Solution :
Given :
[tex]$f(x)=x^3-x^2-18x+19$[/tex]
By using the remainder theorem, if f(x) is divided by (x-k) and the remainder is 'r', then
[tex]$f(x)=(x-k)q(x)+r$[/tex]
Here, k = 4
Therefore, divide the f(x) with (x - 4) to find the q(x) and r.
__________________
[tex]$x-4$[/tex] | [tex]$x^3-x^2-18x+19$[/tex] | [tex]$x^2+3x-6$[/tex]
[tex]$x^3-4x^2$[/tex]
------------------------------------
[tex]$3x^2-18x$[/tex]
[tex]$3x^2-12x$[/tex]
-------------------------------------
[tex]$-6x+19$[/tex]
[tex]$-6x+24$[/tex]
-------------------------------------
[tex]$-5$[/tex]
Therefore,
q(x) = [tex]$x^2+3x-6$[/tex]
r = -5
[tex]$f(x)=(x-4)(x^2+3x-6)-5$[/tex]
[tex]$f(4)=(4-4)(4^2+3 \times 4-6)-5$[/tex]
[tex]$=-5$[/tex]
In a bag in a sports store room, there are
four times as many AFL balls as Rugby
balls and half as many AFL balls as
soccer balls. The number of balls
altogether is 52.
How many AFL balls are in the store room?
Please stop putting links and stuff as the answer.
A dog walking company charges $90 to walk 6 dogs. They charge the same amount of money to walk each dog. Which table represents the relationship between the number of dogs the company walks and the amount of money they charge?
Answer:
15
Step-by-step explanation:
Answer:
its A
Step-by-step explanation:
i did k12
Rob's office recycled a total of 12 kilograms of paper over 2 weeks. How many weeks will it
take Rob's office to recycle a total of 18 kilograms of paper? Assume the relationship is
directly proportional.
weeks
Submit
Answer:
Weeks thats easy man
Step-by-step explanation:
LAST QUESTION!!!!!!!!!!!
segment AB had a mid point at (-1,-1). point A coordinates (3,2). what are the coordinates of B?
Answer:
Just put the opposite coordinates on the other side of the segment and thats your answer!
Step-by-step explanation:
PLEASE HELP
4. Is this a right triangle? Side lengths of 4 in., 6 in., and 9 inches.
O Yes
Ο Νο
Answer:
yes
Step-by-step explanation:
:)
Answer:
no
Step-by-step explanation:
The sides of the given lengths will form a right triangle if they satisfy the Pythagorean theorem.
c² = a² + b²
9² = 4² +6²
81 = 16 +36 . . . . . not true
These side lengths do not form a right triangle. (They form an obtuse triangle.)
Which of the following is a correct interpretation of the expression - 6 + 9?
Answer:
It’s basically 3.
Step-by-step explanation:
Just subtract 9 - 6 which gets you a 3 since there’s a negative sign.
(Surface area) Will give brainliest. Help Needed Asap
Answer:
148
Step-by-step explanation:
Answer:
148ft²
Step-by-step explanation:
Because I just did the question and got it correct.
Hope this helps ;)
65^2 + b^2 = 97^2
what is the length of the missing leg?
[tex] \sf{}b_{1} = - 72 \: \: \: or \: \: \: b_{2} = 72[/tex]
Explain.
[tex] \sf{65}^{2} + {b}^{2} = {97}^{2} [/tex]
[tex] \sf{}4.225 + {b}^{2} = 9.409[/tex]
[tex] \sf {b}^{2} = 9.409 - 4.225[/tex]
[tex] \sf {b}^{2} = 5.184[/tex]
[tex] \sf{}b_{1.2} = ±\sqrt{5.184} [/tex]
[tex] \sf{}b_{1.2} = ±72[/tex]
[tex] \sf{}b_{1} = - 72 \: \: \: or \: \: \: b_{2} = 72[/tex]
.
.
#LearnWithBrainly
Which M.A.D. would show the most variability: 0.5, 1, 1.5, 2
Last question u would love if you could answer!
Answer:
it is a triangles because the other are the name of the triangle.
Step-by-step explanation:
Help please...NO LINKS
$78 is what % of $120?
Answer:
Step-by-step explanation:
see atattchment please answer asap
Answer:
C
Step-by-step explanation:
A trapezoid has a height of 3 meters, a base length of 8 meters, and an area of 30 square meters. What is the length of the base?
Answer:
Length of the second base will be 12 meters.
Step-by-step explanation:
Area of a trapezoid is given by the formula,
Area = [tex]\frac{1}{2}(b_1+b_2)h[/tex]
Here, b₁ and b₂ are the bases of the trapezoid and 'h' is the vertical distance between the bases.
By substituting the values in the formula,
[tex]30=\frac{1}{2}(8+b_2)3[/tex]
[tex]60=3(8+b_2)[/tex]
[tex]20=8+b_2[/tex]
[tex]b_2=12[/tex]
Therefore, length of the second base will be 12 meters.
who wants some points??
is it bad if I've never seen or read Harry Potter... and Star Wars?? lol
Answer:
kinda lol
Step-by-step explanation:
Answer: i have watched harry potter but never read the book. and for star wars i have never read or watched it so your good <3
Step-by-step explanation:
Mary McDonald makes mugs in Miami. She makes two sizes of mugs: a small mug that she sells for
$2.50 and a large mug that she sells for $5.75. Yesterday Mary made $56. Before she opened her shop in the morning, she had 200 mugs in her inventory. At the end of the day she has 188. How many mugs of
each price did she sell?
