Yes , the equation 3x² + 11x + 10 = 0 is a quadratic equation and the roots are x = -5/3 and x = -2
What is Quadratic Equation?
A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c = 0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.
The roots of the quadratic equations are
x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )
where ( b² - 4ac ) is the discriminant
when ( b² - 4ac ) is positive, we get two real solutions
when discriminant is zero we get just one real solution (both answers are the same)
when discriminant is negative we get a pair of complex solutions
Given data ,
Let the equation be represented as A
Now , the value of A is
3x² + 11x + 10 = 0 be equation (1)
Now , the equation is of the form ax² + bx + c = 0 , where the value of a = 3 , b = 11 and c = 10
So , the coefficient a is has the variable x² and equation 3x² + 11x + 10 = 0 is a quadratic equation
The roots of the quadratic equations are
x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )
Substituting the values in the equation , we get
x = [ -11 ± √ ( ( 11 )² - 4 ( 3 ) ( 10 ) ) ] / 2 ( 3 )
On simplifying the equation , we get
x = [ -11 ± √ ( 121 - 120 ) ] / 6
x = ( -11 ± 1 ) / 6
So , the two roots of the equations are
x = ( -11 - 1 ) / 6 and
x = ( -11 + 1 ) / 6
x = -2 and
x = -5/3
Therefore , the values of x are -5/3 and -2
Hence , the roots of the quadratic equations are -5/3 and -2
To learn more about quadratic equations click :
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if one jar of coffee costs $y, what will be the cost of four jars of coffee
Answer:
hi
Step-by-step explanation:
i think so
if one jar of coffee costs y$ then 4 jars of coffee costs
4y$
have a nice day
Helppppp please it’s timed
Answer:
Estimated population of New Hampshire is
A. 35,000
Answer this, please.
Solve the system by substitution 5x+2y=17 -4x+7=y
HELP PLEASEEE
Answer:
y=−9/2 x+12
HEART IF IT HELPED!!
Which of these shapes can be classified as a polygon, quadrilateral, and a parallelogram?
Answer:
Step-by-step explanation:
Solve for x
PLEASE HELP ME DUE IN 10 MINS
Solve for x.
A) 4
C) 1
B) 10
D) 12
Answer:
A) 4
Step-by-step explanation:
3*4 = 12
1+12=13
z
Note: Figure is not drawn to scale,
If x = 4 units, y = 17 units, and z = 3 units, then what is the surface area of the rectangular prism shown above?
OA.
131 units
OB. 330 units
C.
204 units
D
262 units2
Help! Il give brainlest!
A (0,0) B(-6,0)
C (-6, 3)
(x,y) - (x + 6, y + 3)
Answer:
plz send full question
Step-by-step explanation:
according to your book
Express 21/10 as a decimal
Answer:
2.1
Step-by-step explanation:
yall this one too i need help quick guys plz and ty
Answer:
b. (4,2)
Step-by-step explanation:
step one: isolate x in the first equation
substitute x=6-y: [tex]\begin{bmatrix}2\left(6-y\right)-2y=4\end{bmatrix}[/tex]
[tex]\begin{bmatrix}12-4y=4\end{bmatrix}[/tex]
[tex]-4y=-8[/tex]
[tex]y=2[/tex]
step two: isolate y in the second equation, substitute y=2
[tex]x=6-y[/tex]
[tex]x=6-2[/tex]
[tex]x=4[/tex]
Answer:
b
Step-by-step explanation:
Given the 2 equations
3x + 3y = 18 → (2)
2x - 2y = 4 → (2)
Multiplying (1) by 2 and (2) by 3 and adding the result will eliminate the y- term
6x + 6y = 36 → (3)
6x - 6y = 12 → (4)
Add (3) and (4) term by term to eliminate y
12x + 0 = 48
12x = 48 ( divide both sides by 12 )
x = 4
Substitute x = 4 into either of the 2 equations and solve for y
Substituting into (1)
3(4) + 3y = 18
12 + 3y = 18 ( subtract 12 from both sides )
3y = 6 ( divide both sides by 3 )
y = 2
solution is (4, 2 ) → b
Help!! I'll give brainlist...
Answer:
c
Step-by-step explanation:
8 added to the product of 7 and x cubed
Answer:
7x³+8
Step-by-step explanation:
I'm guessing that you are looking for the equation
Olivia is an athlete. During training this morning, she ran three laps. It took her 5 6minute to finish the first lap. The second lap took her 1 12more minutes than the first lap. The third lap took her 1 10less minutes than the second lap. How much time did it take her to finish the third lap?
Answer:
First lap time = 5/6 minute
Second lap time = 11/12 minute
Third lap time = 49/60 minute
Step-by-step explanation:
:))
Olivia is an athlete. During training this morning, she ran three laps. It took her 5 6minute to finish the first lap. it takes her to finish the third lap time in 49/60 minutes.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Olivia is an athlete. During training this morning, she ran three laps. It took her 5 6minute to finish the first lap.
The second lap took her 1 12more minute than the first lap.
