A polynomial of degree at least 3 where one or more of the roots are fractions
#1 p(x)=(x-3)*(x-5)*(x-1)=x3-9x2+23x-15
You try the next one...a fractional root would look like (x-3/2)
Using the Factor Theorem, it is found that an example of a polynomial of degree at least 3 where one or more of the roots are fractions is given by:
[tex]f(x) = x^3 - \frac{7}{2}x^2 + \frac{1}{2}x - 1[/tex]Factor Theorem: The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]
In which a is the leading coefficient.In this problem:
A polynomial of degree 3 will be built, hence it will have 3 roots.A leading coefficient of a = 1 is supposed.Two non-fractional roots, which are x = 1 and x = 2, hence [tex]x_1 = 1, x_2 = 2[/tex].The fractional root is [tex]x_3 = \frac{1}{2}[/tex].Hence:
[tex]f(x) = (x - x_1)(x - x_2)(x - x_3)[/tex]
[tex]f(x) = (x - 1)(x - 2)\left(x - \frac{1}{2}\right)[/tex]
[tex]f(x) = (x^2 - 3x + 2)\left(x - \frac{1}{2}\right)[/tex]
[tex]f(x) = x^3 - \frac{7}{2}x^2 + \frac{1}{2}x - 1[/tex]
To learn more about the Factor Theorem, you can take a look at https://brainly.com/question/24380382
Genevieve spent $56.25 to fill her 15-gallon tank. How much did she pay per gallon?
A. $3.25
B. $3.50
C. $3.75
D. $4.00
Vivi steps off a 10-foot-high diving board and goes 7 3/8 feet below the surface of the swimming pool, then back up to the surface. How far does she travel altogether
Answer:
Your answer is 24 3/4 if you want it decimal wise it would be 24.75
Step-by-step explanation:
Well, let's set up our equation first. 10 (she jumped down 10 feet) + 2(7 3/8) (we are multiplying this by 2 because she first went under the surface then went back up to the surface)
Since distance is never negative you won't add any negative symbols, you'll simply add. First 2(7 3/8) = 59/4 or 14 3/4 | Next we add 10 to it 14+10 = 24 3/4
Your answer is 24 3/4 if you want it decimal wise it would be 24.75
Liam's mom was getting ready to make dinner and
found she was out of potatoes for her famous
smashed potatoes. Liam volunteered to go to the
store and get potatoes for his mom. He spent $11.52
for 12 pounds of potatoes. How much did he spend
per pound?
Answer:
$0.96
Step-by-step explanation:
Take your cost and divide it by your amount.
$11.52/12 = 0.96
Lashonda exercises at least 50 minutes per day. Use t to represent Lashonda's amount of exercise (in minutes per day).
The question is an illustration of inequalities.
The inequality that represents Lashonda's amount of exercise is: [tex]\mathbf{t \ge 50}[/tex]
The given parameter is:
[tex]\mathbf{Minutes = At\ least\ 50}[/tex]
In inequality, at least means greater than or equal to.
So, the above equation becomes:
[tex]\mathbf{Minutes \ge 50}[/tex]
From the question, we understand that the number of minutes should be represented with t.
So, we have:
[tex]\mathbf{t \ge 50}[/tex]
Hence, the inequality is: [tex]\mathbf{t \ge 50}[/tex]
Read more about inequalities at:
https://brainly.com/question/15137133
What is the equation of a line that passes trough (6,-1) and is parallel to the line that has a slope of -2/3?
Answer:
y=-2/3x+3
Step-by-step explanation:
First, identify the slope you need for your equation. The keyword here is "parallel" so the slope you need is the same as the given slope (-2/3).
Next, use the ordered pair (6,-1); it's on the line that you need to find the equation for. Using slope-intercept form (y=mx+b), plug the -1 in for y, plug the 6 in for x, and plug in your slope of -2/3 for m. Solve for b, your y-intercept. You should get 3.
You have your slope and y-intercept now. Create your equation:
y=-2/3x+3.
