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
algol13
2 years ago
5

Select the correct answer. What is the value of x? log^2(x+ 7) = 2

Mathematics
1 answer:
Delvig [45]2 years ago
3 0
Answer: x=-3

Solve the equation by rewriting in exponential form using the definition of a logarithm and simplifying.
You might be interested in
Find the general term of sequence defined by these conditions.
disa [49]

Answer:

\displaystyle  a_{n}  =     (2)^{2n -1}   -   (3) ^{n-1 }

Step-by-step explanation:

we want to figure out the general term of the following recurrence relation

\displaystyle \rm a_{n + 2} - 7a_{n + 1} + 12a_n = 0  \:  \: where :  \:  \:a_1 = 1 \: ,a_2 = 5,

we are given a linear homogeneous recurrence relation which degree is 2. In order to find the general term ,we need to make it a characteristic equation i.e

  • {x}^{n}  =  c_{1} {x}^{n - 1}  + c_{2} {x}^{n - 2}  + c_{3} {x}^{n -3 } { \dots} + c_{k} {x}^{n - k}

the steps for solving a linear homogeneous recurrence relation are as follows:

  1. Create the characteristic equation by moving every term to the left-hand side, set equal to zero.
  2. Solve the polynomial by factoring or the quadratic formula.
  3. Determine the form for each solution: distinct roots, repeated roots, or complex roots.
  4. Use initial conditions to find coefficients using systems of equations or matrices.

Step-1:Create the characteristic equation

{x}^{2}  - 7x+ 12= 0

Step-2:Solve the polynomial by factoring

factor the quadratic:

( {x}^{}  - 4)(x - 3) =  0

solve for x:

x =  \rm 4 \:and \: 3

Step-3:Determine the form for each solution

since we've two distinct roots,we'd utilize the following formula:

\displaystyle a_{n}  = c_{1}  {x} _{1} ^{n }  + c_{2}  {x} _{2} ^{n }

so substitute the roots we got:

\displaystyle a_{n}  = c_{1}  (4)^{n }  + c_{2}  (3) ^{n }

Step-4:Use initial conditions to find coefficients using systems of equations

create the system of equation:

\begin{cases}\displaystyle 4c_{1}    +3 c_{2}    = 1  \\ 16c_{1}    + 9c_{2}     =  5\end{cases}

solve the system of equation which yields:

\displaystyle c_{1}  =  \frac{1}{2}     \\  c_{2}   =   - \frac{1}{3}

finally substitute:

\displaystyle  a_{n}  =  \frac{1}{2}   (4)^{n }   -  \frac{1}{3}  (3) ^{n }

\displaystyle \boxed{ a_{n}  =    (2)^{2n-1 }   -   (3) ^{n -1}}

and we're done!

7 0
3 years ago
Aliens spotted! They have pulled up 97 chickens, 47 cows, and 77 humans. What is the probability, if they randomly select from a
emmainna [20.7K]
The answer would be 0.34. Theres 77 humans out of 221 beings, which means 77/221. Simplifying this fraction gives us 0.34.
4 0
3 years ago
What is the classifications of polynomials -gh4i+3g5
Step2247 [10]

Answer:

The polynomial -gh⁴i + 3g⁵ is a binomial, since it has two terms

Degree of polynomial: degree of a polynomial is the term with highest of exponent.

Degree of binomial -gh⁴i + 3g⁵ = 6

1st term(-gh⁴i ) = (power of g = 1, power of h = 4, power of i = 1)

2nd term(3g⁵) = (power of g = 5)

the polynomial -gh⁴i + 3g⁵ is a 6 degree binomial.

5 0
3 years ago
a fruit salad is made from pineapples, pears, and peaches mixed in the ratio of 2 to 3 to 5, respectively, by weight. what fract
musickatia [10]
2/10 or 1/5, which is 20%
6 0
3 years ago
Can someone help me out please
lbvjy [14]
16 is the answer jxhsjcjaks
5 0
2 years ago
Other questions:
  • The leg of a right triangle is 4 units and the hypotenuse is 9 units. What is the length, in units, of the other leg of the tria
    9·2 answers
  • Triangle ABC and DEF are congruent. Find x.
    13·2 answers
  • Bill at a restaurant came to $136.40 the patrons decide to leave a 15% tip what is the total bill including the tip
    5·2 answers
  • What ordered pair is a solution of the equations y = 4x + 3?
    5·1 answer
  • How would i write the expression as a single power of 10
    12·1 answer
  • Ap calculus help please
    5·1 answer
  • Can someone plz help
    5·2 answers
  • Find the distance between -6 and 8.<br> What is an expression that represents the distance
    15·1 answer
  • PLEASE HELP WILL GIVE BRAINLIEST!?!?!?
    10·2 answers
  • A) side angle side<br> b) side side side <br> c) angle side angle<br> d) not congruent
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!