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3 years ago

Consider function f. f(x) = sqrt 7x- 21

Mathematics

2 answers:

Arada [10]3 years ago

6 0

Answer:

f^-1(x) = (x² + 21)/7

Step-by-step explanation:

Since f(x) = y = √(7x – 21), to find the inverse of f(x) we have to write x in terms of y in order to make x the dependent variable and y the independent variable. The steps involved are:

Step 1: square both sides of the equation, y = √(7x – 21). Doing that, we have:

y² = 7x – 21

Step 2: Add 21 to both sides of the resulting equation. Doing that, we have:

y² + 21 = 7x

Step 3: Divide both sides of the equation by 7. Doing that we have:

x = (y² + 21)/7

Step 4: Replace x with f^-1(x) and y with x. Doing that, we have:

f^-1(x) = (x² + 21)/7

kipiarov [429]3 years ago

4 0

Answer:look at explanation

Step-by-step explanation:

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How to reduce into simpler terms.?

Sveta_85 [38]

Answer:

The simplest form of the fraction $\frac{45}{100}$ is $\frac{9}{20}$ .

i.e.

$\frac{45}{100}=\frac{9}{20}$

Step-by-step explanation:

Here are some simple observations regarding how to reduce a fraction into simpler terms:

A fraction is reduced to lowest or simplest terms by finding an equivalent fraction in which the numerator and denominator are as small as possible.

In order to reduce a fraction to lowest or simplest terms, divide the numerator and denominator by their (GCF). Note that (GCF) is also called Greatest Common Factor .

So, lets take a sample fraction and reduce into simpler terms.

Considering the fraction

$\frac{45}{100}$

$\mathrm{Find\:a\:common\:factor\:of\:}45\mathrm{\:and\:}100\mathrm{\:in\:order\:to\:cancel\:it\:out}$

$\mathrm{Greatest\:Common\:Divisor\:of\:}45,\:100:\quad 5$

$\mathrm{Factor\:out\:}5\mathrm{\:from\:the\:numerator\:and\:the\:denominator}$

$45=5\cdot \:9\mathrm{,\:\quad }100=5\cdot \:20$

$\frac{45}{100}=\frac{5\cdot \:\:9}{5\cdot \:\:20}$

$\mathrm{Cancel\:the\:common\:factor:}\:5$

$=\frac{9}{20}$

Therefore, the simplest form of the fraction $\frac{45}{100}$ is $\frac{9}{20}$ .

i.e.

$\frac{45}{100}=\frac{9}{20}$

4 0

4 years ago

4. Find the length of side EG.

olchik [2.2K]

Answer:

42 cm

Step-by-step explanation:

the first triangle is 7 times bigger than the second triangle. ( 4 x 7 = 28)

so to find out line EG, you times 6 cm by 7. which is 42

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3 years ago

a boat makes a 120-mile trip downstream in 3 hours but makes the return trip in 4 hours. what is the rate of the boat in still w

Tpy6a [65]

Let b equal the speed of the boat in still water.
Let c equal the speed of the current.
Going downstream, we can write the equation:
$b+c=\frac{120}{3}$
which can be rearranged to:
3b + 3c = 120 ............(1)
Going upstream, we can write the equation:
$b-c=\frac{120}{4}$
which can be rearranged to:
4b - 4c = 120 .............(2)
Multiplying equation (1) by 4, and multiplying equation (2) by 3 we get:
12b + 12c = 480 ........(3)
12b - 12c = 360 .........(4)
Adding equations (3) and (4) results in the following equation:
24b = 840
$b=\frac{840}{24}=35\ mph$

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4 years ago

Rewrite 4x − 2y = 10 in slope-intercept form. Give the slope and y-intercept.

Allushta [10]

Add -2y and subtract 10
2y = 4x - 10
Divide by 2
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3 0

3 years ago

Read 2 more answers

A pair of pants costs twice as much as a shirt. The total cost of 1 pair of pants and 1 shirt is $18 . If s represents the cost

dolphi86 [110]

Let the price of 1 shirt be represented by = s

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