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3 years ago

Find all real solutions x to 4^x - 2^x = 56.

Mathematics

2 answers:

Sonbull [250]3 years ago

8 0

Since the bases are the same, set the exponents equal to each other. X = 3

SashulF [63]3 years ago

7 0

$4^{x}$ ↓
$(( 2^{x} )) ^2$ ↓
$y^{x} = w$ ↓
$w^{2} - w - 56 = 0$ ↓
w - 8 & w + 7↓
w(1) = 8 → w(1) = $2^{x1} = 8$ x(1) = 3↓
w(2) = -7 → w(2) = $2^{x2} = -7$
So, therefore the value of "x" would have to be "3"

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2. Check the boxes for the following sets that are closed under the given

son4ous [18]

The properties of the mathematical sequence allow us to find that the recurrence term is 1 and the operation for each sequence is

a) Subtraction

b) Addition

c) AdditionSum

d) in this case we have two possibilities

* If we move to the right the addition

* If we move to the left the subtraction

The sequence is a set of elements arranged one after another related by some mathematical relationship. The elements of the sequence are called terms.

The sequences shown can be defined by recurrence relations.

Let's analyze each sequence shown, the ellipsis indicates where the sequence advances.

a) ... -7, -6, -5, -4, -3

We can observe that each term has a difference of one unit; if we subtract 1 from the term to the right, we obtain the following term

-3 -1 = -4

-4 -1 = -5

-7 -1 = -8

Therefore the mathematical operation is the subtraction.

b) $0. \sqrt{1}. \sqrt{4}, \sqrt{9}, \sqrt{16}, \sqrt{25}$ ...

In this case we can see more clearly the sequence when writing in this way

$0, \sqrt{1^2}. \sqrt{2^2}, \sqrt{3^2 } . \sqrt{4^2} , \sqrt{5^2}$

each term is found by adding 1 to the current term,

$\sqrt{(0+1)^2} = \sqrt{1^2} \\\sqrt{(1+1)^2} = \sqrt{2^2}\\\sqrt{(2+1)^2} = \sqrt{3^2}\\\sqrt{(5+1)^2} = \sqrt{6^2}$

Therefore the mathematical operation is the addition

c) $... \frac{-10}{2}. \frac{-8}{2}, \frac{-6}{2}, \frac{-4}{2}. \frac{-2}{2}. ...$

The recurrence term is unity, with the fact that the sequence extends to the right and to the left the operation is

To move to the right add 1

- $\frac{-10}{2} + 1 = \frac{-10}{2} - \frac{2}{2} = \frac{-8}{2}\\\frac{-8}{2} + \frac{2}{2} = \frac{-6}{2}$

To move left subtract 1

$\frac{-2}{2} - 1 = \frac{-4}{2}\\\frac{-4}{2} - \frac{2}{2} = \frac{-6}{2}$

Using the properties the mathematical sequence we find that the recurrence term is 1 and the operation for each sequence is

a) Subtraction

b) Sum

c) Sum

d) This case we have two possibilities

If we move to the right the sum

If we move to the left we subtract

Learn more here: brainly.com/question/4626313

5 0

3 years ago

Find the roots of f(x)=x^2+10x−96

a_sh-v [17]

Answer:

x = -16 or x = 6

Step-by-step explanation:

To find the roots of a polynomial function, set the polynomial equal to zero and solve for x.

x² + 10x - 96 = 0

We need to factor the left side. The left side is a quadratic polynomial whose first coefficient is 1. We need two numbers whose product is -96 and whose sum is 10. The numbers are 16 and -6.

(x + 16)(x - 6) = 0

If a product of two factors equals zero, then one factor or the other or both must equal zero.

x + 16 = 0 or x - 6 = 0

x = -16 or x = 6

6 0

3 years ago

Can someone help meee

frez [133]

Answer: D or #4: None of the above

Step-by-step explanation: Since the longest angle is 13 x has to be around half because its a 47 degree angle if we round it would be 6 so D

5 0

3 years ago

A machine adds metal bands called ferrules and erasers to one end of a pencil. It takes the machine 2.5 hours to add ferrules an

andreev551 [17]

Answer:

Step-by-step explanation:

Convert 2.5 to minutes = 150 minutes. Then divide 4200/150 which gives you 28 per minute

3 0

3 years ago

a real estate broker sold your house for $72,00. the brokers commission was 6% of the selling pricw. how much would you get afte

worty [1.4K]

$72,00?

I'm assuming you are saying $7200, but if you are saying $72, just replace.

6% = 0.06

7200 / 0.06 = 432

So you would get $432. But trust me, no house is that cheap lol

3 0

3 years ago