The first factor has a degree of 7, the second has a degree of 6, and the third has a degree of 5. The product has a degree of 7, the highest among them.
To determine the degree of each polynomial in the expression[tex]2a^7 - 16a^6 + 18a^5[/tex], we need to understand that the degree of a polynomial is the highest exponent of the variable in that polynomial.
The first factor is[tex]2a^7[/tex]. Here, the highest exponent of the variable 'a' is 7. So, the degree of the first factor is 7.
The second factor is[tex]-16a^6[/tex]. In this case, the highest exponent of 'a' is 6. So, the degree of the second factor is 6.
The third factor is [tex]18a^5[/tex]. Here, the highest exponent of 'a' is 5. So, the degree of the third factor is 5.
Now, to find the degree of the product of these three factors when added together, we need to find the highest degree among them. In this case, the highest degree is 7 (from the first factor). Therefore, the product has a degree of 7.
In summary:
The first factor has a degree of 7.
The second factor has a degree of 6.
The third factor has a degree of 5.
The product has a degree of 7.
These degrees reflect the highest power of 'a' in each term of the polynomial expression.
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What are the names of the eight line section and the six line section that combine to form the 14 lines of a petrarchan sonnet?
The answer is an octave and a sestet. A sestet is the title specified to the second split of an Italian sonnet (as contrasting to an English or Spenserian sonnet), which must contain of an octave, of eight lines and must be followed by a sestet, of six lines. The first recognized user of this poetical type was the Italian poet named Petrarch.
Explain the difference between exponential growth and exponential decay
Final answer:
Exponential growth occurs when a population increases at an increasing rate, whereas exponential decay involves a decrease at a rate proportional to the current size. Logistic growth, adding the concept of carrying capacity, more accurately reflects natural populations with initial exponential increase followed by a plateau as resources become limited.
Explanation:
The key difference between exponential growth and exponential decay lies in the direction and rate at which a quantity changes over time. Exponential growth occurs when a population grows at an increasing rate as time passes, often depicted as a J-shaped curve, whereas exponential decay describes a process of decrease at a rate proportional to the current value, leading to a rapid reduction in size or quantity over time.
In the context of biology and population growth, exponential growth describes how populations can grow dramatically when there are no limits to resources or space. This type of growth can be formalized as a mathematical model where the population after n time periods has increased by a factor of 2n when the base growth rate is 2. In natural populations, this is idealized and does not usually last long as resources become depleted and other limiting factors come into play. On the other hand, exponential decay in biology might refer to the rapid loss of a population due to harsh conditions, lack of resources, or other negative impacts.
Jasmine is 23 years old. jasmine is 3 years less than half of george's age. write and solve an equation to find george's age.
take 23 and multiply by 3 then divide by 2 and your answer should be x34
Use two or three unit fractions to convert. 1515 daysdaysequals=_______ secondsseconds
It is found that Fifteen days is equivalent to 1,296,000 seconds, Or we can say one million two hundred ninety-six thousand seconds.
What is the fundamental principle of multiplication?Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
We need to find the unit fractions to convert 15 days into seconds.
1 day = 24 hour
1 hour = 60 minutes.
1 minutes = 60 seconds
Therefore, 24 hours = 24 x 60 x 60 = 86400 seconds
There are 86400 seconds in one day.
Then 15 days = 15 x 86400 = 1,296,000
Hence, It is found that Fifteen days is equivalent to 1,296,000 seconds, Or we can say one million two hundred ninety-six thousand seconds.
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Can you help me solve #s 43 an 44 pleeeease
PLEASE HELP ASAP!!!!!
Carl, Brian, Dave, and Ashley want to attend the same university. Unfortunately only two spots remain and these four friends have the same GPA, as well as virtually identical community service and leadership experiences. Therefore, the two spots will be determined by their SAT and ACT scores. Carl scored 1,280 on the SAT, while Brian scored 1,325. Dave scored 28 on the ACT, while Ashley scored 30. Use z-scores to determine which two students should be admitted. The mean SAT score was 1,000 with a standard deviation of 175 and the mean ACT score was 20.6 with a standard deviation of 5.2 Both tests are normally distributed.
terrell wants to drive his car at a speed of 50 miles per hour for 2.75 hours. his car has a fuel efficiency of 25 miles per gallon. How many gallons of fuel does terrell need for his journey
suppose the correlation coefficient between the number of the college students in a city and the number of city buses is 0.89. which statement must be true?
Answer:
Step-by-step explanation:
Given that the correlation coefficient between the number of college students in a city and the number of city buses is 0.89.
We find that correlation coefficient is a measure of linear association between two variables.
When the absolute value of correlation coefficient is near 1, there is strong correlation. If correlation has a positive sign, there is a posiitive association between the two variables.
Here the correlation coefficient is positive and also near 1. Thus there is a strong linear correlation between the two variables.
Or whenever there is an increase in one variable there will be an increase in other variable also.
after 5 years what is the total amount of a compound interest investment of 32,000 at 3% interest, compounded quarterly
A.57.795.56
B.32,426.67
C.43,099.36
D.37,157.89
If HE = 3p + 7, /, LP = 5p – 19, and /, find the values of p and q for which quadrilateral HELP is a parallelogram. A. p = 18, q = 13 B. p = 13, q = 8 C. p = 8, q = 18 D. p = 13, q = 1
Which quadrilateral HELP is a parallelogram? The corrsect answer is P=13, q=18
Functions f(x) and g(x) are shown below:
f(x) = -4(x - 6)^2 + 3
g(x) = 2 • cos(2 • x - pi) + 4
Using COMPLETE SENTENCES, explain how to find the maximum value for each function and determine which function has the largest maximum y-value.
What is the area of △ABC?
Enter your answer as a decimal in the box. Round only your final answer to the nearest tenth.
Answer: smh
Step-by-step explanation:
Describe which of the two points lies on the graph of the line
Y-x=4
A. 9,5
B. 5,9
Find y to the nearest tenth.
2.7
2.9
7.5
y = 8 x cos(20)
y = 7.517
y = 7.5
Pleaseeee help!!!!!!!!!
if f(x)=2x-4 find f(q+1)
The value of f(q+1) is 2(q-1).
What is a function?A relation or expression involving one or more variables.
Given that, f(x) = 2x - 4
When x = q+1
f(q+1) = 2(q+1) - 4
f(q+1) = 2q + 2 - 4
f(q+1) = 2q - 2
f(q+1) = 2(q-1)
Hence, the value of f(x) when x = (q+1) is 2(q-1)
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How long will it take for $2800 to grow to $24,900 at an interest rate of 5.6% if the interest is compounded continuously? round the number of years to the nearest hundredth?
Debra travels a distance of 2 miles in 1 minute. how much distance can she cover in 25 minutes? choose the correct equivalent rate.
Debra traveled 50 miles in 25 minutes at a rate of 2 miles per minute.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
Given, Debra travels a distance of 2 miles in 1 minute.
Which is already in unit measure, therefore to determine the distance traveled by Debra in 25 minutes we'll multiply the distance traveled in 1 minute and the total time Debra traveled.
= (2×25) miles.
= 50 miles.
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This graph of a function is a translation of y = 2/x . What is an equation for the function?
A. y = 2/(x - 6) – 3
B. y = 2/(x – 6) + 3
C. y = 2/(x – 3) - 6
D: y = 2/(x – 3) + 6
Answer: The answer is C, the rest of the answers are
1:B
2:C
3:A its a graph
4:C y=2/x-3 -6
5:D19, as of 2019
Step-by-step explanation:
Answer:
The correct option is C) [tex]y=\frac{2}{x-3}-6[/tex]
Step-by-step explanation:
Consider the provided information.
Transformation:
The graph of parent function f(x) move up b unit for f(x)+b.
The graph of parent function f(x) move down b unit for f(x)-b.
The graph of parent function f(x) move left b unit for f(x+b).
The graph of parent function f(x) move right b unit for f(x-b).
Since, the graph of the parent function moves down, Therefore Option Option B and D are incorrect.
Here, we can observe that vertical asymptote shifted from x = 0 to x = 3.
Horizontal Shift: Right 3 Units
Vertical Shift: Down 6 Units
Therefore, the correct option is C) [tex]y=\frac{2}{x-3}-6[/tex]
How does the radius of a positive and negative ion compare to a neutral atom?
A neutral atom contains equal amount of proton and electron.
A negative ion contains extra electrons hence there is additional outer shell so it is expected that the radius is bigger than that of a neutral atom.
While a positive ion contains less electron so there is less outer shell so the radius is smaller than that of a neutral atom.
Arranging the radius in increasing order:
positive ion, neutral atom, negative ion
The initial balance of a mutual fund is $1800. The fund is expected to grow in value at an annual rate of 5%.
Let x represent the number of years since the fund was started. Let y represent the value of the fund x years later.
What equation models the value of the mutual fund x years after it was started?
Joe walked of a mile in of an hour. what is his unit rate in miles per hour? (1 point) = mile per hour = miles per hour = miles per hour = mile per hour
please help and explain to me!
Write the equation of the function whose graph is shown.
Answer:
[tex]y=1(x-5)^2 + 3[/tex]
Step-by-step explanation:
Given : from the graph vertex is (5,3)
Also graph passes through point (8,12)
We use vertex form of quadratic equation
General vertex form is
[tex]y=a(x-h)^2 + k[/tex]
vertex is (5,3)
h= 5 and k =3
So equation becomes [tex]y=a(x-5)^2 + 3[/tex]
Now we need to find out 'a'
We use (8,12) to find out 'a'
Plug in x=8 and y = 12
[tex]12=a(8-5)^2 + 3[/tex]
[tex]12=a(3)^2 + 3[/tex]
12= 9a + 3
subtract 3 on both sides
9 = 9a
divide both sides by 9
so a=1
Final equation is
[tex]y=1(x-5)^2 + 3[/tex]
An equation of the function of this graph is equal to [tex]y=1(x-5)^2 + 3[/tex]
Given the following data:
Points on the x and y-axis = (8, 12).Vertex (h, k)= (5, 3).How to write a function.The vertex form of a quadratic equation can be used to write an equation of the function of a graph.
Mathematically, the vertex form of a quadratic equation is given by this formula:
[tex]y=a(x-h)^2 + k[/tex]
Substituting the given parameters into the formula, we have;
[tex]12=a(8-5)^2 + 3\\\\12=(3a)^2+3\\\\9a^2=12-3\\\\9a^2=9\\\\a^2=1[/tex]
a = 1.
For the equation:
[tex]y=a(x-h)^2 + k\\\\y=1(x-5)^2 + 3[/tex]
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The width of a rectangle is 2m less than the length. the area is 48m squared. find the dimensions
The length of the rectangle is 8m and the width is 6m
This question involves the area of a rectangle and we can use the formula to solve this problem.
Data given;
A = 48m^2w = (L - 2)mAreaThe area of a rectangle is given as
[tex]A = L * W[/tex]
l = lengthw = widthsubstitute the values and solve
[tex]A = lw\\48 = L * ( L - 2)\\48 = l^2 -2l\\l^2 -2l - 48 = 0[/tex]
solve this quadratic equation to find the length
a = 1, b = -2, c = -48
[tex]l = \frac{-b+-\sqrt{b^2 - 4ac} }{2a} \\l = \frac{-(-2)+-\sqrt{(-2)^2-4*1*(-48)} }{2*1} \\l = 8[/tex]
Taking only the positive value of l, l = 8
but we also know that
[tex]w = l -2\\w = 8 -2\\w= 6[/tex]
from the above, the length of the rectangle is 8m and the width is 6m
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Find the quotient and remainder using long division. x6 + 4x4 + 4x2 + 16 x2 + 4
In the diagram below XY is the perpendicular bisector of JK. Which of the following statements must be true?
Answer:
Step-by-step explanation:
A B D F
Determine whether 2y=3x-1 represents a direct variation. if it does, find the constant of variation.
The equation 2y=3x-1 does not represent a direct variation in its strict definition, as it includes a y-intercept. If the y-intercept is ignored, the constant of variation would be k = 3/2.
The equation 2y=3x-1 represents a direct variation if it can be written in the form y = kx, where k is the constant of variation. To determine if this equation represents a direct variation, we can solve it for y:
Divide both sides of the equation by 2 to isolate y:
y = (3/2)x - 1/2.
Since we can express y as an equation of the form y = kx + b, with b being a constant, it does not represent a pure direct variation, as direct variation should have a form y = kx without the constant term.
However, if the question is interpreted to include such linear relationships as direct variations despite the y-intercept, then the constant of variation would be k = 3/2.
Which step should be used to prove that point a is equidistant from points c and b? (1 point)?
Helpppppppppppppppppp