Find the polynomial function in standard form that has the zeros listed. 1(multiplicity 2), -2(multiplicity 3)
Answer:
f(x) = x⁵ +4x⁴ +x³ -10x² -4x+8
Step-by-step explanation:
If p is a zero, then (x -p) is a factor. The multiplicity of the zero tells you how many times that is a factor (its exponent).
f(x) = (x -1)²(x +2)³ = (x² -2x +1)(x³ +6x² +12x +8)
f(x) = x⁵ +4x⁴ +x³ -10x² -4x+8
_____
Additional comment
You can use the distributive property to write out the 12 terms of the product of the two expanded factors, or you can do a little mental arithmetic based on what you know about the exponent of a product term. (It is the sum of the exponents of its factors.)
The mental exercise can be made easier by writing the coefficients of the factors as though they were two cubics. It works well to write them in two rows:
[tex]\left[\begin{array}{cccc}0&1&-2&1\\1&6&12&8\end{array}\right][/tex]
The columns are in order of decreasing powers of x. A relatively simple and symmetrical pattern of sums of cross products is used to find the coefficients of the final polynomial. Working in order of decreasing exponents, we have ...
coefficient of x^6 = (0)(1) = 0
coefficient of x^5 = (0)(6) +(1)(1) = 1
coefficient of x^4 = (0)(12) +(1)(-2) +(1)(6) = 4
coefficient of x^3 = (0)(8) +(1)(1) +(1)(12) +(6)(-2) = 1
coefficient of x^2 = (1)(8) +(6)(1) +(-2)(12) = -10
coefficient of x^1 = (-2)(8) +(12)(1) = -4
coefficient of x^0 = (1)(8) = 8
I need help with numbers 17 and 18.
Answer:
17. D
18. C
Step-by-step explanation:
For both of these questions, you only need a general understanding of what rotation, translation, and dilation do. That is sufficient to let you choose the correct answer.
17.The coordinates of Y are both negative, so it is a point in quadrant III on the graph. Rotating a point in quadrant III 270° clockwise will rotate it through quadrants II and I to quadrant IV, where it will be to the right and below the origin. Translation 9 units right and 5 units down will put it farther to the right and farther below the origin, still in quadrant IV.
As you know, translation right 9 units adds 9 to the x-coordinate. Translation down 5 units subtracts 5 from the y-coordinate. That means the coordinates of Y' must have x > 9 and y < -5. There is only one answer choice like that:
D. Y'(11, -8)
__
18.Dilation about the origin multiplies each coordinate by the scale factor. It does not change the quadrant of a point on the graph. The original coordinates of R are (negative, positive), so it is in quadrant II. The dilated point will still be in quadrant II, but will be closer to the origin. Both coordinate values will change.
R' = (1/3)R = (1/3)(-2, 3) = (-2/3, 3/3)
R' = (-2/3, 1) . . . . . matches choice C
This year the CDC reported that 30% of adults received their flu shot. Of those adults who received their flu shot,
20% still got the flu. Of those who did not receive the flu shot, 65% got the flu.
Use the tree diagram to determine the probability that a person with the flu is a person who received a flu shot.
Enter your answer as a decimal to the ten thousandths place.
=> 0.1165
Using conditional probability, it is found that there is a 0.1165 = 11.65% probability that a person with the flu is a person who received a flu shot.
Conditional Probability
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened. [tex]P(A \cap B)[/tex] is the probability of both A and B happening. P(A) is the probability of A happening.In this problem:
Event A: Person has the flu.Event B: Person got the flu shot.The percentages associated with getting the flu are:
20% of 30%(got the shot).65% of 70%(did not get the shot).Hence:
[tex]P(A) = 0.2(0.3) + 0.65(0.7) = 0.515[/tex]
The probability of both having the flu and getting the shot is:
[tex]P(A \cap B) = 0.2(0.3) = 0.06[/tex]
Hence, the conditional probability is:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.06}{0.515} = 0.1165[/tex]
0.1165 = 11.65% probability that a person with the flu is a person who received a flu shot.
To learn more about conditional probability, you can take a look at https://brainly.com/question/14398287
Answer:
flu shot
flu
no flu
.30
.20
Step-by-step explanation:
trust
what is 100,100,100,987 times 72
Answer: 7207207271064
help me againnnnnnnnnnnnnnnnnnnnnnn
Step-by-step explanation:
(2m + 4) / 8 = w
2m + 4 = 8w
2m = 8w - 4
m = 4w - 2
Step-by-step explanation:
option A is correct.
hope this answer helps you dear! take care
Emika has a monthly budget for her cell phone bill.
