[tex]c=14[/tex]
There is no extraneous solution because as we put the value of c in equation (1), it does not make the equation (1) not define.
Step-by-step explanation:
Given :
[tex]\dfrac {c-4}{c-2} = \dfrac {c-2}{c+2} - \dfrac{1}{2-c}[/tex] --------- (1)
Calculation :
[tex]\dfrac {c-4}{c-2} = \dfrac {(c-2)^2+(c+2)}{(c+2)(c-2)}[/tex]
[tex]c-4 = \dfrac {(c^2-4c+4)+(c+2)}{(c+2)}[/tex]
[tex](c-4)(c+2) = (c^2-3c+6)[/tex]
[tex](c^2-2c-8) = (c^2-3c+6)[/tex]
[tex]c=14[/tex]
There is no extraneous solution because as we put the value of c in equation (1), it does not make the equation (1) not define.
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Answer:
14 and Zero
Step-by-step explanation:
The sum of two integers is 26. The larger of the two integer is 2 more than 3 times the smaller integer
Given: line segment AB is 10 inches long. Find the length of A'B' if AB is dilated to form A'B' with a scale factor of 1 2 . A) 1 2 inches B) 5 inches C) 10 inches D) 20 inches
Answer:
Option (b) is correct.
The length of A'B' is 5 inches.
Step-by-step explanation:
Given : line segment AB is 10 inches long. AB is dilated to form A'B' with a scale factor of [tex]\frac{1}{2}[/tex]
we have to find the length of A'B'
Dilation of a figure is the increase or decrease in the length of the figure by a fixed scaling factor. if scaling factor is greater than 1 , then figure size increases, and if scaling factor is less than 1 , then figure size decreases.
Here, scaling factor is [tex]\frac{1}{2}[/tex] which less than 1 , so line segment A'B' decreases.
New image = scaling factor × original image
that is A'B' = [tex]\frac{1}{2}\times 10=5[/tex]
Thus, the length of A'B' is 5 inches.
Option (b) is correct.
If your front lawn is 15.0 feet wide and 20.0 feet long, and each square foot of lawn accumulates 1450 new snow flakes every minute, how much snow (in kilograms) accumulates on your lawn per hour? Assume an average snow flake has a mass of 1.70 mg.
.. ......
it's my first college chm and I forgot how to do such word problems, would you help me please, thank you
What is the set of all possible outcomes of a probability experiment?
The set of all possible outcomes of a probability experiment is called the sample space. It can be represented as a list, a table, or using set notation.
Explanation:The set of all possible outcomes of a probability experiment is called the sample space. It is denoted by the symbol Ω. The sample space can be represented as a list, a table, or using set notation.
For example, if we are flipping a fair coin, the sample space would be {H, T}, where H represents heads and T represents tails.
In another example, if we were rolling a fair six-sided die, the sample space would be {1, 2, 3, 4, 5, 6}.
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If you were offered a job would you choose the one with the pay increase according to an arithmetic sequence formula or a geometric sequence formula? Justify your response.
Final answer:
For maximizing earning potential over time, a geometric sequence salary increase is typically more beneficial due to exponential growth, while an arithmetic sequence offers steady, predictable increases that may appeal to those who value consistency.
Explanation:
If offered a job with a salary increase tied to either an arithmetic sequence or a geometric sequence, the preferable option typically depends on the long-term financial goals and growth potential you are looking for. An arithmetic sequence will give you steady, predictable increases. However, a geometric sequence formula will often result in larger increases over time, especially if the ratio is 2 or more. Due to the exponential nature of a geometric sequence, your salary could grow significantly faster than with an arithmetic sequence. For example, if you start with a salary of $50,000, and the arithmetic sequence increase is $1,000 each year, after five years you would be earning $55,000. On the other hand, for a geometric sequence with a modest ratio of 1.05 (5% increase each year), you would start at the same $50,000 but after five years be earning approximately $63,814.
Considering this, if your primary goal is to maximize earning potential over time, the geometric sequence would be the more appealing option. However, if you value consistency and predictability in pay increases, or if the progression starts very low, an arithmetic sequence might be more in line with your personal financial planning.
FAST HELP!! 30 POINTS!!!
what type of solutions do the methods for solving systems of equations find and how does this relate to setting the equations equal to each other
Final answer:
Explanation of solutions for systems of equations and how setting equations equal to each other helps find solutions.
Explanation:
Solutions for systems of equations can be classified as unique, no solution, or infinitely many solutions. The method of setting equations equal to each other typically helps find the intersection points where the equations are simultaneously true, representing the solution to the system.
Item 14
POSSIBLE POINTS: 5
The total cost of repairing a car is the sum of the amount paid for parts and the amount paid for labor. You paid $132 for parts and $65 for each hour of labor. The total cost to repair the car was $229.50. How many hours did it take to repair the car?
Which equation best models this problem? Let x = number of hours worked
229.5 – 65 = 132x
132x + 65 = 229.5
132 + 65x = 229.5
132 + 65 = 229.50x
PLEASE HURRY
Line segment CT contains the point C(−2, 5) and a midpoint at A(1, −3). What is the location of endpoint T? T(4, −11) T(3, −8) T(5, −1) T(−0.5, 1)
A farmer has 300 ft of fencing with which to enclose a rectangular pen next to a barn. The barn itself will be used as one of the sides of the enclosed area.
What is the maximum area that can be enclosed by the fencing?
Enter your answer in the box.
ft²
Answer:
The Answer is 11250 ft~
Step-by-step explanation:
I did the test and got it correct
What is the length of the base of a right triangle with an area of 20 m² and a height of 4 m? A.5 m B.10 m C.80 m D.160 m
A theater has 1200 seats. each row has 20 seats. write and solve an equation to find the number xx of rows in the theater. an equation that represents this problem is =1200=1200. there are rows in the theater.
Answer:
The equation is 20x = 1200
x=1200÷20
x=60 rows
Step-by-step explanation:
The speed of an object in space is shown in the graph.
What is the slope of the line?
10
15
20
25
Answer:
Option B is correct
15
Step-by-step explanation:
Formula for slope is given by:
[tex]\text{Slope} = \frac{y_2-y_1}{x_2-x_1}[/tex]
As per the statement:
Form the graph:
Consider two points:
(0.2, 3) and (0.4, 6)
then;
[tex]\text{Slope} = \frac{6-3}{0.4-0.2}[/tex]
⇒[tex]\text{Slope} = \frac{3}{0.2}[/tex]
⇒[tex]\text{Slope}= 15[/tex]
Therefore, the slope of the line is, 15
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What is the equation of a line that is perpendicular to the line represented by y = 3/4 x - 1/2?
BRIANLIESTTTTTTTTTTTT ASAP!
Monica wants to measure the dimensions of her rectangular lawn. If the longer side of the lawn is (x + 3) feet and the diagonal length is (x + 4) feet, which function can be used to find the shorter side of her lawn?
a.] [tex]s(x)= \sqrt{2x+7} [/tex]
b.] [tex]s(x)= \sqrt{2 x^{2} +14x+25} [/tex]
c.] [tex]s(x)= \sqrt{x^{2} +7x+12} [/tex]
d.] [tex]s(x)= {x^{2} +7x+12} [/tex]
can you please help me thank you you will be given brainley
The temperature, T , of a given mass of gas varies inversely with its volume, V . The temperature of a certain gas with volume of 105 cm 3 is 30º C. What will be the temperature of the gas when it is compressed to a volume of 84 cm 3? 18.8º C 48º C 24º C 37.5º C
Final answer:
The temperature of a gas can be calculated using the formula for inverse variation, which is T1*V1 = T2*V2. By substituting the given values into the formula, we can find that the temperature of the gas when it is compressed to a volume of 84 cm^3 is 37.5ºC.
Explanation:
To solve this problem, we can use the formula for inverse variation:
T1*V1 = T2*V2
Given that T1 = 30ºC, V1 = 105 cm^3, and V2 = 84 cm^3, we can solve for T2:
T2 = (T1*V1)/V2 = (30*105)/84 = 37.5ºC
Therefore, the temperature of the gas when it is compressed to a volume of 84 cm^3 will be 37.5ºC.
Quadrilateral ABCD is inscribed in this circle. What is the measure of angle C? Enter your answer in the box.
Answer:
[tex]m<C=62\°[/tex]
Step-by-step explanation:
we know that
In an inscribed quadrilateral opposite angles are supplementary
so
In this problem
[tex]m<D+m<B=180\°[/tex]
[tex]m<C+m<A=180\°[/tex]
step 1
Find the value of x
[tex]m<D+m<B=180\°[/tex]
substitute the values and solve for x
[tex](x+20)\°+(3x)\°=180\°[/tex]
[tex]4x=180\°-20\°[/tex]
[tex]x=160\°/4=40\°[/tex]
step 2
Find the measure of angle A
[tex]m<A=(2x+38)\°=2(40\°)+38\°=118\°[/tex]
step 3
Find the measure of angle C
[tex]m<C+m<A=180\°[/tex]
substitute the values and solve for m<C
[tex]m<C+118\°=180\°[/tex]
[tex]m<C=180\°-118\°=62\°[/tex]
The tables below show two functions. For each set of data:
a) Determine whether the data represents a linear function, exponential function or neither and explain why.
x f(x)
-2 18
-1 22
0 26
1 30
2 34
x g(x)
-2 2
-1 4
0 8
1 16
2 32
Rubric:
Points Concept Addressed
/2 Correctly determines whether each table represents linear, exponential or neither
/2 Correctly explains their answer.
On Friday night, 165 people saw the dinosaur exhibit at the natural history museum. This amount represents 22% of the people who visited the museum that night.
Select from the drop-down menu to correctly identify the total number of people who visited the museum Friday night.
A total of people visited the natural history museum Friday night.
The answer is 750 people visited the natural history musem Friday night.
Answer for function
The price of a gallon of unleaded gas has dropped to $2.81 today. yesterday's price was $2.88 . find the percentage decrease. round your answer to the nearest tenth of a percent.
The percentage decrease is approximately -2.4%.
To find the percentage decrease in price, we can use the formula:
Percentage decrease = ((New price - Old price) / Old price) * 100
Using the given information, we substitute the values into the formula:
Percentage decrease = ((2.81 - 2.88) / 2.88) * 100
Simplifying the expression, we get:
Percentage decrease = (-0.07 / 2.88) * 100
Converting to a decimal and multiplying by 100, we find:
Percentage decrease = -0.0243 * 100 = -2.43%
Rounding to the nearest tenth of a percent, the percentage decrease is approximately -2.4%.
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What is the approximate distance between the points (-3,-4) and (-8,1) on a coordinate grid ?
Rowan raised $640 In a charity walk last year.this year he raised 15% more than he raised last year. How much money did Rowan raise this year?
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the area of a trapezoid is 72.8 square feet. the length of one of its bases is 7.4 feet and the length of its other base is 10.8 feet. what is the height of the trapezoid?
Then in a rectangle the ratio of the width to the length is 4:5 of the rectangle is 45 cm long what is the width
Answer: the answer would be 36:45
Step-by-step explanation: Hope this helps please bore brainlyiest est.
Why are epidemics and pandemics a relatively recent phenomenon in human history?
Sam picked a card from a standard deck. what is the probability that sam picked a heart or a king? one over thirteen sixteen over fifty two