Factor f(x) = 4x2 + 11x? - 104x + 105 into linear factors given that – 7 is a zero of f(x).
f(x) = 4x + 11x2 - 104x + 105 = |
(Factor completely.)
Answers
Answer:
f(x) = 4x + 11x2 - 104x + 105 = (x - 3)(x + 7)(4x - 5)
Step-by-step explanation:
f(x) = 4x^3 + 11x2 - 104x + 105
has the coefficients {4, 11 -104, 105}. We perform synthetic division using the given -7 as divisor:
-7 / 4 11 -104 105
-28 119 -105
-----------------------------------
4 -17 15 0
Since the remainder is zero (0), we have shown that -7 is a zero of f(x). The coefficients of the quotient (above) are {4, -17, 15}. Let's try factoring the corresponding polynomial again using synthetic division. Start out by using 5 as divisor and determining whether or not the remaindeer is zero:
5 / 4 -17 15
20 15
-------------------------
4 3 30 No, the remainder is 30 and so 5 is not a
root of this quadratic. Try the divisor 3 instead:
3 / 4 -17 15
12 -15
---------------------------
4 -5 0 Yes, the remainder is 0 and so 3 is a root.
Thus, the given f(x) = 4x + 11x2 - 104x + 105 factors as follows:
f(x) = 4x + 11x2 - 104x + 105 = (x - 3)(x + 7)(4x - 5). Notice that the coefficients of the last factor come from those we found above when using 3 as a divisor in synthetic division.
Related Questions
Find the slope of the line passing through the points (-7, 4) & (-7, -8)
Answers
Answer:
Undefined
Step-by-step explanation:
The equation for finding the slope is:
y2 - y1
------------
x2 - x1
--------------------------------------------------------------------------------------------------------
4 - (-8)
----------
-7 - (-7)
-----------------------------------------------------------------------------------------------------------
4 + 8
--------
-7 +7
---------------------------------------------------------------------------------------------------------
12
----
0
---------------------------------------------------------------------------------------------------------
The slope is Undefined, so there is no answer
Is it possible to construct a triangle with sides of lengths 40, 8, and 30?
Answers
Answer:
No, the two shorter sides must exceed the longer side.
Step-by-step explanation:
Condense to a single logarithm : log 12 18+3 log 12 2
Answers
Answer:
2 or [tex] \log_{12} 144 [/tex]
Step-by-step explanation:
I assume 12 is the base.
[tex] \log_{12} 18 + 3 \log_{12} 2 = [/tex]
[tex] = \log_{12} 18 + \log_{12} 2^3 [/tex]
[tex] = \log_{12} (18 \times 8) [/tex]
[tex] = \log_{12} 144 [/tex]
[tex] = \log_{12} 12^2 [/tex]
[tex] = 2\log_{12} 12 [/tex]
[tex] = 2 [/tex]
The entire expression simplifies to 2, but if you need the simplest log expression, then you can use
[tex] \log_{12} 144 [/tex]
It takes Diego of an hour to complete a lap on a circular bike track. The track is mile long. What is Diego's bike speed? 8 hours per mile 1/8 mile per hour 8 miles per hour 1/8 hours per mile
PLEASE HELP, I DON'T UNDERSTAND THE WORDING
Answers
Answer:
C. 8 miles per hour
Step-by-step explanation:
It takes Diego [tex]\frac{1}{8}[/tex] of an hour to complete the lap = [tex]\frac{1}{8}[/tex] x 1 hour = [tex]\frac{1}{8}[/tex] hour
Distance of the track = 1 mile long
The speed of an object expresses the ratio of distance moved to time taken to cover the distance.
i.e speed = [tex]\frac{distance}{time taken}[/tex]
= [tex]\frac{1}{\frac{1}{8} }[/tex]
= 8
Speed = 8 mile per hour
Therefore, Diego's bike has a speed of 8 miles per hour.
Rewrite using the
distributive property.
14 + 35?
whats the answer plz
Answers
Answer 7+7+35
Step-by-step explanation:
Answer:
I think (10*1)+4+(10*3)+5??
Step-by-step explanation:
the * represents a multiplication sign btw
What is the measure of arc FG?
PLEASE HELP , i’ll make BRAINLIEST
Answers
The sales tax in one state is 5%. Write a function rule for finding the total cost of an item with selling price x. Then find the total cost of CD player with a selling price of $110
Answers
Answer:
Total Cost = 1.05x
CD Player cost = 110*1.05 = $115.50
Step-by-step explanation:
Which of the following expressions are equivalent to 4 + 36x
Please answer and dont take my points bc i am in a hurry
A
4(1) + 4(36x)
B
4(1 + 36x)
C
2(1) + 4(9x) + 4
D
4(1 + 9x)
Answers
Answer:
The answer would be D.
Answer:
The answer is D 4(1 + 9x) or C depending on what school website you use.
Step-by-step explanation:
Eric and Kelsey each work after school to earn money. Eric charges $10, plus an additional $4 per hour to babysit. Kelsey charges $15, plus an additional $3 per hour to rake. Eric and Kelsey work the same number of hours. Which system of equations can be used to determine how many hours, x, they need to work to earn the same amount of money, y?
Answers
Answer:
the option 3 or c is correct
A hexagonal prism has.............vertices.
Answers
Step-by-step explanation:
A hexagonal prism has 12 vertices.
Hope this answer will help you.
Have a great time
Tan(x) *cos(x)*cos(x)= ( the answer should have sin only ) ASAP
Answers
This doesn't make any sense because you didn't give a value to cos like you did to sin.
Let me guess the actual question is tan(x)*cos(x) write this in term of sin.
Now from trigonometry identities, we know that tan(x)=sin(x)/cos(x)
So the expression can be written as sin(x)/cos(x)*cos(x)
which results in sin(x) as the answer, if I guessed the question wrong, sorry and please tell me in the comments what the correct question is, because this question doesn't seem complete :)
Mariana gets $15 per hour working at McDonald's and Jayvon gets $15 per hour as well. Jayvon had $50 in the
bank to start. After how many weeks will Jayvon and Mariana have the same amount of money in their bank
accounts?
Answers
Answer:
What r the options?
Step-by-step explanation:
How much would a house cost today if it cost $100,000 2 years ago before a 4% increase each year in housing prices?
Answers
Answer:
100000 × 1.04 × 1.04
Step-by-step explanation:
108160
1. In the expression x2, 2 is what we call
A. Base
B. Exponent
C. Multiple
Answers
Answer:
hello! if you're talking about x², then 2 is what we call: B. Exponent.
Una calidad de queso vale los 2/5 de $30.000; una segunda calidad vale 1/3 de $24.000 y una tercera calidad vale el doble de un tercio de $15.000. ¿Cuánto valen juntas las tres calidades de queso?
Answers
Answer:
2/5+1/3=6/15+5/15=11/15
30.000+24.000+15.000 =69.000
Complete the sentence.
Answers
Answer:
50 more
Step-by-step explanation:
Answer:
50 more than............
Having trouble solving this
Answers
opt1.
667/1000
=66.7
hope u understand
Answer:
more like dividing the up ones with bottom ones
EX 717/1000=0.717
There are four hundred twenty-three people attending luncheon. If a table can hold 6 people, how many tables do they need?
Answers
Answer:
the answer is 71
Step-by-step explanation:
423/6
42÷6=7
42-42=0
6÷3=×
30÷6=5
70.5--> 71
PLZ HELP ME I NEED HELP ASAP
Answers
Answer:
75 I hope this helped and brainliest please!
Step-by-step explanation:
The equation for surface area for a square pyramid is A=a squared + 2a times the square root of (a squared over 4) + height squared. Since everything is 5 yd, the answer is 75.
an eagle flew 20 m above sea level.A fish was 35 m vertically below the eagle. find the position of the fish
Answers
Answer:
15m below sea level
Step-by-step explanation:
Given data
Distance of eagle from sea= 20m
Distance of fish from eagle = 35m
Required
The distance of the fish from below the sea level
= 35-20
= 15m
Hence the fish is 15m below sea level
help please I really need it
Answers
Answer:
If x is 6, y is 9
Step-by-step explanation:
In your equation, substitute 6 in for each x. This would be (6) + 3y = 4(6) + y.
This ends up being 6 + 3y = 24 + y.
After that, you can subtract y from both sides to get 6 + 2y = 24.
Then you can subtract 6 from both sides to get 2y = 18.
Finally, divide both sides by 2 to get y = 9.
Photos fast charges a fee of $2.50 plus $0.05 for each picture developed. Photos quick charges a fee of $3.70 plus $0.03 for each picture developed. for how many will the total cost be the same at each shop?
Answers
The total cost will cost be the same at each shop for 60 pictures.
What is word problem?Word problems are often described verbally as instances where a problem exists and one or more questions are posed, the solutions to which can be found by applying mathematical operations to the numerical information provided in the problem statement.
