Answer:
[tex]26a - 10 = 2(13a - 5)[/tex]
a cable tv receiving dish is in the shape of a paraboloid of revolution. find the location of the receiver, which is placed at the focus, if the dish is 6 feet across at its opening and 2 feet deep.
the receiver is located at (0, 0, 2.25 feet) or (0, 0, 27 inches).To find the location of the receiver, we first need to determine the equation of the paraboloid.
The standard equation for a paraboloid of revolution with a vertical axis is:
z = [tex](x^2 + y^2)[/tex]/(4f)
Where:
z is the height at any point (x, y) on the paraboloid.
x and y are the horizontal coordinates of the point.
f is the focal length of the paraboloid, which is half the depth of the dish.
In this case, the dish is 6 feet across at its opening, so the diameter is 6 feet and the radius is 3 feet. Therefore, the maximum value of x and y is 3 feet. The depth of the dish is given as 2 feet.
Using these values, we can solve for the focal length:
2 = [tex](3^2 + 3^2)[/tex]/(4f)
2 = 18/(4f)
f = 18/8 = 9/4 = 2.25 feet
Now that we have the value of f, we can find the location of the receiver, which is placed at the focus of the paraboloid. The focus is located at (0, 0, f).
Therefore, the receiver is located at (0, 0, 2.25 feet) or (0, 0, 27 inches).
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for each increase of one unit on the x-axis (the horizontal axis), the amount on the y-axis (the vertical axis) increases by:
For each increase of one unit on the x-axis (the horizontal axis), the amount on the y-axis (the vertical axis) increases by the slope of the line.
Slope is the amount of change in the y-axis that occurs as a result of a one-unit change in the x-axis. It is also known as the rise over run.
A positive slope indicates that the line rises from left to right, while a negative slope indicates that the line falls from left to right. If the slope is zero, the line is horizontal.
If the line slopes up from left to right, it has a positive slope. As the value of x increases by one, the value of y also increases by the slope. If the line slopes downward from left to right, it has a negative slope. As the value of x increases by one, the value of y decreases by the slope.The slope of a horizontal line is zero, and the slope of a vertical line is undefined because the x or y coordinate does not change as the other changes.
Therefore, the slope of a line represents the amount by which the value on the y-axis increases for every increase of one unit on the x-axis
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Helppppppppppppppppp
(1/32)^x=8^3-x solve for x
We can rewrite the right side of the equation as a power of 2 since 8 = 2^3:
(1/32)^x = (2^3)^3-x
Simplifying the right side:
(1/32)^x = 2^(9-3x)
We can write both sides using a common base, say 2:
2^(-5x) = 2^(9-3x)
Now we equate the exponents and solve for x:
-5x = 9 - 3x
-2x = 9
x = -4.5
Therefore, the solution to the equation is x = -4.5.
a spinner with the colors red, yellow, blue, and green is spun. what is the theoretical probability of stopping on the color blue?
The theoretical probability of stopping on the color blue when spinning a spinner with the colors red, yellow, blue, and green is 25% or 1/4.
A spinner is a tool that spins around an arrow or a pointer that points towards the numbers, colors, or pictures around its edge. The probability of a certain event is the likelihood of that event occurring. In this case, we need to find the theoretical probability of stopping on the color blue.
We have four colors on the spinner, so the probability of stopping on blue can be found using the formula of theoretical probability.
The formula for theoretical probability is:
number of favorable outcomes / total number of outcomes.
Since we have four colors on the spinner, the total number of outcomes is 4. The favorable outcomes are the number of times the spinner will land on blue, which is 1.
So the probability of stopping on the color blue can be calculated as follows:
1 (favorable outcome) / 4 (total number of outcomes) = 1/4
So, the theoretical probability of stopping on the color blue is 1/4. This is because there is an equal chance of landing on any of the four colors, and since there are four colors, each has a 25% chance of being selected.
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Corey spies a bald eagle in a tall tree. He was able to measure the angle of elevation to the bird from where he stands at 62°. The leaves on the tree make it difficult for Corey to watch the bird, so he moves 10 feet further away from the tree to get a better view. Now his angle of elevation is 56°.
