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.
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There are 5,000 books in the town's library. Of these, 4,300 are fiction. To find the percent of the books that are fiction, first set up the percent equation. Then find the percent.
A. 4,300 = m / 5,000
B. 4,300 = m x 5,000
C. 5,000 = m / 4,300
D. 5,000 = m x 4,300
Answer:
B
Step-by-step explanation:
The percent of the books that are fiction is 86% and the percent equation is 4300=m×5000. Therefore, option B is the correct answer.
Given that, there are 5,000 books in the town's library.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Let the percent of the books that are fiction be m
So, m= 4300/5000
4300=m×5000
Percentage =4300/5000 ×100
= 86%
The percent of the books that are fiction is 86% and the percent equation is 4300=m×5000. Therefore, option B is the correct answer.
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find the distance and midpoint of a segment with the following endpoints: (5,-1) and (-9,-1)
Answer:
[tex]d = 14[/tex]
[tex](-2,-1)[/tex]
General Formulas and Concepts:
Order of Operations: BPEMDASDistance Formula: [tex]d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Midpoint Formula: [tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]Step-by-step explanation:
Step 1: Define
(5, -1)
(-9, -1)
Step 2: Find distance d
Substitute: [tex]d = \sqrt{(-9-5)^2+(-1-(-1))^2}[/tex]Simplify: [tex]d = \sqrt{(-9-5)^2+(-1+1)^2}[/tex]Subtract/Add: [tex]d = \sqrt{(-14)^2+(0)^2}[/tex]Evaluate: [tex]d = \sqrt{196}[/tex]Evaluate: [tex]d = \14[/tex]Step 3: Find Midpoint
Substitute: [tex](\frac{5-9}{2},\frac{-1-1}{2})[/tex]Subtract: [tex](\frac{-4}{2},\frac{-2}{2})[/tex]Divide: [tex](-2,-1)[/tex]Which ratio is less than 15 Over 24
A. 1/2
B. 7/8
C. 19/24
D. 6/8
Answer:
A
Step-by-step explanation:
what is the slope in the equation y=2x + 3?
Answer:
the answer is m = 2
Step-by-step explanation:
Try using Symbolab, I use it all the time it gives the correct answer and it gives good explanations.
hope this helps
Answer:
Slope=2
Step-by-step explanation:
Remember the equation: y=mx+b
m: is your slope
b: is your y-intercept
HELP ME ANSWER THESE 2 QUESTIONS MY PARENTS ARE ABOUT TO PUNISH ME IF I DONT DO IT (SHOW WORK OR ANSWER WILL NOT COUNT)
Answer:
what are the questions hurry and tell me
Tristan charges a flat rate of $16 for
each small lawn that he mows. He
decided to increase his rate to $20.
What is the new rate as a percent of
the old rate? Show your thinking.
Answer:
125%
Step-by-step explanation: because 25% of $16 is $4 and it's a $4 increase of the already 100% making 125%
Select the correct locations on the graph. Select the lines that represent functions.
Answer:
bruh there isnt a graph or anything we cant answer it
Step-by-step explanation:
Answer:
where is it
Step-by-step explanation:
3
Lee has -£13 in his bank account. Every week he gets paid £45, and
spends £60. How much will Lee have in his bank account after 3 weeks?
Answer:
Lee has -£13 in his bank account.
Every week he gets paid £45, and spends £60.
IN 3 WEEKS
He gets paid --> £45 · 3 = £135
He spends money --> £60 · 3 = £180
£135 - £180 = -£45
He had -£13 initially
He now has --> -£13 - £45 = -£58
What is the simple interest earned in 4 months on a $300
savings account at an annual rate of 5%?
Answer:
$60
Step-by-step explanation:
Multiply $300 (the total amount of money) by 0.05 (the annual rate)
300 x 0.05 = 15
Then, Multiply the number of months, to 15
15 x 4 = 60
$60 of simple interest earned in 4 months
given the domain (-2,2,4) what is the range for the relation 3x + y = 3?
Answer:
D
Step-by-step explanation:
Aubrey and Charlie are driving to a city that is 120 miles from their house. They have already traveled 20 miles, and they are driving at a constant rate of 50 mi/h. Part A Write the function that models their distance from home as a function of time. f(x) = x + Part B What is a reasonable domain for this situation? ≤ x ≤
their distance from home as a function of time
[tex]f(x)=50x+20[/tex]
The reasonable domain for this situation is
[tex]0\leq x\leq 2[/tex]
Given :
Aubrey and Charlie are driving to a city that is 120 miles from their house. They have already traveled 20 miles, and they are driving at a constant rate of 50 mi/h.
Given driving speed is 50 miles per hour
They already travelled 20 miles. We need to frame linear equation because we are given with constant rate.
Linear equation is [tex]f(x)=mx+b[/tex]
where m is the constant rate and b is the initial miles travelled
m=50 and b=20
the function f(x) is the distance from home
[tex]f(x)= 50x+20[/tex]
Now we find out the domain x. Given that they travelled 120 miles
so f(x) is 120
[tex]120=50x+20\\120-20=50x\\100=5x\\x=2[/tex]
Domain is the number of hours travelled
hours cannot be negative . So the domain x for this situation is
[tex]0\leq x\leq 2[/tex]
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A twelve-hour clock is set at the correct time on the afternoon of May 17th. Somebody knocked the clock off the wall and now it loses 6 minutes per day. How much time will the clock be behind 3 weeks later?
Answer:
126 minutes (or 2 hours and 6 minutes)
Step-by-step explanation:
7 days in a week times 3 weeks = 21 days
6 minutes a day times 21 days = 126 minutes behind
hello! um what is the equivalent to 3/7?
Answer:
9 goes in the blank
Step-by-step explanation:
Since 21 divided by 7 is 3 then you would have to multiply 3 to the numerator to get the equivalent. Hope this helped :)
Answer:
9/21
Step-by-step explanation:
multiply the numerator and denominator by 3 and you will get 9/21
Identify the equation of the line graphed (I need help can someone explain)
Answer:
D.) 5x - 2y = 2
Step-by-step explanation:
1. Find all of the options and convert them to slope-intercept form by isolating y. If you isolate y on all of them, you should get that A is y =-2/5x - 1, B is y = 2/5x - 1, C is y = -5/2x - 1, and D is y = 5/2x - 1.
2. Use logic. This line cannot be negative, because negative lines go up to down, not down to up. That cancels out the possibility of A.) and C.) being answers. Now, we know that the slope has to be more than 1 because it is more compressed than that of a line with a slope of 1. The only slope that is more than 1 is D, so that makes D the answer (If you didn't understand this step, go to step 3).
3. Find the slope (This step does not need to be done if you understood Step 2). Take 2 points to be able to find the slope. Two random points on this line are (2,4) and (0,-1). Next, plug them into the formula to find slope. 4-(-1)/2-0 = 5/2, so the slope is 5/2. The only equation with a slope of 5/2 is D. D is the answer.
Answer: D.) 5x - 2y = 2
Write an equation in point slope form of the line passes through the point (-6,6) ) and has a slope of m=3/2
Answer:
slope intercept would be y=3/2x+15
and
point slope would be y-6=3/2times(x+6)
Step-by-step explanation:
3
..
4) through: (-2,5), slope
2.
Answer:
y - 5 = 2(x + 2)
General Formulas and Concepts:
Point-Slope Form: y - y₁ = m(x - x₁)
x₁ - x coordinate
y₁ - y coordinate
m - slope
Step-by-step explanation:
Step 1: Define
Slope m = 2
Point (-2, 5)
Step 2: Create equation
y - 5 = 2(x + 2)
What is the expected value of the random variable with the given probability distribution? If necessary, round your answer to the nearest hundreth.
A) 0.62
B) 1.62
C) 3.70
D) 4.33
Berks Lanes charges $4 per game of bowling and $5 for the shoe rentals. If Roberto met his friends to play and paid for 5 games and one shoe rental, how much did he pay in all?
What is the y-intercept. Describe how you know in both the table and the graph.