Let for x number of picture, the total cost will cost be the same at each shop.
Total cost of x number of picture on Photos fast shop = $ (2.50 + 0.05x)
Total cost of x number of picture on Photos quick shop = $ (3.70 + 0.03x)
according to the question:
(2.50 + 0.05x) = (3.70 + 0.03x)
0.05x - 0.03x = 3.70 - 2.50
0.02x = 1.20
x = 1.20 ÷ 0.02
x = 60
Hence, for 60 number of picture, the total cost will cost be the same at each shop.
Learn more about word problem here:
brainly.com/question/29027588
#SPJ5
Find The Area of the parallelogram...Explain.
Answers
Answer:
8x17=136, so the area is 136 inches squared.
Step-by-step explanation:
the number of magazine subscriptions decreases by 8% each year.If there are 225,000 this year,how many will there be 7 years from now
Answers
Answer:
I got 147107
Step-by-step explanation:
If the subscriptions decrease by 8% each year then you would times 225000 by 0.08 then take the number you get from that and subtract it from 225000. And repeat until you get to the seventh year.
Other equipment totaled 33000. You earn a commission of 20% on every sale you make. If you put 35% of your earnings on this particular sale into a savings account what is the amount invested
Answers
9514 1404 393
Answer:
2310
Step-by-step explanation:
Assuming "this particular sale" totals 33000 in its entirety, the commission is ...
20% × 33000 = 6600
The amount of that going to the savings account is ...
35% × 6600 = 2310
The amount invested is 2310.
cómo resuelvo estás ecuaciones
6×-5y=-3
3×+2y=12
Answers
Answer:
Y vale 3 x vale 2 ponme
Step-by-step explanation:
Molly bought 10 bags of the same dog food. She had a coupon for $5. She spent a total of $65. Write an equation to determine the cost of each bag of dog food
STEP IT OUT:
Answers
Answer:
7
Step-by-step explanation:
Molly bought 10 bags of the same dog food. She had a coupon for $5. She spent a total of $65. How much money was each bag of the dog food?
example:
ositive numbers
numbers greater than zero
Negative Numbers
numbers less than zero
Integers
whole numbers and their opposites
Absolute Value
The distance a number is from zero on a number line. ALWAYS POSITIVE
equation
A mathematical sentence that contains an equals sign.
more examples:
9- (-9)=
18
121 / -11
-11
2(n + 5) = −2
-6
9
−9x + 1 = −80
253 + 234=
487
−15 = −4m + 5
5
8n + 7 = 31
3
Hope this helps bsf
Write the equations of the line that passes through the point 4,3) and is perpendicular to the line y=2x−4 . Write the equation in slope-intercept form.
Answers
Answer:
y = -¹/₂x + 5Step-by-step explanation:
The product of slopes of perpendicular lines is -1
y = 2x − 4 ⇒ m₁ = 2
m₁m₂ = -1
2m₂ = -1
m₂ = -¹/₂
The Point-Slope form of equation of a line with slope of "m" and passing through point (x₁, y₁) is: y - y₁ = m(x - x₁)
m = -¹/₂
(4, 3) ⇒ x₁ = 4, y₁ = 3
So the equation in point-slope form:
y - 3 = -¹/₂(x - 4)
Therefore:
y - 3 = -¹/₂x + 2
y = -¹/₂x + 2 + 3
y = -¹/₂x + 5A rectangular path 60m and 3m is covered with square tiles of 25 cm. How many tiles wil be used to cover the path ?
Answers
Answer:
2880 tiles
Step-by-step explanation:
A rectangular path has dimensions 60 m and 3 m.
Area of a rectangular path = length × breadth = 60 × 3 = 180 [tex]m^2[/tex]
Use [tex]1\,m^2=10000\,cm^2[/tex]
So,
Area of a rectangular path = 180(10000) = 18,00,000 [tex]cm^2[/tex]
Side of a square tile = 25 cm
Area of a square tile = side × side = 25(25) = 625 [tex]cm^2[/tex]
Number of square tiles = Area of a rectangular path ÷ Area of a square tile
= [tex]\frac{1800000}{625} =2880[/tex] tiles
what does -2x + 9 look like on a graph?
Answers
Answer:
The line of the graph will be going down 2/1 and will pass through the y intercept at 9.
Step-by-step explanation:
Hope this helps a little.
Answer:
this
Step-by-step explanation:
use desmos if u need more help