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The value of x is:
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We can simplify the given rational function into a linear one, the graph is below.

Here we have the rational function:

[tex]f(x) = \frac{4x^2 - 16}{2x - 4}[/tex]

Factorization the numerator, we get:

4x² - 16 = 0

4x² = 16

x² = 16/4 = 4

x = ±√4 = ±2

Then the numerator can be written as:

4*(x - 2)*(x + 2)

And the denominator can be rewritten as:

2x - 4 = 2*(x - 2)

Then the function becomes:

[tex]f(x) = \frac{4*(x + 2)*(x - 2)}{2*(x - 2)} \\\\f(x) = 2*(x + 2) = 2x + 4[/tex]

So we have just a linear equation, so the graph that represents the function is the graph of a line, the one you can see below.

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Answer:

6x-18

Step-by-step explanation:

6*(x-3)

multiply 6 with x and 3

The amount Barbara earned this month is  $1512.

Percentage can be described as a fraction of an amount expressed as a number out of hundred.

Barbara's earnings = percentage commission x worth of goods sold

7% x 21,600

0.07 x 21,600 = $1512

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Answer: 66.8

Step-by-step explanation:

Let the mean height of 16 students in the class = X

Therefore,

[tex]\frac{15*67+63.8}{16} =X[/tex]

[tex]X=\frac{334}{5}[/tex]

X = 66.8

Cost of bench = x

Cost of garden table = x - 50

x - 50 + x = 700

2x - 50 = 700

2x = 750

x = 325

Answer: Option 1

Step-by-step explanation:

The domain is the set of x values that make the radicand non-negative. Since the radicand is a perfect square, it will always be non-negative for any real value of x.

Answer:

[tex]y = -\frac{x}{6} + \frac{14}{3}[/tex]

Step-by-step explanation:

So when you're solving for y you want to get y by it self meaning there should be nothing with y, including any coefficients. The first step is to usually move any terms to the other side and then divide by the coefficient of y so y "technically doesn't" have a coefficient, while it does, but that coefficient 1, so it doesn't really mean much.

Subtract x from both sides

[tex]6y = -x+28[/tex]

Divide both sides by 6

[tex]y = -\frac{x}{6} + \frac{14}{3}[/tex]

The given equation solved for y as y = (28 - x)/6.

The given equation is x+6y=28.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given equation can be solved for y as follows

Here, x+6y=28

⇒ 6y = 28 - x

⇒ y = (28 - x)/6

Therefore, the given equation solved for y as y = (28 - x)/6.

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Answer:

sqrt(172) = hypotenuse

Step-by-step explanation:

IF those are the leg lengths (sides) and not the hypotenuse, then use Pythagorean theorem

c^2 = 7^2 + sqrt (123) ^2

c = sqrt (172)

If sqrt 172 is the hypotenuse :

(sqrt123)^2 = 7^2 + x^2

then  x = sqrt (74 )

Thus, the required capacity lung capacity of hawk is 190.5ml.

robin with a mass of 310 grams has a lung capacity of 46.5 mL
let lung capacity of a 1270-gram hawk = x

Volume, is defined as the ratio of the mass of object to its density.

Here,
The maximum capacity of a bird's lungs varies directly with it size.
So the proportion can be given as
⇒ 310/46.5 = 1270/x
= 190.5

Thus, the required capacity lung capacity of hawk is 190.5ml.

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Answer:

x=0

Step-by-step explanation:

You can combine the equation to get 2sin(3/2 +x) = -2

divide both sides by 2 and you get the equation equal to -1. sin is equal to -1 when the value inside is 3/2 so this is the answer.

The system of equation that will represent her purchase is as follows:

1.39b + 2.49m = 50.73

1.29b + 2.69m = 51.63

At store A she will pay a total sum of $50.73 for bread and milk.

At store B she will pay a total sum of $51.63  for bread and milk.

Therefore, the system of equation that will represent her purchase is as follows:

where

b = number of bread

m = number of milk

Therefore,

1.39b + 2.49m = 50.73

1.29b + 2.69m = 51.63

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The equations that represent linear relationship is y – 5 = 2(x – 1)

Linear functions are functions that has a leading degree of 1. According to the question, we need to determine the function that represents linear equation.

The required equation must have a degree of 1 and must contain both dependent and independent variables.