Answer:
(4,0)
Step-by-step explanation:
The car traveled 42.5 miles per gallon of gas. If the gas tank in the car could hold 16.5 gallons, how far can the car travel on one tank of gas? (Don't round answer)
Please, help I am really confused!
Answer:
2.57575758
Explanation:
42.5 / 16.5
You and your cousin are walking through the lunchroom when you both trip. Your trays hit the ground and both lunches fly through the air in parabolic paths until they hit your friend on the top of the head. If your lunches had not landed on your friend’s head, then your hamburger would have landed on the floor 12 feet away and your cousin’s chili would have landed 16 feet away. Your hamburger reaches a height of 13 feet and your cousin’s chili reaches a height of 6 feet. How tall is your friend? Explain.
Answer: quit
Step-by-step explanation:
The water level of a lake is at 35ft. It is rising at a rate of 3 inches per day. How many days will it take the lake to reach 40 ft?
How does anyone know how to prove parallel lines, especially when there are two pairs of them?
Answer:
Step-by-step explanation:
If two lines are cut by a transversal so that any pair of alternate interior angles are congruent, then the lines are parallel. If two lines are cut by a transversal so that any pair of corresponding angles are congruent, then the lines are parallel. You can use these converses to decide whether two lines are parallel.
PLS HELP ASAP
WILL MARK BRAINLIEST
Answer:
the answer would be clld i am pretty sure yeah hopefully it is right and yeah
Step-by-step explanation:
Question 121 pts
Daniel had $30 to spend at the fair. If the admission to the fair is $8 and the rides cost $1.25 each, what is the greatest number of rides Daniel can go on?
Answer:
17 rides
Step-by-step explanation:
30-8=22
22 divided by 1.25=17.6 and then you cant go on without 1.25 so 17
A group of people planned to go to the amusement
park. Adult tickets are $45.00 and child tickets are $20.
There are two adults in the group. If the budget for the
trip is $600, what is the greatest number of children
that can attend.
Answer:the greatest amount of children that can go is 30
Step-by-step explanation:
$20 x 30= $600
If the dollar store is 5 miles away from my house, and my dad walks at 5 Mph, why has it taken my dad 12 years to come back?
Given that 4x−5y=39
Find y when x=3
Give your answer as an improper fraction in its simplest form.
Answer:
- [tex]\frac{27}{25\\}[/tex]
Step-by-step explanation:
4x−5y=39
for x=3
12 - 5y = 39
-5y = 39 -12
-5y = [tex]\frac{27}{5\\}[/tex]
-y = [tex]\frac{27}{25\\}[/tex]
y = - [tex]\frac{27}{25\\}[/tex] = -1 [tex]\frac{2}{25\\}\\[/tex]
-27/5 or -5 2/5
Step-by-step explanation:
4x-5y=39 while x=3
4(3)-5y=39 add x into bracket
12-5y=39 result of 4*3
12-5y-12=12-39 substrate non variable number to each side
5y = -27 the result from upper substraction
y= -27/5 the result mixed fraction form -5 2/5
help asap pleaseee!!!
Since it is asking you to graph heres what it should look like. Since -4/3 is the slope it should be a negative line (going down) and the 8 is the y-intercept (where the line hits the y axis) And I didnt draw the numbers because it's going by 1's. Hope this helps!
A question on a test asks students to find the speed at which a car travels. The graph shows a proportional relationship between the distance traveled in miles and time in hours. Billy incorrectly says that the speed of the car is 1/60 mile per hour. What is the speed of the car? What error might Billy have made?
Answer:
Step-by-step explanation:
Since, speed of a car = [tex]\frac{\text{Distance traveled}}{\text{Time taken}}[/tex]
From the graph attached,
A point (1, 60) lies on the line shown in graph.
At this point speed of the car = [tex]\frac{\triangle y}{\triangle x}[/tex]
[tex]=\frac{60-0}{1-0}[/tex]
= 60 miles per hour
But Billy says the speed of the car is [tex]\frac{1}{60}[/tex] miles per hour.
So the error in the Billy's answer is that he has used the wrong formula to calculate the speed.
(As per Billy, speed = [tex]\frac{\text{Time taken}}{\text{Distance covered}}[/tex])