Answer:
4 small
8 large
Step-by-step explanation:
s - small mug
l - large mug
Yesterday she had 200 at start of day
at end of day 188 left, so she sold 12 mugs
(1) s + l = 12
(2) 2.50s + 5.75l = 56.00
Solve for l in (1)
l = 12 - s
substitute in l = 12 - s into (2)
2.50s + 5.75(12-s) = 56.00
2.50s + 69.00 - 5.75s = 56.00
-3.25s + 69.00 = 56.00
-3.25s = -13.00
s = 4
to find l substitute s = 4 into (1)
4 + l = 12
l = 8
Which of the following situations are equal to 20%? Select all that apply.
A) 5 out of 25
B) 8 out of 40
C) 2 out of 8
D) 16 out of 80
E) 12 out of 24
Answer:
all except C.
Step-by-step explanation:
Answer: A AND C IT SHOULD BE A BECAUSE IF YOU LOOK AT THE %
Please help
I’m so confused
Please don’t use the link joke
Answer:
i think it's 2.2
Step-by-step explanation:
it looks like (5,11) is a point that the line crosses so when you divide 11 by 5, would get 2.2
A rectangle is 12 cm long and 8 cm broad.
The length and breadth of the rectangle are
both increased by the same amount, dcm.
If the area of the rectangle is now 221 cm,
find the value of d. with a digram
Answer:
17
Step-by-step explanation:
because 17 is the mulitple
One number is 60 more than another. If the larger number is divided by the smaller number, the quotient is 4.
What are the numbers?
Answer:
80 and 20
Step-by-step explanation:
Let the 1st no. be 'x'.
2nd no. should be 'x + 60'.
If the larger no.(x + 60) is divided by the smaller number(x), the quotient is 4.
=> (x + 60)/x = 4
=> x + 60 = 4x
=> 60=4x-x
=> 60=3x
=> 60/3 = x
=> 20 = x
No. are x = 20 and x+60 = 20+60= 80
Help me plzzz I need help
Answer:
It shows the distance travelled, in miles, by the e towboat after 5•15 hours
I really need help with this question
Answer:
where is it at
Step-by-step explanation:
sheeeeeeesh
Suppose you and your friends form a band and you want to record a demo. Studio A rents for $125 plus $50 an hour and Studio B rents for $200 and $30 an hour. Let t = the number of hours and c = cost.
Write an equation to represent the cost at each studio (2 points)
Solve the system (2 points)
Write the solution as a point (x, y) (2 points)
Answer:
Cost A = 125 + 50t
Cost B = 200 + 25t
Step-by-step explanation:
Answer:
Cost A = 125 + 50t
Cost B = 200 + 25t
Step-by-step explanation:
(2,200) And also the graph
Water is being drained from a swimming pool containing 12,000 gallons of water. After
one hour passes, 60% of the water remains. At the start of the fifth hour, how many
gallons of water remain? Round your final answer to the nearest gallon.
933 gallons
560 gallons
1.555 gallons
2,592 gallons
Find the 75th term: 88, 81, 74, 67, 60
Answer:
a₇₅ = - 430
Step-by-step explanation:
There is a common difference between consecutive terms, that is
d = 81 - 88 = 74 - 81 = 67 - 74 = 60 - 67 = - 7
This indicates the sequence is arithmetic with nth term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = 88 and d = - 7 , then
a₇₅ = 88 + ( 74 × - 7) = 88 - 518 = - 430
The 75th term of the arithmetic progression is -430
What is Arithmetic Progression?
An arithmetic progression is a sequence of numbers in which each term is derived from the preceding term by adding or subtracting a fixed number called the common difference "d"
The general form of an Arithmetic Progression is a, a + d, a + 2d, a + 3d and so on. Thus nth term of an AP series is
Tn = a + (n - 1) d, where Tₙ = nth term and a = first term.
Here d = common difference = Tₙ - Tₙ₋₁
Sum of first n terms of an AP : Sₙ = ( n/2 ) [ 2a + ( n- 1 ) d ]
Given data ,
Let the Arithmetic progression be = 88 , 81 , 74 , 67 , 60 ...
The first term of the AP is a ₁= 88
Now , the common difference of the AP d = second term - first term
= 81 - 88
= -7
Now , the nth term of the arithmetic progression is given by ,
Tn = a + (n - 1) d
Substituting the values in the equation , we get
T₇₅ = 88 + ( 75 - 1 ) ( -7 )
= 88 + 74 ( -7 )
= 88 - 518
= -430
Therefore , the value of T₇₅ is -430
Hence , The 75th term of the arithmetic progression is -430
To learn more about arithmetic progression click :
https://brainly.com/question/1522572
#SPJ2
Evan has a book to read that has 144 pages. If he has 12 days to finish the
book, how many pages must he read each day?
Answer:
12 pages a day
Step-by-step explanation:
144/12=12
HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP
Answer:
c the student who missed 14 items
Answer:
The answer is B: The student who missed 14 items caused the distribution to be skewed to the right.
Find an angle between 0 and 360 degrees that is coterminal with 232
Answer:
Hola que hace
:I
Step-by-step explanation:
F(x)=x^2. What is g(x)?
PLZ I NEED THIS SOON:
Sketch the graphs:
y=x; y=−x; y= |x|
Answer:
took a screen shot hope it helps
Step-by-step explanation:
Answer:
y=x slants in between the 1st and third quadrant
y=-x slants in between the second and fouth quadrant
y=|x| am not sure but I think it's the same as y=x