Answer:
[tex]f(x)=x(x-1)(x^2-2x+2)[/tex]
Step-by-step explanation:
The standard polynomial is given by:
[tex]f(x)=a(x-p)(x-q)...[/tex]
Where a is the leading coefficient and p and q are the zeros.
We are given that the zeros are x = 0, 1, and 1 + i.
First, by the Complex Root Theorem, if 1 + i is a zero, then 1 - i must also be a zero.
Therefore:
[tex]f(x)=1(x-(0))(x-(1))(x-(1+i))(x-(1-i))[/tex]
Simplify:
[tex]f(x)=x(x-1)(x-(1+i))(x-(1-i))[/tex]
Expand the third and fourth factors:
[tex](x-(1+i))(x-(1-i))=(x-(1+i))(x)-(x-(1+i))(1-i)[/tex]
Distribute:
[tex]=x^2-x-ix-(x(1-i)-(1+i)(1-i))[/tex]
Expand:
[tex]=x^2-x-ix-x+ix+(1-i+i-i^2)[/tex]
Therefore:
[tex]=x^2-2x+(2)=x^2-2x+2[/tex]
Hence, our polynomial function is:
[tex]f(x)=x(x-1)(x^2-2x+2)[/tex]
WILL MARK BRAINEST IF ANSWER IS CORRECT, ✨
Answer:
2x + 6x + 20 = 180
8x = 160
x = 20
EZ
give brainliest now
40 + 140 = 180 (proof)
Step-by-step explanation:
Answer:
★ The answer is 180
Step-by-step explanation:
Hope you have a great day :)
Divide.
24,350 + 50 =
O A. 478
OB. 487
O C. 527
O D. 587
PLS HURRY IM SUPER CONFUSED
Answer: 487, B.
Step-by-step explanation:
24350 ÷ 50 = 487.
Divide :)
The answer is 487, or B.
On Monday morning, Mr. Descartes asked his Algebra II students whether they had gone to the carnival in town over the weekend.
"I did," said Kristen. "I went on the Teacups ride twice, the rollercoaster twice, and the Spinning Vortex once. I had a lot of fun for only $20."
"I went on those rides, too!" exclaimed Jorge. "Just once each on the Teacups and rollercoaster, but three times on the Spinning Vortex, all for $25."
"I did five Teacup rides," said Lakesha. "And two rollercoaster rides, and one Spinning Vortex. I spent $29."
Marc listed off the same rides. "Three Teacups for me, plus two rollercoasters, plus two rides on the Spinning Vortex, all for – "
"You don't need to say," interrupted Mr. Descartes. "I know how much you spent."
How much are the rides? How much did Marc spend
Answer:
Cost of one Teacup = $3
Cost of one Roller coaster = $4
Cost of one Spinning Vortex = $6
Marc spent = 3x + 2y + 2z = $29
Step-by-step explanation:
Let
Cost of one Teacup = x
Cost of one Roller coaster = y
Cost of one Spinning Vortex = z
In Kristen case -
2x + 2y + z = $20
In Jorge case -
x + y + 3z = $25
In Lakesha case -
5x + 2y + z = $29
In Marc case -
3x + 2y + 2z = ?
Now, we have
2x + 2y + z = $20 ......(1)
x + y + 3z = $25 ........(2)
5x + 2y + z = $29 .........(3)
Now,
Subtract equation (1) from equation (3), we get
5x + 2y + z - ( 2x + 2y + z ) = $29 - 20
⇒5x + 2y + z - 2x - 2y - z = $9
⇒3x = $9
⇒x = $3
Now,
Multiply be 2 in equation (2) , we get
2x + 2y + 6z = $50 ........(4)
Now,
Subtract equation (1) from equation (4), we get
2x + 2y + 6z - ( 2x + 2y + z ) = $50 - 20
⇒2x + 2y + 6z - 2x - 2y - z = $30
⇒5z = $30
⇒z = $6
Now,
Put the values of x and z in equation (2) , we get
$3 + y + 3($6) = $25
⇒$3 + y + $18 = $25
⇒y + $21 = $25
⇒y = $25 - 21
⇒y = $4
∴ we get
Cost of one Teacup = x = $3
Cost of one Roller coaster = y = $4
Cost of one Spinning Vortex = z = $6
Marc spent = 3x + 2y + 2z = 3($3) + 2($4) + 2($6) = $9 + $8 + $12 = $29
HELPPPPPP ANSWER ASAP
2 1/4 + 3/4 =
276x40
Writing an Equation in Slope-Intercept Form
Determine the equation for the given line in
slope-intercept form.
Answer:y=Mx+b
Step-by-step explanation:
What is the y-intercept of the graph of f ?
Answer:
(0,4)
Step-by-step explanation:
y intercept is where the line crosses the y axis
Answer:
4
Step-by-step explanation:
An airline company does not charge an extra fee if the weight of a passenger's luggage is less than 55 pounds.
Part A
On the number line, represent the values when the airline company does not charge an extra fee.
Part B
Create an inequality that represents this situation. Let p represent the weight of a passenger's luggage
Answer:
Let's solve first the part B.
We know that the company does not charge an extra fee is the luggage is less than 55 pounds.
Then if p represents the weight of the passenger's luggage, we need to have:
p is smaller than 55 lb
We also can write this as:
p < 55lb
where the symbol "<"
means that the left side is strictly smaller than the right side.
If we want to be more precise in the notation, we also should have a lower limit.
0lb < p < 55lb
Where the lower limit is because the weight of the luggage can not be zero or smaller than zero.
This is the inequality we wanted.
Now, how we represent this on a number line?
when we have:
x > a
We represent this with a open circle at x = a (this means that x = a is not a solution) and we draw an arrow to the right of a.
and for:
x < a
we represent this with an open circle at a, and we draw an arrow to the left of a.
And if we have:
a < x < b
we draw an open circle at x = a and another at x = b, and all the points between these circles will be solutions.
You can see the graph of the inequality below.
Part A)
(where the point of the arrow should not be there, and both circles should be white)
The weight of water is 62 1/2 lb per cubic foot. Water that weighs 350 lb will fill how many cubic feet?
The question is worded incorrectly. It should say the DENSITY of water is 62 1/2 lbs per cubic foot. Divide the weight by the density to get volume.
(150 lbs) / (62.5 lbs/ft3) = ? ft3 (the two 3's are exponents. so it'd be ft then an exponent of 3.)
Your school club is selling hotdogs at a basketball game. The supplies cost $120. You charge $2.50 for each hotdog. Write a function you can use for finding the profit y for selling x number of hotdogs.
Will mark brainliest!! Look at picture for question please
which expression is equivalent to 6Vg^5, if g> 0
Step-by-step explanation:
Option d is he correct answer.
.....
Please help will give brainliest.
Answer:
D
Step-by-step explanation:
a is false since x could be 0.
b is easy to check, just plug numbers in, and we can see that it's false(you would get 0+0=1 and -0-0=-1 once plugged in)
c is also easy to check, just plot the line or simplify the first equation. since (2x+2y)/2=4/2 is also x+y=2, the second equation is also x+y=2, so it must have infinitely many solutions.
d must be true due to process of elimination but let's check to make sure.
7y=14x, divide both sides by 7 to get y=2x and since they're the same equation it must mean that they have infinitly many solutions and we can see that it is correct
Al simplificar la fraccion 150/600 a su mínima expresión se obtiene 15/6
Answer:
cierto
Step-by-step explanation:
What additional information would be enough to prove
the triangles are similar? Choose all that apply:
A. ZH ZE
B. EF bisects LHFG
C.ZG = ZH
find the value of 2xy+3yz-xyz, when x=2, y=-2, z=4
Answer:
-16
Step-by-step explanation:
2xy + 3yz - xyz
x = 2, y = -2, z = 4
First, plug these values into the equation.
2(2)(-2) + 3(-2)(4) - (2)(-2)(4) = ?
Next, multiply the parentheses.
(-8) + (-24) - (-16) = ?
When you add a negative, you are actually subtracting the number. And when you subtract a negative, you are actually adding the number. Apply this to the equation.
-8 - 24 + 16 = ?
Now, simplify from left to right.
-32 + 16
-16
Your answer is -16.
Hope this helps!
What is 5% of 345? ......
Answer:
17.25
Step-by-step explanation:
5/100 x 345 = 1725/100 = 17.25
Having trouble with this problem
Answer:
True
Step-by-step explanation:
AAAHHHHH!!!!!!! SOMEONE HELP!!!!
Answer:
43.10
Step-by-step explanation:
Je parle une ciart mwoa
All the fractions that are equivalent to 4/5 A. 6/10 B. 8/10 C. 8/15 D. 10/15 E. 12/15
Answer:
B.8/10,E.12/15
Step-by-step explanation:
4/5×2=8/10
4/5×3=12/15
15 PTS NEED ASAP HELP !!!
Answer:
use photo math it helps.......
Answer:
-1
Step-by-step explanation:
Let's simplify this equation one at a time using the order of operations:
|2 - 5| - (12÷4 - 1)^2
3 - (3 - 1)^2
3 - 2^2
3 - 4 = -1
Hope this helps!!
10. John Francis saved P4 on Monday, P16 on Tuesday, P64 on Wednesday and so on. If the
pattern continues, how much will he save on Friday?
Answer:
On Friday it saved 1,024
Step-by-step explanation:
The computation of the amount saved on friday is given below:
GIven that
On Monday it saved P4
On Tuesday it saved P16 (P4 × 4)
On Wednesday it saved P64 (P16 × 4)
On Thursday it saved 256 (P64 × 4)
On Friday it saved 1,024 (P256 × 4)
Pl help It’s for a grade I’ll give you a Brainly
Answer:
8. d
9. c
Step-by-step explanation:
I can give you an explanation if u want
Find the midpoint of the line segment with the endpoints (-6,-8) and (-2,-6)
Answer: (-4,-7)
Step-by-step explanation:
The Midpiont formale is in the picture and add -6 with -2 and add -8 with -6.
-6 + -2 = -8
-8+-6=-14
-8 divided 2 = -4
-14 divided 2 = -7
(-4,-7)
It costs $125.00 to rent the swimming pool, plus $4.50 per person. What would be the total cost to rent the swimming pool for 30 people?
Answer: Hi, I think your answer is gonna be 260 dollars! Have a good day!
Step-by-step explanation:
Rick buys 18 apples for $13. How much would it cost to buy 24 apples?
Answer:
$33.23
Step-by-step explanation:
If 18 apples cost $13, this means that each apple costs 1.38461538. To find the cost of 24 apples, multiply that decimal number by 24. You will get 33.2307692308. You can round this to 33.23.
Fill in the missing number.
6 x 4 =(
x 4) + (3 x 4)
Answer:
6x4= 24
x4)+(3x4)=12
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The complete sentence is 6 x 4 =( 3 x 4) + (3 x 4)
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
6 x 4 =( x 4) + (3 x 4)
Now, split 6 as two equal quantities
6 = 3+ 3
So, 6 x 4 =24
( 3x 4) + (3 x 4)
= 12+ 12
= 24
Hence, LHS = RHS.
Learn more about equation here:
https://brainly.com/question/10413253
#SPJ2
Find the smaller angle (in degrees) between the hands of a clock at 3:25.
Answer:
uhh
Step-by-step explanation:
I'm not sure what It is
Find the area of this circle. Use
3.14 for a
68 mm
The area of the circle is about mm?
(Round to the nearest hundredth as needed.)
Answer:
(3.14)(68)^2=14519.40mm^2 if 68mm is the radius
Step-by-step explanation:
how can I learn to understand it more
Step-by-step explanation:
Well if you dont understand something ask a teacher for help or study on a topic that you struggle with for example math try looking up different math questions and solving them or ask a teacher is you can have pratice questions or problems then show it to him/her so they can check to see if you are right. Hope that help unless you dont understand a certain question that I might have missed.
X-4y=16
5x+4y=8 Math math math
Answer:
(4,-3)
Step-by-step explanation:
x-4y=16
5x+4y=8
find x for one equation
x=4y+16
Now plug this into the other equation
5(4y+16)+4y=8
20y+80+4y=8
24y=-72
y=-3
x=4
Answer:
y=-3
x=4
Step-by-step explanation:
