Solve the following rational equation. Be sure to list the NPV’s and verify your solution(s).
[tex]\frac{2}{2x-6}-\frac{x}{x^2-9} =\frac{3}{x-3}[/tex]
Answer:
NPV: ±3x = -2Step-by-step explanation:
You want the solutions to the rational equation ...
[tex]\dfrac{2}{2x-6}-\dfrac{x}{x^2-9}=\dfrac{3}{x-3}[/tex]
RewriteWe choose to rewrite the equation in the form f(x) = 0. We can start by subtracting the term on the right side (from both sides).
[tex]\dfrac{2}{2x-6}-\dfrac{x}{x^2-9}-\dfrac{3}{x-3}=0\\\\\dfrac{2}{2(x-3)}-\dfrac{x}{(x-3)(x+3)}-\dfrac{3}{x-3}=0\\\\\\\dfrac{(x+3)-x-3(x+3)}{(x-3)(x+3)}=0\qquad\text{cancel 2 in first term; common denominator}\\\\\\\dfrac{-3x-6}{(x-3)(x+3)}=0\qquad\text{collect terms}[/tex]
SolutionThe "not-possible values" will be values of x that make the denominator zero: x = ±3. The solution is ...
[tex]-3(x+2)=0\qquad\text{numerator must be zero}\\\\\boxed{x=-2}\qquad\text{divide by -3, subtract 2}[/tex]
CheckIn the original equation, we have ...
[tex]\dfrac{2}{2(-2)-6}-\dfrac{-2}{(-2)^2-9}=\dfrac{3}{(-2)-3}\\\\\dfrac{2}{-10}-\dfrac{-2}{-5}=\dfrac{3}{-5}\\\\-\dfrac{1}{5}-\dfrac{2}{5}=-\dfrac{3}{5}\qquad\text{TRUE}[/tex]
__
Additional comment
We like to write the equation as a single fraction compared to zero so that any common factors can be cancelled from numerator and denominator. This helps prevent extraneous solutions. Here, there are none.
For the rational function f(x)=5-x/r2 +5+6, solve f(x) = 3.
Answer:
To solve the equation f(x) = 3, we can set the expression for f(x) equal to 3 and then solve for x. In other words, we want to find the values of x that make the equation 5 - \frac{x}{r^2} + 5 + 6 = 3 true.
We can start by simplifying the left side of the equation by combining like terms. This gives us
5 - \frac{x}{r^2} + 5 + 6 = 5 + 5 - \frac{x}{r^2} + 6 = 10 - \frac{x}{r^2} + 6
Next, we set this expression equal to 3 and solve for x:
10 - \frac{x}{r^2} + 6 = 3 \quad \Rightarrow \quad 10 - 6 = 3 - \frac{x}{r^2} \quad \Rightarrow \quad \frac{x}{r^2} = 7
To solve for x, we can multiply both sides of the equation by r^2:
x = 7r^2
Therefore, the solutions to the equation f(x) = 3 are $x = 7r^2$. Note that this is a general solution, and it may not give all the possible values of $x$ that make the equation true. It's also possible that there are no solutions, depending on the value of $r$.
Find the inverse of the following function pairs
Answer:
B
Step-by-step explanation:
This is the only pair of functions where [tex]f(g(x))=g(f(x))=x[/tex].
Shelby wants to buy a car and wants the best deal. Dealer #1 wants $100 down, and payments of $100 per month. Dealer #2 wants $10 down, and payments of $250 per month.
I need help with this fast someone pls I’ll give tons of points
Answer:
look it up
Step-by-step explanation:
Suppose n represents a power of 10.
What is the value of n when 5 is rounded to the nearest power of 10?
Enter your answer in the box.
In the exponent, the value of n when 5 is rounded to the nearest power of 10 will be 100000.
How to illustrate the exponent?The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.
The value of n when 5 is rounded to the nearest power of 10 will be:
= 10^5
= 100000
The value is 10000.
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PLEASE HELP ME PLEASE ASAP!!! I WILL GIVE BRAINLIST PLEASE
ΔABC is rotated 90° clockwise about the origin.
Answer: (12,-6)
Step-by-step explanation:
what is the inverse function below.
(2, 0), (-1, 3), (-5, -4), (0, 6)}
In the broadest sense, inverse functions are those that "reverse" one another.
How to Find the Inverse of a Function?Any function can be solved for by substituting one variable for another to discover the inverse of that function.
Below is an example to help you understand.
Find the inverse of h (x) = (4x + 3)/(2x + 5)
Solution
H (x) should be changed to Y.
h (x) = (4x+3)/(2x+5) y = (4x + 3)/(2x + 5)
Change the order of x and y.
⟹ x = (4y + 3)/ (2y + 5).
The following formula should be used to solve for y in the equation above:
⟹ x = (4y + 3)/ (2y + 5)
Divide both sides by (2y + 5)
⟹ x (2y + 5) = 4y + 3
Distribute the x evenly.
⟹ 2xy + 5x = 4y + 3
isolate y.
⟹ 2xy – 4y = 3 – 5x
⟹ y (2x – 4) = 3 – 5x
Divide through by 2x - 4 to obtain;
⟹ y = (3 – 5x)/ (2x – 4) (2x – 4)
Finally, swap out y for h - 1. (x).
⟹ h – 1 (x) = (3 – 5x)/ (2x – 4) (2x – 4).
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What value of P makes this equation true
2p=-3p-6/4
Answer:
The answer is p = -6/3. This is the value of p that makes the original equation true.
Step-by-step explanation:
To solve this equation, we must first isolate the variable p on one side of the equation. To do this, we can use the properties of equality to add or subtract the same value from both sides of the equation.
First, we can subtract 2p from both sides of the equation to get rid of the 2p term on the left side. This gives us 0 = -3p - 6/4.
Next, we can add 6/4 to both sides of the equation to get rid of the constant term on the right side. This gives us 6/4 = -3p.
Finally, we can multiply both sides of the equation by -4/3 to get rid of the coefficient -3 on the right side. This gives us -6/3 = p.
Therefore, the value of p that makes the equation true is p = -6/3.
What fraction is equal to 100%
Any fraction whose numerator is the same number as its denominator will equal 1, which is 100%. Hence, fraction [tex]\frac{5}{5}[/tex] is a fraction that equals 100%.
Answer:
[tex]\frac{5}{5}[/tex]
Step-by-step explanation:
To get a percentage out of a fraction, you divide the fraction and then move the decimal point two places to the right. [tex]\frac{5}{5} =1[/tex] is also equal to 1.0
Move the decimal two places to the right and you get 100%
which of the following is not a reason that the process being monitored with the chart should be investigated?
By using the concept of control chart, it can be concluded that
A large number of plots are on or near the centerline.
Third option is correct.
What is control chart?
Control chart is used to show how a process changes over time.
There are three lines in a control chart.
They are the central line for the average, upper line for the Upper Control Limit (UCL) and a lower line for the Lower Control Limit (LCL)
It is known that the highest performance of a process is obtained when it is between the LCL and the UCL.
That means to get the best result, samples needs to be concentrated near the centerline.
So the third option is correct
A large number of plots are on or near the centerline.
Third option is correct.
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Complete Question
Quality control charts usually have a central line and upper and lower control limit lines. Which of the following is not a reason that the process being monitored with the chart should be investigated?
A sudden and sustained shift in the plots toward the upper or lower control limit
There is an upward trend in the plots
A large number of plots are on or near the central line
A single plot falls outside of the control limits
Answer the question thank you! :) it’s on the picture.
Answer:
The inequality represented in the given picture is:
[tex]x \le 5[/tex]
Note the inclusive less than sign since the graph has a filled-in dot.
This can be represented in interval notation as:
[tex](-\infty, 5][/tex]
Note the bracket on enclosing the 5, representing inclusiveness.
A conductor is mapping a trip and records the distance the train travels over certain time intervals?
The speed that the train travels is given as follows:
45 miles per hour.
How to obtain the train's velocity?The train travels at a constant speed, hence the distance traveled by the train over time is modeled by the proportional relationship defined as follows:
d = vt.
In which the variables of the equation are defined as follows:
v is the train's velocity.t is the time.Since the velocity is constant, it's equation is defined as follows:
v = d/t.
One point on the table is given as follows:
(1,45).
Hence the constant velocity of the train is calculated as follows:
v = 45/1 = 45 miles per hour.
Missing InformationThe problem is given by the image shown at the end of the answer.
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Which of the following equations have only one solution? Select all correct answers. x 2 - x - 6 = 0 5 x 2 + 20 x + 20 = 0 9 x 2 - 25 = 0 4 x 2 + 4 x = 0 x 2 + 6 x + 9 = 0
The quadratic equations 5x² + 20x + 20 = 0 and x² + 6x + 9 = 0 are the only correct equations having only one solution.
Solutions of a quadratic equationQuadratic equations has it highest power to the degree of two and they have two solutions that makes them true. The solutions could be different or similar ( which implies there is only one solution). From the question we shall concentrate on the equations which have similar solution or rather only one solution.
For the equation 5x² + 20x + 20 = 0;
we divide through by 5 to get;
x² + 4x + 4 = 0
x² + 2x + 2x + 4 = 0 {we group the terms}
x(x - 2) +2(x + 2) = 0 {factorize}
(x + 2)(x + 2) = 0
either; x + 2 = 0 or x + 2 = 0
x = -2 or x = -2 {which are the same solutions}
For the equation x² + 6x + 9 = 0;
x² + 3x + 3x + 9 = 0 {we group the terms}
x(x + 3) + 3(x + 3) = 0 {factorize}
(x + 3)(x + 3) = 0
either; x + 2 = 0 or x + 2 = 0
x = -2 or x = -2 {which are the same solutions}
Therefore, the quadratic equations 5x² + 20x + 20 = 0 and x² + 6x + 9 = 0 each have only one solution which are -2 and -3 respectively.
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Which situation can be modeled by the inequality 3x+7<13?
Answer:
Step-by-step explanation:
x < 2
I think is the answer when you subtract 7 from both sides you get 3x <6 and then you divide both sides by 3 getting x < 2 (not sure if that's how you solve this one but usually it would be solved like this. if wrong then I'm sorry)
The theater was full when the movie began. Seventy-six people left
before the movie ended. One hundred twenty-four people remained.
How many people were in the theater when it was full?
The number of people were 200 in the theater when it was full.
What is a theater?
In architecture, a theatre, usually spelled theatre, is a structure or area where a play can be conducted in front of spectators. The term comes from the Greek theatron, which means "a place of seeing." The actual performance usually takes place on a stage in a theatre.
Given that, the theater was full when the movie began.
76 people leave the theater before end the movie. At the end of the movie, there is 124 people left.
Apply algebraical operation that is addition to find the required answer.
Therefore, the number of people that was present at the beginning of the movie is (76 + 124) = 200.
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help please! I dont understand! :(
brainiest
2n = 10 help pls
Thx
[tex]2n=10[/tex]
Divide both sides by 2:
[tex]\dfrac{2n}{2} =\dfrac{10}{2}[/tex]
[tex]\fbox{n = 5}[/tex]
f(x) = 5x-10 and g(x) = -x+4
Calculate f(-3)
The value of f(-3) if f(x) = 5x - 10 and g(x) = -x + 4 is -25.
What is the equation?Equation: A statement that two variable or integer expressions are equal. In essence, equations are questions, and the motivation for the development of mathematics has been the systematic search for the answers to these questions.
Given:
f(x) = 5x - 10 and g(x) = -x+4
Calculate the f(-3) by putting the value of x = -3 as shown below,
f(x) = 5(-3) - 10
f(x) = - 15 - 10
f(x) = -25
Therefore, the value of f(-3) if f(x) = 5x-10 and g(x) = -x+4 is -25.
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A candy distributor needs to mix a 20% fat-content chocolate with a 60% fat-content chocolate to create 200 kilograms of a 22% fat-content chocolate. How many kilograms of each kind of chocolate must they use?
Answer: They must mix __ Kilograms of the 20% chocolate and __ Kilograms of the 60% chocolate.
Using a system of equations to solve the problem, the candy distributor must mix 190 Kilograms of the 20% chocolate and 10 Kilograms of the 60% chocolate to create 200 Kilograms of a 22% fat-content chocolate.
What is a system of equations?A system of equations means two or more equations solved simultaneously.
They are known as simultaneous equations and can be solved graphically, by elimination, by substitution, or matrix.
The fat-content of one of the chocolate blend = 20%
The fat-content of the second chocolate blend = 60%
The expected mixture will have a fat-content = 22%
The total kilograms of the end mixture = 200 kilograms
Let the 20% fat-content chocolate = x
Let the 60% fat-content chocolate = y
x + y = 200 ... Equation 1
Solving for x, x = 200 - y
0.2x + 0.6y = 0.22(200) ... Equation 2
By substitution in Equation 2:
0.2(200 - y) + 0.6y = 44
40 - 0.2y + 0.6y = 44
40 + 0.4y = 44
0.4y = 4
y = 10
x = 200 - y
x = 190 (200 - 10)
Based on the system of equations, 190 kilograms of the 20%-fat-content chocolate must be mixed with 10 kilograms of the 60% fat-content chocolate.
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Complete the chart for the given proof. GIVEN: the midpoint of AB <AX = <NY NX = BY PROVE: <X = <Y
Two-column proof
See missing statements and reasons below.
Statement Reason
N is the midpoint of AB GivenAN ≅ NB Definition of a midpointAX ≅ NY GivenBX ≅ BY GivenΔAXN ≅ ΔNYB Side-side-side congruency∠X ≅ ∠Y CPCTCProvedIn the data set shown below, what is the value of the quartiles?
{42, 43, 44, 44, 48, 49, 50}
Please Read The Numbers Carefully
A. Q1 = 43.5; Q2 = 44; Q3 = 49
B. Q1 = 43; Q2 = 44; Q3 = 48.5
C. Q1 = 43.5; Q2 = 44; Q3 = 48.5
D. Q1 = 43; Q2 = 44; Q3 = 49
3x-9-4=2 find the value of x
Answer:
x=5
Step-by-step explanation:
or, 3x-9-4=2
or, 3x-13=2
Now, Adding 13 on both sides we get,
or, 3x-13+13=2+13
or, 3x=15
Now, Dividing both sides by 3 we get,
or, (3x)/3=15/3
Therefore, x=5
what are the roots of the quadratic equation y=x^2-10x+125
B would be the answer to this quadratic equation.
Answer:
B. x = 5 ± 10i
Step-by-step explanation:
ax² + bx + c = 0
quadratic formula = (-b ± [tex]\sqrt{b^{2}-4ac }[/tex])/2a
y = x² - 10x + 125
substitute the values:
(-(-10) ± [tex]\sqrt{(-10)^{2}-4(1)(125) }[/tex])/2(1)
= (10 ± [tex]\sqrt{100 - 500}[/tex])/2
= (10 ± [tex]\sqrt{-400}[/tex])/2
= (10 ± 20i)/2
= 5 ± 10i
graph this for free brain
A plane took off from the runway. When the plane had flown 1000 m, it had covered a horizontal distance
of 800 m. Find the measure of the angle to the nearest degree at which the plane rose from the ground.
1000
Answer:
36.9 degrees
Step-by-step explanation:
distance that the plane travels (hypotenuse) = 1000m
horizontal distance (adjacent) = 800m
cos(angle) = adjacent/hypotenuse
cos(angle) = 800/1000
angle = cos-1(800/1000)
angle = 36.9 degrees
A ceramic artist orders two types of clay. She must spend at least $100 to qualify for free shipping. Earthen red clay costs $0.75 per pound, and porcelain white clay costs $1.10 per pound. To summarize the situation, the artist writes the inequality: 0.75r+1.1w>100, where r is the number of pounds of earthen red clay, and w is the number of pounds of porcelain white clay.
