Which of the following rational functions is graphed below?
10-
10
-10
-10-
O A. F(x) =
X-2
x(x + 5)
OB. F(x)=
1
(x+5)(x-2)
O C. F(x) = (x+5)(x - 2)
X
O D. F(x) = (x+5)(x-2)
X

Answer:

No

Step-by-step explanation:

There are multiple coordinates with the same x coordinate

Using translation concepts, the equation for the graph is given as follows:

b. [tex]y = \cos{\left(x + \frac{\pi}{2}\right)} + 1[/tex].

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

In this problem, we have a cosine function(zero at pi/2, this is zero at the origin), shifted pi/2 units to the right and 1 unit up(as the standard amplitude is between -1 and 1, here is between 0 and 2).

Hence the rule is given by:

b. [tex]y = \cos{\left(x + \frac{\pi}{2}\right)} + 1[/tex].

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The solution to the given non linear system of equation is smallest x value , x = 0 , y = 1 , largest x value  x = 3 , y = 8 .

An Equation is a mathematical statement which relates two algebraic expression with an equal sign in between.

The equations given in the question is

y = 2ˣ

This is an exponential function

-7x +3y = 3

This is a linear function

The equations have been plotted and the solution to the non linear system of equation has been determined

The point at which the graphs intersect is the solution to the system of non -linear equations.

(0,1) and (3,8)

x = 0 , y = 1 ; x = 3 , y = 8

The solution to the given non linear system of equation is smallest x value , x = 0 , y = 1 , largest x value  x = 3 , y = 8 .

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Answer:

∠A ≅ ∠D

Step-by-step explanation:

When writing a triangle congruency like ΔABC ≅ ΔDEF, the angles are congurent based on the orders listed. For example the first angle A is congruent with the first angle of the other triangle D.  

∠A ≅ ∠D

∠B ≅ ∠E

∠C ≅ ∠F

Answer:

50 ml

Step-by-step explanation:

50 ml

That's because there's this thing called polite people

Answer:

Because she is nice unlike me

Step-by-step explanation:

give me brainiest pls

see? I am not nice :) But seriously can I get brainliest?

y intercept is 2, which shows while changing the jobs employees bring two customers.

A linear equation is in the form, y = mx + b where m is the rate of change (slope) and b is the y intercept (initial value of y).

The complete question is:

The graph displays the relationship between the length of time an employee works at a company and the number of the employee's monthly customers.

Time Employed (Month)

If the equation for the line of best fit is y = 4.5x + 2, which of the following can be used to interpret the y-intercept in context?

Employee training takes 2 months.

Employee training takes 4.5 months.

Employees are likely to bring 2 customers with them when changing jobs.

Employees are likely to bring 4.5 customers with them when changing jobs.

As, linear equation is

y = mx + b

Let y be the number of customers and x be the length of time.

Then, y = 4.5x + 2

As, y intercept is 2, which shows while changing the jobs employees bring two customers.

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The initial value of the sequence is 1

From the graph, we have the following ordered pairs

(x, y) = (1, 1), (2, 4) and (3, 8)

Remove the x values

y = 1, 4, 8

The first value in the above sequence is 1

Hence, the initial value of the sequence is 1

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Answer:

212

Step-by-step explanation:

Simple addition and subtraction is to be used here.

5, 3 = 28

5-3 = 2 , 5+3 = 8

9 , 1 = 810

9-1 = 8 , 9+1 = 10

8 , 7 = 115

8-7= 1 , 8+7 = 15

6 , 2 = 48

6-2 = 4 , 6+2 = 8

7 , 5 = 212

7-5 = 2 , 7+5 = 12

Answer:

212

Step-by-step explanation:

Rule

5 - 3 = 2

5 + 3 = 8

Therefore: 28

9 - 1 = 8

9 + 1 = 10

Therefore: 810

8 - 7 = 1

8 + 7 = 15

Therefore: 115

6 - 2 = 4

6 + 2 = 8

Therefore: 48

7 - 5 = 2

7 + 5 = 12

Therefore: 212

Answer:

[tex]h(x)=\frac{1}{2}x -\frac{1}{2} .[/tex]

Step-by-step explanation:

if the initial function is f(x)=2x+1, then

x=2*h(x)+1;

2h(x)=x-1;

[tex]h(x)=\frac{x}{2} -\frac{1}{2}.[/tex]

PS. change design according the local requirements.

Answer:

[tex]y^{-1} =\frac{1}{2} x-\frac{1}{2}[/tex]

Step-by-step explanation:

To find the inverse, you want to swap the inputs with the outputs, which is why you have the swapped domain and range between a function and its range.

So, given f(x)=2x+1, its inverse would give,

x=2y+1.

Solve for y,

2y=x-1 -> y=(x-1)/2 -> y=[tex]\frac{1}{2} x-\frac{1}{2}[/tex]

Therefore, [tex]y^{-1} =\frac{1}{2} x-\frac{1}{2}[/tex]

Answer:

y=3x+8

Step-by-step explanation:

First of all, remember what the equation of a line is:

y = mx+b

Where:

m is the slope, and

b is the y-intercept

you find the slope by using this formula:

then we figure out it is 3

then graph to find the y-intercept which is 8

Answer:

y = 3x + 8

Step-by-step explanation:

Below is the image for the formula of the slope.

1. Subtract y values:
17 - 5 - 12
2. Subtract x values:
3 - (-1) = 4
3. Divide y/x
12 / 4 = 3
Therefore, the slope is 3.

Next, you need to find the y-intercept. This is our equation so far:
y = 3x + b
We can substitute any of the points given to us from the problem. I will use the first point: (-1, 5).

When substituting, you get:
5 = 3 ( -1 ) + b
5 = -3 + b
b = 8

Therefore, the equation is y = 3x + 8

Answer:

542

Step-by-step explanation:

So X is the number of finals graded by teacher last year

she graded 83 more finals than the last year

and the total number of finals she graded this year is 625 so we have an equation

X + 83 = 625

and as you solve it for X

X = 625-83

x = 542

Answer:

542,

Step-by-step explanation:

You could solve these types of problems with inverse operations, so if you subtract 83 from 625, you'd get 542.

Answer:

15 drops per minute

Step-by-step explanation:

(drops per minute) flow/drip rate: volume ÷ time × drop factor

note:

volume (mL)

time (minutes)\

30 / 30 = 1

1 * 15 = 15

so, 15 drops per minute will be delivered

hope this helps!! have a lovely day :)

Answer:

15 drops/minute

Step-by-step explanation:

30 ÷ 30 = 1

1 · 15 = 15

hope this is helpful :)

Answer:

6

Step-by-step explanation:

The requried number of passes to reach the maximum is given as 10 passes.

The function which is in format f(x) =aˣ where a is constant and x is variable,  the domain of this exponential function lies   (-∞, ∞).

Here,

We have 5 coins in your purse,
We Gain 1.5x the number of coins in your purse every time you pass the start. The maximum number of coins is 300.

According to the quesiton,
5 . 1.5ˣ = 300

Where x is the number of passes,
1.5ˣ = 60
x ≈ 10

Thus, the requried number of passes to reach the maximum is given as 10 passes.

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The range of the function on the graph is C. all the real numbers greater than or equal to –3 .

We can see by the graph maximum value of y of function is -3 and the graph continues to extend upward .

So, the range contain all the real numbers greater than or equal to –3 .

Therefore, the range contain all the real numbers greater than or equal to –3 .

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Answer:

take 1/2 multiply by sin 91°×2×8

The transformation that can be used to show that ABCDE and its image are congruent is a 90° counterclockwise.

It should be noted that when we rotate a point through 90° counterclockwise, the mapping will be: (x, y) to (-y, x).

In this situation, it van be deduced that the x and y coordinates swapped positions. This illustrates a 90° counterclockwise rotation about the origin..

In this situation, since the rotation is a rigid motion, the two shapes are congruent.

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Answer: B

Step-by-step explanation:

In triangles ABC and CED, CE=AC and AB=ED, but CD>BC, meaning the angle E is smaller than angle A.

We conclude that after 50 days, there will be 67 lily pads.

We know that the number increases by 25% every 10 days.

In 50 days we have 5 groups of 10 days, so there will be five increases of 25%.

We know that the initial number is 22 lily pads, if we apply five consecutive increases of the 25% we get:

N = 22*(1 + 25%/100)*...*(1 + 25%/100%)

( the factor (1 + 25%/100%) appears five times)

So we can rewrite:

N = 22*(1 + 25%/100%)⁵

N = 22*(1 + 0.25)⁵ = 67.1

Which can be rounded to the nearest whole number, which is 67.

So we conclude that after 50 days, there will be 67 lily pads.

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Answer:

050°

Step-by-step explanation:

The bearing of D from C is the angle between the north pole and the line joining C and D when moving in a clockwise direction.

From the diagram, the angle is 050°

Answer:

37.5 m

Step-by-step explanation:

Since the trapezoid area formula is ((base 1+base 2)/2)*height, we can plug in the values.

((8+7)/2)*5

(15/2)*5

7.5*5=37.5

Now we add the unit, "m" to get 37.5 m!

Answer:

7,500

Step-by-step explanation:

When you round you automatically round up unless told otherwise
so find the hundredth, which is 485 and you round that to 500
then put the 7 back → 7,500

Step-by-step explanation:

[tex] = \frac{2 \sqrt{2} - \sqrt{3} }{ \sqrt{2} + \sqrt{3} } [/tex]

[tex] = \frac{2 \sqrt{2} - \sqrt{3} }{ \sqrt{2} + \sqrt{3} } \times \frac{ \sqrt{2} - \sqrt{3} }{ \sqrt{2} - \sqrt{3} } [/tex]

[tex] = \frac{ 2( \sqrt{2} - \sqrt{3} )( \sqrt{2} - \sqrt{3} )}{ { \sqrt{2} }^{2} - { \sqrt{3} }^{2} }[/tex]

[tex] = \frac{2(2 - \sqrt{6} - \sqrt{6} - 3) }{2 - 3} [/tex]

[tex] = \frac{2( - 1 - 2 \sqrt{6} )}{ - 1} [/tex]

[tex] = \frac{ - 2(1 + 2 \sqrt{6} )}{ - 1} [/tex]

[tex] = 2(1 + 2 \sqrt{6} )[/tex]

[tex] = 2 + 4 \sqrt{6} [/tex]

Step-by-step explanation:

hope you can understand

The height of the triangle will be;

⇒ 58.5 mm

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

The base of the triangle = 4.7 mm

The area of triangle = 137.475 mm²

Now,

We know that;

⇒ The area of triangle = 1/2 × Base × Height

Substitute all the values, we get;

⇒ 137.475 = 1/2 × 4.7 × h

⇒ 137.475 = 2.35 × h

⇒ h = 137.475 / 2.35

⇒ h = 58.5 mm

Thus, The height of the triangle = 58.5 mm

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The distances in feet covered in 4 steps, 6 steps, 12 steps, and 30 steps are 10 feet, 15 feet, 30 feet and 75 feet.

When you walk with a normal stride, the average distance covered in 2 steps is about 5 feet

From the question, we have:

Rate = 5 feet per 2 steps

This gives

Rate = 5/2 feet per step

So, we have:

Rate = 2.5 feet per step

The distance is then calculated as:

Distance = Rate * Steps

This gives

Distance = 2.5 * Steps

So, the distances in feet covered in 4 steps, 6 steps, 12 steps, and 30 steps are

Distance = 2.5 * 4 = 10 feet

Distance = 2.5 * 6 = 15 feet

Distance = 2.5 * 12 = 30 feet

Distance = 2.5 * 30 = 75 feet

Hence, the distances in feet covered in 4 steps, 6 steps, 12 steps, and 30 steps are 10 feet, 15 feet, 30 feet and 75 feet.

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Answer:

[tex]\boxed {f(x) = x^{2} - 6x + 1}[/tex]

Step-by-step explanation:

Substituting each x value and checking it corresponds to the table :

x = -6

⇒ f(-6) = (-6)² - 6(-6) + 1

⇒ f(-6) = 36 + 36 + 1

⇒ f(-6) = 73

x = -2

⇒ f(-2) = (-2)² - 6(-2) + 1

⇒ f(-2) = 4 + 12 + 1

⇒ f(-2) = 17

x = 2

⇒ f(2) = (2)² - 6(2) + 1

⇒ f(2) = 4 - 12 + 1

⇒ f(2) = -7

x = 6

⇒ f(6) = (6)² - 6(6) + 1

⇒ f(6) = 36 - 36 + 1

⇒ f(6) = 1

x = 10

⇒ f(10) = (10)² - 6(10) + 1

⇒ f(10) = 100 - 60 + 1

⇒ f(10) = 41

Answer:

1/5 times 100= 20%

Step-by-step explanation:

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