Solve for x
A. Solve using the change of base formula.
Logby= log y/log b
B. Solve using a different method.
C. verify your solutions by substituting your value back into the original equation.
Answers
A) By using the change of base formula, the solution of the expression is,
⇒ x = - 2/3
B) The solution of the expression is,
⇒ x = - 2/3
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ 5³ˣ⁻² = 125²ˣ
Now, We have the change of base formula,
⇒ [tex]log_{b} y = \frac{log y}{log b}[/tex]
Here, The expression is,
⇒ 5³ˣ⁻² = 125²ˣ
⇒ 5³ˣ⁻² = 5⁶ˣ
Take log on both side,
⇒ log 5³ˣ⁻² = log 5⁶ˣ
⇒ (3x - 2) log 5 = 6x log 5
⇒ 3x - 2 = 6x
⇒ - 2 = 6x - 3x
⇒ 3x = - 2
⇒ x = - 2/3
B) By using another method as;
The expression is,
⇒ 5³ˣ⁻² = 125²ˣ
⇒ 5³ˣ⁻² = 5⁶ˣ
By comparing we get;
⇒ 3x - 2 = 6x
⇒ - 2 = 6x - 3x
⇒ 3x = - 2
⇒ x = - 2/3
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Related Questions
area of a sector with 150° and 6ft
Answers
The area of the sector is evaluated to be equal to 15π ft². B) is the correct option.
How to evaluate for the area of the sector.The area of a sector is calculated by multiplying the fraction of the angle for the sector divided by 360° and πr², where r is the radius.
the angle of the sector = 150°
the radius = 6 ft
hence the area of the sector is calculated as follows:
(150°/360°) × π × 6 ft × 6 ft
we simplify by division and multiplication
5/12 × π × 6 ft × 6 ft
5/12 × π × 36 ft²
5π × 3 ft²
15π ft²
Therefore, the area of the sector is evaluated to be equal to 15π ft² square meters.
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Use the expression you wrote in problem 5 to find the
number of centimeters in 9 meters.
Answers
The number of centimeters in 9 meters is 900.
What is metric conversion?Metric Conversion refers to the conversion of the given units to desired units for any quantity to be measured.
Given that, the measure is 9 meters.
We know that, 1 meter = 100 centimeters
Now, 9 meters
= 9×100
= 900 centimeters
Therefore, the number of centimeters in 9 meters is 900.
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What is the value of 1 gallon in litre?
Answers
One gallon is a unit of volume that is equivalent to 3.785 liters. This means that one gallon is equal to 3.785 liters.
The gallon is an imperial unit of measurement, which means that it is not used in most countries outside of the United States and the United Kingdom. In the US customary system, the gallon is divided into four quarts, each of which is equal to two pints. One US gallon is equivalent to approximately 0.83 imperial gallons, which are used in the UK.The gallon originated in medieval England as a measure for ale and other alcoholic beverages. It was adopted by the Romans during their invasion of Britain, and the term "gallon" is derived from the Latin term "galleta," which means "a pailful." The gallon was standardized in the 18th century by the British Imperial System.In the United States, the gallon is used in both the customary and imperial systems. In the customary system, the gallon is equal to 128 fluid ounces, while in the imperial system, it is equal to 160 fluid ounces. The US liquid gallon is divided into four quarts, which is equivalent to eight pints. One US dry gallon is equal to 4.4 liters.
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Jason packs a box full of styrofoam pieces how many square inches of styrofoam can the box fold ?
Answers
The number of styrofoam is 11.
What is a cube?
It is a polygon having six faces.
The volume of a cube is a side³
We have,
The area of the box = 44 square inches
Styrofoam is considered a square shape.
The side length of the styrofoam = 2 in
The area of the foam = 2² = 4 square inches
Now,
The number of styrofoam.
= 44 / 4
= 11
Thus,
11 styrofoam.
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Complete question:
Jason packs a box full of styrofoam pieces in a rectangular shape surface with an area of 44 square inches.
Each styrofoam is a square shape with a side length of 2 inches.
