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3 years ago

What are the solutions to the system of equations?

Mathematics

1 answer:

bogdanovich [222]3 years ago

5 0

Answer:

(0, - 3 ) and (- 1, - 5 )

Step-by-step explanation:

Given the 2 equations

y = 4x² + 6x - 3 → (1)

y = 2x - 3 → (2)

Substitute y = 4x² + 6x - 3 into (2)

4x² + 6x - 3 = 2x - 3 ( subtract 2x - 3 from both sides )

4x² + 4x = 0 ← factor out 4x from each term

4x(x + 1) = 0

Equate each factor to zero and solve for x

4x = 0 ⇒ x = 0

x + 1 = 0 ⇒ x = - 1

Substitute these values into (2) for corresponding values of y

x = 0 : y = 2(0) - 3 = 0 - 3 = - 3 ⇒ (0, - 3 )

x = - 1 : y = 2(- 1) - 3 = - 2 - 3 = - 5 ⇒ (- 1, - 5 )

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Is 1/3x-2y=7 a linear function

Ann [662]

Answer:

The equation is not a linear function.

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3 years ago

What is the directrix of the parabola defined by `(1)/(4)(y + 3) = (x − 2)^2`?

Sauron [17]

The directrix of the parabola is $y = \frac {-49}{16}$

<h3>How to determine the equation of the directrix?</h3>

The parabola equation is given as:

$\frac 14(y + 3) = (x -2)^2$

A parabola is represented as:

$4p(y - k) =(x -h)^2$

By comparing both equations, we have:

4p = 1/4 ==> p = 1/16

-k= 3 ==> k = -3

The directrix is represented as:

y = k - p

So, we have:

$y = -3 - \frac 1{16}$

Take the LCM

$y = \frac {-16 * 3- 1}{16}$

Evaluate

$y = \frac {-49}{16}$

Hence, the directrix of the parabola is $y = \frac {-49}{16}$

Read more about parabola at:

brainly.com/question/1480401

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4 0

2 years ago

Select each pair of equivalent numbers. PLS HELP DUE TMR AND I DONT HOW TO SOLVE IT, PLS SHOW HOW U SET IT UP

BaLLatris [955]

The pairs that are equivalent to each other are 40/1000 and 40%, 6/5 and 120%, 1/8 and 12.5% . They are the correct answers because if we divide for example 6/5 , we would get 1.2 and to turn a decimal into a percent we have to move the decimal point 2 times to the right meaning that the percentage would be 120% and you just do that for all! I hope this helped :)!!

3 0

3 years ago

8m^2+ 40m<br> -------------------<br> 8m

dsp73

Answer:

$(m+5)$