Answer:
x³ + 2x² -3x +6
Step-by-step explanation:
We need to find the polynomial whose roots are ,
-2 , √3 and √3.Say of we have zeroes as , α , β and γ , then the polynomial is ,
=> p(x) = k[ (x - α ) ( x - β) ( x - γ) ]
where k is constant. Substituting the respective values , we have ,=> p(x) = k [ ( x - (-2)) ( x - √3) ( x -√3)]
=> p(x) = k[ (x+2)(x² - 3)]
=> p(x) = k[ x(x² - 3) + 2(x² - 3) ]
=> p(x) = k[ x³ - 3x + 2x² - 6 ]
=> p(x) = k[ x³ + 2x² - 3x - 6 ]
Hence the cubic polynomial is x³ + 2x² - 3x + 6 .Which series is convergent? Check all that apply.
Sigma-summation Underscript n = 1 Overscript infinity EndScripts StartFraction 2 n Over n + 1 EndFraction
Sigma-summation Underscript n = 1 Overscript infinity EndScripts StartFraction n squared minus 1 Over n minus 2 EndFraction
Sigma-summation Underscript n = 1 Overscript infinity EndScripts (one-fifth) Superscript n
Sigma-summation Underscript n = 1 Overscript infinity EndScripts 3 (StartFraction 1 Over 10 EndFraction) Superscript n
Sigma-summation Underscript n = 1 Overscript infinity EndScripts StartFraction 1 Over 10 EndFraction (3) Superscript n
There are 2 correct answers
Answer:
Step-by-step explanation:
c
A right triangle has legs with lenghts of 7 units and 12 units. What is the area of the triangle?
Answer:
area of triangle =1/2 x b x h
Step-by-step explanation:
=1/2 x 7 x 12
= 1/2 x 84
= 42 units
CHECKING YOUR UNDERSTANDING
Choose the letter of the best answer. Write the chosen letter on a separate sheet of
paper
1. A dinner plate has a diameter of 10.2 cm. What is the area of the dinner plate?
A. 81.67 cm
C. 93.84 cm
B. 85.12 cm
D. 100.02 cm
2. A dog is tied to a wooden stake in a yard. His leash is 3 m long, and he runs around
in circles pulling the leash as far as it can go. How much area does the dog have
to run around ?
A. 26.28 m2
C. 29.66 m2
B. 28.26 m2
D. 32.28 m²
3. A storm is expected to hit 7 mi in every direction from a small town of Malabon.
What is the area that the storm will affect?
A. 116.68 mi
C. 150.67 mi
B. 124.83 mi
D. 153.86 mi
4. Every December, an amusement park is constructed in Malabon Robinsons Town
mall. A carousel is the most favorite ride of the kids there. The diameter of the
carousel is 20.5 m. What is the area of the carousel?
A. 329.90 m²
C. 392.90 m2
B. 328.90 m2
D. 391.90 m2
5. A lawn sprinkler sprays water 4.5 ft in every direction as it rotates. What is the area
of the sprinkled lawn?
A. 56.885 ft
C. 63.585 ft
B. 60.855 ft
D. 65.385 ft
Answer:
1) 81.67 cm² (Option A)
2) 28.26 m² (Option B)
3) 153.86 mi.² (Option D)
4) 329.90 m² (Option A)
5) 63.585 ft.² (Option C)
Step-by-step explanation:
GENERAL FORMULAES TO BE USED IN THIS QUESTION :-
Diameter of a circle with radius 'r' = 2r
Area of a circle with radius 'r' = πr²
SOLUTION :-
1) Diameter of the dinner plate = 10.2 cm
Radius of the dinner plate = 10.2/2 = 5.1 cm
⇒ Area of the circle = π(5.1)² = 26.01π cm² ≈ 81.67 cm²
2) Length of his leash = 3m
⇒ Area the dog has to run around = π(3)² = 9π m² = 28.26 m²
3) Radius of the circular range of storm = 7 mi.
⇒ Area of the circular range of storm = π(7)² = 49π mi.² = 153.86 mi.²
4) Diameter of carousel = 20.5 m
Radius of carousel = 20.5/2 = 10.25 m
⇒ Area of the carousel = π(10.25)² = 105.0625π m² ≈ 329.90 m²
5) Radius of the range of sprinkler = 4.5 ft.
⇒ Area of the range of sprinkler = π(4.5)² = 20.25π ft.² = 63.585 ft.²
Aysha got a dress that was on 20% off of the original price of $25.40. How much did she get the dress for?
Answer:
20.32$
Step-by-step explanation:
25.40×.20 = 5.08
25.40- 5.08 = 20.32
so the answer would be 20.32$
will the area be the same or different?
Select the correct answer from each drop-down menu
The table shows the number of books Lucy borrowed from the library each month for a year
Month Number of Books
Month
Number of Books
January
14
6
February
8
July
August
September
19
March
16
12
April
14
October
May
8
November
7
June
7
December
Lucy bomowed the most books in
There were months in which she borowed fewer than 10 books
Answer:
6 Months where she borrowed less than 10,
and he borrowed the most books in August.
Step-by-step explanation:
A woman is thrice as old as her daughter. 12 years hence, she will be twice as old as her daughter find their present age.
help me
with explanation !!!
Answer:
Their present ages are:
Her daughter's age = 12 years Women's age = 36 yearsStep-by-step explanation:
Given that:
A woman is thrice as old as her daughter. 12 years hence, she will be twice as old as her daughter.To Find:
Their present ages.Let us assume:
Her daughter age be x. Women's age = 3xAfter 12 years:
Her daughter's age = x + 12Women's age = 3x + 12Finding their present ages:
According to the question.
⇒ 3x + 12 = 2(x + 12)
⇒ 3x + 12 = 2x + 24
⇒ 3x - 2x = 24 - 12
⇒ x = 12
Their present ages:
Her daughter's age = x = 12 years Women's age = 3x = (3 × 12) = 36 yearsAn airline flying to a Midwest destination can sell 20 coach-class tickets per day at a price of $250 and ten business-class tickets per day at a price of $750. It finds that for each $10 decrease in the price of the coach ticket, it will sell four more per day, and for each $50 decrease in the business-class price, it will sell two more per day. What prices should the airline charge for the coach and business-class tickets to maximize revenue? [Hint: Let x be the number of $10 price decreases for coach tickets and y be the number of $50 price decreases for business-class tickets, and use the methods in this example and this example for each type of car.]
Solution :
Let x = number of coach class tickets sold per day on $ 10 reduced price
y = number of the business class tickets sold per day on $ 50 reduced per price.
Number of the coach class tickets sold = 20 per day at a price of $ 250
Number of the business class tickets sold = 10 per day at a price of $ 750
Decrease in the price of coach class tickets by $ 10 increases the number of tickets sold by 4 per day
Decrease in the price of business class tickets by $ 50 increases the number of tickets sold by 2 per day.
Therefore, the coach price, p(x) = 250 - 10x
Business class price, p(y) = 750 - 50y
Coach tickets, q(x) = 2 + 4x
Business class tickets, q(y) = 6 + 2y
Revenue R(x, y) = p(x) q(x) + q(y) q(y)
R(x, y) = (250-10x)(20+4x)+(750-50y)(6+2y)
R(x) = (250-10x)(0.4)+(20+4x)(-10)+0 = 0
1000-40x-200-40x=0
80x = 800
x = 10
R(y) = 0 + (750 - 50y)(0.2) + (6+2y)(-50) = 0
1500 - 100y+(-300-100y) = 0
200 y = 1200
y = 6
P(x) = 250 - 10(10) = $ 150
P(y) = 780-50(6) = $450
q(x) = 20 + 4(10) = 60
q(y) = 6 + 2(6) = 18
Maximum revenue = 150 x 60 + 450 x 18
= 9000 + 8100
= $ 17100
Using the extreme value theorem, what are the
minimum and maximum values of f(x)?
O minimum value = 1; maximum value = 6
O minimum value = 2; maximum value = 6
minimum value = -1; maximum value = 3
O minimum value = -2: maximum value = 3
Answer:
A
Step-by-step explanation:
Edge
The option A, O minimum value = 1; maximum value = 6 is correct.
We have given that,
Using the extreme value theorem, what are the minimum and maximum values of f(x).
What is the extreme value theorem?Extreme Value Theorem An important application of critical points is in determining possible maximum and minimum values of a function on certain intervals.
Therefore, The option A, O minimum value = 1; maximum value = 6 is correct.
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Two parallel lines cut by a transversal are shown. What is the measure of X"?
9514 1404 393
Answer:
x = 10
Step-by-step explanation:
The marked angles are "alternate interior" angles, so are congruent.
(x° +20°) = (4x° -10°)
30 = 3x . . . . . . . . . . . . . . . divide by °, add 10-x
10 = x . . . . . . divide by 3
Please help faster please
write a function rule for the statement. The output is five times the input.
Answer:
y=5x
Step-by-step explanation:
If the input is x, then the out put is 5x. So y=5x
Domain and range
What is the Domain and Range of the Relation
y = -5
Answer:
D: {all reals}
R: {-5}
Step-by-step explanation:
Reggie needs 24 feet of rope to make a tire swing. He has 10 yards of rope. Is this enough for him to make his swing? Explain.
Answer:
8 yards < 10 yards
He has enough.
Step-by-step explanation:
1 yard = 3 feet
y yards = 24 feet
[tex]\frac{1}{3} :\frac{y}{24}[/tex]
y · 3 = 1 · 24
3y = 24
3y ÷ 3 = 24 ÷ 3
y = 8
24 feet = 8 yards
8 yards < 10 yards
Find the value of x
Answer:
Hello! answer: x = 4
Step-by-step explanation:
Because this is a 180 degree angle it will add up to 180 so 8 × 4 = 32 and 32 + 120 = 152 and 7 × 4 = 28 and 28 + 152 = 180 so 4 is x HOPE THAT HELPS!!
180 degree line-
180 = (8x + 120)
-120
60 = 8x
/8
7.5
x = 7.5
7(7.5) = 52.5
A teacher has a bag of marbles. There are 6 red, 6 blue, 8 green7 purple, and 8 yellow marbles in the bag. As the students enter the classroom, they draw a marble and keep it. If the first student in the room draws a yellowand the second draws a purple, what is the probability that the third student will draw a blue?
25%
18%
22%
33%
Answer:
18%
Step-by-step explanation:
Hope this helps :))
Answer:
the answer is 18%
hope this helps
Answer choices)
A. (2/3x, 2/3y)
B. (3/2x, 3/2y)
C. (1/2x, 1/2y)
D. (2x, 2y)
Please help me :((
9514 1404 393
Answer:
B. (3/2x, 3/2y)
Step-by-step explanation:
It is perhaps easiest to see that B' is 3 grid squares from the origin while B is 2 grid squares from the origin. The scale factor is the ratio of these distances:
3/2
Dilation about the origin multiplies each coordinate value by the scale factor:
(x, y) ⇒ (3/2x, 3/2y)
Plzzzzz help for a brainly
Answer:
20cmStep-by-step explanation:
120/6=20
Answer:
20cm
Step-by-step explanation:
120/6 = 20
Mr. Lauro decided to give a bonus point to the top 25% of students, a
remedial instruction to the bottom 25% of students and a chance for extra credit
to the middle 50% students.
1. Compute the median, lower quartile and upper quartile.
2. How many students will get bonus point that belong to the top 25%?
And who are those students?
3. Who are those students having a chance for extra credit?
4. How many students need to attend the remediation? Who are those
students?
please help po
wag po sana gawing tanga yung sagot
Answer:
Q1 = 23 ; median = 28 ; Q3 = 36
TOP 25% = 3 students (Pauleen ; Vic and Tito).
Extra credit students : (students whose score range between 23 and 36. (score of 23 is not included).
Remediation = 4 students (Pia, Joey, Ryan and Allan
Step-by-step explanation:
Given the scores :
35, 23, 42, 36,36,27,42,28,35,18,42,25,27,18,20
Ordering the scores in ascending order :
18, 18, 20, 23, 25, 27, 27, 28, 35, 35, 36, 36, 42, 42, 42
The lower quartile :
Q1 = 1/4 * (n+1)th term
Q1 = 1/4 * 16 = 4th term
Q1 = 23
The median :
Q2 = 1/2 * (n+1)th term
Q2 = 1/2 * 16 = 8th term
Q2 = 28
The upper quartile :
Q3 = 3/4 * (n+1)th term
Q3 = 3/4 * 16 = 12th term
Q3 = 36
The top 25% refers to the student who scored beyond the 75 percentile score :
Number of students = (15th - 12th) = 3 students students who scored 42
Pauleen ; Vic and Tito.