Last month she spent 120% of her budget, and the bill
was $60.
What is Emika's monthly budget?
Emika's monthly budget is $60.
A percentage can be described as the fraction of a number multiplied by 100. The sign used to represent percentages is %.
Let Emika's cell phone bill budget be represented with x.
In order to determine his monthly budget, divide $60 by 120%
x = $60 / 120%
x = $60 / 1.20
x = $50
To learn more about percentages, please check: https://brainly.com/question/25764815
Which of the following is equivalent to the expression below? (2^5)(2^6)
(A) 2^11
(B) 2^30
(C) 4^11
(D) 4^30
Answer:
(A) 2^11
Step-by-step explanation:
Which numbers between 10 and 99 have digits that differ by 4 and add to 6
Answer:
A
Step-by-step explanation:
Correct option is A)
Let a 3-digit number ABC
Case (1)
If A=7, then B and C can be any digit but not 7
so, total 9 digits (0,1,2,3,4,5,6,8,9) can replace B and C
Then total such combinations =1(9)(9)=81
Case (2)
If B=7 then A can be any digit but not 0 and 7, because if A=0 it will be a 2-digit number.
And C can be any digit but not 7
Then total combinations =(8)(1)(9)=72
Case (3)
If C=7 then A can be any digit but not 0 and 7, because if A=0 it will be a 2-digit number.
And B can be any digit but not 7
Then total combinations =(8)(9)(1)=72
So, total numbers between 99 and 1000 which have exactly one of their digits as 7 are =81+72+72=225
read what on the image and it is so easy
F - 1.47
The largest box represents 100 small cubes or 1. The four pillars represent 10 and there is four of them so it is 40. Then, the individual cubes are 7. So, 1.47.
How can you tell that x and y are NOT directly proportional? A) x is 0 when y is 0. B) y is getting farther away from x. C) x is increasing by the same amount. D) y is increasing by different amounts.
x y
0 0
1 3
2 5
3 9
Answer:
D) y is increasing by different amounts.
Answer:
d
Step-by-step explanation:
cualquier es la siguiente expresiones equivalentes a(4x-5) (3x+7)
Answer:
21
Step-by-step explanation:
21jshe 21jjxjdjdbxhxbdhxbdh21
Construct a bar graph for the relative frequencies given
Dan works in the sales department for sporting goods company. Dan gets a 15% commission on every bike he sells. If Dan sold 227 bikes at $70 each, how much money did Dan make?
The ratio between an exterior angle and the interior angle of a regular polygon is 1: 3. Find the number of sides of that polygon. Please help D:
Answer:
8 sides.
Step-by-step explanation:
The sum of each of the interior and exterior angles = 180 degrees.
Therefore as the ratio is 1:3 the exterior angles are all = 1/4 * 180
= 45 degrees.
So the number of sides = 360/45 = 8. ( As the sum of the exterior angles in all polygons = 360 degrees).
Given f(x) = 3. + 1, solve for when f(3) = 7.
Answer:
The question is incomplete
The grass in Jamie's yard grew 16 centimeters in 10 days. It was growing at a constant rate.How many days did it take the grass to grow 1 centimeter?How many centimeters did the grass grow in 1 day
Answer:
Step-by-step explanation:
16 cm / 10 days = 1.6 cm/day
10 days / 16 cm = 0.625 days/cm
Raisins and nuts were mixed in a bowl. If nuts made up five eighths of the mixture, what was the ratio of raisins to nuts
Answer:
3/8
Step-by-step explanation:
hope this helped
Shonda uses a $10 off coupon to purchase a purse at Chic Mart. At the register, she signs up for a credit card which gives her 20% off her total after the coupon. If Shonda’s total was $60.00, what was the original price of the purse?
Based on the coupon and the discount, we can calculate that the original price of the purse is $85.00
The 20% was applied after the coupon so the price after the coupon was:
= Total price / ( 1 - Discount)
= 60 / ( 1 - 20%)
= $75
The coupon was $10 so before it was attached it the price was:
= Price after coupon + coupon
= 75 + 10
= $85
In conclusion, the original price was $85.
Find out more on this at https://brainly.com/question/14413529.
Write the fraction 35/42 simplest form
Answer:
5/6
Step-by-step explanation:
how do i solve use the GCF and the distributive property to express a sum as a product 52 +20+36
Answer: just add them all up add 50+20+36 then you get 106
Step-by-step explan
A side length of a regular nonagon is an integer. The perimeter of the nonagon is 80
when rounded to the nearest ten. Determine the integer side length.
