What is the sum of the roots of the quadratic $4x^2 - 4x - 4$?
Answers
9514 1404 393
Answer:
1
Step-by-step explanation:
The sum of roots of quadratic ax^2 +bx +c = 0 is -b/a. Here, that means the sum of roots is ...
-(-4)/4 = 1
The sum of the roots is 1.
Answer:
1/2
Step-by-step explanation:
By Vieta's formulas, the sum of the roots of $ax^2 + bx + c$ is given by $\dfrac{-b}{a}$. For this quadratic, that value is
\[ \frac{-b}{a} = \frac{-(-4)}{4} = 1.\]
Since the sum of the roots is $1$, the average of the roots is $\boxed{\dfrac 1 2}$.
Alternately, we could factor $4$ out of every term of this quadratic, giving $4(x^2 - x - 1)$. Since $4 \cdot 0 = 0$, any number that is a root of $x^2 - x - 1$ will also be a root of $4(x^2 - x - 1)$. Thus, the problem can change to finding the sum of the roots of $x^2 - x - 1$.
Since the coefficient of the linear term is $-1$ and this is the opposite of the sum of the roots, we find that the sum of the roots is equal to $1$, and the average is $\boxed{\dfrac 1 2}$.
Related Questions
The school that Eduardo goes to is selling tickets to a fall musical. On the first day of ticket salesthe school sold 3 adult tickets and 7 student tickets for a total of $81. The school took in $94 onthe second day by selling 4 adult tickets and 7 student tickets. Find the price of an adult ticketand the price of a student ticket.A) adult ticket: $6, student ticket: $13B) adult ticket: $13, student ticket: $6C) adult ticket: $17, student ticket: $9D) adult ticket: $19, student ticket: $8
Answers
Answer: B) adult ticket: $13, student ticket: $6
Step-by-step explanation:
Let adults tickets be written as a
Let student tickets be written as s
We then use the information given in the question to form equation. This will be:
3a + 7s = 81 .......... equation i
4a + 7s = 94 .......... equation ii
Subtract equation i from ii
a = 13
Adult tickets cost $13
From equation i
3a + 7s = 81
We put the value of a = 13
3(13) + 7s = 81
39 + 7s = 81
7s = 81 - 39
7s = 42
s = 42/7
s = 6
Students ticket cost $6
what is the domain and range of {(-11,11), (-8,8), (0,0), (13,-13)}
Answers
Answer:
domain = -11,-8,0,13 or the first coordinate
range = 11,8,0,-13 or the second coordinate
Step-by-step explanation:
Find the slope and y-intercept of the following graph.
Answers
Answer: Slope is 2/3, y intercept is 3.
4. Identify the Y-Intercept from the table:
Answers
Answer:
Y-intercept = -1
Step-by-step explanation:
You can find the y-intercept by looking at the value of y when x is 0.
A man sells a mobile set for Rs 5,994 at a loss of 7.5%. How much money has he paid to buy the mobile. Also find his loss amount.
Answers
Answer:
Step-by-step explanation:
Sale price = 5994
Loss % = 7.5%
Remaining % = 92.5%
Purchase price should be = 5994 / 92.5%
Purchase price will be = 6480
Loss is price will be = 6480 - 5994
Loss = 486
Factor 2x^3-12x^2+16x
Answers
Answer:
2x ( x-4) (x-2)Step-by-step explanation:
Each week as part of her workout, Monica walks 0.5 mile, runs 1.6 miles, and then walks 0.75 mile.
How many total miles will Monica walk and run in a year? Reminder: there are 52 weeks in a year.
Enter your answer in the box.
Answers
Answer: 148.20 miles
Step-by-step explanation:
From the question, we are informed that every week as part of her workout, Monica walks 0.5 mile, runs 1.6 miles, and then walks 0.75 mile.
The total miles will Monica walk and run in a year will be calculated as:
Total miles walked in a week = 0.5 + 0.75 = 1.25 miles
Total miles run in a week = 1.6 miles
The total miles Monica walk and run in a year will then be:
= (1.25 + 1.6) × 52
= 2.85 × 52
= 148.20 miles
During one game, the Heat made 12 free throws. If their free throw percentage is 75%, how many free throws were attempted?
Answers
Answer:
16
Step-by-step explanation:
12 = 75%
4 = 25%
4 x 4 = 16
16 = 100%
Sorry if it's confusing but that's just how I think of it.
Answer:
12x100/75 = 16
Step-by-step explanation:
At Alpha's school, lunches cost $2 and the cafeteria cashiers begin to warn you when your account falls below $10. If Alpha has $38 in her account, in how many days will the warnings begin and how long will they continue? Write the inequality to express this.
Answers
Answer:
the warnings will begin in 12 days and last for 5 days
Step-by-step explanation:
38-10=28, 28÷2=12, 10÷2=5, so you get 12 and 5
What is the length of the missing side of this right triangle? WILL GIVE BRAINLIEST
Answers
Answer:
I think its about 9? being as if you look a it its close to 12 but nowhere near it.
a^2+12^2=15^2
a^2+144=225
a^2=81
sqrt(a^2)=sqrt(81)
a=9
a small water bottle holds 75% as much as a large water bottle.
if the small holds 36 units, how much does the large hold?
Answers
Capacity of larger bottle = 48 units
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.
Given,
small bottle holds 36 units of water
Let the large bottle holds x units of water
According to the question,
capacity of small bottle = 75% of capacity of large bottle
36 = 75/100 × x
⇒ x = 36 × 100 / 75
⇒ x = 3600/75
⇒ x = 48 units
Hence the larger bottle holds 48 units of water.
