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MrRissso [65]
2 years ago
7

Determine the number of real solutions for each of the given equations. Equation Number of Solutions y = -3x2 + x + 12 y = 2x2 -

6x + 5 y = x2 + 7x - 11 y = -x2 - 8x - 16 R
Mathematics
1 answer:
rosijanka [135]2 years ago
7 0

Answer:

Step-by-step explanation:

Our equations are

y = -3x^2 + x + 12\\y = 2x^2 - 6x + 5\\y = x^2 + 7x - 11\\y = -x^2 - 8x - 16\\

Let us understand the term Discriminant of a quadratic equation and its properties

Discriminant is denoted by  D and its formula is

D=b^2-4ac\\

Where

a= the coefficient of the x^{2}

b= the coefficient of x

c = constant term

Properties of D: If D

i) D=0 , One real root

ii) D>0 , Two real roots

iii) D<0 , no real root

Hence in the given quadratic equations , we will find the values of D Discriminant  and evaluate our answer accordingly .

Let us start with

y = -3x^2 + x + 12\\a=-3 , b =1 , c =12\\D=1^2-4*(-3)*(12)\\D=1+144\\D=145\\D>0 \\

Hence we have two real roots for this equation.

y = 2x^2 - 6x + 5\\

y = 2x^2 - 6x + 5\\a=2,b=-6,c=5\\D=(-6)^2-4*2*5\\D=36-40\\D=-4\\D

Hence we do not have any real root for this quadratic

y = x^2 + 7x - 11\\a=1,b=7,-11\\D=7^2-4*1*(-11)\\D=49+44\\D=93\\

Hence D>0 and thus we have two real roots for this equation.

y = -x^2 - 8x - 16\\a=-1,b=-8,c=-16\\D=(-8)^2-4*(-1)*(-16)\\D=64-64\\D=0\\

Hence we have one real root to this quadratic equation.

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Is (2,1) a solution of 3y&lt;2x+5
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Answer:

No

Step-by-step explanation:

Plug in the x and y values and you should get 3<9

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A jar contains 2 red and 4 blue marbles. A marble is drawn from the jar. What is the probability that a red marble will be drawn
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Salutations!

<span>A jar contains 2 red and 4 blue marbles. A marble is drawn from the jar. What is the probability that a red marble will be drawn?

So lets solve this! 

Probability is an event of chance; an occurrence of chance.

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Hope I helped :D
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5 0
3 years ago
Read 2 more answers
What is this function written in vertex form? f(x) = (x –1)2 – 7 f(x) = (x 1)2 – 7 f(x) = (x –1)2 – 5 f(x) = (x 1)2 – 5
Maslowich

The vertex form of all expressions is given below.

We have given that the expressions

We have to write the function in vertex form.

<h3>What is the vertex form of the equation?</h3>

The vertex form of a quadratic function is given by f (x) = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.

Therefore the first equation

f(x)=(x-1)^2-7

it can be written as

f(x)=1(x-1)^2+(-7)

The second equation can be written as

f(x) = (x+1)^2 -7

vertex for is,

f(x)=1(x-(-1))^2+(-7)

The third equation is,

f(x) = (x -1)^2 - 5

Vertex form is,

f(x)=1(x-1)^2+(-5)

Forth equation is,

f(x) = (x +1)^2 +(- 5)

Vertex form is,

f(x) =1 (x -(-1))^2 +(- 5)

To learn more about the vertex form visit:

brainly.com/question/17987697

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2 years ago
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Answer: Do you wanna go out with me

Step-by-step explanation:

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