How many square inches of styrofoam can the box fold ?
statistics are often calculated with varying amounts of input data. write a program that takes any number of non-negative integers as input, and outputs the max and average. a negative integer ends the input and is not included in the statistics. assume the input contains at least one non-negative integer.Output the average with two digits after the decimal point followed by a newline, which can be achieved as follows:
System.out.printf("%.2f\n", average);
Ex: When the input is:
15 20 0 3 -1
the output is:
20 9.50
Answers
The average with two digits after the decimal point followed by a newline is 7.4
An integer is a whole number, either positive or negative, that does not have any decimal points. Non-negative integers are those that are greater than or equal to zero.
To write such a program, we can use a loop to continuously read in integers from the user until a negative integer is entered. We then ignore the negative integer and calculate the maximum and average of the non-negative integers that were entered.
The maximum is simply the largest integer in the set. We can use a variable to keep track of the largest integer as we read in the input. At the end of the loop, the variable will hold the maximum value.
The average is the sum of all the integers divided by the total number of integers.
We add each non-negative integer to the sum and increment the count. At the end of the loop, we divide the sum by the count to get the average.
To output the average with two digits after the decimal point, we can use the printf method, which allows us to format our output. The format string "%.2f\n" specifies that we want to output a floating-point number with two decimal places followed by a newline character.
=> (15 + 20 + 0 + 3 - 1) / 5 = 7.4
In summary, a program that takes any number of non-negative integers as input, and outputs the max and average can be written using a loop, variables to keep track of the maximum, sum, and count, and the printf method to format the output. Understanding the basics of integers and how to perform calculations with them is essential for programming and statistical analysis.
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Christa’s mother is 45. Her uncle’s are 35, 35, 30 and her aunt is 36.What is the mean of Christa’s mother, aunt, and uncle’s age
Answers
Answer: 36.2
Step-by-step explanation:
To find the mean, you add up all the values then divide by the number of values present. So, 45+35+35+30+36= 181. 181 divided by 5 is 36.2
Select the correct answer. Which calculation correctly uses prime factorization to write 48 in simplest form? A. 48 = 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 3 = 2 12 B. 48 = 4 ⋅ 12 = 2 12 C. 48 = 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 3 = 4 3 D. 48 = 16 ⋅ 3
Answers
(C) 48 = V2 -2 -2 -2 - 3 = 4√3 correctly uses prime factorization to write V48 in simplest form.
What is Prime Factorization?In number theory, the breakdown of a composite number into a sum of smaller integers is known as integer factorization.
The procedure is known as prime factorization if these factors are further limited to prime numbers.
The technique of expressing all numbers as the product of primes is known as prime factorization.
So, let's take something like the number 20 as an example.
It can be divided into two components.
"Well, that's 4 times 5," we can respond.
Observe that 5 is a prime number. The number 4 is not a prime.
So, it is necessary to write 48 as the product of its prime elements:
2 * 3 * 2 * 2 * 2
Then,
√48 = √(2 * 2 * 2 * 2 * 2)
Lower radical form: √48
Hence, (C) could be the correct option.
Therefore, (C) 48 = V2 -2 -2 -2 - 3 = 4√3 correctly uses prime factorization to write V48 in simplest form.
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Correct question:
Which calculation correctly uses prime factorization to write V48 in simplest form?
A. 48 = V2 -2 -2 -2 - 3 = 2V12
B. 48 = 14 - 12 = 2/12
C. 48 = V2 -2 -2 -2 - 3 = 4V3
D. V48 = 16 - 3 = 4V3
Tony spent a total of 140 minutes studying for his algebra test this total was 5 more than 3 minutes the amount of minutes he spent studying for his biology test how many minutes did Tony spend studying for his biology test
Answers
Proportionately, if Tony spent a total of 140 minutes studying for his algebra test, and this total was 5 more than 3 minutes the amount of minutes he spent studying for his biology test, the time Tony spent studying for his biology test was 132 minutes.
What is proportion?Proportion refers to the equation of two or more ratios.
Ratios show the relative size of a value compared to another.
Proportions are fractional values like ratios.
The total minutes Tony spent studying for his algebra test = 140
5 more than 3minutes = 8 minutes
140 > 132 by 8 minutes (140 - 8)
The time spent studying biology = 132
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If Nathan distributes all of the hot sauce equally among the 7 bottles, how much will be in each bottle?
Answers
The required amount of sauce in each bottle is given by fraction 5/7. Option B is correct.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Sum the total amount of sauce in the 7 bottles present at each booth,
Total sauce = 0 × 2 + 1/2×1 + 1×3 + 1 1/2 × 1
= 1/2 + 3 + 3/2
= 2 + 3 = 5
Now, the ratio of the total sauce to the total number of bottles will give the amount of sauce in each bottle.
So,
= 5/7
Thus, the required amount of sauce in each bottle is given by fraction 5/7.
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Students in Ms. Clark’s class are measuring the lengths of insects. Students are told that 1 inch = 2.5 cm. Ms. Clark tells her students that the longest insect in the world is the Giant Stick Insect that can measure 2 feet long. How many cm long is a Giant Stick Insect that measures 2 feet long?
Answers
Answer:
here u go
Step-by-step explanation:
Sounds like you're very young but here I go!
since 1 inch = 2.5 cm
and 24 inches = 2 feet
multiply inches and cm by 24
answer is 60 cm
i hope it helped it may be wrong tho :(
What is the function graphed below?
y = | x - 1|
y = | x | - 1
y = | x + 1|
y = | x | + 1
Answers
The function represented by the graph is y = |x + 1|
How to determine the function of the graphThe complete question is added as an attachment
From the question, we have the following parameters that can be used in our computation:
The equation of the graph is an absolute value graph
An absolute value graph is represented as
y = |x|
The function is shifted left by 1 units
So, we have
y = |x + 1|
Hence, the function is y = |x + 1|
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A hot-air balloon has a 14
-foot diameter that is being deflated at a rate of 0.25
feet per minute.
How many minutes, x
, will it take before the balloon has shrunk to a diameter of 8
feet?
Answers
Answer:
Step-by-step explanation:
The rate of deflation of the hot-air balloon is 0.25 feet per minute. Let's represent the diameter of the balloon at any time t in minutes as D(t).
We know that D(0) = 14 feet (initial diameter) and we want to find x when D(x) = 8 feet.
Using the fact that the rate of change of D with respect to time is -0.25 (negative because the diameter is decreasing), we can set up a differential equation:
dD/dt = -0.25
Separating variables and integrating, we get:
∫(1/D) dD = ∫(-0.25) dt
ln|D| = -0.25t + C
where C is the constant of integration.
Using the initial condition D(0) = 14, we get:
ln|14| = C
C = ln(14)
Substituting this value of C into the equation, we get:
ln|D| = -0.25t + ln(14)
Taking the exponential of both sides, we get:
|D| = e^(-0.25t + ln(14)) = e^ln(14) e^(-0.25t) = 14 e^(-0.25t)
Since we are only interested in the positive value of D, we can drop the absolute value sign:
D = 14 e^(-0.25t)
Now we can solve for x by setting D = 8:
8 = 14 e^(-0.25x)
Dividing both sides by 14, we get:
e^(-0.25x) = 8/14 = 4/7
Taking the natural logarithm of both sides, we get:
ln(e^(-0.25x)) = ln(4/7)
-0.25x = ln(4/7)
x = -4 ln(4/7) / 0.25
x ≈ 6.21
Therefore, it will take about 6.21 minutes for the balloon to shrink to a diameter of 8 feet.
Solving Right Triangles:
Find the side indicated by the variable. Round to the nearest tenth.
Answers
Answer:
Step-by-step explanation
It seems like you are to use trig functions to find the missing sides.
soh - cah - toa
Sin(what degree angle you have) = opposite of the angle over the hypotenuse
cosine (what degree angle you have) = adjacent (side that is next to angle that isn't hypotenuse) over hypotenuse
tangent (what degree angle you have) = opposite side from angle over adjacent side to angle
for number 1:
sine59 = d/ 37
cross multiply
sin59 multiplied by 37 which equals 31.7
so this means d is 31.7
use the trig functions to find the rest. it is just a pattern and SOH-CAH-TOA will help.
lmk if you have questions
QUESTION 11
Which classification best represents a triangle with side lengths 48 in., 56 in., and 83 in.?