The middle 50% gets extra credit : This is the interquartile range :
This are the students whose score range between 23 and 36. (score of 23 is not included)
Students who have to attend the remedial class are those in the lower quartile, student with score of 23 and below.
4 students and they are : Pia, Joey, Ryan and Allan
the difference of four times a number and 23 is 5 less than the number. Find the number
Answer:
I think it could be 28 because 28 minis 5 is 23
Choose all of the zeros of the function f(x) = 2x² + 5x – 3.
-3, -0.5, 0.5, 1, 3 << those are the answer choices.
Answer:
-3. and -0.5
Step-by-step explanation:
i hope that helps
Is it possible to construct a triangle with the given side lengths?
1 ft, 6 ft, 9 ft
Yes or no?
Order the numbers from least to greatest 41/50, 0.83, 80%
Answer:
80%, 41/50, 0.83
Step-by-step explanation:
80% = 0.80
41/50 = 0.82
0.83 = 0.83
HELP HELP HELP HELP
What is the equation of the trend line in the scatter plot ?
Answer:
y = (4/7)x + 3
Step-by-step explanation:
rise = 7 - 3 = 4
run = 7 - 0 = 7
slope = rise/run = 4/7
y-intercept = 3
---------------------
Slope intercept form is
y = mx + b
m is the slope = 4/7
b is the y-intercept = 3
the equation is
y = (4/7)x + 3
HELP ASAP I WILL MARK BRANLIEST!!!
This probability distribution shows the
number of times a group of people takes
selfies before liking them.
Retakes
o
1
2
3
4
Frequency
27
29
18
14
12
Using this distribution, find the probability that a
person will retake their sexfie exactly 3 times.
p = [?]
Answer:
0.14
Step-by-step explanation:
0.14 is the probability that a person will retake their sexfie exactly 3 times.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Given
Total frequency = 27+29+18+14+12 = 100
frequency of 3 retakes = 14
p(r) = frequency of 3 retakes/ Total frequency
p(r) = 14/100 = 0.14
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Find the length of the third side. If necessary, write in simplest radical form.
3√5
Answer:
3
Step-by-step explanation:
We can use the Pythagorean thorem to solve this question
leg = [tex]\sqrt{hypotenuse^2 - leg^2} = \sqrt{(3\sqrt{5})^2 - 6^2} = \sqrt{45 -36} = \sqrt{9} = 3[/tex]
THIS IS DUE IN LIKE 5 MINUTES I WILL GIVE YOU BRAIN THING IF ITS CORRECT PLEASE HELP NO LINKS THIS IS VERY IMPORTANT I WILL GIVE YOU BRAIN THING IF ITS CORRECT
Answer: A
Step-by-step explanation:
Answer:
a.30
b.12
i cant figure out the rest i am so sry im
trying to figure it out tho
PLZ HELP!!!
I will give you brainliest
Answer:
141
Step-by-step explanation:
CD = | 4-(-2)| = 6
DB = |3-(-7)| = 10
area of a right triangle
A = (leg 1 x leg2)/2 = (6 x 10)/2 = 30
EB = |3-(-3)| = 6
EF = |-8-(-2)| = 6
area of a square = side^2
A = 6^2 = 36
segment G(and a point with same x coordinate of H)
|8-3| = 5
segment H(and the same point)
|-10-(-8)| = 2
A = (5x2)/2 = 5
segment I(and the same point)
|-8-6| = 14
Area of a rectangle
A = base x width
A = (5 x 14) = 70
total area = 70 + 5 + 36 + 30 = 141
if topic A is very sensitive, while topic B is not sensitive at all, which of the following statements is most likely true when surveying people on the two topics?
A. Topic b requires an anonymous answer form, while topic A does not.
B. Both topic A and topic B require an anonymous answer form.
C. Topic A requires an anonymous answer form, while topic B does not.
D Neither topic A nor topic B requires an anonymous answer form.
Answer:
C.
Step-by-step explanation:
Most people do not want personal information about sensitive topics revealed about themselves, so Topic A requires anonymity.
With non-sensitive topics, people are usually comfortable with revealing their identity, so Topic B doesn't require anonymity.
is 12:8 and 18:12 equivalent?
Answer:
no
Step-by-step explanation:
18 is not a multiple of 12
and 12 is not a multiple of 8