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3 years ago

Discuss the nature of the roots x^2+6x=3

2 answers:

8 0

$x^2+6x=3\\
x^2+6x+9-9=3\\
(x+3)^2=12\\
x+3=\sqrt{12} \vee x+3=-\sqrt{12}\\
x=-3+\sqrt{12} \vee x=-3-\sqrt{12}\\
x=-3+2\sqrt{3} \vee x=-3-2\sqrt{3}\\$

Lynna [10]3 years ago

5 0

$x^{2} +6x=3$
$x^{2} +6x-3=0$
using quadratic formula --> $x= \frac{-6± \sqrt{6^{2}-4 *1*-3} }{2*1}$
$x=-3+2 \sqrt{3}$
AND
$x=-3-2 \sqrt{3}$

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A/-8+15>23 isn't this weird to you guys too

yanalaym [24]

Let's solve your inequality step-by-step.

a − 8 + 15 > 23

Step 1: Simplify both sides of the inequality.

−1/8a + 15 > 23

Step 2: Subtract 15 from both sides.

−1/8a + 15 − 15 > 23 − 15

−1/8a > 8

Step 3: Multiply both sides by 8/(-1).

(8/−1) * (−1/8a) > (8/−1) * (8)

a < −64

Therefore, the answer is a < -64! I hope this helped! :)

4 0

3 years ago

A rectangular box has a square base with an edge length of x cm and a height of h cm. The volume of the box is given by V = x2h

Tanya [424]

Answer:

192 cm^3/min

Step-by-step explanation:

Differentiating the volume expression, we get ...

dV/dt = 2xh(dx/dt) +x^2(dh/dt)

We are given that ...

x = 4 cm, dx/dt = 2 cm/min, h = 15 cm, dh/dt = -3 cm/min

Putting these values into the formula for volume rate of change, we get ...

dV/dt = 2(4 cm)(15 cm)(2 cm/min) +(4 cm)^2(-3 cm/min)

= 240 cm^3/min -48 cm^3/min

dV/dt = 192 cm^3/min

8 0

3 years ago

Home Videos Inc. surveys 450 households and finds that the mean amount spent for renting or buying videos is P135 a month and th

adell [148]

SOLUTION:

Case: Hypothesis testing

Step 1: Null and Alternative hypotheses

$\begin{gathered} H_0:\mu=P127.50 \\ H_1:\mu\leq P127.50 \end{gathered}$

Step 2: T-test analysis

$\begin{gathered} t=\frac{\hat{x}-\mu}{\frac{s}{\sqrt{n}}} \\ t=\frac{135-127.5}{\frac{75.25}{\sqrt{450}}} \\ t=2.144 \end{gathered}$

Step 3: t-test with the significance level

$\begin{gathered} t_{\alpha}=? \\ \alpha=0.05 \\ From\text{ }tables \\ t_{0.05}=1.654 \end{gathered}$

Step 4: Comparing

$t>t_{\alpha}$

So tail to reject the null hypothesis. There is enough evidence at a 0.05 level of significance to claim that the mean spent is greater than P127.50.

Final answer:

Yes, there is evidence sufficient to conclude that the mean amount spent is greater than P127.50 per month at a 0.05 level of significance.

6 0

1 year ago

How do you do this? It's geometry

antiseptic1488 [7]

45.

12/18 = 8/x <=> 2/3 = 8/x <=> x = (3*8)/2 = 12;

7 0

3 years ago

7/2x + 1/2x = 7 + 9/2x

lesya [120]

Answer: x=-14

Step-by-step explanation:

5 0

1 year ago