The third lap took her 1 10less minute than the second lap.
First lap time = 5/6 minute
Second lap time = 11/12 minute
Third lap time = 49/60 minute
Learn more about the unitary method;
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Please help, i need it for a test, I'll give you brainliest :]
Answer:
Step-by-step explanation:
C
if u put any links I will report
Answer:
72% increase
Step-by-step explanation:
688-400= 288 increase
288/400= 0.72
0.72x100=
72% increase
Leia is trying to find the best price for 6 pairs of colored shoelaces. If 3 pairs of colored shoelaces cost $20 at Sprint Sneakers, and 2 pairs of colored shoelaces cost $12 at Shoe Sanctuary, how many dollars will Leia save if she buys 6 pairs of colored shoelaces from Shoe Sanctuary instead of Sprint Sneakers?
Answer:16
Step-by-step explanation:
Sprint is 2shoe sanc. 2 for 12
2
4
6 36 - 20 is 16
12
24
36
3m^n+12mn^2 with an explanation please !
Can someone help me figure this out I'm completely lost and this is due in like an hour, the question is "Use the diagram to find the length of GH."
Answer:
GH = 4
Step-by-step explanation:
GH = AB due to congruency markings therefore
5y - 8 = 3y
-8 = =2y
4 = y
Answer:
GH=12
Step-by-step explanation:
You use what this other solution to the answer was. However, they did not include that GH is 3y, so while one y=4, 3y=12. Therefore, GH=12
pls help I need the full working thanks
Answer:
x=3
Step-by-step explanation:
so in order to solve this question we are going to plug in u for 2^x
3((2^x)/2)=2^x+4
3u/2=u+4
3u=2u+8
u=8
we can put 2^x back into the equation in order to find x
2^x=8
2^x=2^3
x=3
PLS HELP ME! I’m tired.
Answer:
30.5*10=350$
Step-by-step explanation:
you have to multiply the number without the decimal point then add it later but if its tenn u must move the place value of the decimal point 1 to the right.
hope it helps
Find the probability of getting 3 heads and 1 tail when flipping a coin 4
times. (write your answer as a reduced fraction)
pls
Answer:
The probability is 4/16 = 1/4
Step-by-step explanation:
To get 3 heads, means that one gets only one tail. This tail can be either the 1st coin, the 2nd coin, the 3rd, or the 4th coin. There are only 4 outcomes which have three heads....hope this helped
Lightning strikes Earth 1000 times in 10 seconds. How many seconds does it take for lightning to strike 7250 times? It takes seconds for lightning to strike 7250 times.
Answer:
1000 / 10 = 100 strikes per second. Now, multiply by 12 to find the number of strikes that occurred. 100 * 12 = 1200 strikes in 12 seconds. Part B: Divide the number of seconds to the number of lightning strikes to find the average rate. 10 / 1000 = 0.1 seconds per strike. Now, multiply by 7250 to find the number of seconds that passed.
Step-by-step explanation:
What is the surface area of the cylinder with height 6 in and radius 7 in? Round your answer to the nearest thousandth.
Answer:
571.77
Step-by-step explanation: I might be wrong so don't really trust me
The difference of 1 and twice a number is at most one third the
number(Which of the following models this description?
A. 21 – 2x<_ 1/3x
B. 21 – 2x = 1/3x
C. 21 – 2x >_ 1/3x
D. 21 – 2x < 1/3x
Answer:
Step-by-step explanation:?
MULTIPLE CHOICE !! HELP
Answer:
Its D
Step-by-step explanation:
Write two different
expressions to find the total cost of an item
that costs $a if the sales tax is 6%. Explain
why the expressions give the same result.
Answer:
Total cost = $a + 0.06a
Total cost = a(1 + 0.06)
Step-by-step explanation:
Given that :
Cost of item = $a
Sales tax = 6%
Total cost = cost of item + sales tax
Total cost = $a + (6% of a)
Equation 1:
Total cost = $a + 0.06a
Equation 2:
Total cost = $a + 0.06a
Total cost = a(1 + 0.06)
The population of town is 32600. about 27% are over 60 years old. About 19% are 16 or under. How many are between 16 and 60?
Answer:
Number of population between 16 and 60 =17,604
Step-by-step explanation:
population of town = 32600
Percentage of people over 60 years old=27%
Percentage of people 16 or under =19%
Percentage of people between 16 and 60= 100%-(27% +19%)
100-(46) =54%
Number of population between 16 and 60 =Percentage of people between 16 and 60 x population of town
=54% x 32600
=17,604
Aliyah rode her bike at a speed of 10 miles per hour for 1.5 hours and then traveled at a speed of 7.5 miles per hour for 2 hours. What is the total distance that Alyah rode her bike during this time?
Answer:
Step-by-step explanation:
S(peed) = 10 mph
time = 1.5 hours
distance = s * time
distance = 10 * 1.5 = 15 miles
s = 7.5 mph
t = 2 hours
d = s * t
d = 7.5 * 2 = 15
Here total distance = 15 + 15 = 30 miles.