All categories

2 years ago

Find all solutions of the system of equations algebraicllally. Write your solutions as coordinate points Y=3x^2- 2x-1 2x+y=11

Mathematics

1 answer:

zloy xaker [14]2 years ago

8 0

Answer:

(- 2, 15 ) and (2, 7 )

Step-by-step explanation:

Given the 2 equations

y = 3x² - 2x - 1 → (1)

2x + y = 11 → (2) ← subtract 2x from both sides

y = 11 - 2x → (3)

Substitute y = 3x² - 2x - 1 into (3)

3x² - 2x - 1 = 11 - 2x ( subtract 11 - 2x from both sides )

3x² - 12 = 0 ( add 12 to both sides )

3x² = 12 ( divide both sides by 3 )

x² = 4 ( take the square root of both sides )

x = ± $\sqrt{4}$ = ± 2

Substitute these values into (3) for corresponding values of y

x = - 2 : y = 11 - 2(- 2) = 11 + 4 = 15 ⇒ (- 2, 15 )

x = 2 : y = 11 - 2(2) = 11 - 4 = 7 ⇒ (2, 7 )

You might be interested in

What is the awnser to 9 1/3 ÷ 8

Ostrovityanka [42]

Answer:

$\frac{7}{6}$ is the answer for this question.

Step-by-step explanation:

You'll get your answer By reducing the expression, if possible, by cancelling the common factors.

And that'll be your final answer - $\frac{7}{6}$

8 0

2 years ago

Read 2 more answers

If she is going x amount of miles an hour how many is she going in 90 minutes

Ne4ueva [31]

<h3>✽ - - - - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - - - - ✽</h3>

➷ 90 - 60 = 30

This time is x + 1/2x

You can write this as 1.5x

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬ ʜᴀɴɴᴀʜ ♡

8 0

3 years ago

Find the measure of ΔABC. Show your work.

valina [46]

Answer:

Step-by-step explanation:

7 0

3 years ago

A certain ball is dropped from a height of x feet. It always bounces up to 2/3 x feet. Suppose the ball is dropped from 10 feet

galina1969 [7]

Given that if a ball is dropped from x feet, it bounces up to 2/3 x feet.

And the ball is dropped from 10 feet, that is x=10 feet,

So,before the first bounce it travels 10 feet distance.

Between first and second bounce it travels $\frac{2}{3}* 10 + \frac{2}{3} * 10 = 20*(\frac{2}{3})$

Between second and third bounce, it travels $20*(\frac{2}{3})^{2}$

Between third and fourth bounce, it travels $20*(\frac{2}{3}) ^{3}$

Like that between 29th and 30th bounce, it travels $20*(\frac{2}{3} )^{29}$

Hence total distance traveled is

$10+20*(\frac{2}{3} )+20*(\frac{2}{3})^{2} + 20*(\frac{2}{3}) ^{3}+......+20*(\frac{2}{3})^{29}$

= $10+20[(\frac{2}{3}) +(\frac{2}{3}) ^{2} +(\frac{2}{3}) ^{3} +.....+(\frac{2}{3} )^{29} ]$

= $10+20[\frac{\frac{2}{3}*(1-(\frac{2}{3})^{29}) }{1-\frac{2}{3} }]$

= 10+20*2*(1- $(\frac{2}{3}) ^{29}$ )

= 49.9997 feet ≈ 50 feet approximately.

7 0

2 years ago

Read 2 more answers

What are the values that satisfy the trigonometric equation for: 0 ≤ q ≤ 2Π ?

bagirrra123 [75]

Answer: 0, π, 2π

Nevertheless, that is not an option. I see two possibilities: 1) the options are misswirtten, 2) the domain is not well defined.

If the domain were 0 ≤ θ < 2π, then 2π were excluded of the domain ant the answer would be 0, π.

Explanation:

1) The first solution, θ = 0 is trivial:

sin (0) - tan (0) = 0

0 - 0 = 0

2) For other solutions, work the expression:

sin(θ) + tan (-θ) = 0 ← given

sin (θ) - tan(θ) = 0 ← tan (-θ) = tan(θ)

sin(θ) - sin (θ) / cos(θ) = 0 ← tan(θ) = sin(θ) / cos(θ)

sin (θ) [1 - 1/cos(θ)] = 0 ← common factor sin(θ)

⇒ Any of the two factors can be 0

⇒ sin (θ) = 0 or (1 - 1 / cos(θ) = 0,

sin(θ) = 0 ⇒ θ = 0, π, 2π

1 - 1/cos(θ) = 0 ⇒ 1/cos(θ) = 1 ⇒ cos(θ) = 1 ⇒ θ = 0, 2π

⇒ Solutions are 0, π, and 2π

In fact if you test with any of those values the equation is checked. The only way to exclude one of those solutions is changing the domain.

7 0

3 years ago

Read 2 more answers