1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Ludmilka [50]
3 years ago
7

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

Mathematics
1 answer:
slavikrds [6]3 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}

You might be interested in
How do I solve 5x+1=7x+19
notsponge [240]

Answer:

x=-9

Step-by-step explanation:

5x+1=7x+19

1 = 7x-5x +19

1-19 = 2x

-18/2 = x

x = -9

Hope this helps!

Please mark brainliest if you think I helped! Would really appreciate!

5 0
3 years ago
The range of the function f(x) = x + 5 is {7, 9}. What is the function’s domain?
mina [271]
** x + 5 = 7 x = 2 ** x + 5 = 9 x = 4 {2,4}
4 0
3 years ago
Santiago wants to walk at least 500 miles before the end of this year. He has already walked 437 miles, and there are 36 days le
Mrrafil [7]

Answer:

437+36x>=500

Step-by-step explanation:

This basically shows that 437 plus the x miles he will walk per day for 36 will total to more than or equal to 500

7 0
3 years ago
Read 2 more answers
Can some explain this to me do i need to covert something or can someone explain it to me how in gonna get the answer i try to d
solniwko [45]
Cross multiply:

2.5 ft x 16.5 ft = 41.25 ft

now divide:

41.25 / 8.25 = 5

L = 5 feet 
7 0
3 years ago
The sum of the first two terms of an infinite GP is 6 and each term is 5 times the sum of the succeeding termsthen the second te
kozerog [31]

Answer:

\dfrac{6}{7}.

Step-by-step explanation:

It is given that the sum of first two terms of an infinite GP is 6.

nth term of a GP is

a_n=ar^{n-1}

a+ar=6     ...(1)

Each term is 5 times the sum of the succeeding terms.

a_n=5(a_{n+1}+a_{n+2}+...+\infty)

ar^{n-1}=5(ar^n+ar^{n+1}+...+\infty)

ar^{n-1}=5ar^n(1+r+r^2+...+\infty)

Divide both sides by a.

r^{n-1}=5r^n(\dfrac{1}{1-r})    [\text{Sum of infinite GP}=\dfrac{a}{1-r}]

\dfrac{r^n}{r}=\dfrac{5r^n}{1-r}

\dfrac{1}{r}=\dfrac{5}{1-r}

1-r=5r

1=6r

\dfrac{1}{6}=r

The common ratio is 1/6.

Put r=1/6 in (1).

a+a(\dfrac{1}{6})=6

6a+a=36

7a=36

a=\dfrac{36}{7}

Second term ar=\dfrac{36}{7}\times \dfrac{1}{6}=\dfrac{6}{7}

Therefore, the second term is \dfrac{6}{7}.

4 0
2 years ago
Other questions:
  • Alice has a total of 12 dimes and nickels. She has 2 more nickels than dimes. Which equation represents the given problem situat
    6·2 answers
  • Use the drop-down menus to complete these statements.
    14·2 answers
  • 3.5^2+2.6×3-6 anybody explain this please.
    8·1 answer
  • I only need help with #15
    13·2 answers
  • What’s 6r+3=4r-11?????
    14·2 answers
  • WILL MARK BRAINLIEST!!!!!! HELP ASAP!!!!
    12·2 answers
  • Answer the mathmatics question below, and please give me an accurate answer. Thank you!
    12·2 answers
  • length of a rectangle is 2 metre and the breadth is 50 find the ratio of a length to the breadth of a rectangle​
    12·1 answer
  • 165 is what percent of 150 ?
    8·2 answers
  • Help someone how do you solve this
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!