Any proposed solution of a rational equation that causes a denominator to equal _______ is rejected.
Answer:
Any proposed solution of a rational equation that causes a denominator to equal __ZERO__ is rejected.
Step-by-step explanation:
We will show this statement is true by an example:
Consider the expression : [tex]\frac{x}{x-4}=\frac{x}{x-4}+4[/tex]
Now, solved the rational expression and check its proposed solution
[tex]\frac{x}{x-4}=\frac{x}{x-4}+4[/tex]
x cannot equal to 4, as it makes both denominators equal to zero.
Multiply both the sides by (x-4),
[tex]\left ( x-4 \right )\cdot \frac{x}{x-4}=\left (x-4 \right )\cdot\left ( \frac{x}{x-4}+4 \right )\\[/tex]
Now, use the distributive property on Right hand side,
[tex]\left ( x-4 \right )\cdot \frac{x}{x-4}=\left (x-4 \right )\cdot \left ( \frac{x}{x-4} \right )+\left (x-4 \right )\cdot 4\\[/tex]
Simplify the above expression,
[tex]x=x+4x-16[/tex]
Combine like terms,
[tex]x-x-4x=-16[/tex]
[tex]-4x=-16[/tex]
Divide both sides by -4, we get
[tex]\frac{-4x}{-4}=\frac{-16}{-4}[/tex]
[tex]x=4[/tex].
As we know that x cannot equal to 4, replacing x=4 in the original expression causes the denominator equal to 0.
Check the solution: [tex]\frac{x}{x-4}=\frac{x}{x-4}+4[/tex]
Substitute the value of x=4 in the original expression,
[tex]\frac{4}{4-4}=\frac{4}{4-4}+4[/tex]
[tex]\frac{4}{0}=\frac{4}{0}+4[/tex]
Thus, 4 must be rejected as the solution, and the solution set is only 0.
A proposed solution of a rational equation that causes a denominator to equal zero is rejected because division by zero is not possible.
Explanation:Any proposed solution of a rational equation that causes a denominator to equal zero is rejected. When the denominator of a rational equation is zero, the fraction becomes undefined because division by zero is not possible. In mathematics, division by zero is an undefined operation.
what is 77.0 divided by 200
Find f(5) for f(x). ... .. ... ....
Need help with number 6. Also could you tell me if I did number 5 right? Thanks
The function d(x) =3x +2 determine how many donuts need to be purchased for a meeting, where x is the number of people at the meeting. The office manager uses h(d(x)) to find the amount of money to bring for the donuts purchase. The function h(x) = 2x + 7 . Solve for how much money to bring when there are 8 people In the meeting.
A.25
B.26
C.52
D.59
use multiplication and the Distributive property to find the quotient
70 divided by 5 =
What Is 22/55 in lowest terms
wes has six errands to run (picking up the dry cleaning, going to the grocery store, getting gas, going to the bank, going to the library, and going to the video store). he only haves time to run 3 errands this afternoon. how many different combinations of three errands could he choose to run?
Answer: 120 different combinations .
Step-by-step explanation:
The combination of n things taking m things at a time is given by :-
[tex]C(n,m)=\dfrac{n!}{m!(n-m)!}[/tex]
Given : The total numbers of errands = 6
Now, the combination of 6 errands taking 3 at a time is given by :-
[tex]C(6,3)=\dfrac{6!}{3!(6-3)!}\\\\=\dfrac{6\times5\times4\times3!}{3!}=120[/tex]
Hence, he could choose to run 120 different combinations of three errands .
The decimal equivalent to the binary number 0 0 0 1 0 1 1 0 is ______________.
Maree is 8 years older than Aaron.
Aaron is twice as old as Rick.
All their ages add up to 28.
What are their ages?
Maree is
Aaron is
Rick is
what is the answer? this is hard
Use the result from part c to find the two solutions to the equation 2x2−3x−5=0. enter the two solutions separated by a comma. (the order is not important.)
The quadratic formula can be used to find the solutions of a quadratic equation. In this case, the equation is 2x² - 3x - 5 = 0. Using the quadratic formula, the two solutions are x = 2 and x = -1.
Explanation:To find the solutions to the equation 2x² - 3x - 5 = 0, we can use the quadratic formula. The formula states that the solutions of any quadratic equation ax² + bx + c = 0 can be calculated using the formula:
x = (-b ± √(b² - 4ac)) / 2a
In this case, a = 2, b = -3, and c = -5. Substituting these values into the formula, we get:
x = (-(-3) ± √((-3)² - 4(2)(-5))) / (2(2))
Simplifying further, we have:
x = (3 ± √(9 + 40)) / 4
x = (3 ± √49) / 4
x = (3 ± 7) / 4
Therefore, the two solutions to the equation 2x² - 3x - 5 = 0 are x = (3 + 7) / 4 = 2 and x = (3 - 7) / 4 = -1.
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An automotive repair center charges $45 for any part of the first hour of labor, and $25 for any part of each additional hour. Which of the following is a correct cost?
A. C(t) = 145 for 5 < x ≤ 6
B. C(t) = 145 for 6 < x ≤ 7
C. C(t) = 170 for 5 < x ≤ 6
D. C(t) = 170 for 6 < x ≤ 7
what is 150% as a fraction
F(x)=x-2/x^3+x find the domain
Do I add the lenghs of the sides of a figure and multiply them by the height to get the area?
Suppose that it costs $25 to place a classified advertisement in the newspaper, plus $3 for each line. Then the cost to place an ad x lines long is given by y dollars, where y=3x+25. Express an ordered pair the fact that a 2 line ad cost $31
A couple has 4 children. what is the probability they would have four boys
The number of sofas a factory produces varies directly with the number of hours the machinery is operational. Suppose the factory can produce 455 sofas in 48 hours. What is an equation that relates the number of sofas produced, n, with the amount of time, t, in hours? What is the graph of your equation?
Let a and b be the solutions of the quadratic equation $2x^2 - 8x + 7 = 0. Find 1/(2a)+(1/2b).
Please help me!
How can knowing the multiplication properties help you multiply 5x(2x6)?
Train A and train B leave a central station at the same time. They travel the same speed, but in opposite directions, with train A heading towards station A, and train B heading towards station B. Train A reaches station A after 4 h. Train B reaches station B after 312 h. Station A and Station B are 562.5 mi apart. What is the rate of the trains? Enter your answer in the box.
the answer is 75 mph i took the test and it said 75 not 1.78
Answer:
its 75 i did the math a calaculator
Step-by-step explanation:
In October Greg and Thomas had the same amount of money in their savings account in November Greg deposited $120 into his account Thomas increased the money in his account by 20% when they compare their bounces they found out they were still equal
Use this equation to find dy/dx. 3y cos x = x2 + y2
Ceremonies help individuals cope with loss as they facilitate the grieving process. Please select the best answer from the choices provided. T F
Answer:
True
Step-by-step explanation:
Ceremonies do help individuals cope with loss as they facilitate the grieving process.
Over last week,the daily low temperature in degrees Fahrenheit have been -4,6.2,18 1/2,-5.9,-1/4,and1.75.list these numbers in order from least to greatest
Time measured in minutes is an example of a(n) _______________ scale.
The answer can be written in statement form as,"Time measured in minutes is an example of a(n) interval scale."
What is an interval scale?A numerical scale known as an interval scale is one in which both the order of the variables and their differences are known. Using the Interval scale, variables with recognizable, consistent, and calculable differences are categorized.
It is easy to remember the primary role of this scale too, ‘Interval’ indicates ‘distance between two entities’, which is what Interval scale helps in achieving.
The value of time is given in minutes.
The given quantity can be measured on interval scale.
Hence, the required scale is known as interval scale.
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Find parametric equations for the line through the point ( 0,3,2 ) that is perpendicular to the line ! ! x =1+t , ! ! ! y = 3−t , ! ! z = 4t , and intersects this line. (use the parameter t ).
Which of the following gives an example of a set that is closed under multiplication? CHOOSE ALL THAT APPLY !!!! 15 PTS
A. The product of an even number and an even number
B. The product of 0 and 0
C. The product of a negative number and a negative number
D. The product of a perfect square and a perfect square
what is the exponent used in cubing a number
A tank can be filled by one pipe in four hours and by a second pipe in six hours; and when it is full, the tank can be drained by a third pipe in three hours. If the tank is empty and all three pipes are open, in how many hours will the tank be filled?
A. 8 hours
B. 12 hours
C. 24 hours