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2 years ago

Can you answer this and simplify this?

Mathematics

1 answer:

BARSIC [14]2 years ago

7 0

Answer and Step-by-step explanation:

The length of the rectangle is 3 + w (w represents the width).

The polynomial representing the area of the rectangle:

a (area) = w(3 + w) = w^2 + 3w

a = 1

b = 2

c = 3

d = 1

w = 4

(4)^2 + 3(4) = 8 + 12 = 20

e = 20

#teamtrees #PAW (Plant And Water)

I hope this helps!

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2 years ago

Find the equation of the line passing through the points (6,3) and (-4,3) Y=

Molodets [167]

${ \qquad\qquad\huge\underline{{\sf Answer}}}$

Equation of line passing through given points :

Let's proceed with two point form ~

$\qquad \sf \dashrightarrow \: y - y1 = \cfrac{y2 - y1}{x2 - x1} (x - x1)$

Assume :

$\qquad \sf \dashrightarrow \: y - 3= \cfrac{3 - 3}{ - 4 - 6} (x - 6)$

$\qquad \sf \dashrightarrow \: y - 3= \cfrac{0}{ - 10} (x - 6)$

$\qquad \sf \dashrightarrow \: y - 3 = 0$

$\qquad \sf \dashrightarrow \: y = 3$

So, the equation of required line is : y = 3 ~

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9 months ago

Graphing exponential functions and then State the domain, range and asymptote

Luda [366]

9514 1404 393

Answer:

D: all real numbers

R: f(x) > 0

A: f(x) = 0

(-∞, 0), (+∞, +∞)

vertical stretch by a factor of 2; left shift 2 units

Step-by-step explanation:

The transformation ...

g(x) = a·f(b(x -c)) +d

does the following:

vertical stretch by a factor of 'a'
horizontal compression by a factor of 'b'
translation right by 'c' units
translation up by 'd' units

For many functions, horizontal coordinate changes are indistinguishable from vertical coordinate changes. Exponential functions tend to be one of those.

Using the above notation, you seem to have f(x) = 3^x, and g(x) = 2f(x+2). The transformation is a vertical stretch by a factor of 2, and a translation left 2 units.

As with all exponential functions, ...

the domain is "all real numbers"
the range is all numbers above the asymptote: f(x) > 0
the horizontal asymptote is f(x) = 0

The function is a growth function, so ...

x → -∞, f(x) → 0
x → ∞, f(x) → ∞

_____

Additional comment

The left shift is equivalent to an additional vertical stretch. The function could be rewritten as ...

f(x) = 18(3^x)

with no left shift and a vertical stretch by a factor of 18 instead of 2.

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2 years ago

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vlada-n [284]

Answer:

If a rug was 5 times as long as this record sheet. The length of this record sheet in centimeters is 100x centimeter

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Given that a rug was 5 times than the record sheet.

Let assume the length of the record sheet = x units

Then from given information,

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Suppose the given length is in meters, than need to multiply the given length by 100 to get the length in centimeter that is

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Conversion factor will change accordingly to the unit of given length which needs to be convert into centimeter.

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