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2 years ago

Simplify the expression 2(x-6)+2(8)

Mathematics

1 answer:

jolli1 [7]2 years ago

8 0

Answer:

2x+4

Step-by-step explanation:

Distribute:

=(2)(x)+(2)(−6)+(2)(8)

=2x+−12+16

Combine Like Terms:

=2x+−12+16

=(2x)+(−12+16)

=2x+4

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For the function g(x)=3-8(1/4)^2-x

Reika [66]

Using function concepts, it is found that:

a) The y-intercept is y = 2.5.

b) The horizontal asymptote is x = 3.

c) The function is decreasing.

d) The domain is $(-\infty,\infty)$ and the range is $(-\infty,3)$ .
e) The graph is given at the end of the answer.

------------------------------------

The given function is:

$g(x) = 3 - 8\left(\frac{1}{4}\right)^{2-x}$

------------------------------------

Question a:

The y-intercept is g(0), thus:

$g(0) = 3 - 8\left(\frac{1}{4}\right)^{2-0} = 3 - 8\left(\frac{1}{4}\right)^{2} = 3 - \frac{8}{16} = 3 - 0.5 = 2.5$

The y-intercept is y = 2.5.

------------------------------------

Question b:

The horizontal asymptote is the limit of the function when x goes to infinity, if it exists.

$\lim_{x \rightarrow -\infty} g(x) = \lim_{x \rightarrow -\infty} 3 - 8\left(\frac{1}{4}\right)^{2-x} = 3 - 8\left(\frac{1}{4}\right)^{2+\infty} = 3 - 8\left(\frac{1}{4}\right)^{\infty} = 3 - 8\frac{1^{\infty}}{4^{\infty}} = 3 -0 = 3$

--------------------------------------------------

$\lim_{x \rightarrow \infty} g(x) = \lim_{x \rightarrow \infty} 3 - 8\left(\frac{1}{4}\right)^{2-x} = 3 - 8\left(\frac{1}{4}\right)^{2-\infty} = 3 - 8\left(\frac{1}{4}\right)^{-\infty} = 3 - 8\times 4^{\infty} = 3 - \infty = -\infty$

Thus, the horizontal asymptote is x = 3.

--------------------------------------------------

Question c:

The limit of x going to infinity of the function is negative infinity, which means that the function is decreasing.

--------------------------------------------------

Question d:

Exponential function has no restrictions in the domain, so it is all real values, that is $(-\infty,\infty)$ .
From the limits in item c, the range is: $(-\infty,3)$

--------------------------------------------------

The sketching of the graph is given appended at the end of this answer.

A similar problem is given at brainly.com/question/16533631

8 0

2 years ago

Of the total number of spectators at a circus show, 1/4 are men. 2/5 of the remaining number of spectators are women. There are

ch4aika [34]

Answer: There are $198$ children at the circus show.

Step-by-step explanation:

Let be "x" the total number of spectators at the circus show and "c" the number of children at the circus show.

Knowing that $\frac{1}{4}$ of the spectators are men, we can find the remaining:

$x-\frac{1}{4}x=\frac{3}{4}x$

Since $\frac{2}{5}$ of the remaining number of spectaros are women and there are a total of 132 women, we can write the following equation:

$(\frac{2}{5})(\frac{3}{4}x)=132$

Solving for "x", we get:

$x=(132)(\frac{20}{6})\\\\x=440$

Therefore, we get that "c" is:

$c=440-\frac{1}{4}(440)-132\\\\c=198$

8 0

3 years ago

Use the expression shown below. 1 = (4 x 4 x 4 x 4 x 4) What is the value of the expression.

jeka57 [31]

Answer:

1024

Step-by-step explanation:

5 0

2 years ago

What is the total quotient of 6476 divided by 12

olga55 [171]

1619/3 as a fraction

539.666667 as a decimal

4 0

3 years ago

What is the area of this figure? 168 102 132 340

JulsSmile [24]

Area of square =6*6= 36 cm^2
Area of trapezoid =1/2( base1+base2)*height
base 1=7
base2=21-6=15
height=6
Area of trapezoid =1/2( 7+15)*6= 66
whole area = area of square + area of trapezoid= 36+66=102
Answer 102

8 0

2 years ago