The rational equation [tex]x^2 - 36 / (x+6)[/tex], when x is not -6, simplifies to x - 6. The correct answer is D.) x - 6.
Explanation:This is a Mathematics problem related to algebraic expressions and rational expressions. Given the equation [tex]x^2 - 36 / (x+6)[/tex], when x is not equal to -6, we can simplify this equation by factoring. Note that x^2 - 36 is a difference of two squares, which factors into (x-6)(x+6). So we now have [tex](x-6)(x+6) / (x+6).[/tex]
Since x is not -6, we can cancel out the (x+6)s, leaving us with x-6. Therefore, the answer is D.) x - 6. It's important to be careful with the conditions given in the problem, as they can affect the result.
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In a geometric sequence, a4=54 and a7=1458. What is the 12th term?
a. 5,616
b. 354,294
c. 14,350,365
d. 234,812,358
Answer-
[tex]\boxed{\boxed{a_{12}=354294}}[/tex]
Solution-
If there are 2 terms of a Geometric Sequence [tex]a_n[/tex] and [tex]a_k[/tex] where (n > k), then
[tex]a_n=a_k\cdot r^{n-k}[/tex]
where, r = common ration of the G.P.
Here,
[tex]a_4 = 54\\\\a_7=1458[/tex]
Putting in the equation,
[tex]\Rightarrow a_7=a_4\cdot r^{7-3}[/tex]
[tex]\Rightarrow a_7=a_4\cdot r^3[/tex]
[tex]\Rightarrow 1458=54\cdot r^3[/tex]
[tex]\Rightarrow r^3=\dfrac{1458}{54}[/tex]
[tex]\Rightarrow r^3=27[/tex]
[tex]\Rightarrow r=3[/tex]
Again putting the values in the equation,
[tex]\Rightarrow a_{12}=a_7\cdot r^{12-7}[/tex]
[tex]\Rightarrow a_{12}=a_7\cdot r^5[/tex]
[tex]\Rightarrow a_{12}=1458\cdot 3^5[/tex]
[tex]\Rightarrow a_{12}=354294[/tex]
The 12th term of the geometric sequence is 354,294
The nth term of a geometric sequenceThe nth term of a geometric progression is given by the formula:
[tex]a_n = ar^{n-1}[/tex]
For n = 4
[tex]a_4=ar^{4-1}\\\\a_4=ar^3\\\\ar^3=54..................(1)[/tex]
For n = 7
[tex]a_7=ar^{7-1}\\\\a_7=ar^6\\\\ar^6=1458................(2)[/tex]
Divide equation (2) by equation (1)
[tex]\frac{ar^6}{ar^3} =\frac{1458}{54} \\\\r^3=27\\\\r^3=3^3\\\\r = 3[/tex]
Substitute r = 3 into equation (1)
[tex]a(3)^3=54\\\\27a=54\\\\a=\frac{54}{27}\\\\a=2[/tex]
The 12th term of the sequence is therefore calculated below
[tex]a_{12}=ar^{11}\\\\a_{12}=2(3^{11})\\\\a_{12}=354294[/tex]
The 12th term of the geometric sequence is 354,294
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Double vision can be the result of _________________.
Wearing glasses that are too strong
Looking directly into bright headlights Passing other cars
Eye muscles relaxed from fatigue, drugs, or alcohol
Rapid eye blinking
Final answer:
Double vision can be caused by wearing glasses that are too strong, eye muscles being relaxed from fatigue, drugs, or alcohol, or by rapid eye blinking. Nearsightedness and farsightedness are common vision defects related to the eye's focusing ability but do not usually cause double vision, which can also be a result of misalignment.
Explanation:
Double vision can be the result of several factors including wearing glasses that are too strong, eye muscles relaxed from fatigue, drugs, or alcohol, or rapid eye blinking. It is not typically caused by looking directly into bright headlights or the action of passing other cars, which are more likely to cause temporary glare or flash blindness rather than persistent double vision.
Common vision defects such as nearsightedness (myopia) and farsightedness (hyperopia) are related to the focusing ability of the eyes. Myopia occurs when the eye over-converges the rays from a distant object in front of the retina, causing distant objects to appear blurry. Hyperopia, on the other hand, happens when the eye does not converge rays from a close object sufficiently, making close objects appear blurry. Misalignment can also cause double vision, and this can be due to a variety of factors including strabismus or nerve damage. Correction of vision defects often involves the use of glasses or contact lenses with the appropriate lens power or surgery for more severe cases.
Jill spend $15 on diapers. If they cost $5 a package, how many packages did she buy ?
How to solve; you roll a pair of number cubes what is the probability of rolling a number less than 4 on both cubes?
