Answer:
Step-by-step explanation:
f(x) = 2x³ + ax² - 7a²x - 6a³
= 2x³ - 2a²x + ax² - a³ - 5a²x - 5a³
= 2x(x² - a²) + a(x² - a²) - 5a²(x+a)
= (2x+a)(x - a)(x + a) - 5a²(x + a)
= (x + a)[(2x + a)(x - a) - 5a²]
= (x + a)(2x² - ax - 6a²)
= (x + a)(2x + 3a)(x - 2a)
x-a is the factor of the equation and x + a is not a factor of the equation,
All the roots of the equation are x + a, 2x+3a, x-2a.
What is a cubic equation ?"In algebra, a cubic equation in one variable is an equation of the form
ax^3+bx^2+cx+d=0
in which a is nonzero.
The solutions of this equation are called roots of the cubic function defined by the left-hand side of the equation. If all of the coefficients a, b, c, and d of the cubic equation are real numbers, then it has at least one real root (this is true for all odd-degree polynomial functions). "
Given equation is [tex]f(x) = 2x^3 + ax^2 - 7a^2x - 6a^3[/tex]
Now,
[tex]f(x) = 2x^3 + ax^2 - 7a^2x - 6a^3\\\\= 2x^3 - 2a^2x + ax^2 - a^3 - 5a^2x - 5a^3\\\\= 2x(x^2 - a^2) + a(x^2 - a^2) - 5a^2(x+a)\\\\= (2x+a)(x - a)(x + a) - 5a^2(x + a)\\\\= (x + a)[(2x + a)(x - a) - 5a^2]\\\\= (x + a)(2x^2 - ax - 6a^2)\\\\= (x + a)(2x + 3a)(x - 2a)[/tex]
Hence, the roots of the equation are x + a, 2x +3a, x - 2a.
To know more about cubic equation here
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Find the value of X in the triangle
Answer:
44°Step-by-step explanation:
[tex]m\angle BAC=180^o-124^o=56^o\\\\\overline{AB}=\overline{BC}\quad\implies\quad m\angle BCA=m\angle BAC=56^o\\\\m\angle ABC=180^o-2\cdot56^o=68^o[/tex]
[tex]m\angle DBE=m\angle ABC=68^o[/tex] {vertical angles}
[tex]\overline{BD}=\overline{DE}\quad\implies\quad m\angle DEB=m\angle DBE=68^o\\\\m\angle x=180^o-2\cdot68^o=44^o[/tex]
Please help with question 4 thank you !!
Answer:
I would have to go with B.) 129
Step-by-step explanation:
because 54+130+130+97 is 411 and 540-411 is 129
What is the slope of the line that passes through the points (-6 , -4) and ( -12 , -4)? Write in simplest form plssss!
Answer:
the slope is zero
Step-by-step explanation:
Answer:
I think that: slope (m) = 0
Step-by-step explanation:
the equation of slope is m = y2-y1/x2-x1
so, y2 = -4, y1 = -4, and x2=-12, and x1= -6
Just substitute them into the equation:
m = -4 - -4 / -12- -16
m = 0
The slope is equal to 0
I hope this helps!
Solve for y.
4(y - 8) + 6 = 58
Answer:
[tex]4(y - 8) + 6 = 58 \\ or \: 4y - 32 + 6 = 58 \\ or \: 4y - 26 = 58 \\ or \: 4y = 58 + 26 \\ or \: 4y = 84 \\ or \: y = \frac{84}{4} \\ or \: y = 21[/tex]
21 is the answer.....Hopes to get BRAINLIEST......Hopes it helps you.......Thank you ☺️
The scale of a map is 2/5 inches represents 3 miles. How much does 1 inch represent?
Answer:
DEEEEEEZ NUTTTTTTZ
Step-by-step explanation:
There are 6 people in George's family. How much did George's mom pay for tickets? Show how you found your solution.
Answer:
$75
Step-by-step explanation:
To find out how much George's mom paid for the 6 tickets, first find the unit rate, that is cost per ticket.
The unit rate/constant of proportionality between cost of tickets (y) and number of tickets (x) can be calculated using the coordinates of any points on the graph.
Using (4, 50), this means that 4 tickets cost $50.
Unit rate/constant of proportionality = y/x = 50/4 = 12.5
This means a ticket costs $12.5.
Therefore, 6 tickets would cost:
6 tickets × $12.5 = $75.
George's mom paid $75 for the tickets?
Last question I think HELP ME ITS FIXING TO BE OVER DUE!!!
Answer:
I am not good at this but a good app for math is Math
way
~Hope this helps!!Stay safe~
g(x) = x + 2h (x) = x^2 – 4Find: g(x) • h(x)
See attachment for math work and answer.
Hey can you please help me
What is the domain of the function in this table
The main fuction is mulitiply by 2 each 1 point
Step-by-step explanation:
The width of a rectangle is its length. The perimeter of the rectangle is 300 ft. What is the length, in feet, of the rectangle?
Answer:
It's simple. All you need to do is subtract 2 from 40.
