The polynomial of degree 3 is given by x³-3x²-40x+84.
The degree of a polynomial is the highest degree of the variables present with non-zero coefficients.
For example the polynomial [tex]{\displaystyle 2x^{2}y^{3}+8x+10}[/tex] has three terms. The first term has a degree of 5 (the sum of the powers 2 and 3), the second term has a degree of 1, and the last term has a degree of 0. Therefore, the polynomial has a degree of 5, which is the highest degree of any term.
A degree 3 polynomial having zeros α,β and γ and the coefficient of x³ equal a is
a(x-α)(x-β)(x-γ)
So the given zeroes of the polynomial are -6,8 and 7 and the coefficient of x³ is 1. So the desired polynomial is given by:
1(x+6)(x-2)(x-7)
=(x²-4x-12)(x-7)
=x³-3x²-40x+84
Hence the polynomial of degree 3 is given by x³-3x²-40x+84.
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A data set had values ranging from 117 to 139. A new data point of 30 was
added to the data set. Would this point affect the mean or the median more? How
(increase/decrease) and why? (2 points)
Answer:
This point would affect the mean more because the median is less sensitive to outliers.
Step-by-step explanation:
Hope this helps!
Write 4,000,000 in scientific notation
4 × 10 then put a 6 by the 10 as an exponent.
What is
1
4
+
9
10
y
−
3
5
y
+
7
8
written in simplest form
Find the perimeter of the regular polygon ?
The perimeter of the regular polygon is 232
How to find the perimeter of the regular polygon?The side lengths of the regular polygon are given as
4/3x - 1/3 and x + 7
The sides of regular polygon are equal
So, we have:
4/3x - 1/3 = x + 7
Multiply both sides by 3
4x - 1 = 3x + 21
Collect like terms
4x - 3x = 1 + 21
Evaluate the like terms
x = 22
Substitute x = 22 in x + 7
Side = 22 + 7
Side = 29
The perimeter of the regular polygon is calculated as:
Perimeter = Number of sides x Side length
So, we have
Perimeter = 8 * 29
Evaluate
Perimeter = 232
Hence, the perimeter of the regular polygon is 232
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Find the perimeter of the equilateral triangle.
9x16
8-3x
The perimeter is
The perimeter of the equilateral triangle will be 27x - 48.
How to calculate the perimeter?It should be noted that the perimeter of an equilateral triangle is the addition of all its sides or multiplying by three since they're equal.
Therefore, the perimeter of the equilateral triangle will be:
= 3(9x - 16)
= 27x - 48
Therefore, the perimeter of the equilateral triangle will be 27x - 48.
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Find the perimeter of the equilateral triangle.
9x - 16
Just need these answers for an assignment help would be nice
Answer:
below
Step-by-step explanation:
25)-ab
=-(-1/2)(3/4)
=3/8
26)b÷c
=(3/4)×1/-6
=3/-24
=-1/8
27)c÷a
=-6÷-1/2
=6×2/1
=12
12345678901234567890
Yes; The construction demonstrates how to bisect an angle correctly using technology because Circles D & E have the same radius
How to properly bisect an angle?
In construction of angles and lines, bisection means dividing either a given angle or line segment into two equal parts. This means after the construction, the two parts must have equal measure.
The steps to bisect a line segment are as follows;
1. Draw the required length of the line segment AB.
2. With point A and radius of the compass greater than half of AB, describe arcs above and below the segment.
3. With the same radius as in step 2 and point B, describe two arcs above and below the segment. These would intersect that of step 2 at C and D.
4. Join the points of intersection of the arcs with a straight line CD.
Now, in this given question with the circle, we can see that line AG is the line that bisects the angle EAD.
Now, we see that circles C and D have the same radius and as such the construction demonstrated is correct for that very reason.
Answer: yes
Step-by-step explanation: the construction correctly shows how to bisect an angle using technology because circles D and E have the same radius.
What is the solution set of the quadratic inequality 4(x + 2)²(less than equal to)0
Answer:
{-2}
Step-by-step explanation:
You want the solution set for the inequality 4(x +2)² ≤ 0.
SolutionThe expression on the left cannot be negative, but it can be zero when ...
x +2 = 0 ⇒ x = -2
The only solution to this inequality is x = -2.