O A. acute, because 832> 48² +56²
O B. acute, because 832 < 48² +56²
OC. obtuse, because 832> 48² +56²
O D. obtuse, because 832 < 482 +56²
h
Answers
The triangle with side lengths of 48 in., 56 in., and 83 in. is obtuse, because 832> 48² +56²
What is triangle?A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.
here, we have,
The side lengths of the triangles are 48 in., 56 in., and 83 in
The smallest side lengths are: 48 in., 56 in
The sum of the squares of these side lengths is
48^2+ 56^2
For the triangle to be obtuse, then the following must be true
83^2> 48² +56²
Evaluate the exponents
6889> 5440
The above inequality is true.
Hence, the triangle is obtuse, because 83^2> 48² +56²
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Which is the value of the 3rd term in the expansion of (x+6)*6?
Answers
Answer:
540x⁴
Step-by-step explanation:
You want the 3rd term of the expansion of (x +6)⁶.
Binomial expansionThe k-th term of (a +b)^n is ...
C(n, k)a^(n-k)b^k
where terms are numbered 0 to n.
Third termThe third term of (x+6)⁶ is the above expression with k=2:
C(6, 2)a⁴b²
Where a=x and b=6, this is ...
15x⁴6² = 540x⁴
__
Additional comment
C(n, k) is the function that represents the number of combinations of n things taken k at a time:
C(n, k) = n!/(k!(n-k)!)
C(6, 2) = 6!/(2!·4!) = 6·5/(2·1) = 15
What is the best approximation for the perimeter of the pentagon ABCDE? A Pentagon ABCDE image on the graph with E intercepts at (0, 1), vertices A (4, 3), B (7, 3), C (8, 0), and D (2, minus 3) 25 units 22 units 17 units 54 units
Answers
The Perimeter of the pentagon ABCDE is 17 units.
What is Distance Formula?If two points in coordinates plane P(a, b) and Q(c, d) then the distance between these points are
PQ = √(c-a)² + (d-b)²
Given:
The coordinates of Pentagon are A (4, 3), B (7, 3), C (8, 0), and D (2, -3) and E(0, 1).
Using Distance formula
AB = √(7-4)² + (3-3)²
AB = √9
AB = 3
BC = √(8-7)² + (0-3)²
BC = √1 + 9
BC = √10
CD = √(2-8)² + (-3-0)²
CD = √36 + 9
CD = √45
CD = 3√5
DE = √(0-2)² + (-3-1)²
DE = √4 + 16
DE = √20
DE = 2√5
So, Perimeter of the pentagon ABCDE = AB+BC+CD+DE+EA
= 3 + √10 + 3√5 + 2√5
= 3 + √10 + 5√5
= 17.342 unit
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Answer: 22
Step-by-step explanation:
Just because it is right yk.
a quarter pound hamburger counts as how many servings
Answers
A quarter pound hamburger is counted as one servings which is four ounces.
A pound is usually a unit which is used to measure the weight of a body. It is known as one pound is approximately equal to 454 grams. One kilogram is roughly the same as equal to 2.2 lbs. There are 16 ounces in one pound which is mentioned.
This question can be solved due to the rule of proportions.
A pound is an imperial unit of mass or weight measure, it is abbreviated as lb, lbm and one pound is considered to be equal to 0.4535 kilograms.
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The figure is cut into 6 equal pieces. Shade 2/3 of the figure.
Answers
Label the following on the coordinate plane below: quadrant I, II, III, and IV; the origin, the x‐axis, and
the y‐axis. Also, label the sign of the coordinate points found in each quadrant.
Answers
Answer:
Quadrant I is located on the top right of the graph (Positive x, Positive y)
Quadrant II is located on the top left of the graph (Negative x , Positive y)
Quadrant III is located on the bottom left of the graph (Negative x, Negative y)
Quadrant IIII is located on the bottom right of the graph (Positive x, Negative y)
The origin is at the center of the graph with (0,0) as its x and y components
Step-by-step explanation: ^^ Please give 5 star and thanks.
