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2 years ago

\ sqrt {x ^ 2 + 4x + 7} = \ sqrt {x ^ 2-2x + 4

Mathematics

1 answer:

slavikrds [6]2 years ago

6 0

First note the domain of the expressions on either side of the equation,

$\sqrt{x^2 + 4x + 7} = \sqrt{x^2 - 2x + 4}$

√x is defined only for x ≥ 0, so we need to have

$x^2 + 4x + 7 \ge 0 \\\\ (x^2+4x+4) + 3 \ge 0 \\\\ (x+2)^2 \ge -3$

and

$x^2 - 2x + 4 \ge 0 \\\\ (x^2 - 2x + 1) + 3 \ge 0 \\\\ (x-1)^2 \ge -3$

but x ² ≥ 0 for all real x, so both conditions will always be satisfied.

Back to the equation - take the square of both sides and solve for x :

$x^2 + 4x + 7 = x^2 - 2x + 4 \\\\ 4x + 7 = -2x + 4 \\\\ 6x = -3 \\\\ \boxed{x=-\dfrac12}$

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Which of the following is not equal to sin⁡(-230°)?

xenn [34]

From trigonometry we know that:

if $sin(\theta)=sin(\alpha)$

then, $\theta=n\pi+(-1)^n\alpha$ (where $n$ is an integer)

This can be rewritten in degrees as:

$\theta=n(180^{\circ})+(-1)^n\alpha$ .............(Equation 1)

Now, in our case, $\alpha=-230^{\circ}$

Therefore, (Equation 1) can be written as:

$\theta=n(180^{\circ})+(-1)^n(-230^{\circ})$ ..........(Equation 2)

Now, to find the correct options all that we have to do is replace n by relevant integers and find the values of $\theta$ that match.

For n=2, (Equation 2) gives us: $\theta=2\times 180^{\circ}+(-1)^2(-230^{\circ})=360^{\circ}-230^{\circ}=130^{\circ}$ .

Thus, $sin(230^{\circ})=sin(130^{\circ})$

Now, we know that: $-sin(-50^{\circ})=sin(50^{\circ})$

Let n=-1, then:

$\theta=(-1)\times 180^{\circ}+(-1)^{-1}(-230^{\circ})=-180^{\circ}+230^{\circ}=50^{\circ}$

Thus, $sin(-230^{\circ})=-sin(-50^{\circ})$

Likewise, $sin(-230^{\circ})=sin(50^{\circ})$

Only the last option $sin(-50^{\circ})$ will never match $sin(-230^{\circ})$ because no integral value of $n$ will ever give $\theta=-50^{\circ}$

Thus the last option is the correct option.

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2 years ago

Read 2 more answers

Please answer this correctly

sineoko [7]

Answer:

Chicken: 36%

Beef: 34%

Black Bean: 30%

Hope this helps!

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ZanzabumX [31]

Answer:

360 mi/h

Step-by-step explanation:

The speed for the outbound trip was ...

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(715 mi)/(1 5/6 h) = 390 mi/h

The airspeed of the plane is the average of these two ground speeds, so is ...

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Aleksandr-060686 [28]

A) 0.8
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For A, since 1 in 5 is dry, 4 in 5 are not; 4/5 = 0.8

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0.3(0.8) = 0.24

For C, 100%-30%=70% of wells that are not dry are not contaminated; 0.7(0.8) = 0.56

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3.4 is what percent of 4.25? Enter your answer in the box.

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Step-by-step explanation:

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