If x + 2 and x - 3 are factors of the following polynomial, then find the values of a and b. F(x) = x^2 + ax^2- 7x + b
Answers
[tex]\text{Given that,}\\\\f(x) = x^3+ax^2-7x+b \\\\\text{Since}~ (x+2)~ \text{and}~ (x-3)~ \text{are factors of f(x),}\\\\f(-2) = 0 ~ \text{and}~ f(3)=0\\\\\\ \text{Now,}\\\\f(-2)=0\\\\\ \implies (-2)^3+a(-2)^2-7(-2)+b =0\\\\\implies -8 +4a +14+b =0\\\\\implies 4a +b +6 =0~~~....(i)\\\\\\f(3) = 0\\\\\implies 3^3+a(3^2) -7(3) +b =0\\\\\implies 27 +9a -21 +b =0\\\\\implies 9a +b +6 =0~~....(ii)\\\\\\(ii)-(i):\\\\9a+b+6 - 4a-b - 6 = 0\\\\\implies 5a =0\\\\\implies a = 0\\[/tex]
[tex]\text{Substitute a=0 in equation (i):}\\\\4(0) +b +6 =0\\\\\implies b+6 =0\\\\\implies b =-6\\\\\text{Hence, a = 0 and}~ b =-6[/tex]
Related Questions
Solve it (Easy question) :
[tex]\lim_{x \rightarrow 1} \cfrac{x {}^{2} - 25 }{x {}^{2} - 5 }[/tex]
Answers
The solution to the limit expression [tex] \lim_{x \to 1} \frac{x^2 - 25}{x - 5} [/tex] is 6
The limit expression is given as:
[tex] \lim_{x \to 1} \frac{x^2 - 25}{x - 5}[/tex]
Express 25 as 5^2
[tex] \lim_{x \to 1} \frac{x^2 - 5^2}{x - 5}[/tex]
Express the numerator as the difference of two squares
[tex] \lim_{x \to 1} \frac{x^2 - 25}{x - 5} = \lim_{x \to 1} \frac{(x - 5)(x +5)}{x - 5}[/tex]
Evaluate the quotient
[tex] \lim_{x \to 1} \frac{x^2 - 25}{x - 5} = \lim_{x \to 1} (x +5)[/tex]
Remove bracket
[tex] \lim_{x \to 1} \frac{x^2 - 25}{x - 5} = \lim_{x \to 1} x +5\\ [/tex]
Substitute 1 for x
[tex] \lim_{x \to 1} \frac{x^2 - 25}{x - 5} = 1 +5[/tex]
[tex] \lim_{x \to 1} \frac{x^2 - 25}{x - 5} = 6[/tex]
Hence, the solution to the limit expression [tex] \lim_{x \to 1} \frac{x^2 - 25}{x - 5} [/tex] is 6
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0.15% of what number is 10.5
Answers
Answer:
70
Step-by-step explanation:
10.5/0.15 = 70
Check:
70 · 0.15 = 10.5
The password must consist of a vowel followed by 3 letter and 2 odd digits. How many passwords are possible if repetition is allowed?
Answers
There are 5 vowels, AEIOU
Then followed by 3 letters
There are 26 options for the first letter, second letter and third letter
And then followed by two odd digit, there are 5 odd digits, 1,3,5,7,9
5x26x26x26x5x5 = 2197000
-6+ (-19) =
Evaluate
Answers
Martina's fish tank has 15 liters of water in it. She plans to add 5 liters per minute until the tank has at least 60 liters. What are the possible numbers of minutes
. :
Martina could add water?
Use t for the number of minutes
Write your answer as an incqua ty solved fort
Answers
Answer:
9 minutes
Step-by-step explanation:
60=15+5t
45=5t : subtract 15 from both sides
9=t : divide by 5 for both side
67*25 helpppp pleaseeee
Answers
Answer:
1675
Step-by-step explanation:
do people not have calculators?
Equation 2
T
.
X
-
Show
2(4k + 3) - 13 = 2(18 – k) - 13
Answers
Answer:
Step-by-step
= 2 ( 1 8 − ) − 1 3 -13=2(18-k)-138 + 6 − 1 3
= 2 ( 1 8 − ) − 1 3
h=-16t^2+72t+100 solve for t
Answers
Answer:0
Step-by-step explanation:
hey i'm in the six grade i'm not sure but pls try it
Cassidy is selling popcorn for a fundraiser sale at the price shown. he purchases a total of 150 containers of popcorn to sell. after he sells 25 containers, he will make a total profit, after his upfront costs, of $5.50 cassidy's profit, after upfront costs, can be modeled by a linear function in the form of y=mx+b.
C. Will the function be discrete or continuous? Explain.
D. Write the function that models Cassidy's profit.
E. What is the domain of the function?
F. What is Cassidy's profit or loss if he does not sell any popcorn?
G. What is cassidy's profit if he sells all the popcorn?
H. What is the range of the function?
Answers
The domain and the range of the function describes the possible profit or
loss from the sale of popcorn and the number of popcorn units.