36
30
60
33°
(3x-3)
60
Answers
Answer:
please give the complete question..
Step-by-step explanation:
please give the complete question..
what is 127kg to lbs
Answers
Answer:
279.987
Step-by-step explanation:
Answer:
279.987073 lbs
Step-by-step explanation:
1 kg = 2.20462262 lbs
2.20462262 * 127 = 279.987073
PLEASE HELP IMMEDIATELY (WILL GIVE 30 POINTS!!!) Use your answer to problem 2 to find the measure of /LOM and /MON. (The answer to problem 2 is x = 9)
Answers
Each interior angles of a rectangle is equal to 90° so m∠MON and m∠LOM are complementary as they add up to 90°. The value of x = 9. Angles m∠MON = 72° and m∠LOM = 18°. The angle m∠POQ = 18° because m∠LOM and m∠POQ are vertical angles.
How to calculate the angles of the rectangle.The angles m∠MON and m∠LOM form one of the interior angles of a rectangle, hence they are complementary as they add up to 90°.
we shall solve for x as follows:
2x + 7x + 9 = 90
9x + 9 = 90
9x = 90 - 9 {subtract 9 from both sides}
9x = 81
x = 81/9 {divide through by 9}
x = 9
m∠MON = 7(9) + 9 = 72°
m∠LOM = 2(9) = 18°
The angles m∠LOM and m∠POQ are vertical angles formed by the two straight lines MA and LP, hence;
m∠LOM = m∠POQ = 18°
In conclusion, each interior angles of a rectangle is equal to 90° so m∠MON and m∠LOM are complementary as they add up to 90°. The value of x = 9. Angles m∠MON = 72° and m∠LOM = 18°. The angle m∠POQ = 18° because m∠LOM and m∠POQ are vertical angles.
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Solve the system {-x+y=-3
3x+3y=9 check your solution by graphing
Answers
The solution of the equation is (3, 0).
How to solve equations with 2 variables?A specific point on the graph represents the solution of a linear equation in two variables, ax+by = c, where the total of these two values will equal c when the x-coordinate is multiplied by a and the y-coordinate by b. Basically, there are infinitely many solutions to a linear equation with two variables.
Given:
-x+y=-3....................(1)
3x+3y=9...................(2)
Solving Equation (1) and (2) we get
3x + 3(-3 + x) = 9
3x - 9 + 3x= 9
6x = 18
x= 18/ 6
x= 3
and, y= -3+ x
y= -3 + 3
y= 0
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Use decomposition to find the area of the figure.
A drawing of a right-angled trapezoid with length of two parallel sides measuring 10 yards and 13 yards. The height of the trapezoid is 8 yards.
The area is
square yards.6th grade
Answers
The area of given trapezoid is 92 square yards.
What is area of the trapezoid?The area of a trapezoid can be calculated if the length of its parallel sides and the distance (height) between them is given. The formula for the area of a trapezoid is expressed as, A = ½ (a+b)×h.
where (A) is the area of a trapezoid, 'a' and 'b' are the bases (parallel sides), and 'h' is the height (the perpendicular distance between a and b).
Given that, a right-angled trapezoid with length of two parallel sides measuring 10 yards and 13 yards.
The height of the trapezoid is 8 yards.
Here, area = 1/2 (10+13)×8
= 23×4
= 92
Therefore, the area is 92 square yards.
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13. Taxpayers with an office in their home may deduct a percentage of their home-related expenses. This percentage is based on the ratio of the office's area to the area of the home. A taxpayer with a 2400 square-foot home maintains a 20-foot by 19 foot office If the yearly electricity bills for the home come to $4800 how much of this is deductible?
How much money is deductible from the bill? (simplfy your answer)
Answers
Based on the ratio of the office's area to the area of the home, the deductible amount is $760.
What is the ratio?The ratio refers to the relative quantity of one value contained in another.
