Using the factor theorem, the equation for q is:
[tex]q(x) = 4(x^5 - 14x^4 + 51x^3 - 14x^2 + 50x)[/tex]
The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, ..., x_n[/tex] is given by:
[tex]f(x) = a(x - x_1)(x - x_2)...(x - x_n)[/tex]
In which a is the leading coefficient.
In this problem:
Passes through the origin, so x = 0 is a zero, that is [tex]x_1 = 0[/tex].x = i is a zero, and thus, it's conjugate also is, that is, x = -i, hence [tex]x_2 = i, x_3 = -i[/tex]x = 7 - i is a zero, and thus, it's conjugate also is, that is, x = 7 + i, hence [tex]x_4 = 7 - i, x_3 = 7 + i[/tex]Then, the equation is:
[tex]q(x) = a(x - 0)(x - i)(x + i)(x - 7 + i)(x - 7 - i)[/tex]
[tex]q(x) = ax(x^2 - i^2)((x-7)^2 - i^2)[/tex]
Considering that [tex]i^2 = -1[/tex]
[tex]q(x) = ax(x^2 + 1)(x^2 - 14x + 50)[/tex]
[tex]q(x) = ax(x^4 - 14x^3 + 51x^2 - 14x + 50)[/tex]
[tex]q(x) = a(x^5 - 14x^4 + 51x^3 - 14x^2 + 50x)[/tex]
q(-1) = -520 means that when [tex]x = -1, q = -520[/tex], and this is used to find a.
[tex]q(x) = a(x^5 - 14x^4 + 51x^3 - 14x^2 + 50x)[/tex]
[tex]-520 = a(-1 - 14 - 51 - 14 - 50)[/tex]
[tex]130a = 520[/tex]
[tex]a = \frac{520}{130}[/tex]
[tex]a = 4[/tex]
Hence, the equation is:
[tex]q(x) = 4(x^5 - 14x^4 + 51x^3 - 14x^2 + 50x)[/tex]
A similar problem is given at https://brainly.com/question/24380382
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Answer:
Step-1 : Multiply the coefficient of the first term by the constant 1 • 7 = 7
Step-2 : Find two factors of 7 whose sum equals the coefficient of the middle term, which is -8 .
-7 + -1 = -8 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -7 and -1
x2 - 7x - 1x - 7
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-7)
Add up the last 2 terms, pulling out common factors :
1 • (x-7)
Step-5 : Add up the four terms of step 4 :
(x-1) • (x-7)
Which is the desired factorization
Step-by-step explanation:
x = 7 or 1
this is algebra 1 id appreciate it if you could help me thx!
Answer:
Option 4: 0
Step-by-step explanation:
Given the function, f(x) = 3x, and the domain. {-3, 1, 4}:
Substitute the values of each domain as inputs into the function:
x = -3f(-3) = 3(-3)
f(-3) = -9
x = 1f( 1 ) = 3( 1 )
f( 1 ) = 3
x = 4f(4) = 3(4)
f(4) = 12
Therefore, the correct answer is option 4) 0, because there is no input value that provides an output of 0. You were only given three domain values that provided its corresponding outputs.
그if Ella runs 1 mile Monday and runs 3 miles Tuesday and runs 4 miles Thursday and skipped Wednesday how many miles she run in all ➗ it all up
Find the missing angle measure.
Can someone tell me the answer to this please
Answer:
sum of all angles of a triangle= 180°
Let angle A be x,
then 63°+90°+x=180°
x=17°
Please help meeeee how do you rotate this?????
Answer:
Hello,
Here is the answer,
After rotating your graph would look like this with P being at (1, -2) and C still being at (-2, 5). The Upper point is C the lower point is P
Step-by-step explanation:
For brainily please help
Answer:
z is 11 and all angles are the same so all sides are 11
to write
algebraically
following expressions:
the
1. Double an X number.
2. Triple an X number.
3. Double a number x plus 5.
4. The square of the triple of a
number x.
5. Three-quarters of a
number x.