Two numbers that will multiply to -45 and also add to 4
Answer:
your numbers are -5 and 9, since 9 * -5 = -45 but 9 + (-5) = 9 - 5 = 4
Answer:
The numbers are 9 and -5
Step-by-step explanation:
9×-5= -45
9-5 = 4
25,812-4.2d=31.311-5.5d
Answer:
d=−19831.299231
Step-by-step explanation:
Evaluate. 4^3⋅(100÷25)−5^0
[tex]4 {}^{3} .(100 \div 25) - 5 {}^{0} [/tex]
Solution[tex] {4}^{3} \times (100 \div 25) - {5}^{0} \\ \\ = 64 \times 4 - 1 \\ \\ = 256 - 1 \\ \\ = 255[/tex]
[tex] \fbox \red{Hope This Helps }[/tex]
Answer:
255
Step-by-step explanation:
1) Simplify 100 ÷ 25 to 4.
4³ × 4 - 5⁰
2) Use Rule of Zero: x⁰=1
4³ × 4 - 1
3) Use Product Rule
4⁴ - 1
4) Simplify 4⁴ to 256
256 - 1
5) Simplify
255
hyun is on a game show. points are added for the correct answer and subtracted for incorrect answers. at the end of the second round he has five points and the third round he loses 5 points how many points does hyun have after the third round ?show your work
[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]
The number of points at the end of second round is :
5 pointsand if he loses all the 5 five points in the third round then the number of point he is left with is :
5 - 5 0 pointsHow to give a fraction of an hour
Answer:
An hour is 60/1
Step-by-step explanation:
Solve for x. x/3 < -6
-
Answer:
x < -18
Step-by-step explanation:
x/3 < -6
3 × x/3 < 3 × (-6)
x < 3 × (-6)
x < -3 × 6
x = -18
5/3=x/6 can you find out what x is pls
Answer:
Hey mate....
Step-by-step explanation:
This is ur answer....
5/3 = x/6
= 5×6/3 = x
= 30/3 = x
= 10 = x
= x = 10
Hope it helps!
Brainliest pls!
Follow me! ♧
Answer:
x=10
Step-by-step explanation:
3*2=6 and using giant one its 5*2 which is 10
10/6
Mary and Jeff both have jobs at a baseball stadium selling bags of peanuts. They each get paid $12 per game
and $1.75 for each bag of peanuts they sell. (A-CED.1)
a.) How many bags of peanuts does Jeff need to sell to earn $54?
b.) How much will Mary earn if she sells 70 bags of peanuts at a game?
Please please help me please please I will give you brainless
I keep getting it wrong help
5. What number is in the ones place of a product of 10 and
another number? Explain.
A product of 10 has a number in one's position, and another figure will be 0.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
It is also known as the product. If the object n is given to m times then we just simply multiply them.
The one number is 10.
And let the other number of two digits will be xy.
Then the product of 10 and another number will be
10 × xy = xy0
The number at ones place when the product of 10 and another number will be 0.
More about the Algebra link is given below.
https://brainly.com/question/953809
#SPJ2
help plz help
send photo
plz
Answer:
See belowStep-by-step explanation:
9 a)
8 + 3/4 = 8.75 cmb)
10 + 5 + 3 = 18 kgc)
1 + 1/5 = 1.2 l10 a)
65 - 1 = 64 cmb)
100 + 100 * 2.5/4 = 162.5 mlc)
20 + 4.2 = 24.2° CMandy is making a bouqet of flowers. She goes to a flower shop and finds 3 types of rose, 2 types of peony, 3 types of lily and 5 types of carnation. She only wants to buy 2 flowers. How many possible flower combinations can she choose from?
Answer:
Mandy is making a bouqet of flowers. She goes to
Answer:
possible flower combinations can she choose from?
Step-by-step explanation:
possible flower combinations can she choose from?
What is the distance between the points (1,-6) and (5,-3)?
Answer: 5 is the answer
Use the distance formula to determine the distance between two points.
Answer:
[tex]\displaystyle d = 5[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Coordinate Planes
Coordinates (x, y)Algebra II
Distance Formula: [tex]\displaystyle d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
Step-by-step explanation:
Step 1: Define
Identify
Point (1, -6)
Point (5, -3)
Step 2: Find distance d
Simply plug in the 2 coordinates into the distance formula to find distance d
Substitute in points [Distance Formula]: [tex]\displaystyle d = \sqrt{(5 - 1)^2 + (-3 + 6)^2}[/tex][Order of Operations] Evaluate: [tex]\displaystyle d = \sqrt{25}[/tex]Simplify: [tex]\displaystyle d = 5[/tex]Arnold finished reading 2/3 part of the assigned book for his book report. Greg, on the other hand, has read 3/4 part of the assigned book/novel. Which boy has read more pages?
Answer:Greg has read more pages because 3/4 is bigger then 2/3
Step-by-step explanation:
Simplify (23)-2
- -13
2
ОО
O 64
DONE
9514 1404 393
Answer:
(b) (correct choice is marked)
Step-by-step explanation:
The expression can be evaluated according to the Order of Operations and the rules of exponents.
(2^3)^-2 = 8^-2 = 1/8^2 = 1/64
__
The applicable rule of exponents is ...
a^-b = 1/a^b
Answer:
The correct answer choice is option b. 1/64
Step-by-step explanation:
(2^3)^-2
= 2^3(^-2)
= 2^-6
= 1/2^6
= 1/64
2. rx + h = -k
solve for x?
Answer:
x=(-k-h)/r
Step-by-step explanation:
rx+h=-k
subtract h from both sides.
rx=-k-h
divide both sides by r.
x=(-k-h)/r
Devan stand s926 meters
Answer:
I believe your missing part of the question.
Each unit in the graph above is one block. How far would you have to walk from the harbor to the magic shop and then return to the harbor?
Question 3 options:
A)
5 blocks
B)
9 blocks
C)
3 blocks
D)
6 blocks
Solve for w.
–1.01 = 1.4(w + 2) − 2.41
I SWEAR TO GOD PLEASE SOME ANSWER
Answer:
w= -1
Step-by-step explanation:
-1.01 = 1.4(w + 2) - 2.41
add 2.41 to both sides
1.4 = 1.4(w + 2)
divide by 1.4 on both sides
1=w+2
subtract 2 on both sides
-1 =w
Lucy has read 500 pages of her summer reading assesment, and Angie has read 460 pages. Lucy has reads 10 per week for the remainder of the summer, and Angie reads 20 pages per week for the remainder of the summer. Write and solve an equation to show how many weeks it will take before the girls have read the same amount of pages.
Answer:
It would take four more weeks before the two read the same number of pages.
Step-by-step explanation:
Let [tex]x[/tex] denote the number of extra weeks required before the two read the same number of pages.
Express the number of pages each would read between now and [tex]x[/tex] weeks into the future:
Lucy reads [tex]10[/tex] pages per week. Thus, she would have read [tex]10\, x[/tex] additional pages after [tex]x[/tex] more weeks.
Angie reads [tex]20[/tex] pages per week. She would've read [tex]20\, x[/tex] additional pages after [tex]x[/tex] more weeks.
It is also given that Lucy has already read [tex]500[/tex] pages. After reading [tex]10\, x[/tex] pages in the upcoming [tex]x[/tex] weeks, Lucy would have read a total of [tex](500 + 10\, x)[/tex] pages.
Likewise, after reading [tex]20\, x[/tex] pages in the upcoming [tex]x[/tex] weeks, Angie would have read a total of [tex](460 + 20\, x)[/tex] pages.
It is assumed that the two would have read the same number of pages after these [tex]x[/tex] more weeks. In other words:
[tex]500 + 10\, x = 460 + 20\, x[/tex].
Solve this equation for [tex]x[/tex]:
[tex]x = 4[/tex].
In other words, Lucy and Angie would have read the same number of pages after four more weeks.
16 teams of hockey are playing. each team plays two matches against another team. how many matches are played
Answer:
240
Step-by-step explanation:
Find the intercepts of the following equation
7x^2+y=7
Which of the following is the area of a rectangle with a length of 7 feet and a width of 5 feet?
Answer:
D) 35 sq ft
Step-by-step explanation:
The options are:
A) 24 sq ft B) 70 sq ft C) 12 sq ft D) 35 sq ft
So, when calculating the area of a regular rectangle or square, you need to multiply the base by the height (area=base*height)
So it is as simple as 7 multiplied by 5 which is 35 (7*5=35), so the answer is D) 35 square feet.
The graph shows the amount of money paid when purchasing bags of candy at the zoo:
What is the constant of proportionality of the image shown below?
A. 1/2
B. 3/4
C. 1
D. 2
Answer:
D
Step-by-step explanation:
The proportions is 2
hope this helps