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
when x varies directly as 2y and x=6 when y=20 find y when x=9
Answer:
x=k×2y
substitute x for 6 and y for 20
6=2(20)×k
6=40k
Divide both sides by the coefficient of k
6/40=40k/40
3/20=k
To find y, when x=9
9=3/20×2y
9=6y/20
cross multiply
9×20=6y×1
180=6y
Divide both sides by the coefficient
y=30
Please help me
if v=6, w=-9, and x=7
Answer:
im sorry but r u even trying..... bc i just answer one of ur questions
Step-by-step explanation:
A community hall is in the shape of a cuboid.
The hall is 20m long, 15m wide, and 4m high.
Answer:
The total paint cost is £380. The total tiles cost is £1800. The total cost is £2180.
Step-by-step explanation:
To know the cost, you need to calculate the area of the community hall.
Area of the ceiling/floor: 40m x 15m = 600m2So together, their area is 1200m2.
Area of the small walls of the community hall: 15m x 3m = 45m2/each wallTogether the two walls have an area of 90m2
Area of the big walls of the community hall: 40m x 3m = 120mTogether the two big walls have an area of 240m2
So, therefore, the total area of the community hall: 1530m2Painting:
They are going to paint the walls and the ceiling and each 10L tin covers 25m2 so:
Area of the walls and ceiling = 600m2 + 90m2 + 240m2 = 930m2
930m2 ÷ 25m2 = 37.5 tins. Since you can't have half a tin, they will need 38 10L tins.
38 x £10 = £380
Floor:
1m2 floor tiles costs £3 so 600m2 x £3 = £1800
Total:
£1800 + £380 = £2180
Danielle pays $35 for 6 1/3 pounds of coffee.Charyn pays $60 for 9 1/4 of coffee. Whose coffee cost more per pound . What is the difference per pound in the coffee
Answer:
Charyn's coffee is the dearest.
Difference per pound is $0.96.
Step-by-step explanation:
Price per pound = total price / pounds bought
For Danielle this
is 35 / 6 1/3
= 35 / 19/3
= 35 * 3 / 19
= $5.526.
For Charyn this
is 60 / 9 1/4
= 60 / 37/4
= 60 * 4 / 37
= $6.486.
Difference = $0.96.
What is the distance between -9and -2 on the number line
Answer:
7 units
Step-by-step explanation:
Calculate the distance using the absolute value function
| - 9 - (- 2) | = | - 9 + 2 | = | - 7 | = 7
or
| - 2 - (- 9) | = | - 2 + 9 | = | 7 | = 7
Expand and simplify
3(4a - 5b) + 2(2a - 3b)
Answer:
a = 5/2
b = 1
I hope it correct
Step-by-step explanation:
Thank you
Answer:
answer is 5ab
Step-by-step explanation:
3(4a-5b)+2(2a-3b)
3(ab)+2(ab)
3ab +2ab
5ab
The perimeter of the figure below is 140 ft.
Find the length of the missing side.
Answer:
9.2 ft
Step-by-step explanation:
140 - 9.6 - 10.2*8 - 19.8*2 = 9.2
mark me as brainliest PLEASE
Hello could someone help me I don’t get this? Will name brainliest :D if correct answer please no links
Answer:
A -- only
Step-by-step explanation:
A segment bisector intersects a segment at its midpoint.
S is the midpoint of segment PQ, so ST is a segment bisector. (It intersects PQ at its midpoint, S.)
No other midpoints are shown in this drawing.
__
A perpendicular bisector is perpendicular to the segment it bisects. None are shown in this drawing.
__
An angle bisector divides an angle into two congruent parts. None are shown in this drawing.
__
The vertex of a right angle is often marked with a small square. Only point P is the vertex of a right angle in this drawing. (We cannot assume OPQR is a square.)
m
Which of the
following proves
these triangles
are congruent?
B
SSA
SAA
neither
Help plz
Can someone please help me with this one? Tysm!!
Answer:
-26
Step-by-step explanation:
well add the negative numbers first so you get
-17-18=(-35)
then you add 9 so its (-35)+9=26
Answer:
Step-by-step explanation:
-17 + 9 +(-18) = -8 -18 = -26 final answer
What is the percent of decrease from 100 to 38?
Answer: 62
Step-by-step explanation:
100 - x = 38
x =62
What is the area of this figure?
6 in
4 in
1 in
2 in
7 in
6 in
square inches
Answer:
wheres the figure
aaah
good morning
For what value of y is the perimeter of the Shape 220 cm? and given sides are 5y+4 and 2y+36
Given that:
Length of the rectangle = (5y+4) cm
Breadth of the rectangle = (2y+36) cm
We know that formula for
Perimeter of a rectangle = 2(l+b) units
⇛P = 2(5y+4+2y+36) cm
⇛ P = 2(7y+40) cm
⇛ P = 14y+80 cm
According to the given problem
The perimeter = 220 cm
⇛ 14y+80 = 220
⇛14y = 220-80
⇛14y = 140
⇛y = 140/14
⇛y = 10 cm
Therefore, the value of y = 10 cm Ans.
also read similar questions: A rectangular prism has a volume of 220 cubic cm and a height of 5 cm. Its base might have sides that measure:
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If the ratio of the measures of the sides of a triangle is 5:6:9 and its perimeter is 220. what are the measures of the sides
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Please help I need help by the end of today
Answer:
A. x = 7, y = 3
Step-by-step explanation:
The triangles are congruent by HL if the hypotenuses are congruent, and if the marked legs are congruent.
3x -1 = 6y +2 . . . . hypotenuses are congruent
2x = 5y -1 . . . . . . .legs are congruent
Subtracting 2 times the first equation from 3 times the second gives ...
3(2x) -2(3x -1) = 3(5y -1) -2(6y +2)
6x -6x +2 = 15y -3 -12y -4
9 = 3y . . . . . . . . . . . add 7 and simplify
y = 3 . . . . . . . . divide by 3
This value of y matches only answer choice A.
Plz, Help me!
What is the equation of a circle with a radius of 5 and a center located at (7,9)?
a. (x - 9)^2 + (y - 7)^2 = 5
b. (x - 7)^2 + (y - 9)^2 = 5
c. (x - 7)^2 + (y - 9)^2 = 25
d. (x - 9)^2 + (y - 7)^2 = 25
Answer:
(x-7)^2 + (y-9)^2 = 25
Step-by-step explanation:
PLEASE ANSWER QUICKLY 100 POINTS!!!! Simplify the expression below. (See picture below) What is the numerator of the simplified expression?
Answer:
13N+26/9n-26/3
Step-by-step explanation:
Answer:
13N+26/9n-26/3
Step-by-step explanation:
Mark as brainliest
Helps me please ill give brainliest to the best ! this is supposed to be easy(not for me)
Which congruence criteria is met in the following scenario?
ASA
SSS
AAS
HL
SAS
Which expression are equivalent to -1+12x^2+x
Answer:
(3x+1)(4x-1)
Step-by-step explanation:
you can reorder the terms to make it less confusing to 12x^2+x-1
write x as a different 12x^2+4x-3x-1
factor out 4x 4x(3x+1)-3x-1
factor out the negative sign 4x(3x+1)-(3x+1)
factor out 3x+1
(3x+1)(4x-1)
Find the gradient of the line segment between the points (3,-2) and (5,-5). Give your answer in its simplest form.
Answer:
2/7
Step-by-step explanation:
gradient y²-y¹/x²-x¹=4-2/4-(-3)
=2/7
{Taking (x¹,y,¹)=(-3,2)
and(x²-y²)=(4,4)
Koala Airlines carries an average of 272 passengers on its Dallas-Perth flight. It runs 620 such flights each year. How many passengers does it carry on those flights each year?
Answer:
272×620=168,640
Step-by-step explanation:
If koala airlines carries 272 in average then the answer is 168,640
If two terms of an arithmetic sequence are a11 = 23 and a15 = −5, what is a28?
The value of a28 given a11 = 23 and a15 = −5 is -96
Given:
a11 = 23
a15 = −5
Where,
a1 = first term
d = common difference
a11 = a + 10d = 23
a15 = a + 14d = -5
a + 10d = 23 (1)
a + 10d = 23 (1)a + 14d = -5 (2)
subtract (1) from (2) to eliminate a
14d - 10d = -5 - 23
4d = -28
d = -28 / 4
d = -7
Substitute d = -7 into (1)
a + 10d = 23 (1)
a + 10(-7) = 23
a - 70 = 23
a = 23 + 70
a = 93
So,
a28 = a + 27d
= 93 + 27(-7)
= 93 + -189
= 93 - 189
= -96
Therefore, the value of a28 given a11 = 23 and a15 = −5 is -96
Learn more about arithmetic sequence:
https://brainly.com/question/6561461
Giving brainliest
Write the inequality that represents the possible values for x
Answer:
6x +12 < 10
Step-by-step explanation:
Will give brainly,5 stars,and thanks
Answer:
Give the person above me brainliest
Step-by-step explanation:
question attached , need help~
thx for answering ~
kindly stay away if u don't know the ans :) ~
Answer:
I FOUND IT ACTUALY 22.857 lacs $2,285,714
Step-by-step explanation:
do the formula
is/of = %/100
[tex]\frac{17.5}{100} = \frac{4}{x}[/tex]
100*4=400
400/17.5=22.857
Answer:
Total worth of assets of the man = 22.86 lacs
Step-by-step explanation:
Let the man's assets = 100%
Given to the wife = 50%, so leftover 50%
From it given to 4 sons = 15%, so leftover 35%
From it given equally to 2 daughters, so each daughter gets 35% / 2 = 17.5%
17.5% = 4 lacs
100% = 4 x (100/17.5) = 22.8571
Round off to 2nd decimal place = 22.86 lacs
expand: -4(2x + 2) +3
Answer:
-8x-8+3
-8x-5
that is the answer for this question and I will send you the link to mp3 and
Answer two questions
Answer:
3) a = 9
4) v = 16
Step-by-step explanation:
Assuming here that the two questions you're talking about are problem 3 and problem 4, here is my work to find each answer.
Problem 3
First, let's distribute the 5 onto both terms in the parentheses.
5(a - 3) = 30
5(a) - 5(3) = 30
5a - 15 = 30
Next, we can add 15 to both sides to isolate a.
5a - 15 = 30
5a = 45
Finally, divide both sides by 5 to find the value of a.
5a = 45
a = 9
Problem 4
First, let's remove 2 from both sides of the equation.
v/2 + 2 = 10
v/2 = 8
Then, we can multiply both sides by 2 to find the value of v.
v/2 = 8
v = 16
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\text{Number 1}[/tex]
[tex]\text{QUESTION: 5(a - 3) = 30}\\\\\large\textsf{DISTRIBUTE 5 WITHIN the PARENTHESES}\\\\\rm{5(a) + 5(-3) = 30}\\\\\rm{5a - 15 = 30}\\\\\large\textsf{ADD 15 to BOTH SIDES}\\\\\rm{5a - 15 + 15 = 30 + 15}\\\\\large\textsf{CANCEL out: -15 + 15 because it gives you 0}\\\large\textsf{KEEP: 30 + 15 because it helps solve for the a-value}\\\\\text{NEW EQUATION: 5a = 30 + 15}\\\\\large\textsf{SIMPLIFY IT!}\\\\\rm{5a = 45}\\\\\large\textsf{DIVIDE 5 to BOTH SIDES}\\\\\rm{\dfrac{5a}{5} = \dfrac{45}{5}}[/tex]
[tex]\large\textsf{CANCEL out: }\mathsf{\dfrac{5}{5}}\large\textsf{ because it gives you 1}\\\large\textsf{KEEP: }\mathsf{\dfrac{45}{5}}\large\textsf{ because it helps solve for the a-value}\\\\\text{YOUR NEW EQUATION: }\rm{a = \dfrac{45}{5}}\\\\\large\textsf{SIMPLIFY IT!}\\\\\large\text{a = 9}\\\\\huge\text{Therefore, your answer is: \boxed{\textsf{a = 9}}}\huge\checkmark[/tex]
[tex]\huge\text{NUMBER 2}[/tex]
[tex]\text{QUESTION: }\rm{\dfrac{v}{2} + 2 = 10}\\\\\rm{\rightarrow \dfrac{1}{2}v + 2 = 10}\\\\\large\textsf{SUBTRACT 2 to BOTH SIDES}\\\\\rm{\dfrac{1}{2}v + 2 - 2 = 10 - 2}\\\\\large\textsf{CANCEL out: 2 - 2 because it gives you 0}\\\large\textsf{KEEP: 10 - 2 because it helps solve for the v-value.}\\\\\text{YOUR NEW EQUATION: }\rm{\dfrac{1}{2}v = 10 - 2}\\\\\text{SIMPLIFY IT!}\\\\\rm{\dfrac{1}{2}v = 8}\\\\\large\textsf{MULTIPLY 2 to BOTH SIDES}\\\\\rm{2\times \dfrac{1}{2}v = 2\times8}[/tex]
[tex]\large\textsf{CANCEL out: }\mathsf{2\times\dfrac{1}{2}}\large\textsf{ because it gives you 1}\\\large\textsf{KEEP: }\mathsf{2\times8}\large\textsf{ because it helps solve for the v-value}\\\\\text{YOUR NEW EQUATION: }\rm{v = 2\times8}\\\\\large\textsf{SIMPLIFY IT!}\\\\\rm{v = 16}\\\\\huge\text{Therefore, your answer is: \boxed{\textsf{v = 16}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
When is new years????????????
Answer:
21 day
Step-by-step explanation:
EASY MArk as brainliest
Answer:
January 1 is new years day! can I get branliest:>
What is the value of cos (150°)?
PLEASE NO WEBSITES!
Thank you
Answer:
Cos (150) = -√3/2
Step-by-step explanation:
You can find this using a calculator. You will get −0.866025403 which is equal to -√3/2
It is a Saturday morning, and Jeremy has discovered he has a leak coming from the water heater in his attic. Since plumbers charge extra to come out on weekends, Jeremy is planning to use buckets to catch the dripping water. He places a bucket under the drip and steps outside to walk the dog. In 20 min, the bucket is 1/8 of the way full. What is the rate at which the water is leaking per hour? and what is the longest time he can be away from the house before the bucket will overflow?
Step-by-step explanation:
You start by asking yourself or as I call it crossmultiply
if 20 min the bucket is 1/8 full what about 8/8 or a whole
20×8/8×1/8
=160 min or 2.6 hrs
Answer:
[tex]2\frac{1}{2} hours[/tex]
Step-by-step explanation:
What is the rate at which the water is leaking per hour?
rate: [tex]\frac{1}{5} buckets = \frac{1}{5}/ \frac{1}{2} buckets/ hr\\ ----\\\frac{1}{2} hour = \frac{2}{5} buckets/ hr[/tex]
Write an equation that represents the relationship between the number of buckets filled, , in hours.
[tex]y=\frac{2}{5}x[/tex]
What is the longest that Jeremy can be away from the house before the bucket will overflow?
[tex]\frac{5}{2}[/tex] or [tex]2\frac{1}{2} hours[/tex]