The correct responses are;
C. The function is discreteD. The function is; y = 1.5·x - 32E. The domain is; 0 ≤ x ≤ 150F. The loss when non of the popcorn is sold is $-32G. The profit is $193H. The range is; -32 ≤ y ≤ 193Reasons:
The question parameters are;
The price of a popcorn = $1.5
Number of popcorn he purchases = 150
Total profit made = $5.50
The number of containers sold = 25
Therefore;
C. Given that the number of containers sole is countable, the function will be discrete.
D. Cost of the containers = Revenue - Profit
Which gives;
Cost of the containers = 1.5 × 25 - 5.5 = 32
The given function is therefore;
y = 1.5·x - 32
E. The domain is the 150 containers which gives;
The domain = 0 ≤ x ≤ 150
F. When no popcorn is sold, we have;
x = 0, which gives;
y = 1.5 × 0 - 32 = -32
If he does not sell any popcorn, the loss is $32
G. If all the popcorn are sold, we have;
x = 150
Therefore;
y = 1.5 × 150 - 32 = 193
The profit if all the popcorn are sold = $193
H. The range of the function are the possible y values, which is the possible profit or loss, which gives;
The range = -32 ≤ y ≤ 193
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Help me with this plzzzzzzzzz
Answers
in the pediatric unit of a hospital has 165 beds how many are there if each room holds 3 beds
Answers
Answer:
There are 55 rooms
Step-by-step explanation:
There are 165 beds in the hospital. Each room contains 3 beds. In order to find the number of beds per room, take the total number of beds and divide it by the number of rooms in each bed. 165/3=55. There are 55 rooms in the hospital, all containing 3 beds.
Hope this helps!
Whats the solution(X-1)=5x+2
Answers
Answer:
X= - ¾ X= - 0.75
Step-by-step explanation:
thats all i can do hope it help :D
Hey! I really need help with this question:
Giving out brainiest to best answer and 100 points. <3
Please help.
Question: How do I memorize words faster and better? And- how do I study faster and quicker?
Answers
Answer:
Idea one, if you want to memorize words fast and better, you can put part of it in your password of something and then try to log in to whatever you set the password on everyday. Idea two, if you want to study fast and quicker you need to spend big half of the day learning what you need to learn and reading books.
Hope this helps!
The best way I could explain this is that everyone has there own pace at doing things. Like me I learn very fast but I have to read over something to memorize them.
The only way I could say is that maybe take more notes and go over them everyday. It helped me a lot when I wanted to learn more and get better grades. Also another way is taking you time at first and when you get use to it you'll be able to read faster learn quicker but you have to go slow first to go fast.
find the angle of rotation that maps point D onto point A
Answers
Answer:
A - 144
Step-by-step explanation:
everything else would be too far. thx
in the actual room, the distance between the front and back walls is 8 feet. what is the actual length of the front wall, in feet?
Answers
Answer:
8 feet
Step-by-step explanation:
it actually will be 8 feet
Put the following equation of a line into slope-intercept form, simplifying all fractions.
9
x
−
3
y
=
9x−3y=12
Answers
Answer: 3y = 9x -12
Step-by-step explanation:
2. Use the conversion table to convert the following metric units into the given English units.
Round your answers to two decimal places.
a. 12 mm to inches
b. 75 km to miles
C. 150 m to feet
d. 63 square meters to square feet
e 45 meters per second to feet per second
1.9 L (liters) to U.S.quarts
Answers
Answer:
I need only 5 brainlisted please give meStep-by-step explanation:
please anyone please I request you allThe conversion is a. 12 mm ≈ 0.47 inches
b. 75 km ≈ 46.60 miles
c. 150 m ≈ 492.13 feet
d. 63 square meters ≈ 678.13 square feet
e. 45 meters per second ≈ 147.64 feet per second
f. 1.9 L ≈ 2.01 U.S. quarts
To convert the metric units into the given English units, we'll use the following conversion factors:
1 inch = 25.4 mm
1 mile = 1.60934 km
1 meter = 3.28084 feet
1 square meter = 10.7639 square feet
1 meter per second = 3.28084 feet per second
1 liter = 1.05669 U.S. quarts
a. 12 mm to inches:
12 mm * (1 inch / 25.4 mm) ≈ 0.47 inches
b. 75 km to miles:
75 km * (1 mile / 1.60934 km) ≈ 46.60 miles
c. 150 m to feet:
150 m * (3.28084 feet / 1 meter) ≈ 492.13 feet
d. 63 square meters to square feet:
63 square meters * (10.7639 square feet / 1 square meter) ≈ 678.13 square feet
e. 45 meters per second to feet per second:
45 meters per second * (3.28084 feet per second / 1 meter per second) ≈ 147.64 feet per second
f. 1.9 L (liters) to U.S. quarts:
1.9 L * (1.05669 U.S. quarts / 1 liter) ≈ 2.01 U.S. quarts
So, after rounding to two decimal places:
a. 12 mm ≈ 0.47 inches
b. 75 km ≈ 46.60 miles
c. 150 m ≈ 492.13 feet
d. 63 square meters ≈ 678.13 square feet
e. 45 meters per second ≈ 147.64 feet per second
f. 1.9 L ≈ 2.01 U.S. quarts
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What is -3/4+2 3/4 O 3 1/2 O 3 3/4 O 2 1/2 O 2
Answers
Answer:
D. 2
Step-by-step explanation:
Common denominator is already presented which is 4.