The inequality to use to find the number of pounds for Earthen red clay and Porcelain white clay is:
0.75r + 1.1w ≥ 100
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal = ≤
Greater than and equal = ≥
We have,
A ceramic artist orders two types of clay.
Earthen red clay
Porcelain white clay
Amount to spend = $100 or more
Earthen red clay costs = $0.75 per pound
Porcelain white clay costs = $1.10 per pound.
The inequality to use to find the number of pounds for Earthen red clay and Porcelain white clay.
= 0.75r + 1.1w ≥ 100
where r is the number of pounds of earthen red clay, and w is the number of pounds of porcelain white clay.
Thus,
The number of pounds for Earthen red clay and Porcelain white clay can be found using the inequality:
0.75r + 1.1w ≥ 100
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The excel cable company has a monthly fee of $32 an additional charge of $8 for each premium channel. The best cable company has a monthly fee of $26 and an additional charge of $10 for each premium channel. The Horton family is deciding which of these 2 cable companies to subscribe to.
(A) For what number of premium channels will the total monthly subscription fee for the excel and best cable companies be the same?
The Horton family decides to subscribe to 2 premium channels for a period of one year.
(B) Which cable company should they subscribe to in order to spend less money, Excel or Best? Explain your reasoning.
(C) How much money will the Hortons save in one year by using the less expensive company?
The Horton family subscribes to 3 premium channels. The total monthly subscription fee for the excel cable company is 48 dollars. The Horton family will save 24 dollars in one year by using the less expensive company.
(A) To find the number of premium channels for which the total monthly subscription fee for the excel and best cable companies will be the same, we set these two expressions equal to each other and solve for x:
32 + 8x = 26 + 10x
8x - 10x = 26 - 32
-2x = -6
x = 3
Therefore, the Horton family subscribes to 3 premium channels.
(B) The total monthly subscription fee for the excel cable company is 32 + 8 × 2 = 48 dollars if the Horton family subscribes to 2 premium channels. The total monthly subscription fee for the best cable company is 26 + 10 × 2 = 46 dollars if the Horton family subscribes to 2 premium channels.
Since the total monthly subscription fee for the best cable company is less than the total monthly subscription fee for the excel cable company, the Horton family should subscribe to the best cable company in order to spend less money.
(C) If the Horton family subscribes to the best cable company for one year, they will save 48 - 46 = 2 dollars per month. Over the course of one year, they will save 2 × 12 = 24 dollars.
Therefore, the Horton family will save 24 dollars in one year by using the less expensive company.
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Find the Missing Side Lengths
Instructions: Use the ratio of a 45-45-90 triangle to solve for the variables. Leave your answers as radicals in simplest form.
x=____
y=_____
The value of x is 13 units and the value of y is 13 units
The given triangle is right triangle
The ratio of the given triangle angles = 45-45-90 degrees
To find the length of the sides we have to use the trigonometric functions
sin θ = Opposite side / hypotenuse
cos θ = Adjacent side / hypotenuse
tan θ = Opposite side / adjacent side
Find the value of x
sin 45 = Opposite side / 13[tex]\sqrt{2}[/tex]
Opposite side = 13[tex]\sqrt{2}[/tex] × sin 45
= 13 units
Similarly
cos 45 = Adjacent side / 13[tex]\sqrt{2}[/tex]
Adjacent side = 13[tex]\sqrt{2}[/tex] × cos 45
= 13 units
Therefore, the length of the side x and y is 13 units
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Chris needs to drive 24 miles to work. So far, he has driven 5.4 miles. How many more miles must he drive?
Answer:
18.6 miles
Step-by-step explanation:
Subtract Distance traveled from total distance
Total distance: 24 miles
Distance Traveled: 5.4 miles
24 - 5.4 = 18.6