Length: 40 ft
Width: 38 ft
Hopefully that helped! :)
Step-by-step explanation:
pls help me, i’ll give brainliest
Answer:
the set of integers
Step-by-step explanation:
Using the number line above, write the integer that each point represents
Pls answer number 3
Answer:
E= -6
D= 4
B =- 4
Step-by-step explanation:
Answer:
The answers are:
E: -6
D: +4
B: -4
equivalent ratio to 2:5
Answer:
4:10
8:20
16:40
1:2.5
Step-by-step explanation:
PLEASE HELP ME I ONLY HAVE 10 MINS TO FINISH ALL MY ASSIMENTS, WILL GIVE BRAINLIEST AND 15 POINTS
question:The baseball infield has an area of 90^2 square feet. What is the area of the infield?
Answer:
8100 square feet
Step-by-step explanation:
Express the tangent of
Answer:
Step-by-step explanation:
TANGERINES
Answer:
of what ? finish the question
The driver of a car traveling at 60 ft/sec suddenly applies the brakes. The position of the car is s(t) = 50t - 2t2, t seconds after the driver applies the brakes. How many seconds after the driver applies the brakes does the car come to a stop? (4 points)
Answer:
t=12.5s
Step-by-step explanation:
s(t) = 50t - 2t^2
v(t) = 50 - 4t
a(t) = -4
When v(t) = 0, the car stops.
v = u +at
0 = 50 + (-4)t
t = 12.5
Write the equation of a line with a slope of 5 and contains the point (-6, 2)
-3-(0.5) on a number line
Answer:
-3.5
Step-by-step explanation:
mark on the left side of the number line where -3.5 is.
Sophie bikes s miles per hour. Her friend, Rana, is slower. Rana bikes r miles per hour.
c
Rana and Sophie went for a 20-mile bike ride today. Each girl biked at her usual speed. How long did Sophie wait for Rana at the end of the route?
Answer:
C x 20 + R x 20
Step-by-step explanation:
C x 20 + R x 20 or
20c + 20r
the table below represents a proportional relationship the unit rate of the relationship is ______?
Answer:
It is 3
Step-by-step explanation:
I know it is 3 because multiply every nimber on the and you will get the number frome the bottom.
Help me plzzzzzzzzzz
Answer:
∠f=34°
Step-by-step explanation:
Find the value of missing angles
Help me out here pleaseeeeeeeee.
Answer:
[tex]\frac{4}{5}[/tex]
Step-by-step explanation:
A fraction is in simplest form when no other factor but 1 will divide into the numerator/ denominator
[tex]\frac{5}{10}[/tex] ← divide numerator/ denominator by 5
=[tex]\frac{1}{2}[/tex]
[tex]\frac{4}{5}[/tex] ← is in simplest form
[tex]\frac{6}{10}[/tex] ← divide numerator/denominator by 2
= [tex]\frac{3}{5}[/tex]
[tex]\frac{8}{12}[/tex] ← divide numerator/denominator by 4
= [tex]\frac{2}{3}[/tex]
[tex]\frac{4}{5}[/tex] is the only fraction given in simplest form
The price of a DVD is $24.00 plus 8% sales tax.What is the sales tax on this DVD in dollars and cents?
A) 25
B) 0.8
C) 1.92
D) 30
Answer:
Your answer is C) 1.92
Hope this helps ^_^
Answer:
Sales tax is $1.92 or 192 cents.
Step-by-step explanation:
Given the price of a DVD is $24.00 plus 8% sales tax.
we have to find the sales tax on this DVD in dollars and cents.
The sales tax is 8% can be calculated as
8/100 X $24
1.92
In cents
as one dollar equals 100 cents
∴ 1.92 dollar = $1.92 = 192 cents
Hence, sales tax is $1.92 or 192 cents.
So your answer is C!!
Rich and Betsy Cuik started a small business. They manufacture a microwavable coffee-to-go cup called Cuik Cuppa Coffee. It contains spring water and ground coffee beans in a tea-bag-like pouch. Each cup costs the company $1.00 to manufacture. The fixed costs for this product line are $1,500. Rich and Betsy have determined the demand function to be q = -1,000p + 8,500, where p is the price for each cup.
Write the expense equation in terms of the demand, q.
Express the expense equation found in part (a) in terms of the price, p.
Answer: E= 1.00q + 1,500
Step-by-step explanation:
Find the third, fifth, and tenth terms of the sequence described by the rule.
A(n)= -5+ (n - 1)(6)
A(3) =
(Simplify your answer.)
A(5) =
(Simplify your answer.)
A(10) =
(Simplify your answer.)
Find the area of the circle.
Answer:
8.938
Step-by-step explanation:
Answer:
dont at me if its wrong but i think its the second one
Step-by-step explanation:
PLEASE WILL GIVE BRAINLIEST!!
Step-by-step explanation:
Hey there!
According to the figure;
9v = 31° + 4v + 44° { The exterior angle is equal to the sum of opposite adjacent interior angles}
9v-4v = 44°+31°
5v = 75°
v = 75°/5
Therefore, v= 15°.
Hope it helps...
Find all multiples of 6 that are less than 40
Multiply 6 by numbers 1 -6:
To get:
6, 12, 18, 24, 30,36