this is represented by the figure below, therefore:

$(12+x)(14+x)=252 \\ \\ 168+12x+14x+x^2-252=0 \\ \\ x^2+26x-84=0 \\ \\ \\ Using \ quadratic \ formula: \\ \\ x=\frac{-b \pm \sqrt{b^2-4ac}}{2a} \\ \\ a=1 \\ \\ b=26 \\ \\ c=-84 \\ \\ \\ x=\frac{-26 \pm \sqrt{26^2-4(1)(-84)}}{2(1)} \\ \\ x=\frac{-26 \pm \sqrt{1012}}{2} \\ \\ \\ Two \ solutions: \\ \\ x_{1}=-13+\sqrt{253} \approx 2.9\\ \\ x_{2}=-13-\sqrt{253} \approx -28.9 \\ \\ x_{2} \ is \ discarded \ because \ it \ can't \ be \ negatives$

Finally:

In order to increase the area of a rectangular garden that measures 12 feet by 14 feet by 50% Jake must increase each dimension by equal lengths, x:

$x\approx 2.9ft$

<h2>Learn more:</h2>

Dilation: brainly.com/question/10945890

#LearnWithBrainly

6 0

2 years ago