What is the height of the tree? Round your answer to the nearest foot.
pls help
The height of the tree is approximately 76 feet.
What is the angle of elevation?
The angle of elevation is the angle created between the line of sight and the horizontal. The angle created is an angle of elevation if the line of sight is upward from the horizontal line.
We can use tangent to set up the following two equations based on the given angles of elevation:
tan(62°) = h/x
tan(56°) = h/(x+10)
We can rearrange the first equation to solve for "h":
h = x * tan(62°)
tan(56°) = (x * tan(62°)) / (x+10)
We can solve for "x" by multiplying both sides by (x+10) and rearranging:
x = 10 * (tan(62°) - tan(56°)))
Now we can substitute this value for "x" into either of the two equations we set up earlier to find the height of the tree "h". Using the first equation, we get:
h = x * tan(62°) ≈ 76 feet
Therefore, the height of the tree is approximately 76 feet.
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What is the standard form of the equation of the circle with the center and a radius of square 2 divided by 4
The standard form of the equation of the circle with center and radius of square 2 divided by 4 is (x - 1/2)² + (y + 1/2)² = 1/8.
The standard form of the equation of a circle is (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius.
To use this formula, we first need to find the values of h, k, and r for the given circle with center and radius of square 2 divided by 4.
We know that the center of the circle is (h, k) = (2/4, -2/4) = (1/2, -1/2).
This means that h = 1/2 and k = -1/2.
The radius of the circle is r = square 2 divided by 4.
We can write this as r² = (square 2 divided by 4)² = 2/16 = 1/8.
Now we can substitute these values into the standard form equation to get:
(x - 1/2)² + (y + 1/2)² = 1/8
So the standard form of the equation of the circle with center and radius of square 2 divided by 4 is (x - 1/2)² + (y + 1/2)² = 1/8.
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A child earns $2 per completed household chore and an additional $12 per month if the child completes all the chores on the chore list. If the child completed the entire chore list last month and earned a total of $44, which statement is true?
Hence, C) The child performed every task on the list last month is the right answer.
what is unitary method ?Mathematicians utilize the unitary approach as a tool for solving proportionality-related problems. Given certain known values, it entails applying ratios and proportions to find unknown quantities. According to the unitary technique, if two quantities are connected to one another in a particular way, we can determine the value of one quantity by knowing the value of the other. This is accomplished by first determining the unit value of the given quantity, which is then multiplied or divided to yield the desired value.
given
Let's name the quantity of housework the youngster performed "x".
The total earnings can be expressed by the equation below, where the child earns an additional $12 if they finish all the chores on the chore list:
Total income = 2x plus 12
We are informed that the child accomplished all of the chores on the list for the previous month and earned $44. We may set this equal to 44 and find x by using the equation above:
2x + 12 = 44
2x = 32
x = 16
The kid finished 16 housework tasks last month.
Now that we know which of the following is true:
A) The youngster finished ten domestic duties.
This is untrue, since we determined that the child accomplished 16 domestic duties.
A) The youngster received $4 for finishing all the tasks on the list.
This is untrue because the child receives $12 for finishing the chores on the list.
B) Last month, the youngster finished all of the chores on the list.
This is accurate because we were told the child accomplished every task on the list and discovered that there were 16 in all.
Hence, C) The child performed every task on the list last month is the right answer.
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who in 1706 first gave the greek letter pi its current mathematical definition
The mathematician William Jones is credited with first using the Greek letter π
The mathematician William Jones is credited with first using the Greek letter π to represent the ratio of a circle's circumference to its diameter in a 1706 publication. He wrote, "there is no other more proper than Pi," and thus the symbol caught on among mathematicians. However, it's important to note that the concept of pi and its calculation had been around for thousands of years prior to Jones' use of the symbol.
Ancient Egyptian, Babylonian, and Indian mathematicians all had methods for approximating pi, and Archimedes famously used a geometric method to calculate it to a high degree of accuracy in the third century BCE.
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Luca owns a food truck called The Muffin Man, and this week, he is making a specialty flavor by adding cheddar cheese and hot peppers to corn muffin mix. The mix comes in a box shaped like a rectangular prism with a volume of 60 cubic inches. The box has a length of 5 inches and a height of 8 inches
The width of the rectangular prism box is 1.5 inches if the length of the box is 5 inches and the height of the box is 8 inches.
The volume of a rectangular prism = 60 cubic inches.
The length of the box = 5 inches
The height of the box = 8 inches
To calculate the width of the rectangular prism, we can use the formula for volume:
Volume = length * width * height
Mathematically,
V = l*w*h
60 = 5w * 8
w = 60 / (5 * 8)
w = 1.5 inches
Therefore we can conclude that the width of the rectangular prism box is 1.5 inches.
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Luis models a can of ground coffee as a right cylinder. He measures its height as 51/1
3
in and its radius as in. Find the volume of the can in cubic inches. Round your
4
answer to the nearest tenth if necessary.
Answer:
Step-by-step explanation:
Answer: I can’t find it please help
Step-by-step explanation:
the order is for 35 mg of zantac iv now. how many milliliters of zantac will the nurse administer to the patient?: enter only the numeral (not the unit of measurement) in your answer.
Numeric (continuous) variable: the amount of zantac in milliliters that the nurse will administer.A millilitre is a unit of capacity measurement. It is one thousandth of a litre in size. In other words, a one-liter container may hold [tex]1,000[/tex] millilitres.
What zantac will the nurse administer to the patient?A millilitre is a more manageable unit of measurement for liquid volume or capacity in the metric system. It is used to measure smaller amounts of liquid and is equal to one thousandth of a litre (1 litre = 1000 millilitres).
To calculate how many millilitres of Zantac will the nurse administer to the patient, you need to know the concentration of Zantac in the dosage form and the prescribed dose for the patient.
For example, if the patient is prescribed 150 mg of oral Zantac twice daily and has a bottle of syrup that contains 15 mg/mL of ranitidine, then the nurse will administer [tex]10 mL (150 mg / 15 mg/mL)[/tex] of syrup per dose.
Therefore, If the patient is prescribed 50 mg of intravenous Zantac every 8 hours and has a vial of solution that contains 25 mg/mL of ranitidine, then the nurse will administer 2 mL (50 mg / 25 mg/mL) of solution per dose.
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Last year, 89 musicians attended a jazz camp, and 15 of them were bassists. What is the experimental probability that the first musician to sign up will be a bassist?
There is a roughly 16.85% chance that a bassist will be the first musician to register for the jazz camp.
What is experimental probability?Experimental probability is a type of probability that is based on actual observations or experiments. It is also called empirical probability
According to question:The ratio of the frequency of an occurrence to the total number of trials or observations is known as the experimental probability. In this case, the event is the first musician to sign up being a bassist.
Since there were 15 bassists out of 89 musicians who attended the camp last year, the experimental probability of the first musician to sign up being a bassist is:
Experimental probability = Number of bassists / Total number of musicians
Experimental probability = 15 / 89
Experimental probability = 0.1685 or approximately 16.85%
As a result, there is a roughly 16.85% chance that a bassist will be the first musician to register for the jazz camp.
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The sum of two numbers is 25, and the larger is 3 less than three times the smaller. What is the number?
The smaller number is 5.5 and the larger number is 15.5.
Let's start by assigning variables to the two unknown numbers. Let x be the smaller number and y be the larger number.
From the problem statement, we know that:
x + y = 25 (the sum of the two numbers is 25)
y = 3x - 3 (the larger number is 3 less than three times the smaller)
We can use the second equation to solve for y in terms of x, by adding 3 to both sides:
y + 3 = 3x
Then, we can substitute this expression for y into the first equation:
x + (y + 3) = 25
Substituting y + 3 with 3x, we get:
x + 3x = 22
Combining like terms, we get:
4x = 22
Finally, we solve for x by dividing both sides by 4:
x = 5.5
Now that we know x, we can use the equation y = 3x - 3 to find y:
y = 3(5.5) - 3 = 15.5
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the value of a boat is 21 200. it loses 6 of its value every year. find the approximate monthly percent decrease in value.
The approximate monthly percent decrease in value of the boat is 0.5%.
