Answer:
[tex]P(x) = x^3 - 10x^2+ 34x-40[/tex]
Step-by-step explanation:
Given
[tex]p =1[/tex] -- Leading coefficient
[tex]Zeros: 4\ and\ 3 - i[/tex]
Required
Determine the polynomial
Represent the zeros with a and b
Such that
[tex]a = 4[/tex]
[tex]b = 3 - i[/tex]
The polynomial is:
[tex]P(x) = p * (x - a) * (x - b)[/tex]
[tex]P(x) = 1 * (x - 4) * (x - (3 - i))[/tex]
However, to solve further: We need to symmetrise over 3-i and its conjugate
[tex]P(x) = 1 * (x - 4) * (x - (3 - i))* (x - (3 + i))[/tex]
[tex]P(x) = (x - 4) * (x - (3 - i))* (x - (3 + i))\\\\[/tex]
To define a suitable function, the expression becomes
[tex]P(x) = (x - 4) * ((x - 3)^2+1)[/tex]
[tex]P(x) = (x - 4) * ((x - 3)(x - 3)+1)[/tex]
[tex]P(x) = (x - 4) * (x^2 - 6x + 9+1)[/tex]
[tex]P(x) = (x - 4) * (x^2 - 6x +10)[/tex]
Open bracket
[tex]P(x) = x^3 - 6x^2 +10x - 4x^2 + 24x-40[/tex]
[tex]P(x) = x^3 - 6x^2 - 4x^2+10x + 24x-40[/tex]
[tex]P(x) = x^3 - 10x^2+ 34x-40[/tex]
What is the product of (x − 3) and (x + 7)? A. x^2 + 4x − 21 B. x^2 − 4x − 21 C. x^2 − 10x − 21 D. x^2 + 10x − 21
Answer: (x−3)(x+7)
Step-by-step explanation:
=(x+−3)(x+7)
=(x)(x)+(x)(7)+(−3)(x)+(−3)(7)
=x^2+7x−3x−21
=x^2+4x−21
Answer:
A. X^2+4x-21
Step-by-step explanation:
(x−3)(x+7)
=(x+−3)(x+7)
=(x)(x)+(x)(7)+(−3)(x)+(−3)(7)
=x2+7x−3x−21
=x2+4x−21
I hope this helps :) I got it CORRECT also i added the Steps if your teacher asked for steps :)
3.
Write the slope-intercept form of the equation for the line.
A. y = 2x – 1
B. y = [tex]\frac{1}{2}[/tex]x – 1
C. y = [tex]\frac{1}{2}[/tex]x + 1
D. y = –2x – 1
Answer:
I'm gonna go with letter A. y= 2x - 1
Step-by-step explanation:
Answer:
y = 2x -1
Step-by-step explanation:
the line passes through -1 on the graph
it rises 2
and moves right once
Hope this helps ! (:
A university has 40,110 students. In a random sample of 210 students, 14 speak three or more languages. Predict the number of students at the university who speak three or more languages. The expected number of students at the university who speak three or more languages is .
plsss help i’ll give brainliest if you give a correct answer
Answer:
it a
Step-by-step explanation:
Answer:
A (7)
Step-by-step explanation:
9w = 63
9 x 7 is 63,
9 x 6 = 54,
9 x 8 = 72,
9 x 9 = 81,
Find the area of the shaded polygons
PLS HELP ASAP AGAIN!!!
9514 1404 393
Answer:
9 square units
Step-by-step explanation:
Pick's theorem is a useful relationship in circumstances like these. It tells you the area is ...
A = i + b/2 - 1
where i is the number of interior points (8), and b is the number of points on the border (4).
The area of this figure is ...
A = 8 + 4/2 -1 = 9
The area of the polygon is 9 square units.
_____
You can also get there by realizing the bounding rectangle is 4 units square. From that, corner triangles are cut. CW from upper left, those triangles have (base, height) dimensions of (3, 2), (1, 3), (3, 1), and (1, 2). So, the total of their areas is (1/2)(6 +3 + 3 +2) = 7 square units. The shaded area is then 16-7 = 9 square units, same as above.
Which characteristics best describe an acute isosceles triangle
Answer:
answer is A i and iv
two sides meet at 90°
two sides are equal in lenght
Solve the equation -5x + 3 = 2x - 1
Step-by-step explanation:
Given
- 5x + 3 = 2x - 1
or, 2x + 5x = 3 + 1
or, 6x = 4
or, x = 4/ 6
Therefore x = 2 /3
Hope it will help :)❤
Step-by-step explanation:
Subtract
3
3
3
from both sides of the equation
−
5
+
3
=
2
+
1
−
5
+
3
−
3
=
2
+
1
−
3
2
Simplify
Subtract the numbers
Subtract the numbers
−
5
=
2
−
2
3
Subtract
2
2x
2x
from both sides of the equation
−
5
=
2
−
2
−
5
−
2
=
2
−
2
−
2
4
Simplify
Combine like terms
Combine like terms
−
7
=
−
2
5
Divide both sides of the equation by the same term
−
7
=
−
2
−
7
−
7
=
−
2
−
7
6
Simplify
Cancel terms that are in both the numerator and denominator
Divide the numbers
=
2
7
What's the answer to this?
Answer:
The answer to this equation is 3 3/16
Step-by-step explanation:
Enter the value for that makes the given equation true.
20−5(6+4)=4−6
Answer:
hi, there is no variable
Use what you know about the angle sum theorem for triangles and your algebra skills to solve for x and find the measure of all three angles:
Answer:
2x° = 45°, 3x° = 67.5°
Step-by-step explanation:
Sum of angles in a triangle = 180°
2x+3x+3x=180°
8x=180°
x=22.5°
2x=22.5°x2=45°
3x=22.5°x3=67.5°
help answer both plz!
Answer:
3.6666 (I didn't round)
Repeating decimal
Step-by-step explanation:
We know that
2/3
is the same as
2÷3
Therefore:
3 2/3 = 3+(2÷3) = 3 + 0.6666 =3.6666
A repeating decimal is one that keeps going and repeats a pattern. This is decimal keeps going and repeats a pattern so it is a repeating decimal.
A terminating decimal is one that terminates or ends. This decimal does not terminate or end. It keeps going.
Hope this helped.
in the sequence 113, 93, 77, 65, 57,…, what number should come next?
a) 55
b) 54
c) 53
d) 51
Your answer is:
C) 53
THANK YOU!!
∝ Sidhdi
Order the side from greatest to least.
Η.
28°
118°
K
J
side [Select ]
Answer:
HJ>KJ>HK
Step-by-step explanation:
Side opposite to the largest angle is the largest.
Side opposite to smallest angle is the smallest.
ang K = 118° ang J = 28°
ang K + ang J + ang H = 180° (Sum of all the angles in the triangle is 180°)
118°+28°+angH=180° (Putting the values of ang K & ang J)
146°+angH=180°
ang H=180°-146°
ang H=34°
128°>34°>28°
ang K>ang H>ang J
Here, ang K is the largest, so the side opposite to it i.e. HJ will be the largest side.
Smaller than ang K and bigger than ang J is ang H, so the side opposite to it i.e. KJ will be smaller than HJ but bigger than HK.
Ang J is the smallest angle, so the side opposite to it i.e. HK will be the smallest.
HJ>KJ>HK.
if margrate has a basket of apples and pears. the number of apples equals three more than twice the number of pears. if there are 15 pieces ot fruite altogether how many apple and pears are there?
Answer:
There are 6 pears and 9 apples.
Step-by-step explanation:
The equation would be a=3+2p
Please! No one got the right answer here and i need it
In their last game, the New England
Patriots scored 9 points in the first half. In
the second half, they scored twice the
amount of points in the first half. What is
the ratio of points scored in the second half
to the total number of points scored?
Answer:
3:5
Step-by-step explanation.
The first half: 9
The second half is: 15
9:15 =3:5
For ΔJNM, the following facts are given: KL || MN
KL = 8 ft MN = 10 ft JL = 3.2 ft MK = 1.5 ft
Answer the following:
a) Is ΔJNM ~ ΔJLK? Support your answer with a postulate or theorem. b) Find the length of JN. Show all your work.
c) Find the length of JK. Show all your work.
d) What is the area ratio of ΔJNM to ΔJLK? Show all your work.