6 numbers per cube
3 numbers are less than 4 ( 1, 2 & 3)
so you have a 3/6, reduce to 1/2 probability of rolling a number less than 4 on each cube
2 cubes
so 1/2 * 1/2 = 1/4 probability
True or false? the point at which a tangent line meets a circle is called the point of tangency
Final answer:
The statement is true; a tangent line meets a circle at the point of tangency, which is the unique point where the tangent touches the circle without intersecting it.
Explanation:
True, the point at which a tangent line meets a circle is indeed called the point of tangency. This is a fundamental concept in geometry, where a tangent line is defined as a line that touches a curve at exactly one point, without crossing through it. This distinct point is known as the point of tangency.
For example, if we have a circle and a line that touches the circle at just one point and does not intersect it at that point, that line is a tangent to the circle, and the point of contact is the point of tangency. The tangent line is always perpendicular to the radius of the circle at the point of tangency, as can also be seen from the properties of the director circle, which is the locus of points of intersection of perpendicular tangents to the curves like ellipses and hyperbolas.
In the context of a director circle, perpendicular tangents to an ellipse would intersect on this special circle. Although for this particular question, we are focusing on the tangent line to a single circle and its point of tangency. It's interesting to note that according to the properties of circles, every point on a circle allows for exactly one tangent line. Whenever such a line is drawn, it illustrates the concept of tangency.
Given that x = 7, write an equation that contains two different equivalent expressions each including at least one variable (x) and the operations: addition, subtraction, multiplication, and division.
Well here are two equivalent different expressions of my making that you could use for this question.
f(x) = 2x - 7
g(x) = 3x - 28 / 2
When x = 7, these two different expressions will equate to the same value of 7. If you meant something else let me know, otherwise this is what you should put for your essay-question.
If H(x)=4x^2-16 were shifted 9 units to the right and 1 down, what wold be the new equation?
A. H(x)= 4(x+9)^2-17
B. H(x)= 4(x-7)^2+16
C. H(x)= 4(x-17)^2-9
D. H(x)= 4(x-9)^2-17
Answer: H(x)=4(x-9)^2-17
Step-by-step explanation:
A bicyclist travels at the rate of 8 miles in an hour. If the bicyclist continues at this rate, how many miles can the bicyclist travel in seven hours?
A. 54 miles
B. 55 miles
C. 45 miles
D. 56 miles
Explain how to write and evaluate an algebraic expression.
one more than the product of a number and seven decreased by five; evaluate when n=6
Answer:
Replace critical words with variables, numbers, and operations. More than is addition, the product is multiplication and decreased by is subtraction. The constants are 1, 7, and 5. The expression is 1 + 7n – 5. To evaluate the expression, substitute 6 for the variable and then simplify the order of operations. The value when n = 6 is 38.Step-by-step explanation:
A car uses an average of 8 litres of fuel for every 100 km travelled. At this rate, how many litres would the car use to travel 250 km?
The car would use 20 litres to travel 250 km.
Explanation:To determine the number of litres the car would use to travel 250 km, we can set up a proportion using the average fuel consumption rate of 8 litres per 100 km:
8 litres / 100 km = x litres / 250 km
To solve for x, we can cross-multiply and then divide:
x litres = (8 litres * 250 km) / 100 km
x litres = 20 litres
Therefore, the car would use 20 litres to travel 250 km.
Final answer:
The car would use 20 liters of fuel to travel 250 km.
Explanation:
To determine how many liters of fuel the car would use to travel 250 km, we can set up a proportion using the given information:
8 liters ÷ 100 km = x liters ÷ 250 km
Cross multiplying, we get:
x = (8 liters × 250 km) ÷ 100 km
x = 2000 liters ÷ 100 km
x = 20 liters
Therefore, the car would use 20 liters of fuel to travel 250 km.
The base of a cone can be
A. a triangle.
B. a pentagon.
C. a square.
D. an ellipse.
Find the sum of the three expressions and choose the correct answer.
-8a 3 b + 3a2 b 2 - 5
2 + 5a 2 b 2
3a 3 b + 7 - 9a 2 b 2
Choices:
A.) -5a3b - a2b2 + 2
B.) -5a3b + 8a2b2 + 4
C.) -5a3b - a2b2 + 4
Answer:
Sum of -8a³b+3a²b²-5,2+5a²b² and 3a³b+7-9a²b² is:
-5a³b-a²b²+4
Step-by-step explanation:
We have to find the sum of:
-8a³b+3a²b²-5,2+5a²b² and 3a³b+7-9a²b²
-8a³b+3a²b²-5+2+5a²b²+3a³b+7-9a²b²
= -5a³b-a²b²+4
Hence, sum of -8a³b+3a²b²-5,2+5a²b² and 3a³b+7-9a²b² is:
-5a³b-a²b²+4
Margie and four friends are eating lunch at a restaurant. The total bill is $52.50 before tax and tip. Margie has a coupon good for $10off their total purchase. If sales tax of 6 percent is collected on the discount amount, what is the total cost after tax?
If a stimulus plus a response results in a satisfying outcome, the probability of that response occurring again ________.
In terms of operant conditioning, if a response to a stimulus results in a satisfying or rewarding outcome, the probability of the response recurring to that stimulus in the future increases. Conditioning behavior is controlled by their consequences.
Explanation:If a stimulus plus a response results in a satisfying outcome, the probability of that response occurring again increases. This concept is central to the idea of operant conditioning in behavioral psychology. Operant conditioning is a type of learning where behavior is controlled by consequences. If the response to a stimulus results in a rewarding or satisfying outcome, this acts as positive reinforcement.
In operant conditioning, when a response yields a rewarding outcome (reinforcement), the likelihood of the behavior recurring in the future is increased. Take, for instance, the case of a dog that has learned if it sits when commanded, it receives a treat. The command ('Sit') is the stimulus, sitting is the response, and receiving a treat is the reinforcement. This scenario typically increases the likelihood of the dog sitting when given the command in the future.
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In terms of operant conditioning, if a response to a stimulus results in a satisfying or rewarding outcome, the probability of the response recurring to that stimulus in the future increases. Conditioning behavior is controlled by their consequences.
Explanation:If a stimulus plus a response results in a satisfying outcome, the probability of that response occurring again increases. This concept is central to the idea of operant conditioning in behavioral psychology. Operant conditioning is a type of learning where behavior is controlled by consequences. If the response to a stimulus results in a rewarding or satisfying outcome, this acts as positive reinforcement.
In operant conditioning, when a response yields a rewarding outcome (reinforcement), the likelihood of the behavior recurring in the future is increased. Take, for instance, the case of a dog that has learned if it sits when commanded, it receives a treat. The command ('Sit') is the stimulus, sitting is the response, and receiving a treat is the reinforcement. This scenario typically increases the likelihood of the dog sitting when given the command in the future.
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What is the height, h, of one of the triangles?
Answer:
8ft
Step-by-step explanation:
How many solutions can be found for the equation −4x − 11 = 2(x − 3x) + 13?
Answer:
it is no solutions
Step-by-step explanation:
A circle has a diameter of 13 centimeters and a central angle EOG that measures 280 degrees. What is the length of the intercepted arc EG? Use 3.14 for pi and round your answer to the nearest tenth. A) 10.1 cm B) 15.9 cm C) 31.7 cm D) 63.5 cm
If you buy something at a 20% discount off the listed price of $ 97, but pay a sales tax of 10% after the discount is applied, how much do you end up paying? $
You are saving money to buy a new game system you received $50 as a birthday gift from your grandparents. You want to save $25 a week from mowing lawns.
Event A is rolling a five on a six sided die and event B is rolling an odd number on the same die. Are the events dependent or independent, why?
Solve for x. 12x = 2x^2 + 18
A. x = –3
B. x = 3
C. x = –3 or x = 0
D. x = 0 or x = 3
Use the graph below to answer the following question:
What is the average rate of change from x = 1 to x = 4?
−3
−1
1
3
Answer:
Step-by-step explanation:
_______
Good evening ,
_______________
f(1)=3 and f(3) = -1 so the average rate of change from x = 1 to x = 4 is 1.
Look at the photo below for more details,
________________________________
:)
How much carpet is needed to cover 2 rooms, one of which is 12 ft by 6 ft and the other 10 ft by 8 ft?
Answer:
152 square feet
Step-by-step explanation:
The area of a rectangle is the product of its length and width. The total area of carpet required is the sum of the areas of the two rooms:
carpet area = (12 ft)(6 ft) +(10 ft)(80 ft) = 72 ft^2 +80 ft^2
carpet area = 152 ft^2
During a recent snowstorm in red hook ny Jaime notice that there were 4 inches of snow on the ground at 3:00p.m and there were 6 inches of snow on the ground at 7:00p.m. If she were to graph these data what does the slope of the line connecting these two point represent in the context of this problem
Complete the square to solve the equation below.
x²+x =7/4
A.)x=3, x= -1
B.)x= -2+ √2, x= -2- √2
C.) x= -1/2+√2, x= -1/2- √2
D.) x=1+ √-2, x= 1- √2
Answer: The correct answer is C
Step-by-step explanation: APPEX learning quiz
A coin collector bought a set of coins for $500, and then sold the set for $850, making a profit of $50 per coin. how many coins were in the set?
For this case, the first thing we must do is calculate the total profit.
We have then:
[tex] P = 850 - 500 [/tex]
[tex] P = 350 [/tex]
Then, we look for the number of coins.
For this, we need the total profit (which we already calculate) and the amount of profit per coin.
We have then:
[tex] N = \frac{350}{50} [/tex]
[tex] N = 7 [/tex]
Answer:
The amount of coins that was on the set is:
[tex] N = 7 [/tex]
Final answer:
The coin collector bought and sold a set of coins, making a total profit of $350. Dividing this profit by the $50 profit per coin reveals that there were 7 coins in the set.
Explanation:
The coin collector made a profit of $50 per coin by selling a set of coins. To find out how many coins were in the set, we need to calculate the total profit made from selling the coins and then divide that by the profit per coin.
The total profit is the selling price minus the buying price, so $850 - $500 = $350. If the collector made $50 profit per coin, then the number of coins in the set can be found by dividing the total profit by the profit per coin: $350 / $50 per coin = 7 coins.
37. A juice pitcher holds 1.5 gallons of liquid. How many 8-ounce glasses of juice can be poured from a full pitcher? (1 gallon 128 ounces) Explain your answer by writing or describing the steps you used to solve the problem.
1 gallon = 128 ounces
multiply 128 by 1.5 gallons:
1.5 x 128 = 192 ounces total
divide total ounces by 8 to get number of glasses:
192/8 = 24
you can pour 24 eight ounce glasses
What is the result of isolating y2 in the equation below? 9x2 + 7y2 = 42
Isolating a variable involves changing the subject of the equation.
The result of isolating y^2 is: [tex]\mathbf{y^2 = \frac{42 - 9x^2}7}[/tex]
The equation is given as:
[tex]\mathbf{9x^2 + 7y^2 = 42}[/tex]
Subtract 9x^2 from both sides
[tex]\mathbf{7y^2 = 42 - 9x^2}[/tex]
Divide through by 7
[tex]\mathbf{y^2 = \frac{42 - 9x^2}7}[/tex]
Hence, the result of isolating y^2 is: [tex]\mathbf{y^2 = \frac{42 - 9x^2}7}[/tex]
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20 is what percent of 50?
Hey!
Hope this helps...
~~~~~~~~~~~~~~~~~~~~~~~
First, you need to do 20 divided by 50 (or in your calculator 20/50)...
Second, you would do long division (or in the calculator, press 'enter')...
And boom-bada-boom, your answer is: 20 is 40% of 50
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For future reference, please try to avoid asking/posting questions that can be answered using the calculator...
25 POINTS PLZ HELP ASAP!!!
Match the functions with their inverse functions.
We know that when we are given a inverse function as: [tex]f^{-1}(x)[/tex]
Then we find the function by the method:
Put [tex]f^{-1}(x)=y[/tex]
Then we switch the places of x and y and solve for y.
1)
[tex]f^{-1}(x)=\dfrac{2x-3}{5}[/tex]
Hence, we find the function as follows:
[tex]\dfrac{2x-3}{5}=y[/tex]
Then we switch for x and y
[tex]\dfrac{2y-3}{5}=x\\\\\\i.e.\\\\2y-3=5x\\\\\\i.e.\\\\\\2y=5x+3\\\\\\i.e.\\\\\\y=\dfrac{5x+3}{2}[/tex]
Hence, inverse function is:
[tex]f(x)=\dfrac{5x+3}{2}[/tex]
2)
[tex]f^{-1}(x)=\dfrac{x+8}{2}[/tex]
Hence, we find the function as follows:
[tex]\dfrac{x+8}{2}=y[/tex]
Then we switch for x and y
[tex]\dfrac{y+8}{2}=x[/tex]
[tex]y=2x-8[/tex]
Hence, inverse function is:
[tex]f(x)=2x-8[/tex]
3)
[tex]f^{-1}(x)=\dfrac{x+2}{7}[/tex]
Hence, we find the function as follows:
[tex]\dfrac{x+2}{7}=y[/tex]
Then we switch for x and y
[tex]\dfrac{y+2}{7}=x[/tex]
[tex]y=7x-2[/tex]
Hence, inverse function is:
[tex]f(x)=7x-2[/tex]
4)
[tex]f^{-1}(x)=\dfrac{1-2x}{x}[/tex]
Hence, we find the function as follows:
[tex]\dfrac{1-2x}{x}=y[/tex]
Then we switch for x and y
[tex]\dfrac{1-2y}{y}=x[/tex]
i.e.
[tex]1-2y=xy\\\\xy+2y=1\\\\i.e.\\\\y(x+2)=1\\\\y=\dfrac{1}{x+2}[/tex]
Hence, inverse function is:
[tex]f(x)=\dfrac{1}{x+2}[/tex]