The given value of a boat is 21 200, and it loses 6% of its value every year. We are to find the approximate monthly percent decrease in value.
The given information is as follows: The value of a boat = $21,200The percentage decrease in value = 6%We are to find the approximate monthly percent decrease in value. Annual decrease in value of a boat is 6% of $21,200= $1,272Monthly decrease in value of a boat will be 1/12 of the annual decrease = $1,272/12≈ $106Thus, the approximate monthly percent decrease in value of the boat will be
[tex]$\frac{106}{21,200}*100\%=0.5\%$[/tex]
Therefore, the approximate monthly percent decrease in value of the boat is 0.5%.
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Your question is incomplete, but probably the complete question is :
The value of a boat is $21,200. It loses 6% of its value every year. Find the approximate monthly percent decrease in value. Round your answer to the nearest hundredth of a percent.
PLEASE HELP!
The sum of the roots of a monic quadratic is -6, and the product of its roots is 7. What is the quadratic?
Answer with a quadratic expression using the variable x such as x^2 + 10x + 20
Answer:
x^2 +6x+7
Step-by-step explanation:
for roots a and b
x^2 - (a+b)x + ab = (x-a)(x-b)
An angle measures 62° more than the measure of its complementary angle. What is the measure of each angle?
Use the rational zeros theorem to find all the real zeros of the polynomial function. use the zeros to factor f over the real numbers. f(x)=x^3-5x^2-61x-55???
The polynomial function f(x) = x³ - 5x² - 61x - 55 has the following
Real zeros: x = -5, x = -1, and x = 11.
To find the rational zeros of a polynomial, we use the rational zeros theorem. We look at the factors of the leading coefficient and the factors of the constant coefficient.
The states that if a polynomial function is defined as P(x) = anxn + an-1xn-1 + ... + a1x + a0 with integers, then each rational zero of the polynomial can be expressed in the form p/q where p is a factor of a0 and q is a factor of an.
For example, if P(x) = 2x³ - 5x² + 3x + 6 then p can be any factor of 6 and q can be any factor of 2.
The factors of the leading coefficient, 1, and the factors of the constant coefficient, -55, are: ±1, ±5, ±11, ±55. So the possible rational zeros are: ±1, ±5, ±11, ±55, ±1/1, ±5/1, ±11/1, ±55/1, ±1/1, ±5/1, ±11/1, ±55/1.
Simplifying the results, we have that the potential rational zeros are: ±1, ±5, ±11, ±55, ±1, ±5, ±11, and ±55.
By testing each possible rational zero, we find that x = -5, x = -1, and x = 11 are the real zeros of f(x).
Hence, using synthetic division, we get:
(x + 5)(x + 1)(x - 11) = x³ - 5x² - 61x - 55
Thus, the function can be factored over the real numbers as
f(x) = (x + 5)(x + 1)(x - 11).
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an old piano has 88 keys, and 56 of them are out of tune, while the remaining keys are tuned properly. a child strikes a key on the piano at random. what is the probability that the child strikes a properly tuned key?
Answer: I think It is 63.64%. If I'm wrong I'm sorry.
Step-by-step explanation:
Ask yourself what is 56% out of 88%. I did it in my head, but I got 63.6363636% then I rounded it to 63.64%.
A triangular pyramid has a base shaped like an equilateral triangle. The legs of the equilateral tris are all 9 feet long, and the height of the equilateral triangle is 7.8 feet. The pyramid's slant heigh feet. What is its surface area?
If a triangular pyramid has a base shaped like an equilateral triangle. its surface area is: 120.41 square feet.
How to find the surface area?To solve this problem, we can use the formula for the surface area of a pyramid:
Surface area = base area + (1/2) x perimeter of base x slant height
First, we need to find the area of the base, which is an equilateral triangle. The formula for the area of an equilateral triangle is:
Area = (square root of 3) / 4 x (side length)^2
Substituting the given values, we get:
Area = (square root of 3) / 4 x 9^2
Area = (square root of 3) x 20.25
Area = 11.06 (rounded to two decimal places)
Next, we need to find the perimeter of the base, which is simply 3 times the side length:
Perimeter = 3 x 9
Perimeter = 27
Finally, we can use the given slant height to find the surface area:
Surface area = 11.06 + (1/2) x 27 x 8.1
Surface area = 11.06 + 109.35
Surface area = 120.41 square feet (rounded to two decimal places)
Therefore, the surface area of the triangular pyramid is approximately 120.41 square feet.
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John is making apple pies and apple cobblers to sell at his stand at the Farmer's Market.
A pie uses 4 cups of apples and 3 cups of flour.
A cobbler uses 2 cups of apples and 3 cups of flour.
John has 16 cups of apples and 15 cups of flour.
When John sells the pies and cobblers at the Farmer's Market, he will make $3.00 profit per pie and $2.00 profit per cobbler.
Let x = the number of pies John makes.
Let y = the number of cobblers John makes.
Enter the four constraints into the graphing calculator.
What are the vertices of the feasible region?
Hint: input your answers from questions 3, 4, and 5 into Desmos to find the vertices.
Answers from questions 3, 4, and 5
[tex]4x+2y≤16\\3x+3y≤15\\x≥0\\y≤0[/tex]
Answer:huh,
Step-by-step explanation:I don’t understand you’re saying
Find the sum of and .2푥+1
Answer:
2*22/7/27+1
Step-by-step explanation:
2*22/7*27+1
2*(594+1)/7
2*595/7
2*85
170 ans..
Which of these is a pythagorean triple?
Responses
9, 40, 41
7, 26, 89
1, 2, 3
36, 48, 62
Answer:
The first one
Step-by-step explanation:
Use the pythagoras theorem=a ^2+b^2 =c^2
Use a is 9 b is 40 because the largest value is always the hypotenuse and the hypotenuse is always c.
so you do 9 squared add 40 squared to find c squared.
Square root the answer and you get 41 so it is a pythagoras triple
caden is 208 miles away from rahquez. they are traveling towards each other. if rahquez travels 6 mph faster than caden and they meet after 8 hours, how fast was each traveling?
Caden's speed is 10 mph and Rahquez's speed is 16 mph faster, which is 16+6 = 32 mph
Let's use the formula: distance = rate x time
Since Caden and Rahquez are traveling towards each other, their combined distance will be 208 miles. Let's call Caden's speed "x" and Rahquez's speed "x+6", since Rahquez is traveling 6 mph faster than Caden.
Using the formula above, we can set up the equation:
208 = (x + x + 6) * 8
Simplifying, we get:
208 = (2x + 6) * 8
208 = 16x + 48
160 = 16x
x = 10
Therefore, Caden's speed is 10 mph and Rahquez's speed is 32 mph.
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PLEASE HELP MARKING BRAINLEIST JUST ANSWER ASAP AND BE CORRECT
Answer:
4t - 22
Step-by-step explanation:
To find:-
Perimeter of the given figure.Answer:-
To find out the perimeter we can simply add all the side lengths of the given figure. Since the given figure here is a rectangle, we can add up all the four sides to find the perimeter.
The four sides given to us are t-6 , t-5 , t-6 and t-5 .
Hence the perimeter of the quadrilateral would be ,
Perimeter = t-5 + t-6 + t-5 + t-6
Perimeter = 4t - 10 - 12
Perimeter = 4t - 22
Hence the perimeter of the given figure us 4t - 22.
[tex]\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\put(0.03,0.02){\framebox(0.25,0.25)}\put(0.03,2.75){\framebox(0.25,0.25)}\put(4.74,2.75){\framebox(0.25,0.25)}\put(4.74,0.02){\framebox(0.25,0.25)}\multiput(2.1,-0.7)(0,4.2){2}{$\sf\large t-5$}\multiput(-1.4,1.4)(6.8,0){2}{$\sf\large t-6$}\put(-0.5,-0.4){\bf A}\put(-0.5,3.2){\bf D}\put(5.3,-0.4){\bf B}\put(5.3,3.2){\bf C}\end{picture} [/tex]
a bag contains marbles, marbles, and marbles. if a marble is drawn from the bag, replaced, and another marble is drawn, what is the probability of drawing first a marble and then a marble?