If the side length is n, then the perimeter is 9n. The closest multiple of 9 to 80 is 81, so n = 9.
Step-by-step explanation:
A nonagon is a shape with 9 sides. A regular shape means that all angles and sides of the shape is equal. That means let call the side of the nonagon, n. That means the perimeter which is 80, which means all side, n will add up.
[tex]n + n + n + n + n + n + n + n + n = 80[/tex]
or
[tex]9n = 80[/tex]
Solve for n
[tex]n = \frac{80}{9} [/tex]
This rounded would make our interger side, 9
1,7,19,37,61,91,127,169…
Answer:
Sequence sum? but it has no right sequence
The yellow submarine was at sea level when the passengers boarded. The journey began with a descent of 40 meters. After examining the sea life, they rose 30 meters. Zach thought he saw an octopus, below. They dove again, a distance of 25 meters to watch the eight ‘legged’ sea creature.
a) Write an expression to describe the journey of the yellow submarine. _________________________________
b) At what depth did they stop to look at the octopus? ______________________
Answer:
20 meters
Step-by-step explanation:
..................
Max points i need this for finals
Answer:
[tex]Slope (m) = \frac{y}{x} = \frac{3}{1} =3[/tex]
Step-by-step explanation:
[tex]Slope (m) = \frac{y}{x} = \frac{3}{1} =3[/tex]
[tex]0 = arctan(\frac{y}{x}) + 180^o = 251.56505117708^o[/tex]
X = -4 – -2 = -2
Y = 4 – 10 = -6
[tex]Distance (d) = \sqrt{x^2+y^2}=\sqrt{40} = 6.3245553203368[/tex]
Equation of the line:
y = 3x + 16
When x=0, y = 16
When y=0, x = -5.3333333333333
10 < 2 - d solve for d
Answer:
d< -8
Step-by-step explanation:
10 < 2 -d
Add d to both sides: 10 + d < 2 -d + d
Simplify: 10+d<2
Subtract 10 from both sides: 10 + d - 10 < 2 - 10
Simplify: d < -8
Sorry if I'm wrong or didn't explain right. I tried my best. Enjoy your answer and have a great day. Thanks :)
equivalent ratio tables
Answer:
11, 44, 24
Step-by-step explanation:
On the right side column you are adding 11 every time you add 4 on the left side column
For example :
4:11
8:22
12:33
16:44
20:55
24:66
Hope this helps!!! :)))
write the equation of the line given the two points. (1,-2) and (1,5)
Answer:
x=1
Step-by-step explanation:
y=mx+b
5--2/1-1
7/0
Plz I need help! On these 3 questions!
Answer: 1. Angle MHG 2. Angle LHM 3. Angle LHK and KHJ and the measures are 35 each
Step-by-step explanation:
1. The order you put the angle points in isn’t super important, as long as the middle point of the angle stays between the two letters, so angle ABC can be angle CBA as long as the b stays in the middle
2. You can find out the LHM is a right angle by looking at the protractor and counting
3. Congruent = Equal and both angles equal 35 degrees.
Answer:
1. Acute Angle
2. MHL
3. LHK and KHJ
Step-by-step explanation:
1. Since GHM has an angle less than 90˚ it is an acute angle
2. MHL is an Right Angle as 110-20 is 90˚ and an right angle is 90˚
3. LHK and KHJ both has an angle of 35˚
Hope this helps!
A printer is printing photos. For every 8 photos, the printer takes 2 minutes. Complete the table below showing the number of photos and the time it takes to print them.
The statue of liberty casts a 122 foot shadow at the same time ryan casts a 2 foot shadow. If the statue of liberty is 305 feet tall how tall is ryan?
Step-by-step explanation:
2 objects and their shadows create 2 similar right-angled triangles.
that means all angles are the same, and the side lengths of one triangle correlate to the corresponding side lengths of the other triangle via the same factor.
so,
122 × f = 2
f = 2/122 = 1/61
therefore, Ryan is
305 × f = 305 × 1/61 = 5 ft
tall.
If the Statue of Liberty is 305 feet tall, Ryan is 5 feet tall.
What is proportion?A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio.
Given that,
The length of shadow of Statue of Liberty = 122 foot.
The length of shadow of Ryan = 2 foot.
Also, the height of Statue of Liberty = 305 feet.
Let the height of Ryan = x
To find the value of x,
Use ratio and proportion method,
122 / 305 = 2 / x
x = 2 x 305 / 122
x = 305 / 61
x = 5
The height of Ryan is 5 feet.
To know more about Proportion on:
https://brainly.com/question/7096655
#SPJ5