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3 years ago

The drawing plan for an art studio shows a rectangle that is 19.2 inches by 8

Mathematics

1 answer:

vazorg [7]3 years ago

4 0

Answer:

24 ft by 10 ft

240 ft

Step-by-step explanation:

19.2/4 = 4.8

4.8 · 5 = 24

8/4 = 2

2 · 5 = 10

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The table shows the number of students that are enrolled in Geometry at Eastlake High School If the pattern continues, how many

vaieri [72.5K]

Answer:

Step-by-step explanation:

8 0

3 years ago

What is the extraneous solution found in solving the equation log2 4x + log₂ (x + 1) = 3

yan [13]

Answer:

x = -2

Step-by-step explanation:

We are given the logarithmic base 2 equation of:

$\displaystyle{\log_2 (4x) + \log_2 (x+1) = 3}$

Apply logarithm property of addition where:

$\displaystyle{\log_a M + \log_a N = \log_a MN}$

Therefore, we will write new equation as:

$\displaystyle{\log_2 [4x(x+1)] = 3}$

Apply logarithm to exponential form using:

$\displaystyle{\log_a M = N \to a^N = M}$

Thus, another new rewritten equation is:

$\displaystyle{2^3 = 4x(x+1)}\\\\\displaystyle{8 = 4x(x+1)}\\\\\displaystyle{2=x(x+1)}$

Expand the expression in and arrange the terms in quadratic expression:

$\displaystyle{2=x^2+x}\\\\\displaystyle{0=x^2+x-2}\\\\\displaystyle{x^2+x-2=0}$

Solve for x:

$\displaystyle{(x+2)(x-1)=0}\\\\\displaystyle{x=-2,1}$

These are potential solutions to the equation. To find extraneous solution, you’ll have to know the domain of logarithm function. We know that logarithm’s domain is defined to be greater than 0. Henceforth, anti-logarithm must be greater than 0.

( 1 ) 4x > 0, x > 0

( 2 ) x + 1 > 0, x > -1

Therefore, our anti-log must be greater than 0, so any solutions that are equal or less than 0 will be considered as extraneous solution.

Hence, x = -2 is the extraneous solution.

7 0

2 years ago

What decimal is greater than 8.5

Valentin [98]

9.5 cause it brought a ten up to show the decimel

8 0

3 years ago

Read 2 more answers

Find the rational roots f(x) =3x3+ 2x2 + 3x + 6

Ann [662]

The rational roots of f(x) = 3x^3 + 2x^2 + 3x + 6 are ±(1, 2, 3, 6, 1/3, 2/3)

<h3>How to determine the rational root of the function f(x)?</h3>

The function is given as:

f(x) = 3x^3 + 2x^2 + 3x + 6

For a function P(x) such that

P(x) = ax^n +...... + b

The rational roots of the function p(x) are

Rational roots = ± Possible factors of b/Possible factors of a

In the function f(x), we have:

a = 3

b = 6

The factors of 3 and 6 are

a = 1 and 3

b = 1, 2, 3 and 6

So, we have:

Rational roots = ±(1, 2, 3, 6)/(1, 3)

Split the expression

Rational roots = ±(1, 2, 3, 6)/1 and ±(1, 2, 3, 6)/3

Evaluate the quotient

Rational roots = ±(1, 2, 3, 6, 1/3, 2/3, 1, 2)

Remove the repetition

Rational roots = ±(1, 2, 3, 6, 1/3, 2/3)

Hence, the rational roots of f(x) = 3x^3 + 2x^2 + 3x + 6 are ±(1, 2, 3, 6, 1/3, 2/3)

The complete parameters are:

The function is given as:

f(x) = 3x^3 + 2x^2 + 3x + 6

The rational roots of f(x) = 3x^3 + 2x^2 + 3x + 6 are ±(1, 2, 3, 6, 1/3, 2/3)