Learn more about percentage here:
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plsss helppppp i need this answer rlly bad!!
Answers
Answer:20
Step-by-step explanation:
set it up like 4/5 = x/25 and cross multiply
Sneaks-R-Us buys sneakers from the manufacturer for $24.50 each. The store adds a 50% markup. What is the selling price, the retail price?
Answers
Answer:
Sneaks r us sells the sneakers for $36.75
Step-by-step explanation:
Write the equation of the line with a slope of -2/5 and goes through the point
(-15, 5)
Answers
Answer:
y=[tex]-\frac{2}{5} x[/tex]-1
Step-by-step explanation:
Lightening Pizza has a special: If customers order 4 pizzas, each pizza will cost $4.44. Mr.Peele orders 4 pizzas and wants to tip the driver 20% of the cost of the order. How much should Mr. Peele tip, round up to the nearest cent?
Answers
Answer:
21.31
Step-by-step explanation:
First do 4.44x4 then you get 17.76
and 20% of 17.76 is 3.552
you add 17.76 and 3.552 to get 21.312 which you round to the hundrenth which is 21.31
If 15 hamburgers cost $75.00, what is the cost of 1 hamburger?
Answers
Answer:
75.00 divided by 15 equals 5 dollars for 1 burger
Step-by-step explanation:
Answer:
$5
Step-by-step explanation:
75 ÷ 15 = 5
Evaluate if k = 21 and j = 9
Answers
Answer:
16
Step-by-step explanation:
k/3 + j = 21/3 + 9 = 7+9=16
Answer:
16
Step-by-step explanation:
so the problems is 21/3+9
so i write it down first
21/3+9
then ima divide 21 by 3 which equals 7
21/3=7
then im add 7+9
7+9=16
so the answer is 16
what’s 2/7x-7 = 9x-4
Answers
Step-by-step explanation:
[tex] \frac{2}{7} x - 7 = 9x - 4[/tex]
[tex] \frac{2}{7} x - 9x = - 4 + 7[/tex]
[tex] \frac{2}{7} x - \frac{63}{7} x = 3[/tex]
[tex] \frac{ - 61}{7} x = 3[/tex]
[tex]x = 3 \times \frac{7}{ - 61} [/tex]
[tex]x = - 0.344[/tex]
Find the slope of the line passing through the points (3, 8) and (-2, 5).
Answers
Answer:
3/5
Step-by-step explanation:
m = y2 - y1
x2 - x1
m = 5-8
-2 - 3
m = 3/5
Find the minimum, maximum, and range for the given set of data.
{23.5, 22.1, 24.0, 28.6, 26.3, 29.2, 21.0, 22.7, 25.5, 22.3, 21.6}
A.
minimum = 21.0, maximum = 29.2, range = 50.2
B.
minimum = 21.0, maximum = 29.2, range = 8.2
C.
minimum = 22.1, maximum = 26.3, range = 48.4
D.
minimum = 22.1, maximum = 26.3, range = 4.2
Answers
Answer:B
Step-by-step explanation:
1. 9
2. 6
3. 3
4. 81
Help plz giving out brianlest and god bless you
Answers
Help ASAP if you want brainliest, five stars, thanks, and friends list.
Answers
Answer:
11(r+t)+32
Step-by-step explanation:
I need help please
Answers
Answer:
the answer would be 81
Step-by-step explanation:
6 to the second power would be 36 then you would multiply 36x2 and it would equal 72. then you would do 2x6 which is 12. then 72+12-3= 81
ANY MATH EXPERTS PLS HELP RN I GOT 30 MIN LEFT I PUT 100 POINTS
Answers
Answer:
Step-by-step explanation:
x y
0 6
24 0
Points are (0,6) and (24,0)
Answer:
that what i got
Step-by-step explanation:
uhm which one idk thankssss
Answers
Answer:
The answer is A and C
Step-by-step explanation:
Supplementary angles added together = 180.
Special right triangles
Find j
Thank you for any help ;)
Answers
a = 12.12436 = 7√3
j = 24.24871 = 14√3
∠α = 30° = 0.5236 rad = π/6
h = 10.5
area = 127.30573 = 147√3/2
perimeter = 57.37307
inradius = 4.43782
circumradius = 12.12436 = 7√3
Answer is
j = 24.24871 = 14√3
If you left $25.00 on your table for a $21.50 meal, what was the percent of the tip?
16.3%
15.0%
14.0%
18.4%
Answers
Answer:
16.3
Step-by-step explanation:
The percent of the tip was 14%.
The correct option is C.
What is a percentage?A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.
Given:
If you left $25.00 on your table for a $21.50 meal,
the tip = 25 - 21.50 = 3.5
Let the percentage is n.
Then applying percentage formula,
n = 3.5 x 100/25
n = 14
Therefore, 14% is the required percentage value.
To learn more about the percentage;
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Put the following equation of a line into slope-intercept form, simplifying all fractions.
9x+6y=36
Answers
Answer:
x= -2/3 y +4
Step-by-step explanation:
[tex]x = \frac{ - 2}{3} y + 4[/tex]
Answer: y = 3/2x - 6
Write an equation for the line in slope-intercept form.
Answers
Answer:
The equation of the line is y = -4x + 2
712.8036 rounded to the nearest
Answers
Answer:
To the nearest whole number = 713
To the nearest tenth = 712.8
To the nearest hundredth = 712.804
Step-by-step explanation:
You didn't finish writing what you were going round it to so I'm going to give you several answers.