The equations that represent linear relationship is y – 5 = 2(x – 1)  

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Answer:

The anser is:

A

C

D

E

Step-by-step explanation:

I hope this helps, have a blessed day :)

Answer:

(x+3)(x+2)

Step-by-step explanation:

x^2 + 5x+6

To factor this problem, we need to determine which two numbers multiply to 6 and add to 5

3*2 = 6

3+2 -5

(x+3)(x+2)

Step-by-step explanation:

x² + 5x + 6

= x² + 2x + 3x + 6

= x ( x + 2 ) + 3 ( x + 2 )

= ( x + 2 ) ( x + 3 )

Hence factorized.

Thus we can conclude that if Will is 34% higher than Wanda, then Will's height is 134% (100% + 34%) of Wanda's height.

Will is 34% taller than Wanda, so Will's height is 134% of Wanda's height.

If Will is 34% of Wanda's height, we can conclude that he has all of Wanda's height plus 34% of that height.

All the height of Wanda represents 100% as it is referring to a complete system.

Height is a way to measure someone or something from base to top or head to toe.

From this, we can conclude that Will is 100% more than 34% of Wanda's height.

Thus we can conclude that if Will is 34% higher than Wanda, then Will's height is 134% (100% + 34%) of Wanda's height.

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Answer:

[tex]57[/tex]

Step-by-step explanation:

You just plug in 8 as a, and 7 as b. This gives you the following equation: [tex](8)^2-7[/tex] which becomes [tex]64-7[/tex] by squaring the 8, Then subtract 7 and you get [tex]57[/tex]

Answer:

57

Step-by-step explanation:

a = 8

b = 7

a² - b

= 8² - 7

= (8*8) - 7

= 64 - 7

= 57

The interval that function f(x)=x³-9x has a positive average rate of change is [ -4, -1 ].

Option D) is the correct answer.

To determine whether the average rate of change is positive, f(max) - f(min) must be greater than zero.

Given the function; f(x) = x³ - 9x

We determine f(max) - f(min)

At interval [ -2, 1 ]

(x³ - 9x) - ( x³ - 9x )

( (1)³ - 9(1) ) - ((-2)³ - 9(-2))= -8 - 10 = -18 NOT POSITIVE

At interval [ -2, 3 ]

(x³ - 9x) - ( x³ - 9x )

( (3)³ - 9(3) ) - ((-3)³ - 9(-3))= 0 - 0 = 0 NOT POSITIVE

At interval [ -1, 2 ]

(x³ - 9x) - ( x³ - 9x )

( (2)³ - 9(2) ) - ((-1)³ - 9(-1))= -10 - 8 = -18 NOT POSITIVE

At interval [ -4, -1 ]

(x³ - 9x) - ( x³ - 9x )

( (-1)³ - 9(-1) ) - ((-4)³ - 9(-4))= 8 - (-28) = 36 POSITIVE

Therefore, the interval that function f(x)=x³-9x has a positive average rate of change is [ -4, -1 ].

Option D) is the correct answer.

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Answer:

no

Step-by-step explanation:

you have done your part by helping in their study session,if you help them cheat you will suffer the consequences if he/she is caught,

This is an academic integrity violation because it is against honesty rules, the best would be to offer assistance to your friend.

Academic integrity encompasses principles of honesty, fairness, and trustworthiness in academic pursuits. It generally includes a commitment to originality and independent work. Assisting someone in completing an exam, especially a take-home exam, where individual effort and understanding are expected, would likely violate academic integrity policies.

Handling the situation ethically and responsibly would involve respecting the academic rules and ensuring fairness for all students. Instead of directly completing the exam for your friend, you can offer assistance by explaining concepts, providing guidance on problem-solving approaches, or reviewing their completed work to identify errors or areas for improvement. This way, you can help your friend learn the material and develop their own understanding, without compromising academic integrity.

Encourage your friend to seek additional help from their professor, teaching assistants, or tutoring services provided by the institution. They can also engage in group study sessions or form study groups with classmates, which promote collaborative learning while maintaining individual effort.

