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Aleonysh [2.5K]
2 years ago
15

Two functions are shown below.

Mathematics
2 answers:
vodka [1.7K]2 years ago
6 0

Answer:

  x = 6

Step-by-step explanation:

We assume your functions are ...

  • f(x) = (1/2)(2^x)
  • g(x) = 5x+2

In general, mixed polynomial and exponential functions have no algebraic solution. That means we need to solve f(x) = g(x) using a table of values, or by graphing.

__

Attached is a graphical solution. It shows the largest value of x for which f(x) = g(x) is x=6.

<em>Check</em>: f(6) = 1/2(2^6) = 32 = g(6) = 5(6) +2

__

<em>Additional comment</em>

We can start with f(x) = g(x) and subtract g(x) from both sides of the equation. This gives ...

  f(x) -g(x) = 0

Many graphing calculators readily identify the zeros of a function or expression. We have used that fact to find the two values of x where these functions are equal: ≈0.32 and 6.

For x>6, the exponential function increases without bound, so the graphs never cross again. Likewise, for x < -0.32, the linear function decreases without bound, so the graphs never cross again.

The lower value of x where the graphs cross is an irrational number near −0.319886722135.

ELEN [110]2 years ago
5 0

Answer:

x = 6

Step-by-step explanation:

As the function f(x) is an exponencial function, it will grow faster than g(x), that is a linear function.

For small values of x, we have that f(x) < g(x). For example:

f(1) = 1/2 * 2 = 1

g(1) = 5*1 + 2 = 7

f(2) = 1/2 * 4 = 2

g(2) = 5*2 + 4 = 14

So we just need to check some integer values and see when f(x) will be bigger than g(x). It will not be a big value, as the exponencial function grows very fast.

For x = 5, we have:

f(5) = 1/2 * 32 = 16

g(5) = 5*5 + 4 = 29

For x = 6, we have:

f(6) = 1/2 * 64 = 32

g(6) = 5*6 + 4 = 34

For x = 7, we have:

f(7) = 1/2 * 128 = 64

g(7) = 5*7 + 4 = 39

So the largest integer value of x for f(x) ≤ g(x) is x = 6.

Another way to solve this is by plotting both equations, and then checking where they cross, that is, where f(x) = g(x).

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One solution to the problem below is 5. What is the other solution? c^2 - 25 = 0
topjm [15]

Answer:

c = -5

Step-by-step explanation:

Plug in -5 to c in the equation:

c² - 25 = 0

(-5)² - 25 = 0

Simplify. First, solve the power, then solve the subtraction:

(-5)² - 25 = 0

(-5 * -5) - 25 = 0

(25) - 25 = 0

0 = 0 (True)

~

4 0
3 years ago
Read 2 more answers
Let f be a functions of degree 4 whose coefficients are real numbers: two of its zeros are - 3 and 4 - i. Explain why one of the
kvasek [131]

Answer:

Step-by-step explanation:

We have the following theorem, if f is a polynomial with real coefficients, we can factor it completely in factors of the degree at most 2.

Consider first a polynomial of degree two, hence it is a polynomial of the form ax^2+bx+c. The cuadratic formula tells us that the solutions are of the form

x = \frac{-b\pm \sqrt[]{b^2-4ac}}{2a}.

Note that square root, over the reals, tells us that the are only real solutions if b^2-4ac \geq 0. If that is not the case, say it's negative, the solution are complex. Then, the solutions are of the form

x = \frac{-b \pm i \sqrt[]{4ac-b^2}}{2a}. NOte that this means that if we have a complex number of the form a+bi that is a solution, then the number a-bi (who is called the complex conjugate) is also a solution.

Recall that when we have a polynomial f(x) whose a zero is the number c, then we can factor f as follows f(x) = (x-c) * p(x) where p(x) is another polynomial of lesser degree .

So far, we know that -3 and 4-i are zeros of the function f. Note that we are missing two zeros. But, since complex numbers are zeros of polynomial only by pairs (that is the number and its conjugate are zeros), then, we must have that one of the missing 2 zeros is a real number. We have 4-i as a zero, then, its complex conjugate must be also a zero, i.e 4+i is a zero.

8 0
3 years ago
Solve −2x − 15 = 6x + 9.
Sindrei [870]

Answer: x=-3

Step-by-step explanation:

Given the equation:

-2x - 15 = 6x + 9

You must solve for "x" to find its value.

You can follow these steps:

- Add 2x to both sides of the equation:

-2x - 15+2x= 6x + 9+2x

- 15 = 8x +9

- Subtract 9 from both sides of the equation:

- 15-9 = 8x +9-9

-24 = 8x

- Divide both sides of the equation by 8. Then you get:

\frac{-24}{8}=\frac{8x}{8}\\\\x=-3

6 0
3 years ago
1. Write a division sentence that tells what the<br> model represents.
boyakko [2]

Answer:

Since there are two of 112 blocks, it will be 112 ÷ 2

8 0
3 years ago
there are 25 students in Hansels class and 17 of the students went on the class trip to the zoo. what percentage of students wen
drek231 [11]
It is given in the problem that out of 25 students in Hansels class 17 students went to the class trip to the zoo. From the above information it is easy to find the percentage of students that went for the class trip to the zoo.
Total number of students in the class = 25
Number of students that went for the class trip to the zoo = 17
Then
Percentage of students that went to the zoo = (17/25) * 100
                                                                       = (17 * 4) percent
                                                                       = 68 percent
So 68% of the students in Hansels class went for the class trip to the zoo.
6 0
3 years ago
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