Given the functions f(x) = –4x + 5 and g(x) = x3 + x2 – 4x + 5, what type of functions are f(x) and g(x)? Justify your answer. What key feature(s) do f(x) and g(x) have in common? (Consider domain, range, x-intercepts, and y-intercepts.)

Start at 3 and multiply by -4 each time.

well, at the beginning of the 6th year, you've been there for 5 whole years, so you've gotten 5 increases hmmm

[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &16000\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ t=years\dotfill &5\\ \end{cases} \\\\\\ A=16000(1 + 0.03)^{5}\implies A=16000(1.03)^5\implies A\approx 18548.39[/tex]

Answer:

-1/2 is correct

Step-by-step explanation:

Among the given options, option C [tex](\( \frac{1}{2} \))[/tex] is the closest to [tex]\( \frac{24}{49} \)[/tex]. Therefore, the answer is: C. [tex]\( \frac{1}{2} \)[/tex]. To evaluate the expression (g - f)(2), you need to first find the values of g(2) and f(2), and then subtract f(2) from g(2).

Given:

[tex]\( f(x) = \frac{x + 3}{x^2 + 2x - 3} \) \\ \( g(x) = \log_4(x) \)[/tex]

Let's start by calculating the values of f(2) and g(2): 1. [tex]\( f(x) = \frac{x + 3}{x^2 + 2x - 3} \)[/tex]

Substitute (x = 2):   [tex]\( f(2) = \frac{2 + 3}{2^2 + 2 \cdot 2 - 3} = \frac{5}{7} \)[/tex]

2. [tex]\( g(x) = \log_4(x) \)[/tex]  Substitute ( x = 2):  [tex]\( g(2) = \log_4(2) \)[/tex]

Now, evaluate the expression [tex]\( (g - f)(2) \):[/tex]

[tex]\( (g - f)(2) = g(2) - f(2) = \log_4(2) - \frac{5}{7} \)[/tex]

To determine which option matches this value, calculate [tex]\( \log_4(2)[/tex]) and subtract [tex]\( \frac{5}{7} \)[/tex] from it.

Approximately,[tex]\( \log_4(2) \)[/tex] is around 0.5.

So, [tex]\( (g - f)(2) \approx 0.5 - \frac{5}{7} \)[/tex]. To compare this result with the options provided, convert the fractions to a common denominator:

[tex]\( \frac{5}{7} = \frac{35}{49} \)[/tex]. So, [tex]\( (g - f)(2) \approx 0.5 - \frac{35}{49} \)[/tex].

Now, simplify the subtraction: [tex]\( 0.5 - \frac{35}{49} = \frac{24}{49} \)[/tex]

Among the given options, option C [tex](\( \frac{1}{2} \))[/tex] is the closest to [tex]\( \frac{24}{49} \)[/tex]. Therefore, the answer is: C. [tex]\( \frac{1}{2} \)[/tex]

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Answer:

34 cm

Step-by-step explanation:

Keep in mind that the perimeter of a rectangle is the sum of the measures of its sides. This means that the sum of the longer sides and the shorter sides is the perimeter of the rectangle.

Let "L" represent the longer side (length) of the rectangle and "S" represent the shorter side (width) of the rectangle.

⇒ Perimeter of rectangle = L + S + L + S

⇒ Perimeter of rectangle = 2(L) + 2(S)

⇒ Perimeter of rectangle = 2(L + S)

Now, let's substitute the length and the width in the perimeter and simplify.

⇒ Perimeter of rectangle = 2(10 + 7)                                                [L = 10; S = 7]

⇒ Perimeter of rectangle = 2(17)

⇒ Perimeter of rectangle = 34 cm

Answer: 70 cm

Step-by-step explanation: 10 x 7 = 70

hope this helps

Answer:

25

Step-by-step explanation:

5 > x/5

5 × 5 > (x/5) × 5

25 > x

Answer:

10

Step-by-step explanation:

The least common denominator can be found by finding the LCM of the 2 denominators:

First let's list the multiples of the first denominator :

10,20,30,40,50

Now let's list the multiples of the second denominator :

5,10,15,20,25

As we can see the lowest number that appears in both lists is 10.

