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3 years ago

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Point N ( , 2 9) is on RS. A translation moves point N to its image, N'(6 3 , ). What is the distance, in units, between any poi

nt on RS and its image? A 10 B 40 C 52 D 130

1 answer:

KatRina [158]3 years ago

7 0

Hello!

Distance between two points (2,9) and (6,3) -

<span>1. Take the Absolute Difference between the X points 2 and 6. The Absolute Difference is 4. </span>
<span>2. Square 4 = 16 </span>
<span>3. Take the Absolute Difference between the Y points 9 and 3. The absolute Difference is 12. </span>
<span>4. Square 12 = 144 </span>
<span>5 Add 144 + 16 = 160 </span>
<span>6. Take the Square root of 160 </span>

<span>12.6491106407

Hope this Helps at least! :)</span>

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The exponential function f(x) = 3(5)x grows by a factor of 25 between x = 1 and x = 3. What factor does it grow by between x = 5

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<h2> Question # 1</h2>

Answer:

25 is the factor which grows by between x = 5 and x = 7.

Step-by-step explanation:

Considering the exponential function

$f\left(x\right)\:=\:3\left(5\right)^x$

The growth factor between $x=1$ and $x=3$ is given by:

$\left[3\left(5\right)^3\right]\div \left[3\left(5\right)^1\right]$

$\mathrm{Calculate\:within\:parentheses}\:\left[3\left(5\right)^3\right]\::\quad 375$

$\mathrm{Calculate\:within\:parentheses}\:\left[3\left(5\right)^1\right]\::\quad 15$

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= $375\div \:15$

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Similarly, growth factor between $x=5$ and $x=7$ is given by:

$\left[3\left(5\right)^7\right]\div \left[3\left(5\right)^5\right]$

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<h2> Question # 2</h2>

Answer:

The population be in 24 years will be 27000.

Also, the population growth modeled by an exponential function as $y=A\cdot \left(b\right)^t$ is an exponential function.

The graph for $y=A\cdot \left(b\right)^t$ is also shown in attached figure.

Step-by-step explanation:

If a city that currently has a population of 1000 triples in size every 8 years.
what will the population be in 24 years?
Is the population growth modeled by a linear function or an exponential function?

As the city that currently has a population of 1000 triples in size every 8 years.

So, for this case

$y=A\cdot \left(b\right)^t$

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$A$ = Initial population amount

$b$ = growth rate

$t$ = time

Substituting the values in the function

$y=A\cdot \left(b\right)^t$

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So, the population be in 24 years

$y=1000\cdot \:\:3^{\frac{1}{8}24}$

As

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Therefore, the population be in 24 years will be 27000.

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<h2 /><h2> Question # 3</h2>

Answer:

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Step-by-step explanation:

We have to find the effect on the graph of the function $f(x)=2x$ when it is replaced by f(x- 3/5).

We already have an idea that rule for horizontal translation:

Given a function $f(x)$ , and a constant c > 0, the function $g(x) = f(x - a)$ represents a horizontal shift c units to the right from f(x). The function $h(x) = f(x + a)$ represents a horizontal shift c units to the left.

As 3/5 > 0, so the graph of the function will translate horizontally 3/5 units right.

Therefore, the graph of the function will translate horizontally 3/5 units right.

Keywords: exponential function, translation function, growth factor

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