Generally, ratios are depicted as fractions, decimals, or percentages.
Total home area = 2400 ft²
Office area =380 ft² (20 x 19)
The ratio of office to home area = 380/2400
The percentage of office use of the home-related expense = 15.83% (380/2400 x 100)
The Electricity bill for the year = $4,800
The deductible amount for office use = $760 ($4,800 x 380/2400) or ($4,800 x 15.83%)
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I need help plssssssssssssss
Answers
Work Shown:
[tex]\tan(\text{angle}) = \frac{\text{opposite}}{\text{adjacent}}\\\\\tan(26) = \frac{x}{5.7}\\\\x = 5.7*\tan(26)\\\\x \approx 2.78007575482541\\\\x \approx 2.8\\\\[/tex]
Make sure your calculator is in degree mode.
Riley planted flowers in some of her garden. Then, she planted
vegetables in 2/8 of her garden. Now, 7/8 of Riley's garden is planted. What
fraction of Riley's garden is planted with flowers?
O2/8 of her garden
O 3/8 of her garden
4/8 of her garden
O 5/8 of her garden
Answers
Answer
Step-by-step explanation:
Malcolm trains on his kayak every weekend. He paddles upstream (against current) for 3 ½ hours and then returns downstream (with current) in 2hrs 6 minutes. If the river flows at 3km/ h, find:
* The paddling speed in still water
* The distance he paddles upstream.
Answers
If Malcolm trains on his kayak every weekend. The speed is 12km/h and the distance is 31.5km.
How to find the speed and distance?Let's call Malcolm's paddling speed in still water "v".
When paddling upstream, Malcolm is fighting the current, so his effective speed is v - 3 km/h. And when paddling downstream, his effective speed is v + 3 km/h.
The time it takes for him to paddle upstream= 3.5 hours
Distance he covers in this time = (v - 3) * 3.5.
The time it takes for him to paddle downstream = 2.1 hours
Distance he covers in this time = (v + 3) * 2.1.
Let set the sum of these two distances equal to each other and solve for v:
(v - 3) * 3.5 = (v + 3) * 2.1
Expanding both sides:
3.5v - 10.5 = 2.1v + 6.3
Subtracting 2.1v from both sides:
1.4v - 10.5 = 6.3
Adding 10.5 to both sides:
1.4v = 16.8
Dividing both sides by 1.4:
v = 12 km/h
So Malcolm's paddling speed in still water is 12 km/h. To find the distance he paddles upstream, we can use the formula (v - 3) * 3.5, which gives us:
(12 - 3) * 3.5 = 9 * 3.5 = 31.5 km
Therefore the distance Malcolm paddles upstream is 31.5 km.
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find the value of 16/4
Answers
Answer:
2
Step-by-step explanation:
sqrt 16/4 is 4/2
4/2 is 2
How do you find the end behavior of a polynomial?
Answers
The end behavior of this the end behavior of this polynomial is positive, meaning that as x approaches positive and negative infinity, the y values approach positive infinity.
The end behavior of a polynomial can be determined by looking at the degree (highest exponent) and the leading coefficient (coefficient of the highest degree term). If the degree is even and the leading coefficient is positive, the end behavior of the polynomial is positive, meaning that as x approaches positive and negative infinity, the y values approach positive infinity. Similarly, if the degree is even and the leading coefficient is negative, the end behavior of the polynomial is negative, meaning that as x approaches positive and negative infinity, the y values approach negative infinity. If the degree is odd and the leading coefficient is positive, the end behavior of the polynomial is positive, and if the degree is odd and the leading coefficient is negative, the end behavior of the polynomial is negative.For example, consider a polynomial of degree 5, f(x) = 3x5 + 2x4 - 3x2 + 4. The leading coefficient is 3, which is positive, and the degree is 5, which is odd. Therefore, the end behavior of this polynomial is positive, meaning that as x approaches positive and negative infinity, the y values approach positive infinity. This can be verified by using the formula: End Behavior = Leading Coefficient x ∞limitx→±∞ End Behavior = 3 x ∞limitx→±∞ End Behavior = +∞.
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