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3 years ago

PLEASE HELP ITS TIMED which is the graph of a logarithmic function?

Mathematics

2 answers:

RSB [31]3 years ago

7 0

D is the graph of logarithmic function

Elodia [21]3 years ago

3 0

Answer:

Choice D

Step-by-step explanation:

You are given for graphs.

A. This graph is translated graph of the graph of inverse proportion function

$y=\dfrac{k}{x}.$

B. This graph is the graph of linear function

$y=kx+b.$

C. This graph is the graph of quadratic function

$y=(x-a)^2.$

D. This graph is the graph of logarithmic function

$y=\log_ax.$

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The recyclables have been sorted into plastic and glass. The number of plastic items is 30 less than nine times the number of gl

Colt1911 [192]

Answer:

B, 9

Step-by-step explanation:

Let g represent the number of glass items. Then the number of plastic items is (9g -30). If 85% of items are plastic, then 100%-85% = 15% of items are glass. The ratio of plastic to glass is ...

85%/15% = (9g -30)/g

17/3 = 9 -30/g . . . . simplify

30/g = 9 -17/3 = 10/3 . . . . . . add 30/g -17/3

g = 30(3/10) = 9 . . . . . . . . . . multiply by 3g/10

There are 9 glass items.

_____

Additional comment

The number of plastic items is 9(9) -30 = 51, and the total number of items is 51+9 = 60. The percentage of plastic items is 51/60 = 85%.

There are many other ways the equation(s) could be written, including using a system of two equations. For example ...

p = 9g -30
p/(p+g) = 0.85 . . . . . plastic is 85% of the total

6 0

2 years ago

Using the Rational Root Theorem, what are all the rational roots of the polynomial f(x) = 20x4 + x3 + 8x2 + x – 12?

igomit [66]

Answer:

Option 1 is correct.

Step-by-step explanation:

The given polynomial is

$f(x)=20x^4+x^3+8x^2+x-12$

we have to find all the rational roots of the polynomial f(x)

The Rational Root Theorem states that the all possible roots of a polynomial are in the form of a rational number i.e in the form of $\frac{p}{q}$

where p is a factor of constant term and q is the factor of coefficient of leading term.

In the given polynomial the constant is -12 and the leading coefficient is 20.

$\text{All possible factor of -12 are }\pm1,\pm2, \pm3, \pm4,\pm6,\pm12$

$\text{All possible factor of 20 are }\pm1,\pm2,\pm4,\pm5,\pm10,\pm20$

So, the all possible rational roots of the given polynomial are,

$\pm1,\pm2, \pm3, \pm4,\pm6,\pm12,\pm\frac{1}{2},\pm\frac{3}{2},\pm\frac{1}{4},\pm\frac{3}{4},\pm\frac{1}{10},\pm\frac{1}{5},\pm\frac{3}{5},\pm\frac{3}{10},\pm\frac{2}{5},\pm\frac{6}{5},\pm\frac{1}{20},\pm\frac{3}{20},\pm\frac{4}{5},\pm\frac{12}{5}$

Now, the rational roots of polynomial satisfy the given polynomial

$f(-\frac{4}{5})=20(-\frac{4}{5})^4+(-\frac{4}{5})^3+8(-\frac{4}{5})^2-\frac{4}{5}-12=\frac{256}{625}\times 20-\frac{64}{125}+\frac{128}{125}-\frac{4}{5}-12$