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
madam [21]
3 years ago
10

What is the solution or solutions of 2^x=7

Mathematics
1 answer:
alina1380 [7]3 years ago
4 0
The answer is x=2.80735
You might be interested in
according to the fundemental theorem of algebra, how many roots exist for the polynomial function? f(x) = (x^3-3x+1)^2
Svetradugi [14.3K]

Answer:

6

Step-by-step explanation:

First, we can expand the function to get its expanded form and to figure out what degree it is. For a polynomial function with one variable, the degree is the largest exponent value (once fully expanded/simplified) of the entire function that is connected to a variable. For example, x²+1 has a degree of 2, as 2 is the largest exponent value connected to a variable. Similarly, x³+2^5 has a degree of 2 as 5 is not an exponent value connected to a variable.

Expanding, we get

(x³-3x+1)²  = (x³-3x+1)(x³-3x+1)

= x^6 - 3x^4 +x³ - 3x^4 +9x²-3x + x³-3x+1

= x^6 - 6x^4 + 2x³ +9x²-6x + 1

In this function, the largest exponential value connected to the variable, x, is 6. Therefore, this is to the 6th degree. The fundamental theorem of algebra states that a polynomial of degree n has n roots, and as this is of degree 6, this has 6 roots

3 0
3 years ago
Can anyone help me on this problem? Please it doesn’t make sense to me...
Sav [38]

Answer:

6

Step-by-step explanation:

Cost per item is found by dividing the cost by the number of items. If the woman bought n items for $120, the cost of each item is $120/n. If the woman bought 24 more items, n+24, at the same price, then the cost per item is $120/(n+24). The problem statement tells us this last cost is $16 less than the first cost:

120/(n+24) = (120/n) -16

Multiplying by n(n+24) gives ...

120n = 120(n+24) -16(n)(n+24)

0 = 120·24 -16n^2 -16·24n . . . . . . subtract 120n and collect terms

n^2 +24n -180 = 0 . . . . . . . . . . . . . divide by -16 to make the numbers smaller

(n +30)(n -6) = 0 . . . . . . . . . . . . . . factor the quadratic

The solutions to this are the values of n that make the factors zero: n = -30, n = 6. The negative value of n has no meaning in this context, so n=6 is the solution to the equation.

The woman bought 6 items.

_____

Check

When the woman bought 6 items for $120, she paid $120/6 = $20 for each of them. If she bought 6+24 = 30 items for the same money, she would pay $120/30 = $4 for each item. That amount, $4, is $16 less than the $20 she paid for each item.

3 0
3 years ago
a driver had 18 2/3 gallons of gas in his car before the trip. when he arrived he had only 9 1/2 gallons left. the trip used 9 1
Ksju [112]

Answer:

IT IS YES AND MORE YESES yo tango

Step-by-step explanation:

5 0
3 years ago
A savings accouny has 50 dollars in it at the start of the year and 20 dollars is deposited each week. After x weeks, there are
Diano4ka-milaya [45]
I’m assuming you need to write an equation to display the relationship.
y=20x+50
3 0
2 years ago
Solve the equation. StartFraction dy Over dx EndFraction equals5 x Superscript 4 Baseline (1 plus y squared )Superscript three h
dangina [55]

Answer:

Step-by-step explanation:

To solve the differential equation

dy/dx = 5x^4(1 + y²)^(3/2)

First, separate the variables

dy/(1 + y²)^(3/2) = 5x^4 dx

Now, integrate both sides

To integrate dy/(1 + y²)^(3/2), use the substitution y = tan(u)

dy = (1/cos²u)du

So,

dy/(1 + y²)^(3/2) = [(1/cos²u)/(1 + tan²u)^(3/2)]du

= (1/cos²u)/(1 + (sin²u/cos²u))^(3/2)

Because cos²u + sin²u = 1 (Trigonometric identity),

The equation becomes

[1/(1/cos²u)^(3/2) × 1/cos²u] du

= cos³u/cos²u

= cosu

Integral of cosu = sinu

But y = tanu

Therefore u = arctany

We then have

cos(arctany) = y/√(1 + y²)

Now, the integral of the equation

dy/(1 + y²)^(3/2) = 5x^4 dx

Is

y/√(1 + y²) = x^5 + C

So

y - (x^5 + C)√(1 + y²) = 0

is the required implicit solution

5 0
3 years ago
Other questions:
  • )Simplify the following expression: (−1)(−7)(4)
    9·1 answer
  • Another problem I need help setting up:/
    9·1 answer
  • Y=x-6 and y=8x+1 need help
    11·2 answers
  • Which expression is equivalent to (125^2/125^4/3)​
    11·1 answer
  • The diagram of the hexagon below displays all the lines of symmetry for the hexagon. True or false
    6·2 answers
  • A weather balloon is released and rises vertically such that its distance s (t) above the ground during the first 10 sec of flig
    8·1 answer
  • The increase in length of an aluminum rod is twice the increase in length of an Invar rod with only a third of the temperature i
    7·1 answer
  • Pls help me I don’t know this!!!
    12·2 answers
  • Plz answer this question
    11·2 answers
  • Which equation best represents the relationship between x and y in the graph
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!