Given the exponential equation 2X = 8, what is the logarithmic form of the equation in base 10? (5 points)

Select the correct difference. -3z 5 - (-7z 5) -10z5 -4z5 4z5 4z

Alinara [238K]

-10z5 is the answer.

3 0

3 years ago

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Find the slope from the graph shown. A. -1 B. undefined C. 1 D. 0

zimovet [89]

Answer:

it is underfined because if you look closely there is no slope in the graph

8 0

2 years ago

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42:15 = What is the ratio

vfiekz [6]

The ratio is 14:5, as 42 divided by 3 is 14 and 15 divided by 3 is 5.

8 0

2 years ago

Could the inverse of a non-function be a function? Explain or give an example.

Kitty [74]

Answer:

The inverse of a non-function mapping is not necessarily a function.

For example, the inverse of the non-function mapping $\lbrace (0,\, 0),\, (0,\, 1),\, (1,\, 0),\, (1,\, 1) \rbrace\!$ is the same as itself (and thus isn't a function, either.)

Step-by-step explanation:

A mapping is a set of pairs of the form $(a,\, b)$ . The first entry of each pair is the value of the input. The second entry of the pair would be the value of the output.

A mapping is a function if and only if for each possible input value $x$ , at most one of the distinct pairs includes $x\!$ as the value of first entry.

For example, the mapping $\lbrace (0,\, 0),\, (1,\, 0) \rbrace$ is a function. However, the mapping $\lbrace (0,\, 0),\, (1,\, 0),\, (1,\, 1) \rbrace$ isn't a function since more than one of the distinct pairs in this mapping include $1$ as the value of the first entry.

The inverse of a mapping is obtained by interchanging the two entries of each of the pairs. For example, the inverse of the mapping $\lbrace (a_{1},\, b_{1}),\, (a_{2},\, b_{2})\rbrace$ is the mapping $\lbrace (b_{1},\, a_{1}),\, (b_{2},\, a_{2})\rbrace$ .

Consider mapping $\lbrace (0,\, 0),\, (0,\, 1),\, (1,\, 0),\, (1,\, 1) \rbrace\!$ . This mapping isn't a function since the input value $0$ is the first entry of more than one of the pairs.

Invert $\lbrace (0,\, 0),\, (0,\, 1),\, (1,\, 0),\, (1,\, 1) \rbrace\!$ as follows:

$(0,\, 0)$ becomes $(0,\, 0)$ .
$(0,\, 1)$ becomes $(1,\, 0)$ .
$(1,\, 0)$ becomes $(0,\, 1)$ .
$(1,\, 1)$ becomes $(1,\, 1)$ .

In other words, the inverse of the mapping $\lbrace (0,\, 0),\, (0,\, 1),\, (1,\, 0),\, (1,\, 1) \rbrace\!$ would be $\lbrace (0,\, 0),\, (1,\, 0),\, (0,\, 1),\, (1,\, 1) \rbrace\!$ , which is the same as the original mapping. (Mappings are sets. There is no order between entries within a mapping.)

Thus, $\lbrace (0,\, 0),\, (0,\, 1),\, (1,\, 0),\, (1,\, 1) \rbrace\!$ is an example of a non-function mapping that is still not a function.

More generally, the inverse of non-trivial ellipses (a class of continuous non-function $\mathbb{R} \to \mathbb{R}$ mappings, including circles) are also non-function mappings.

3 0

2 years ago

Two ships leave the same port in different directions, forming a 120° angle between them. One ship travels 70 mi. and the other

kondaur [170]

Answer : Distance between the ships to the nearest miles = 106.03 ≈ 106 mi.

Explanation :

Since we have shown in the figure below :

a=70 mi.

b=52 mi.

c=x mi.

$\text{Since two ships leaves the same port in different directions forming a }120\textdegree\text{angle between them.}$

So, we use the cosine rule , which states that

$c^2=a^2+b^2-2ab.cosC\\\\x^2=70^2+52^2-2\times 70\times 52\times cos(120\textdegree)\\\\x^2=4900+2704-7280\times (-0.5)\\\\x^2=7604+3640\\\\x^2=11244\\\\x=\sqrt{11244}\\\\x=106.03$

So, c = x= 106.03 mi.

Hence, distance between the ships to the nearest miles = 106.03 ≈ 106 mi.

8 0

3 years ago