-3/4 and 3/4 cancel each other out.
you can also convert to decimal form -3/4 + 2 3/4 is the same as:
-0.75 + 2.75 = 2.
help me please please
Answers
Answer:
11/14
Step-by-step explanation:
Have a nice day !!!
Answer:
its B, its 11/14
Step-by-step explanation:
Yosef typed a 36 word paragraph in 2/3 minute. What is his typing speed, in words per minute?
Answers
Answer:
the answer is:
Yousef typing speed, in words per minute is
equal to
54 words
minute
3x-9=2(x-14)
show me the steps to do this
Answers
Answer:
x=-19
Step-by-step explanation:
3x-9=2(x-14)
3x-9=2x-28
x-9=-28
x=-19
the product of seven non-zero factors. of which only three are positive. is
a) positive
B) negative
c) null
Answers
Answer:
The answer is A
Step-by-step explanation:
This is one of those sneaky questions where you think there is no definite answer, but don't despair. There is an answer.
You have 7 numbers
3 of them are positive which means greater than 0. Let's pick them
3 4 5 = 60
That part's easy. Those 3 numbers give a plus result.
Now try the other 4 numbers
-3 - 2 - 1 - 4
Do you see what's going to happen. You have -3 * - 2 = 6
then you get - 1 * - 4 = 4
All of a sudden you get a positive result 6 * 4 = 24
60 * 24 = 1440
So the answer is any 3 plus numbers multiplied by 4 minus numbers gives a plus result.
Answer:
a) positive
Step-by-step explanation:
If 3 of the 7 numbers are positive, the other 4 are negative. The product of an even number of negative factors is positive. The product of any number of positive factors is positive.
The product is positive.
3. Let Angle ABC be an isosceles triangle with AB = AC. Which of the following describes
LB of the triangle?
A. Exterior Angle
B. Base Angle
C. Vertex Angle
D. Remote Interior Angle
Will mark Brainiest
Answers
It’s should be D because
Step by step explanation
What is the value
of m when p= 32
3p + 2 = m
m =
O
11
00
8
O
5
3
Answers
3(32)+2=m
96+2=m
M=98
7. Which of the lists of three lengths cannot form a triangle?
7,7,20
13,13, 20
13,13,13
7,7,7
7,13,13
Answers
Answer:
7,7,20 I think
Step-by-step explanation:
7+7 is less then 20
Caleb’s receipt for lunch is shown below is Caleb pays with a $10 bill how much change will he receive
Answers
Answer:
Please attach the screenshot for the receipt so people can answer
Answer:
3.08
Explanation
3.79
+1.45
1.24
-----------
6.53
+ .39
-----------
6.92 Now
10.00
- 6.92
3.08
PLEASE HELP ME!!!!!
Laura earns an hourly rate of $14.50 for the first 40 hours that she works in a week. She earns one- and-a-half times her hourly rate for any hours over 10. If she earned $775.75 in one week, how many hours did she work?
a. 35.7
b. 53.5
c. 45
d. 49
Answers
Answer:
I'm not 100% sure but I believe the answer is A
The total hours of work done by Laura is 39 hours.
What are Mathematical operators?A collection of numbers and operations is an expression in mathematics. The following are the parts of a math expression that do a math operation:
Operands: Operands are the numbers that an operator uses. The terms that are given to the operands vary according to the kind of operation.
Given the hourly income Laura = $14.50
total hours she works in a week = 40
increase in rate after working after 10 hours is 1.5 times
the hourly rate after 10 hours = 14.50 x 1.5 = $21.75
amount earned in 10 hours = 10 x 14.5 = $145
total earning = $775.75
the amount left after reducing the amount of 10 hours = 775.75 - 145 = $630.75
$630.75 is earned in = 630.75/21.75 hours = 29 hours
total hours Laura worked = 10 + 29 = 39 hours.
Hence Laura worked 39 hours in a week.
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A movie theater is splitting
cups 30 of popcorn into 18
bags. How much popcorn
will each bag holde
Answers
Answer:
30/18=1 2/3 cups of popcorn in each bag
Hope This Helps!!!
9. Sofija buys a bracelet for $14.50 plus 8% tax.
Momoka buys a necklace for $12 plus 8% tax.
Enter the sum, in dollars, that Sofija and
Momoka paid, including tax.
Answers
Answer:
$12.96
Step-by-step explanation:
Before Tax Price: $12.00
Sale Tax: 8.00% or $0.96
After Tax Price: $12.96
There is a rack of 7 billiards balls, numbered from 1 to 7. If one ball is selected at random, determine the odds against it being an odd-numbered ball.
The odds are 0:0
(Type whole numbers. Simplify your answer.)
Answers
Answer:
Step-by-step explanation:
seven options 1, 2, 3, 4, 5, 6, 7
three successes for it being even. 2, 4, 6
odds are 3:7 of against randomly drawing an odd numbered ball.