Therefore 10 is the least common denominator.

Nandyan na po

Step-by-step explanation:

Answer:

Step-by-step explanation:

12y = 2x + 12

y = 2/12x + 12/12

y = 1/6x + 1

The slope intercept form is y = (1/6)x + 1.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

12y - 2x = 12

The slope intercept form is y = mx + c.

So,

12y - 2x = 12

Add 2x on both sides.

12y = 12 + 2x

12y = 2x + 12

Divide both sides with 12.

y = (2/12)x + (12/12)

y = (1/6)x + 1

Thus,

The slope intercept form is y = (1/6)x + 1.

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The work done by the machine is the product of force and distance

The amount of work done by the machine is 10 joules

The amount of work done is calculated using:

W = Fd

Where:

The distance moved to the living room is the same when you move the chair or a machine does is the same.

Also, if the force applied in moving the chair remains unchanged, the amount of work done would be the same.

Hence, the amount of work done by the machine is 10 joules

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Answer:

477 square foot

Step-by-step explanation:

cause yea

Answer:

[tex]\sf \dfrac{1}{10}[/tex]

Step-by-step explanation:

From the table:

[tex]\sf Probability \ of \ an \ event \ occurring = \dfrac{Number \ of \ ways \ it \ can \ occur}{Total \ number \ of \ possible \ outcomes}[/tex]

[tex]\sf \implies P(Sophomore)=\dfrac{10}{37}[/tex]

[tex]\sf \implies P(Boy \cap Sophomore)=\dfrac{1}{37}[/tex]

[tex]\begin{aligned}\sf P(Boy | Sophomore) & = \sf\dfrac{P(Boy \cap Sophomore)}{P(Sophomore)}\\\\ & = \sf \dfrac{1}{37} \div \dfrac{10}{37}\\\\ & = \sf\dfrac{1}{37} \times\dfrac{37}{10}\\\\ & = \sf\dfrac{1}{10}\end{aligned}[/tex]

Answer:

1/10

Explanation:

Given Boy Sophomores: 1

Given Total Boy: 3 + 1 + 4 + 2 = 10

So

⇒  P(Boy|Sophomore)  

⇒  Boy Sophomore/Total Boy

⇒  1/10

Answer:

x = 15

Step-by-step explanation:

Since m and n are parallel to the line t.

Then (7x - 10) + (6x - 5) = 180° supplementary angles for a linear pair.

(7x - 10) + (6x - 5) = 180°

13x -15 = 180°

13x = 195°

x = 15

Plug x into the angles to solve for angle.

(7x - 10)

(7*15 - 10) = 105 - 10 = 95°

(6x - 5) =

(6*15 - 5) = 90 - 5 = 85°

Answer:

The answer is shown in the picture. you basically have to do integration by parts 2 times to get final answer.

Let's write this verbal phrase as an inequality.

First of all, let the number be n.

"three times n" can be written like so:-

[tex]\pmb{3n}[/tex]

Now, 18 is greater than 3n:-

[tex]\pmb{18 > 3n}[/tex]

Which means 3n is less than 18:-

[tex]\bigstar{\boxed{\pmb{3n < 18}}}[/tex]

Hope everything is clear; if you need any explanation/clarification, kindly let me know, and I'll comment and/or edit my answer :)

Answer:

  surface area

Step-by-step explanation:

Wrapping paper covers the surface of an object.

To know how much paper he needs, Landry will need to determine the surface area of the present.

Answer:

$37.5+$3r

Step-by-step explanation:

We can assume that the number of rides is r. Since each ride is $3.00, all rides are $3r ($3xr).

We also know that there are FIVE people going to the fair, with Tory being one and each of her friends. Since the entrance fee is 7.50, we can do 7.50x5 which is $37.5.

Then, you can add it which is $37.5+$3r

Answer:

Mean Absolute Deviation (MAD): 3

Step-by-step explanation:

Answer:

no idea

is the answer

if you like my answer please like comment and mark me as brilliant

The mean amount of money Sadie saves each month is $10,724.29.

Mean is a measure of central tendency that is used to determine the average of a set of numbers. It is determined by adding the numbers together and dividing it by the total number

Mean = sum of the numbers / total number

(10150 + 102211 + 10424 + 10769 + 11155 + 11477) / 7 =  $10,724.29.

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The answer to this question is D 2/4

Answer:

Yes;

Step-by-step explanation:

5/2 = 2 1/2

2 1/2 > 1

Yes, 5/2 is to the right of 1 on a number line.

Answer:

Step-by-step explanation:

Use the order of operations to solve this problem.

[tex]\Longrightarrow: \sf{\sqrt{28-3(4)} }[/tex]

Remove parentheses.

→ (4)=4

Rewrite the problem down.

[tex]\Longrightarrow:\sf{\sqrt{28-3*4} }[/tex]

PEMDAS stands for:

→ 28-3*4

Multiply.

→ 3*4=12

→ 28-12

Subtract.

→ 28-12=16

[tex]\Longrightarrow:\sf{\sqrt{16} }[/tex]

[tex]\Longrightarrow\sf{\sqrt{16}=4^2 }[/tex]

Use the radical rule.

[tex]\Longrightarrow: \sf{4^2=\boxed{\sf{4}}[/tex]

I hope this helps you! Let me know if my answer is wrong or not.

Answer:

[tex]\±4[/tex]

Step-by-step explanation:

Given expression: [tex]\sqrt{28 - 3(4)}[/tex]

Here, we can see that the terms, 28 and 3(4) are inside the root. Since the two terms are inside the root, we can subtract them. Therefore:

Usually, [tex]\sqrt{16}[/tex] can also be written as [tex]\sqrt[2]{16}[/tex]. Therefore:

Therefore, the simplified expression is ±4.

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Answer:

Below in bold.

Step-by-step explanation:

Supplementary angles add up to 180 dgrees, so we have the equation:

3x + 19 + 7x - 9 = 180

10x + 10 = 180

10x = 180 - 10

10x = 170

x = 17.

So m <ABC = 3(17) + 19 = 70 degrees

and m < DBC = 7(17) - 9 = 110 degrees.

Answer:

3x + 19+7x-9=180

10x+10=180

10x=180-10

10x=170

x =17

Step-by-step explanation:

oh that is again something you can nicely envision :

the inner circle has a radius of 59 ft.

so, because of the 2 ft wide track the outer circle has a radius of 59+2 = 61 ft.

the circumference of a circle is

2×pi×r

the answer to the question is simply the difference bergen the 2 circumference values.

inner circle :

2×pi×59 = 118pi

outer circle :

2×pi×61 = 122pi

the difference is

122pi - 118pi = 4pi = 12.56637061... ft ≈ 12.6 ft

the wheel on the outer track travels about 12.6 ft farther than a wheel on the inner track in one full turn.

Answer:

Step-by-step explanation:

r (2 x + 8) - x - 4

(2 r - 1) x + 8 r - 4

Answer:

[tex]y = \frac{2}{3}x + 4[/tex]

Step-by-step explanation:

The rule for graphs is:

[tex]y = mx + c[/tex]

Where [tex]m[/tex] is the gradient and [tex]c[/tex] is the y-intercept (where the line crosses the y-axis)

We can work out c by looking at our graph.

Our line crosses the y-axis at (0, 4). So... [tex]c=4[/tex]

To work out our gradient of a straight line (which is what we have)

We use the formula:

[tex]m = \frac{\triangle y}{\triangle x}[/tex]

The triangle [tex]\triangle[/tex] just means the "change in" the coordinates between any two points.

To calculate the change in y, we can pick any two points on our line!

Let's go for (0, 4) and (-6, 0)

To work out the gradient:

[tex]m = \frac{\triangle y}{\triangle x} = \frac{0 - 4}{-6 - 0} = \frac{-4}{-6} = \frac{4}{6} = \frac{2}{3}[/tex]

Using our formula

[tex]y = mx + c[/tex]
[tex]y = \frac{2}{3}x + 4[/tex]