To find the probability of drawing a marble and then another marble from the bag, we need to multiply the probabilities of the individual events. This is because the two events are independent, and the outcome of the first event does not affect the outcome of the second event.
Let P(R) denote the probability of drawing a red marble, and P(B) denote the probability of drawing a blue marble. We are given that the bag contains red, blue, and green marbles, but we do not know the exact numbers of each color.
Since we replace the marble after each draw, the probability of drawing a red marble and then a blue marble can be found as:
P(RB) = P(R) x P(B)
To find P(R), we need to divide the number of red marbles in the bag by the total number of marbles. Similarly, to find P(B), we need to divide the number of blue marbles in the bag by the total number of marbles. However, since we do not know the exact numbers of each color, we cannot compute these probabilities exactly.
Therefore, we can only say that the probability of drawing a marble and then another marble is equal to the product of the probabilities of drawing each marble separately. In other words, the probability of drawing a red marble and then a blue marble is:
P(RB) = P(R) x P(B)
where P(R) and P(B) are the probabilities of drawing a red marble and a blue marble, respectively, which we cannot determine without more information about the contents of the bag.
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How do you fine the blank for infinitely many solutions
To determine if a system of linear equations has infinitely many solutions, you need to solve the system and check the resulting equations.
Here are the general steps:
Write the system of linear equations in standard form: ax + by = c, where a, b, and c are constants.Use any method (substitution, elimination, or matrix) to solve the system of equations and obtain the solution set.If you get an equation that is always true (such as 0 = 0), then the system has infinitely many solutions.If you get an equation that is always false (such as 0 = 1), then the system has no solution.If you obtain a valid solution for each variable, then the system has a unique solution.
If you have two or more variables and only obtain a solution for some of them, then the system has infinitely many solutions.
It's also important to note that if you have a system with fewer equations than variables, it may also have infinitely many solutions.
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Work out m and c for the line: y = 5 − x
Answer:
m = -1, c = 5
Step-by-step explanation:
Provided in the attachment.
Mitchelle and Angela won R18000 in a competition and they decided share the money in the ratio 2:3how much will each get
Mitchelle will receive R7200 and Angela will receive R10800.
How to find the value of one part by dividing the total amount won by the total number of parts?
To determine how much Mitchelle and Angela will each receive in the ratio of 2:3, we need to first find the total number of parts in the ratio, which is 2 + 3 = 5.
Value of one part = R18000 ÷ 5 = R3600
Therefore, one part of the ratio 2:3 is equal to R3600.
How to find out how much Mitchelle and Angela will each receive?
we can multiply their respective parts by the value of one part:
• Mitchelle's share = 2 parts × R3600 per part = R7200
• Angela's share = 3 parts × R3600 per part = R10800
Therefore, Mitchelle will receive R7200 and Angela will receive R10800.
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A student solved the equation extraneous? Explain. 5/x-4 = x/x-4 and got 4 and 5 as solutions. Which, if either, of these is extraneous? Explain.
Therefore , the solution of the given problem of equation comes out to be x = 5 is a correct answer to the problem.
What is equation?Complex algorithms frequently employ variable words to demonstrate coherence between two opposing assertions. Equations are academic expressions that are used to demonstrate the equality of different academic figures. In this instance, normalization results in a + 7 rather than a separate algorithm who divides 12 onto two separate components and is able to evaluate data obtained from x + 7.
Here,
We can begin by making the provided equation simpler:
=> 5/(x - 4) = x/(x - 4)
=> 5 = x
Consequently, x = 5 is the answer to the problem.
The result of adding x = 4 to the initial equation is:
=> 5/(4 - 4) = 4/(4 - 4)
That amounts to:
=> 5/0 = 4/0
However, since division by zero is undefinable, the answer x = 4 is superfluous and does not satisfy the equation.
The result of the initial equation with x = 5 is:
=> 5/(5 - 4) = 5/(5 - 4)
That amounts to:
=> 5/1 = 5/1
As a result, x = 5 is a correct answer to the problem.
In conclusion, only one of the solutions -x = 5 is correct, and the other
-x = 4 is unnecessary because it results in a divide by zero.
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