What is the difference quotient of the function, g (x) = startroot x endroot, x greater-than-or-equal-to 0?

Using linear functions, it is found that:

A linear function is modeled by the following rule:

y = mx + b

In which:

For Shop A, we have that the slope is of 3, as the cost increases by $3 an hour, hence:

yA(x) = 3x + b.

When x = 1, y = 8, hence we find the intercept b as follows:

8 = 3 + b

b = 5.

Hence:

yA(x) = 3x + 5.

For Shop B, the rule is given as follows:

yB(x) = 2x + 8.

Due to the lower slope, we have that:

Shop B charges less per hour.

The costs will be the same when:

yA(x) = yB(x).

Hence:

3x + 5 = 2x + 8

x = 3.

The total costs are the same when a pair of skis is rented for 3 hours.

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Answer: 53.05

Step-by-step explanation: Simply divide both using the division method. Show your work as the method. (would recommend drawing out the problem)

Answer:

60.5

Step-by-step explanation:

60.5

8 424

-42

0

4.0

4.0

0

An advantage of a weighted moving average (WMA) is that recent actual results can be given more importance than what occurred a while ago is a "true" statement because "Weighted moving averages could be adjusted to emphasize more recent data in forecasting."

Moving averages are popular tools for measuring momentum among active traders. The formula used to calculate the average is the primary distinction between a simple moving average, a weighted moving average, and an exponential moving average.

Some key features regarding the weighted moving average are-

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The function g(x) = - |x| + 2 is the result of applying a reflection about the x-axis and a translation 2 units up.

In this problem we find a resulting expression, that is, the function g(x) = - |x|   + 2. This is the result of a sequence of rigid transformations done on the parent absolute value function, that is, the function f(x) = |x|. Rigid transformations are transformations applied on functions such that Euclidean distance is conserved in the entire function.

After a quick inspection, we find that two rigid transformations were used in the following order:

Now we proceed prove this procedure:

f(x) = |x|

Step 1

f'(x) = - |x|

Step 2

g(x) = - |x| + 2

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An equation for the perpendicular bisector of the line segment whose endpoints are (−4,−1) and (8,-5) is [tex]y=-\frac{1}{3} x-\frac{7}{3}[/tex]

Find the line [tex]$y=m x+b$[/tex] passing through [tex]$(-4,-1),(8,-5)$[/tex]

Compute the slope [tex]$(-4,-1),(8,-5): \quad m=-\frac{1}{3}$[/tex]

Compute the [tex]$y$[/tex] intercept: [tex]$\quad b=-\frac{7}{3}$[/tex]

Construct the line equation [tex]$y=m x+b$[/tex] where [tex]$m=-\frac{1}{3}$[/tex] and [tex]$b=-\frac{7}{3}$[/tex]

[tex]y=-\frac{1}{3} x-\frac{7}{3}[/tex]

A perpendicular bisector can be defined as a line that intersects another line segment perpendicularly and divides it into two parts of equal measurement. We can draw a perpendicular bisector using a rule, a compass and a pencil.

Two lines are said to be perpendicular to each other when they intersect each other at 90 degrees or at right angles. And, a bisector is a line that divides a line into two equal halves. Thus, a perpendicular bisector of a line segment AB implies that it intersects AB at 90 degrees and cuts it into two equal halves.

A line segment that bisects another line segment at a 90° angle is known as a perpendicular bisector. In other words, a perpendicular bisector divides a line segment into two equal parts by intersecting it at a 90° angle.

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14 is the largest integer.

Let x, x+2 & x+4 be the 3 integers.

x + 2 (x+2)= (x+4)+20

x + 2x + 4 = x + 4 + 20

3x + 4 = x + 24

3x - x = 24 - 4

2x = 20

x = 20/2

x=10 for the smallest integer.

10 + 2 = 12 for the middle integer.

10 + 4 = 14 for the largest integer.

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Answer:

7√3

Step-by-step explanation:

Answer:

983,040

Step-by-step explanation:

4×5=20

6×32=192

4×4=16

4×4=16

20×192×16×16

=983,040

Answer:

0.02

Step-by-step explanation:

Answer:

first option

Step-by-step explanation:

They are cumulative because they are constant functions.

Answer: 227 is a rational number because it can be expressed as the quotient of two integers: 227 ÷ 1.

Step-by-step explanation:

The expression in scientific notation is given as follows:

3.5 x 10³.

A number in scientific notation is given by:

[tex]a \times 10^b[/tex]

With the base being [tex]a \in [1, 10)[/tex].

For this problem, the expression is given by:

[tex]\frac{5 \times 10^2 \times 4.2 \times 10^4}{6 \times 10^3}[/tex]

When two factors of a multiplication have the same base and different exponent, we keep the base and add the exponents, hence:

[tex]10^2 \times 10^4 = 10^6[/tex]

5 x 4.2 = 21, hence the expression is:

[tex]\frac{5 \times 10^2 \times 4.2 \times 10^4}{6 \times 10^3} = \frac{21 \times 10^6}{6 \times 10^3}[/tex]

When we divide two terms with the same base and different exponents, we keep the base and subtract the exponents, hence:

[tex]\frac{21 \times 10^6}{6 \times 10^3} = 3.5 \times 10^3[/tex]

Which is the simplified expression.

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The value of m is 3

The expression can be written as follows

The sum of 5 times a number m and 12 is equal to 27

5m + 12 = 27

collect the like terms

5m= 27-12

5m= 15

Divide both sides by the coefficient of m which is 5

5m/5 = 15/5

m= 3

Hence the value of m is 3

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Answer:

Rs 984

Step-by-step explanation:

Principal (P) = Rs 9,600

Time (T) = 2 years

Rate (R) = 5%

Simple Interest (SI) = [tex]\frac{PTR}{100}[/tex]

SI = [tex]\frac{9600*2*5}{100}[/tex]

SI = [tex]\frac{9600}{10} = Rs 960[/tex]

Compound Interest (CI) = 9600 * [tex]\frac{41}{100} = 24*41 = Rs 984[/tex]

Answer:

16

Step-by-step explanation:

x=-3

g(x)=4(-4(-3)-8)

g(x)=4(4)

g(x)=16

Answer:

1 : 4 1/2 :: 8 1/5 : x            proportion

x = (4 1/2)(8 1/5)                product of means/extremes

x = (9/2)(41/5)                   change improper fraction

x = 369/10                         multiply

x = 36.9                              change to decimal

Answer:

278

Step-by-step explanation:

First, add 85+95=180.

Then, add 56+42=98

Add 180+98=278

The order from least to greatest of the numbers will be D. one fifth, thirty percent, 0.8, four thirds.

It should be noted that 1/5 = 0.2

It should be noted that 30% = 0.3

It should be noted that 4/3 = 1.33

Therefore the order from least to greatest of the numbers will be one fifth, thirty percent, 0.8, four thirds

In conclusion, the correct option is D.

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Answer:

2c+2

The number that will go in the green box is 2.

Step-by-step explanation:

3c-1-c+3

Combine the like terms.

3c-1-c+3=2c+2

Hope this helps!

Please mark as brainliest if correct!

The y values from:

1. ₋6

2. ₋3

3. 0

4. 3

Given the x values and y value as y = 3x

1. when x = ₋2 then y = 3x

y = 3(₋2)

y = ₋6

2. when x = ₋1 then y = 3x

y = 3(₋1)

y = ₋3

3. when x = 0 then y = 3x

y = 3(0)

y = 0

4. when x = 1 then y = 3x

y = 3(1)

y = 3

therefore we get the points as (₋2 , ₋6) (₋1 , ₋3) (0,0) (1 , 3).The graph is pltted and attached.

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Answer: d=12

Step-by-step explanation:

[tex]\displaystyle\\\frac{3d-2}{8} =-d+16\frac{1}{4} \\\\\frac{3d-2}{8} =-d+\frac{16*4+1}{4} \\\\\frac{3d-2}{8} =-d+\frac{64+1}{4} \\\\\frac{3d-2}{8} =-d+\frac{65}{4}[/tex]

Multiply both parts of the equation by 8:

[tex]\displaystyle\\3d-2=(-d+\frac{65}{4} )(8)\\\\3d-2=-8d+65*2\\\\3d-2=-8d+130\\\\3d-2+2=-8d+130+2\\\\3d=-8d+132\\\\3d+8d=-8d+132+8d\\\\11d=132\\[/tex]

Divide both parts of the equation by 11:

[tex]d=12[/tex]

Step-by-step explanation:

[tex] - 4x + 3(2x - 5) = 31 \\ - 4x + 6x - 15 = 31 \\ 2x - 15 = 31 \\ 2x = 31 + 15 \\ 2x = 46 \\ x = 46 \div 2 \\ x = 23[/tex]

The domain at which the function f(x) = x² - 4•x + 2, and the inverse of the function, f(x), is given by the option;

The given function is f(x) = x² - 4•x + 2.

The points through which the parabola passes are;

The inverse of the function is found as follows;

f(x) = x² - 4•x + 2

The standard form of a quadratic equation is f(x) = a•(x - h)² + k

Where;

(h, k) = The coordinates of the vertex

a = The coefficient of x²

Comparing, we have;

(h, k) = (2, -2)

a = 1

Which gives;

f(x) = x² - 4•x + 2 = (x - 2)² - 2

f(x) = (x - 2)² - 2

Let f(x) = y

y = (x - 2)² - 2

y + 2 = (x - 2)²

x - 2 = √(y + 2)

x = √(y + 2) + 2 = 2 + √(y + 2)

x = 2 + √(y + 2)

Therefore, f(x) has an inverse when y > -2, which gives;

The domain where f(x) has an inverse is x > 2, given that the expression, 2 + √(y + 2), is always positive.

The inverse of the function is obtained by changing x to [tex] f^{-1}(x) [/tex] and y to x in the equation, x = 2 + √(y + 2), to give;

The correct option is therefore;

x > 2, f superscript negative 1 Baseline (x) = 2 + StartRoot x + 2 EndRoot

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Answer:

Its D.x > 2; f Superscript negative 1 Baseline (x) = 2 + StartRoot x + 2 EndRoot

Step-by-step explanation:

The cinnamon-scented jar candle brunt faster.

Relativity means observing some action with different perspective.

Suppose you are moving in a bus at 100 km/hr and you are reading a book.To an observer which you are passing by you and the book he observes moving at a speed of 100 km/hr.But for you the book is not moving at all because both you and the book is moving at a speed of 100 km per hour.

According to the given question Andrei had cinnamon-scented jar candle that burned for 303030 hours and a berry-scented pillar candle that burned for 888888 hours.

From the given data of burning hours we can observe that berry-scented pillar candle that burned for 888888 hours which is more that of Andrei had cinnamon-scented jar candle that brunt for 303030 hours because

30303030 < 888888.

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Answer:

true

Step-by-step explanation:

needed to eliminate bias

Answer: x=6.5

Step-by-step explanation:

3(2x - 4) = 8 + 2x + 6

6x-12=14+2x

4x-12=14

4x=26

x=26/4

x=6.5

Given equation g = x-1/k in terms of x would be x = 1 + gk

for given question,

we have been given an equation g = x-1/k

Dyani began solving the equation g = x-1/k for x by using the addition property of equality.

We solve given equation for x.

⇒ g = x-1/k                      ..........(Given)

⇒ gk = (x - 1/k)k               .........(Multiply both the sides by k)

⇒ gk = x - 1

⇒ gk + 1 = x - 1 + 1           .........(Add 1 to each side)

⇒ gk + 1 = x

⇒ x = 1 + gk

Therefore, given equation g = x-1/k in terms of x would be x = 1 + gk

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Answer: 1

Step-by-step explanation:

How big is the table? 1 table can fit all 17 people if the table is big enough.

1)

In this question, we have been given Tank A initially contained 124 liters of water. It is then filled with more water, at a constant rate of 9 liters per minute.

1 minute = 9 liters

⇒ 60 seconds = 9 liters

⇒ 20 seconds = 3 liters

We need to find the amount of water in the tank A

a) when 4 minutes

Given that, 1 minute = 9 liters

Let y1 liters of water in the tank A after 4 minutes

So, we get an equation,

y1 = 9 × 4

y1 = 36 liters

36 + 124 (initial water level) = 160 liters

Hence, 160 liters of water in the tank A after 4 minutes been passed.

b) when 80 seconds

From given information, 20 seconds = 3 liters

Let y2 liters of water in the tank A after 80 seconds

So, we get an equation,

20 (y2) = 3 × 80

y2 = 12 liters

12 + 124 (initial water level) = 136 liters

Hence, 136 liters of water in the tank A after 80 seconds been passed.

Now we need to find the amount of time passed when Tank A contains the following amounts of water.

i) 151 liters

151 - 124 = 27 liters of more water filled.

As we know,  1 minute = 9 liters ..............................(Given)

Let t1 be the required time.

so, we get an equation,

9 × t1 = 1 × 27

t1 = 27 / 9

t1 = 3 minutes

This means, 3 minutes have passed when Tank A contains 151 liters of water.

ii) 191.5 liters

191.5 - 124 = 67.5 liters of more water filled.

As we know,  1 minute = 9 liters ..............................(Given)

Let t2 be the required time.

so, we get an equation,

9 × t2 = 1 × 67.5

t2 = 67.5 / 9

t2 = 7.5 minutes

t2 = 7 minutes 30 seconds

This means, 7 minutes 30 seconds have passed when Tank A contains 191.5 liters of water.

iii) 270.25 liters

270.25 - 124 = 146.25 liters of more water filled.

As we know,  1 minute = 9 liters ..............................(Given)

Let t1 be the required time.

so, we get an equation,

9 × t1 = 1 × 146.25

t3 = 146.25 / 9

t3 = 16.25 minutes

t3 = 16 minutes 15 seconds

This means, 16 minutes 15 seconds have passed when Tank A contains 270.25 liters of water.

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

2)

In this question, Tank B, which initially contained 80 liters of water, is being drained at a rate of 2.5 liters per minute.

⇒ 1 minute = 2.5 liters of water drained

⇒ 60 seconds = 2.5 liters

⇒ 10 seconds = 0.42 liters

We need to find the amount of water drained from tank B

a) after 30 seconds

Let x1 be the amount of water drained after 30 seconds

Given that, 1 minute = 2.5 liters

So, we get an equation.

10 (x1) = 30 × 0.42

x1 = 3 × 0.42

x1 = 1.26 liters

b) after 7 minutes

Let x2 be the amount of water drained after 30 seconds

Given that, 1 minute = 2.5 liters

So, we get an equation.

x2 = 7 × 2.5

x2 = 17.5 liters

Now, we need to find the time in which the water is draining when Tank B contains

i) 75 liters

80 - 75 = 5 liters of more water drained.

As we know,  1 minute = 2.5 liters water drained       ............(Given)

Let t1 be the required time.

so, we get an equation,

2.5 × t2 = 5

t1 = 5 / 2.5

t1 = 2 minutes

This means, after 2 minutes Tank B contains 5 liters of water.

ii) 32.5 liters

80 - 32.5 = 47.5 liters of more water drained.

As we know,  1 minute = 2.5 liters water drained       ............(Given)

Let t2 be the required time.

so, we get an equation,

2.5 × t2 = 47.5

t2 = 47.5 / 2.5

t2 = 19 minutes

This means, after 19 minutes Tank B contains 32.5 liters of water.

iii) 18 liters

80 - 18 = 62 liters of more water filled.

As we know,  1 minute = 2.5 liters water drained       ............(Given)

Let t3 be the required time.

so, we get an equation,

2.5 × t3 = 62

t3 = 5 / 2.5

t3 = 24.8 minutes

t3 = 24 minutes 48 seconds

This means, after 24 minutes 48 seconds Tank B contains 18 liters of water.

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