Answer:
I havn't gotten c and d yet, but:
a) They are similar because of the Angle Angle Theorem
b) JN=4ft
Answer this question to get marked as brainliest!!!
1
3x +2y - 5z
If
y-42
X
=
find the value of x when y = 6 and z
2
3y
Answer:
hmmmm i saw something about 13?????
Step-by-step explanation:
Together Mike and Sara ran 42 laps on the
track. Sara ran twice as many laps as
Mike did. Write a system of equations and
solve it to see how many laps they each ran.
Answer:
i dont know the system of equations since i only calculated it until i got the right answer but sara did 28 laps and mike did 14
Which expression is equivalent to 99 + 22? A. 11(9) + 2(1) B. 11(9 + 2) C. 9 + 2(11) D. (8 × 9) + (6 × 7)
Answer:
B
Step-by-step explanation:
They both equal 121
Which expression shows the total area of 5 rooms, if the
sides of 3 rooms measure 17 feet each, and the sides of
2 rooms measure 15 feet each?
Answer:
3084 sq. ft
Step-by-step explanation:
for the first three rooms,
area= 6l² = 6× 17² = 1734
for the next two rooms,
area= 6l² = 6×15² = 1350
total area = 3084
What is a common factor for the two fractional terms
11
001 01
x and
?
The terms can be written as 5)
(x) and (11)
log
(x) y).
O 5
100 100
Weißt du Deutsch, ich kann vielleicht helfen
I don't know what this is.
Show work and please
On the grid below, draw the graph of y = 2 - 3x for the values of x from - 3 to 3
Step-by-step explanation:
slop -3
(x ,y) point that throgh the x,y axis
(0,2), (1,-1), (2, -4),( -1, 5), ( -2, 8) etc you can make the graph by connect the co ordinat point
Write the expression as StartFraction a Over 90 EndFraction. Write the expression as 90 – a. Write the expression as a – 90. Substitute 102 in for the variable, a. Simplify by subtracting 90 from 102. Simplify by dividing 102 by 90. The answer is 1.13. The answer is 12.
Answer:
Write the expression as a – 90
Simplify by subtracting 90 from 102.
The answer is 12.
Step-by-step explanation:
Write and evaluate the expression. Then, check all that
apply
the difference of a number and ninety;
o Write the expression as
90
when a = 102
Subtraction Words
Write the expression as 90-a.
Write the expression as a -90,
O Substitute 102 in for the variable, a.
Simplify by subtracting 90 from 102.
Simplify by dividing 102 by 90.
decreased by
difference
fewer
The answer is 1.13.
less than
The answer is 12.
subtract
Let
The unknown number = a
The expression is
a - 90
Substitute a = 102
a - 90
= 102 - 90
= 12
The answer is - /C, D, E, H/
- /3, 4, 5, 8/
- "Write the expression as a – 90.",
"Substitute 102 in for the variable, a.",
"Simplify by subtracting 90 from 102.",
"The answer is 12."
I hope it makes sense, you're welcome!
Help me with this!!!
Answer:
Yes
Step-by-step explanation:
You can use the perpendicular bisector theorem, because the bisecting line is intersecting at a right angle, which means it is actually perpendicular. Along with IJ and IH being congruent (equal)
Parallel Lines cut by a transversal
Answer:
-4
Step-by-step explanation:
1. They are alternate exteriors meaning they are supposed to be the same so you sort the equation like 134+x=130
2. Then you pass 134 both side like ×=130
-134
3. Which will equal :-4
I -9I = ____
HELP HELP ME ME ASAP PLEASE
Answer:
9
Step-by-step explanation:
l l means absolute value
the absolute value of any negative number is the same number but positive
so the absolute value of -9 is positive 9
Answer:
9
Step-by-step explanation:
Absolute value (or the lines) makes everything inside of it positive, so |-9| = 9
Solve for x. 5:1::6:x
Answer:
Step-by-step explanation:
5/1 = 6/x
5x = 6
x= 6/5
Answer:
x
=
15
Step-by-step explanation: