is (0,0) a solution to this system y> x2+x-4 y <x2+2x+1

Question

oreoluwae oreoluwae

07-04-2018
Mathematics

contestada

is (0,0) a solution to this system y> x2+x-4 y <x2+2x+1

is 00 a solution to this system ygt x2x4 y ltx22x1 class=

Respuesta :

Otras preguntas

Divide. (4x²+22x+31)+ (2x+5) Your answer should give the quotient and the remainder.

A compound of carbon and hydrogen and oxygen (ethylene glycol- antifreeze) is determined to be 38. 7% C, 51. 6% O, and 9. 7% H. Calculate the molecular formula

How did the Dust Bowl disaster during the 1930's affect population density? A. Population density lowered in the Midwest, but increased out West. B. Only Califo

Did I do this right?

the process where an external qualitative methodology or topic area specialists (such as subject matter experts) are asked to review the research analysis is kn

Find a polynomial function f with real coefficients that satisfies the given conditions. leading coefficient a= -1, degree n= 3, Zeros include -4 and -1i. f(x)

what reasons did explorers have for traveling north

What are two types of prewritting?

the four elements of comparison used in the sales comparison approach include the terms and time of sale, as well as location and physical elements about the pr

A different mass of sodium hydroxide was used to make another 25.0 cm' solution. 35.0 cm' of 0.250 mol/dm' hydrochloric acid was required to neutralise this sol

calculista calculista · Answer 1 · 2019-11-18T22:45:40+01:00

Answer:

Yes, the ordered pair (0,0) is a solution of the system

Step-by-step explanation:

we have

[tex]y\geq x^{2}+x-4[/tex] ----> inequality A

[tex]y < x^{2} +2x+1[/tex] ----> inequality B

we know that

If a ordered pair is a solution of the system of inequalities, then the ordered pair must satisfy both inequalities

Verify

For x=0,y=0

Inequality A

[tex]0\geq (0)^{2}+0-4[/tex]

[tex]0\geq -4[/tex] ----> is true

so

The ordered pair satisfy inequality A

Inequality B

[tex]0 < (0)^{2} +2(0)+1[/tex]

[tex]0 < 1[/tex] ----> is true

so

The ordered pair satisfy inequality B

therefore

The ordered pair (0,0) is a solution of the system

johanrusli johanrusli · Answer 2 · 2019-11-19T04:15:41+01:00

(0,0) is a solution to this system y ≥ x² + x - 4 and y < x² + 2x + 1

Further explanation

Discriminant of quadratic equation ( ax² + bx + c = 0 ) could be calculated by using :

D = b² - 4 a c

From the value of Discriminant , we know how many solutions the equation has by condition :

D < 0 → No Real Roots

D = 0 → One Real Root

D > 0 → Two Real Roots

An axis of symmetry of quadratic equation y = ax² + bx + c is :

[tex]\large {\boxed {x = \frac{-b}{2a} } }[/tex]

Let us now tackle the problem!

Given:

[tex]y \geq x^2 + x - 4[/tex]

[tex]y \leq x^2 + 2x +1[/tex]

[tex]\texttt{ }[/tex]

If we put the coordinate (0 , 0) into the two inequality above then:

[tex]y \geq x^2 + x - 4[/tex]

[tex]0 \geq 0^2 + 0 - 4[/tex]

[tex]0 \geq - 4[/tex] → true

[tex]\texttt{ }[/tex]

[tex]y \leq x^2 + 2x +1[/tex]

[tex]0 \leq 0^2 + 2(0) +1[/tex]

[tex]0 \leq 1[/tex] → true

[tex]\texttt{ }[/tex]

Since the two inequality values are true when the coordinate is (0,0), then it can be concluded that (0,0) is a solution to this system.

[tex]\texttt{ }[/tex]

Learn more

Solving Quadratic Equations by Factoring : https://brainly.com/question/12182022
Determine the Discriminant : https://brainly.com/question/4600943
Formula of Quadratic Equations : https://brainly.com/question/3776858

Answer details

Grade: High School

Subject: Mathematics

Chapter: Quadratic Equations

Keywords: Quadratic , Equation , Discriminant , Real , Number