Answer:
1. 2x
2. 3x
3. 2x+5
4. (3x)^2
5. 3\4(x)
I hope it makes sense
have a great day
if any questions pls ask
The following relation is a function: {(-1,0), (1,3), (-2,0), (0,4)}.
True
False
Answer:
My answer is true hope this'll help
the oblique pyramid has a square base with an edge length of 5 cm. the height of the pyramid is 7 cm. an oblique pyramid has a square base with an edge length of 5 centimeters. the height of the pyramid is 7 centimeters. what is the volume of the pyramid? 11two-thirds cm3 43three-fourths cm3 58one-third cm3 87one-half cm3
The volume of a square base pyramid with edge length of 5 cm and height of 7 cm is 58. 33 cm³
Volume of a pyramidThe volume of a pyramid is decribe as follows:
volume of a pyramid = 1 / 3 Bh
where
B = base areah = height of the pyramidTherefore,
B = 5² = 25 cm²
volume of the pyramid = 1 / 3 × 25 × 7
volume of the pyramid = 175 / 3
volume of the pyramid = 58.3333333333
volume of the pyramid = 58. 33 cm³
learn more on pyramid here:https://brainly.com/question/3399922
Answer:
C. 58 1/3 cm^3
Step-by-step explanation:
Solve and graph x - 2 > -5 and x - 2 < 4 on a number line
Answer:
dont take my word for it but
Step-by-step explanation:
x<-7
Which number line represents the solution set for the given inequality?
x + 1 ≤ -3 or -4x < -8
The solution to the system of equations is x≤ -4 and x > 2. Find the number line attached below:
Given the set of inequalities expressed as;
x + 1 ≤ -3 or -4x < -8
For the inequality expression x + 1 ≤ -3
x ≤ -3 - 1
x ≤ -4
For the inequality expression:
-4x < -8
Divide both sides by -4
-4x/-4 > -8/-4
x > 2
Hence the solution to the system of equations is x≤ -4 and x > 2. Find the number line attached below:
Learn more here: https://brainly.com/question/15816805
are two of the same looking triangle but different sizes mean they are congruent?
Answer:
No
Step-by-step explanation:
They are similar
Answer:
Congruent triangles Two or more triangles that have the same size and shape are called congruent triangles. The four triangles are congruent with each other regardless whether they are rotated or flipped. The congruence of two objects is often represented using the symbol
Step-by-step explanation:
The angle measurements in the diagram are represented by the following expressions.
ZA = 5x + 34°
ZB = 2x + 76°
Solve for x and then find the measure of ZA:
ZA=
point A (-1-1) point B(-2-1)
In seventh grade, Emile grew 3 9/10cm,and in eight grade he grew 4 2/5cm. How much did his height increase during these two years?
Answer:
8 3/10 cm
Step-by-step explanation:
Add Emile's 7th and 8th grade growth amounts together:
3 9/10 cm
4 4/10 cm (This is equivalent to 4 2/5 cm.)
-----------------
7 13/10 cm, or
8 3/10 cm
can someone please help me with this
Answer:
Perimeter = 18m
Area = 18m²
Step-by-step explanation:
On a rectangle, opposite sides have equal lengths. This means to find the perimeter you would do (3 × 2) + (6 × 2) which is 6 + 12 = 18
The perimeter is 18m
To find the area, you would do length × width. The length is 6 and the width is 3 so 6 × 3 is 18
The area is 18m²
Hope this helps!
Which of the following is not true?
p+q = q+p
p x q = q x p
p x (q x r)=(p x q ) x r
p - q = q - p
Plz answer my exam is going on right now
Step-by-step explanation:
the number 4 is false
p-q =-(q-p)
please answer by 10 pm
Answer:
1/2n + 3
One half times a number
Step-by-step explanation:
In a regular deck of cards, there are 52 total cards, 26 red, 26 black, and 13 of each of the four suits (hearts, clubs, spades, and diamonds). What is the probability, if you draw a card randomly, that the card will be a heart?
Answer:
13/52 (25%)
Step-by-step explanation:
There are 13 hearts in the deck, and 52 cards in the deck. This means that the probability is 13/52.
A coordinate plane with a line passing through (negative 3, 0), (0, negative 2) and (3, negative 4).
What is the equation of the graphed line written in standard form?
2x + 3y = –6
2x + 3y = 6
y equals negative StartFraction 2 Over 3 EndFraction x minus 2.
y equals StartFraction 2 Over 3 EndFraction x minus 2.
Answer:
2x+3y=-6
Step-by-step explanation:
the intercepts are (-3,0) (x intercept) and (0,-2) (y intercept)
this means that when x = 0, y = -2 and when y = 0, x = -3.
the last two are not in standard form, so we can eliminate those.
the answer also cannot be the second one because both intercepts are negative. when we solve it, the intercepts would be (3,0) and (0,2). the answer must be 2x+3y=-6.
sorry for the late reply!
Answer:
I believe its A. 2x+3y=-6
Step-by-step explanation:
What is the domain in (6-4),(8,-4), (8,-8)}?
a) 2,4.13
c) -4,-8}
b) {6,8}
d) (-2,00)
Answer:
B
hope this helps
Finding the nth term of this sequence: (by the way I'm learning quadratic sequences=
-2 -8 -18 -32 -50
Answer:
n^2+2n+1
Step-by-step explanation:
-2-8-18-32-50
difference=-6-10-14-18
common differences=-4-4-4-4-4
-2-8-18-32-50
n^2=1,4,9,16,25
minus it
=-1,-4,-9,-16,-25
differences 2,5,7,9
common differences=2
2,4,6,8
so 2n+1
so the answer is n^2+2n+1
Bath and Body Works is having a special promotion on fall candles. Every 12th guest is receiving a free pumpkin scented candle and every 36th guest is receiving a free Carmel waffle scented candle. Which number of guests will receive both the pumpkin and caramel waffle scented candles?
Answer:
i d k but now i want candles from bath and body works
Step-by-step explanation:
Triangle ABC is a right triangle
Answer:
Okay.........so what's the problem???
Which of the following ratios are equivalent to the ratio 4: 8?
Answer:
11:22,8:16,9:18...…Step-by-step explanation:
All of the given above are same as 4: 8. because the answer of all is 1 : 2.Look at the point in the picture. What is the y coordinate?
(3,-2)
Answer:
-2
Step-by-step explanation:
It's (x,y)
Here, (3,-2)
-2 is y
:)
which is perpendicular to the line x-2y=2
Answer:
y=-2x+5
Step-by-step explanation:
x-2y=2
2y=x-2
y=(x-2)/2
so the slope is 1/2
for lines to be perpendicular m1m2=-1 so the line must have a slope satisfying the condition
(1/2)m=-1
m=-2
the only line with a slope of -2
If is wrong i'm sorry
5^-1 = blank * 5^4 find the missing factor
Answer:
1/3125 or, 5^-5
Step-by-step explanation:
5^-1 = blank * 5^4
1/5/625= blank or, 5^-1/5^4=blank
blank=1/3125 5^-5=blank
Which blocks should go in Space A and Space B?
Answer:
2 in A 0 in B
Step-by-step explanation:
Vertical and horizontal numbers add up to 8, going by this logic, it's 2 and 0.
A teacher wants to buy the same number of colored markers and pencils. Markers come in packs of 12, and pens come in packs of 16. What is the fewest number of markers and pens the teacher needs to buy?
Answer:
if the teacher buys 4 packa of markers and 3 packs of pens she would have the same amount
Molly is helping her younger sister run a lemonade stand. They earn $2 for each cup of
lemonade they sell.
Write an equation that shows how their total earnings, y, depend on the number of cups sold,
X.
Do not include dollar signs in the equation.
y =
Answer:
y= x • 2
Step-by-step explanation:
The amount of money they make is dependent of how many 2 dollar cups they sell.
(please crown me brainleist I need to level up)