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Answer:

a) 60,000 cubic cm; b) 60,000 mL; c) 60 L

Step-by-step explanation:

a) V = l x w x h

V = 50 cm x 40 cm x 30 cm = 60,000 cubic cm

b) 1 cubic cm = 1 mL, therefore 60,000 cubic cm = 60,000 mL

c) 1000 mL = 1 L; 60,000 mL = 60 L

The equation of line that passes through a pair of points: (2, 3), (4, -2).is option B. y = -5/2 x + 8.

Suppose the given points are (x_1, y_1) and (x_2, y_2),

then the equation of the straight line joining both two points is given by

[tex](y - y_1) = \dfrac{y_2 - y_1}{x_2 - x_1} (x -x_1)[/tex]

We need to find the equation of the line that passes through a pair of points: (2, 3), (4, -2).

So, the equation would be

[tex](y - y_1) = \dfrac{y_2 - y_1}{x_2 - x_1} (x -x_1)[/tex]

[tex](y - 3) = \dfrac{-2 - 3}{4- 2} (x -2)\\\\\\(y - 3) = \dfrac{-5}{2} (x -2)\\\\\\2(y - 3) = -5 (x -2)\\\\2y - 6 = -5x + 10\\\\2y = -5x + 16\\\\y = -5/2 x + 8[/tex]

Hence, the equation of line is option B. y = -5/2 x + 8.

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Answer:B

Step-by-step explanation:

The amount loaned at 8% is  $4800.

The amount loaned at 18% is $6,200.

a + b - 11,000 equation 1

0.08a + 0.18b = 1500 equation 2

Where:

a = amount loaned at 8%

b = amount loaned at 18%

Multiply equation 1 by 0.08

0.08a + 0.08b = 880 equation 3

Subtract equation 3 from equation 2

0.10b = 620

b = 620 / .10

b = $6200

a = 11,000 - 6200 = $4800

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Answer:

36

Step-by-step explanation:

I think it’s a trick question because “legs” can also mean like chair legs that hold it up. Therefore:

2 dogs = 8 legs

4 horses = 16 legs

1 giraffe = 4 legs

And a bed: 4 legs(things that hold it up)

And a chair: 4 legs (things that hold it up)

This is assuming that the bed is a normal bed with stools holding it up

And the chair has 4 piles aswell as no missing legs in the animals… lol

Answer:

a.) P(HH|C)=2/5

Explanation:

Given following:

Solving steps:

[tex]\sf P(HH|C) = \dfrac{P(HH \cap C) }{P(C)}[/tex]

[tex]\sf P(HH|C) = \dfrac{4 }{10}[/tex]

[tex]\sf P(HH|C) = \dfrac{2 }{5}[/tex]

The area of the given right trapezoid ​is 40 ft².

Area of the trapezium = ½(a + b) × h

Given;

base 1 = 9 feet

base 2 = 7 feet

Height h = 5 feet

Area of the trapezium = ½(a + b) × h

Area = (9 + 7) x 5/2

Area = 16 x 5/2

Area = 8 x 5

Area = 40 Square feet.

Hence, the area of the given trapezium ​is 40 ft².

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The height of a triangle with a hypotenuse of 23 and angle between base and hypotenuse of 75° is h= 23sin(75)

An equation is an expression that shows the relationship between two or more variables and numbers.

Trigonometric ratio shows the relationship between the sides and angles of a right angle triangle.

Let us assume that the right triangle has a altitude h, hypotenuse of 23 and angle between base and hypotenuse is 75°, hence:

sin(75) = h/23

h= 23sin(75)

The height of a triangle with a hypotenuse of 23 and angle between base and hypotenuse of 75° is h= 23sin(75)

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the effects of the given transactions on the accounting equation are:

an investment would increase assets (cash) and also increase equity. every expense such as salaries would decrease assets and equity.

incurring debt would increase assets and liabilties while paying off debt would decrease both asset (cash) and liabilities.

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The point that is labeled H on this graph is the point where Chana's and Josiah's distance from the starting line at the time when Chana catches up with Josiah.

At the point H, there is an intersection between the distance covered by both of these individuals.

This point is the point where we are shown that Chana has caught up with Josiah as they are skating.

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It would take 2 hours for me at level 6 to be on the same level with my friend which is initially at level 5.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let t represent the time it would take to be on the same level with your friends. I am at level 6 and my friend is on level 4, hence:

5t = 4t + 2

t = 2 hours

It would take 2 hours for me at level 6 to be on the same level with my friend which is initially at level 5.

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