Expressed as a set of solutions, we have ...
x ∈ {-2}
Find the sum of (6.9 × 106) and (5.9 × 105). Write the final answer in scientific notation.
The sum of (6.9 × 10^6) and (5.9 × 10^5) written in scientific notation is 12.8 × 10^11
Scientific notation(6.9 × 10^6) and (5.9 × 10^5)
Sum
= (6.9 × 10^6) + (5.9 × 10^5)
= (6.9 + 5.9) × 10^(6+5)
= 12.8 × 10^11
Therefore, the sum of (6.9 × 10^6) and (5.9 × 10^5) written in scientific notation is 12.8 × 10^11
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Rewrite as a simplified fraction 0.7 repeating
Answer:
7/10
Step-by-step explanation:
Rewriting 0.7 as a fraction would be 7/10. 0.7 can also be 0.70, and 70/100
in the grid below what is the distance between point a and b. round to the nearest tenth
The graph of f(x) is shown.
How many horizontal tangent lines does f(x) have?
0
1
2
3
4
Check the picture below.
The following table shows the estimated number of millionaire households (households with a net worth of at least $1 million, not including primary residence) in a certain country for selected years.
Year Millionaire Households
2015 9,200,000
2016 9,350,000
2017 9,620,000
2018 9,970,000
If the percentage increase between 2017 and 2018 continued for 2018 and 2019, how many millionaire households would there be in 2019? Round to the nearest ten thousand.
If the percentage increase between 2017 and 2018 continued for 2018 and 2019, there would be 10332908 millionaire households in 2019
How many millionaire households would there be in 2019? Round to the nearest ten thousand?The given parameters are:
Year Millionaire Households
2015 9,200,000
2016 9,350,000
2017 9,620,000
2018 9,970,000
From the question, we have
The percentage increase between 2017 and 2018 continued for 2018 and 2019
The percentage increase between 2017 and 2018 is calculated as
Percentage = (2018 - 2017)/2017 * 100%
So, we have
Percentage = (9,970,000 - 9,620,000)/9,620,000 * 100%
Evaluate
Percentage = 3.64%
The number of millionaire households in 2019 is calculated as
2019 = 2018 * (1 + percentage)
So, we have
Households = 9,970,000 * (1 + 3.64%)
Evaluate
Households = 10332908
Hence, if the percentage increase between 2017 and 2018 continued for 2018 and 2019, there would be 10332908 millionaire households in 2019
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need help with 36.01 x 0.06
Answer: 2.1606
Step-by-step explanation:
36.01 x 0.06 =
3601/100 x 6/100=
3601 x 6/(100 x 100)=
21606/10000=2.1606
A sun in a distant galaxy has an estimated Mass of 1.55272 x 10³1 kg and the earth has a mass of
5.972 x 1024
kg, how many earths would it take to equal the mass of the sun? Write your answer in
scientific notation.
It would take
earths to equal the mass of the sun
A sun in a distant galaxy has an estimated Mass of 1.55272 x [tex]10^{31}[/tex] kg and the earth has a mass of 5.972 x [tex]10^{24}[/tex] kg,26x[tex]10^{5}[/tex] earths would it take to equal the mass of the sun.
A sun in a distant galaxy has an estimated Mass of 1.55272 x [tex]10^{31}[/tex]kg
earth has a mass of 5.972 x [tex]10^{24}[/tex]kg
Let x number of earths equal the mass of the sun
x (5.972 x [tex]10^{24}[/tex]) = 1.55272 x [tex]10^{31}[/tex]
x= 1.55272 x [tex]10^{31}[/tex] / 5.972 x [tex]10^{24}[/tex]
x= 26x[tex]10^{5}[/tex]
The wavelength of light emitted by a far-off galaxy extends and is "redshifted" toward the infrared region of the electromagnetic spectrum as it moves away from us. This means that by the time the light from a very distant galaxy that emits mostly visible or ultraviolet light reaches Earth, it will appear as infrared light.
Webb's ability to detect infrared light and the cosmos' expansion, which extends light to redder wavelengths, make it a good tool for identifying galaxies that originated at the beginning of the Universe's existence.
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Determine which integer in the solution set will make the equation true.
3s − 12 = −9
S: {−1, 0, 1, 2}
A: −1
B: 0
C: 1
D: 2
Answer:
c) 1
Step-by-step explanation:
Solving for the value of s,
→ 3s - 12 = -9
→ 3s = -9 + 12
→ s = 3/3
→ [ s = 1 ]
Thus, option (c) is correct.
(a) Write the next whole number after 222three in the base-three system.
Answer:
1000
Step-by-step explanation:
You want the next number after 222 in base 3.
Counting sequenceIn any useful number base, the counting at any given integer position is ...
0, 1, 2, 3, ..., (base -1), 0 and add 1 to the next number position
For base 3, this is ...
0, 1, 2, 10
When the digit in the next higher position is also (base -1), then it gets incremented to 0 and the carry is propagated to the left.
In base 10, the equivalent is ...
999 +1 = 99(9+1) = 99(10) = 9(9+1)0 = 9(10)0 = (9+1)00 = 1000
In base 3, your incremented value is ...
222 +1 = 22(2+1) = 22(10) = 2(2+1)0 = 2(10)0 = (2+1)00 = 1000
The next whole base 3 number after 222 is 1000.
Jared estimates that his houseplant is as heavy as a 5 kilogram bowling ball. Draw a tape diagram to estimate the weight of 3 houseplants.
3 houseplants will weigh 15 kg (Refer to the tape diagram below).
What is a tape diagram?A tape diagram is a visual model that looks like a piece of tape and is used to aid in the calculation of ratios, addition, subtraction, and, most commonly, multiplication. It is also referred to as a divided bar model, a fraction strip model, a length model, or a strip diagram. It is used in elementary school mathematics education to solve word problems.The weight of 3 household plants will be about 15 kg.
5 kg × 3 = 15 kg(Refer to the tape diagram given below)Therefore, the weight of 3 household plants will be about 15 kg (Refer to the tape diagram below).
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Select the part of speech for the underlined words below. I WAS afraid of roller coasters when I was younger, but I AM a huge fan of them now. preposition, adverb, verb, adjective
Answer: I'm pretty sure its a verb
Step-by-step explanation:
Can you guys help me solve this?
Answer:
Step-by-step explanation:
97
Answer:
$97 per/tire
Step-by-step explanation:
Long division[tex]Borrow\:8\\4 \cdot 9 = 36\\= 38 - 36\\= 2\\4 \cdot 7 = 28\\28 - 28 = 0\\\\= 97\:\mathrm{R0}[/tex]
find the area of the circle
The circle has an area of 28.26 ft².
It is assumed that the circle's radius is 3 feet.
The circle's area must be determined.
What is radius of a circle ?
A line segment from a circle's center to its perimeter is known as the radius.
As per the question ;
Radius of circle , r = 3 ft
Area of the circle is given by ;
A = πr²
A = π × 3²
A = 9π
or
A = 9 × 3.14
or
A = 28.26 ft²
Thus , the area of the circle will be 28.26 ft².
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A rectangular tiled floor is composed of 70 square tiles. The rectangular floor is rearranged so that 2 tiles are removed from each column and 4 tiles are added to each row. After the change in layout, the floor will still have 70 tiles, and still be rectangular. How many columns are in the tile floor before the change in layout?
The number of columns is in the title floor before the change in layout is 10
Given that A rectangular tiled floor is composed of 70 square tiles. The rectangular floor is rearranged so that 2 tiles are removed from each columns and 4 tiles are added to each row. After the change in layout, the floor will still have 70 tiles, and still be rectangular asked to find the number of columns in the tile floor before the change in layout.
Let's assume the number of rows is x
The number of columns will be [tex]\frac{70}{x}[/tex]
After the changing, the rows can be x+4
The number of columns will be [tex]\frac{70}{x}[/tex]-2
The equation will be (x+4)([tex]\frac{70}{x}[/tex]-2)=70
⇒[tex]x^{2} +4x-140=0[/tex]
⇒x=10
Therefore,The number of columns is in the title floor before the change in layout is 10
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Zan needs 28 centimeters of ribbon for each bow she makes. What is the greatest number of bows Zan can make with 9 feet of ribbon?
