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1 year ago

PLEASE HURRY WILL GIVE POINTS AND BRAINLYEST TO FIRST RIGHT!!!

Mathematics

2 answers:

zysi [14]1 year ago

7 0

Answer:

(0, 4) and (-1, 0)

Step-by-step explanation:

Given system of equations:

$\begin{cases}y=2x^2+6x+4\\y=-4x^2+4\end{cases}$

Solve by substitution

Substitute the first equation into the second:

$\implies 2x^2+6x+4=-4x^2+4$

Add 4x² to both sides:

$\implies 2x^2+6x+4+4x^2=-4x^2+4+4x^2$

$\implies 6x^2+6x+4=4$

Subtract 4 from both sides:

$\implies 6x^2+6x+4-4=4-4$

$\implies 6x^2+6x=0$

Factor out 6x from the left side:

$\implies 6x(x+1)=0$

Therefore:

$\implies 6x=0 \implies x=0$

$\implies x+1=0 \implies x=-1$

To find the y-coordinates of the found x-values, substitute the found values of x into one of the equations:

$x=0 \implies -4(0)^2+4=4 \implies (0,4)$

$x=-1\implies -4(-1)^2+4=0\implies (-1,0)$

Therefore, the solutions to the system of equations are:

(0, 4) and (-1, 0)

Eva8 [605]1 year ago

7 0

Answer:

Solutions:

a) x = 0, y = 4 ⇒ (0, 4)

b) x = -1, y = 0 ⇒ (-1, 0)

Step-by-step explanation:

Given system of equations:

a) y = 2x² + 6x + 4

b) y = -4x² + 4

1. Substitute the value of y in the second equation into the first equation:

⇒ -4x² + 4 = 2x² + 6x + 4

2. Solve for x:

⇒ -4x² + 4 = 2x² + 6x + 4 [subtract 4 from both sides]

⇒ -4x² + 4 - 4 = 2x² + 6x + 4 - 4

⇒ -4x² = 2x² + 6x [subtract 2x² from both sides]

⇒ -4x² - 2x² = 2x² - 2x² + 6x

⇒ -6x² = 6x [subtract 6x from both sides]

⇒ -6x² - 6x = 6x - 6x

⇒ -6x² - 6x = 0 [factor out -6x from the equation]

⇒ -6x(x + 1) = 0

Two cases:

⇒ -6x = 0 [divide both sides by -6]

⇒ -6x ÷ -6 = 0 ÷ -6

⇒ x = 0

⇒ x + 1 = 0 [subtract 1 from both sides]

⇒ x + 1 - 1 = 0 - 1

⇒ x = -1

3. Find the value of y by substituting the found x values into one of the given equations:

a) x = 0:

⇒ y = -4x² + 4

⇒ y = -4(0)² + 4

⇒ y = -4(0) + 4

⇒ y = = 0 + 4

⇒ y = 4

coordinate: (0, 4)

b) x = -1:

⇒ y = -4x² + 4

⇒ y = -4(-1)² + 4

⇒ y = -4(1) + 4

⇒ y = -4 + 4

⇒ y = 0

coordinate: (-1, 0)

Learn more here:

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3 years ago

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2 years ago

Which sentence can represent the inequality 2.4 (6.2 minus x) greater-than negative 4.5?

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Answer: Choice B

Two and four tenths multiplied by the difference of six and two tenths and a number is more than negative four and five tenths.

======================================================

Explanation:

2.4 = 2 + 0.4

2.4 = 2 and 4/10

2.4 = 2 and 4 tenths

2.4 = two and four tenths

-------------------

Through similar reasoning,

6.2 = six and two tenths

And also,

-4.5 = negative four and five tenths

---------------------

Notice how 6.2 - x translates into "difference of six and two tenths and a number"

We then multiply that by 2.4, aka two and four tenths.

So that's how we get the phrasing "Two and four tenths multiplied by the difference of six and two tenths and a number"

All of this is greater than -4.5 aka negative four and five tenths.

This points us to Choice B as the final answer.

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2 years ago

Read 2 more answers