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Ludmilka [50]
2 years ago
7

\ 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}

√<em>x</em> is defined only for <em>x</em> ≥ 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 <em>x</em> ² ≥ 0 for all real <em>x</em>, so both conditions will always be satisfied.

Back to the equation - take the square of both sides and solve for <em>x</em> :

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

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zepelin [54]
3 cookies for pouch because each x and y factor can be divided by 3
7 0
3 years ago
Read 2 more answers
The population of California is approximately 38,040,000. The population of Texas is about 2.606 × 107. What is the approximate
liubo4ka [24]

Answer:

The total population of these two states is:

3.804\times \:\:10^7+2.606\times \:\:10^7\:=10^7\times \:\:6.41

Therefore, option C is correct.

Step-by-step explanation:

  • The population of California is approximately 38,040,000.
  • The population of Texas is about 2.606 × 10⁷.

Writing the population of California i.e.38,040,000  in scientific notation by moving the decimal point 7 places to the left and dropping the 0's on the right  side as they're after the decimal point now.

i.e.

38,040,000 = 3.804 x 10⁷

So adding 3.804 x 10⁷ and 2.606 × 10⁷

i.e.

3.804\times \:10^7+2.606\times \:10^7

\mathrm{Add\:similar\:elements:}\:10^7\times \:3.804+10^7\times \:2.606=10^7\times \:6.41

Thus, the total population of these two states is:

3.804\times \:\:10^7+2.606\times \:\:10^7\:=10^7\times \:\:6.41

Therefore, option C is correct.

4 0
3 years ago
Make U the subject of the formula <br> D = ut + kt2
natali 33 [55]

Remark

I'm going to interpret this equation as

D = ut + kt²  The only difference is the 2.

Solution

Subtract kt² from both sides.

D - kt² = ut   Now divide by u on both sides.

\dfrac{D - kt^2}{t} = \dfrac{ut}{t}

The t's cancel out. on the right.  You are left with u on the right.

\dfrac{D - kt^2}{t} =\text{u}


6 0
3 years ago
What is the answer to #3?
FrozenT [24]
I think it’s 2 but I’m not sure
5 0
2 years ago
I don't understand this. please help me, much appreciated !!
nevsk [136]

Apparently, the calculator at the link in your lesson is fully capable of giving you the necessary numbers. My own TI-84 work-alike gives me the account balances, but the rest of the numbers need to be figured.

In 30 years, there are 12×30 = 360 months, or 4×30 = 120 quarters. See the calculator results below. Your table can be filled in using the given information to find the contribution amount. The calculator gives the final balance. The interest amount is found by subtracting the contribution amount from the final balance.

\begin{array}{cccc}\text{Opt}&\text{Contributions}&\text{Int}&\text{Final Bal}\\1&360\cdot 25=9000&6250.50&15250.50\\2&120\cdot 75=9000&8467.04&17467.04\\3&1000&5489.17&6489.17\end{array}


3 0
3 years ago
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