Answer:
3
Step-by-step explanation:
i think its 3 because 28 divided by 9 is 3
Find all the numbers that satisfy the fol-
lowing descriptions:
The number has seven digits.
The number is between 1,000 and
10,000.
The digit in the tenths place is 150%
of the digit in the thousandths place.
The digit in the hundredths place is
of the sum of the digit in the
tenths place and the digit in the
thousandths place.
The sum of all the digits in the num-
ber is 17.
None of the digits are zero.
There is no number which is satisfying the given conditions.
The first condition is that the number has seven digits.
The second condition is that the number lies between 1000 and 10000.
From these two conditions, we can conclude that there is no number which satisfies all the given conditions. Because there is no seven-digit number which is less than 10000.
Let us assume that the second condition is the number lies between 1000000 and 10000000.
And let the required number be "abcdefg".
The third condition is the digit in the tenth place is 150% of the digit in the thousandth place.
⇒ f = 150 × (d) / 100 = 1.5 × d
The fourth condition is the digit in the hundredth place is the sum of the digit in the tenth place and the digit in the thousandth place.
⇒ e = f + d = 1.5d + d = 2.5d
The fifth condition is the sum of all the digits in the number is 17.
⇒ a + b + c + d + e + f + g = 17
⇒ a + b + c + d + 2.5d + 1.5d + g = 17
⇒ a + b + c + 5d + g = 17
And the last condition is none of the digits is zero.
Using the last condition the possible values for d are either 1 or 2.
Because, if d is 3, then if we take the least possible digit(1) for others, the sum on the LHS is 19, which is greater than 17.
And d can not be 1. Because, if d is 1, then f and e are 1.5 and 2.5 respectively. 1.5 and 2.5 are not valid digits.
Therefore, the value of d = 2.
f = 1.5d = 3
e = 2.5d = 5
If d = 2, then we get a + b + c + g + 10 = 17
⇒ a + b + c + g = 17 - 10
⇒ a + b + c + g = 7
⇒ The possible values for (a, b, c, g) are (4, 1, 1, 1), (1, 4, 1, 1), (1, 1, 4, 1), (1, 1, 1, 4), (2, 2, 2, 1), (2, 2, 1, 2), (2, 1, 2, 2), (1, 2, 2, 2), (2, 3, 1, 1), (3, 2, 1, 1), (1, 1, 2, 3), and (1, 1, 3, 2)...
Therefore there are more than 12 possible answers that satisfy the assumption made.
411253114125311142531111253422225312212532212253212225322312531321253112325311322531Learn more about number here:
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100 points + first decent answer gets brainliest
The mean of a distribution of selected theme park admission prices is $59 with a standard deviation of $3.99. The mean cost of a distribution of a specific home stereo system sold at many different stores is $1,499 with a standard deviation of $4.
Which distribution has the lower standard deviation?
Which distribution is more spread out? Explain.
Answer:
See explanation
Step-by-step explanation:
Selected theme park admission prices has the lower standard deviation.
Specific home stereo system's distribution is more spread out since the ratio between the standard deviation and the mean is greater compared to that of selected theme park admission prices.
specific home stereo system: 3.99/59=0.0676.
selected theme park admission prices: 4/1499=0.002668
0.0676>0.002668
Answer:
The theme park ahs the lower standard deviation
if a(x + 1) = 2x + 3a, and a ≠ 0, then what is x in terms of a
Answer:
[tex]x = \frac{2a}{a - 2} [/tex]
Josue is the youngest of three siblings whose ages are consecutive even integers. If
the sum of their ages is 78, find Josue's age.
Answer:
39 is the sum of their ages
Step-by-step explanation:
Hope this helps :)
Please help !
What is the coefficient in the term 4w?
4
w
0
1
Answer:
4
Step-by-step explanation:
the coefficient is usually a constant factor for a variable.
so, the answer here is 4.
Evaluate the expression ab, for a = 4 and b = 7.
Answer:
28
Step-by-step explanation:
4 x 7 = 28
beth and ann are joking that their combined ages equal sams age. if beth is twice anns age and sam is 69. what are beth and anns age
Answer: ann is 69 and beth is 138
Step-by-step explanation: