Answer:
The very end of the line at the coordinates (7, -5)
Step-by-step explanation:
The absolute minimum point of a graph is the lowest point in the domain of a function's graph. The lowest point on this functions graph is at the very end of the graph at the coordinates (7, -5)
suppose a finite model for an incidence geometry satisfies the additional axiom: every line has exactly three points lying on it. what is the minimum number of points needed for such a geometry? why?
In an incidence geometry with the additional axiom that every line has exactly three points lying on it, the minimum number of points required is 4.
This is because a line must have at least two-points to exist, and if it has only two points, it is not possible to have another point lying on it (since every line must have exactly three points).
Hence, there must be at least 4-points to create two lines such that each line contains exactly three points.
Also, with 4 points, it is possible to create 6 lines such that each line contains exactly 3 points, forming a configuration known as the Fano-plane, which is the smallest example of an incidence geometry that satisfies the given axiom.
Learn more about geometry:
https://brainly.com/question/28359671
#SPJ4
Scavenger Hunt
heard F. Use your answer to card F. to find the next
A
12 - x - 2x = -12
Answer:
Hi! The answer to your question is \(x = 8\)!
Step-by-step explanation:
☆*: .。..。.:*☆☆*: .。..。.:*☆☆*: .。..。.:*☆☆*: .。..。.:*☆
☆Brainliest is greatly appreciated!☆
Hope this helps!!
Stay Safe!!!
- Brooklynn Deka
1/8 divided by 5 = ??
Answer:
\(\frac{1}{40}\)
Step-by-step explanation:
Answer:
1/40
Step-by-step explanation:
\(\frac{1}{8}\) ÷ \(\frac{5}{1}\)
\(\frac{1 x 1 }{8 x 5}\) = 1/40
Factor and Solve.
x^4+7x^2+10=0
Answer:
second one
Step-by-step explanation:
Answer:
the second one
Step-by-step explanation:
x^4+7x^2+10=2
use the quadratic formula
hope this helps
brainliest?
carla believed that her teammates on the track team were faster than she was, so she began putting in extra practices in order to become just as fast as them. this is an example of . a. compensation b. rationalization c. regression d. displacement please select the best answer from the choices provided a b c d
Carla's behavior of putting in extra practices to become faster can be seen as an example of (Option A.) compensation. This is because she is trying to make up for her perceived lack of speed by working harder to become as fast as her teammates.
Carla began putting in extra practices in order to become just as fast as them. This is an example of: Option A. CompensationCarla's behavior of putting in extra practices to become faster can be seen as an example of compensation. This is because she is trying to make up for her perceived lack of speed by working harder to become as fast as her teammates.
By engaging in extra practices, Carla is attempting to compensate for her lack of speed and improve her performance. This is different from rationalization, which is the act of making excuses for one's behavior, or from regression, which is the act of reverting to a younger age in response to a stressful situation.
Finally, displacement is the act of redirecting one's emotions or anger onto another person or object.
Learn more about Compensation: https://brainly.com/question/13978016
#SPJ4
Suppose y varies jointly as x and z. Find y when x = –10 and z = 20, if y = 179 when x = –5 and z = –11. Round your answer to the nearest hundredth, if necessary
The value of y = -651. To find the value of y when x = -10 and z = 20, given that y varies jointly as x and z and y = 179 when x = -5 and z = -11, follow these steps:
Step 1: Understand that "y varies jointly as x and z" means y = kxz, where k is the constant of variation.
Step 2: Use the given values (y = 179, x = -5, z = -11) to find k. Substitute these values into the equation:
179 = k(-5)(-11)
Step 3: Solve for k:
179 = 55k
k = 179 / 55
k = 3.2545 (rounded to the nearest hundredth)
Step 4: Use the found value of k (3.2545) and the new values of x (-10) and z (20) to find the new value of y:
y = (3.2545) (-10)(20)
Step 5: Calculate y:
y = -651
So, when x = -10 and z = 20, y = -651.
Learn more about value here:
brainly.com/question/10987396
#SPJ11
A triangle has two angle measures of 20 degrees and 30 degrees. Find the third angle. This triangle is a(n) ________ triangle
Answer:
an obtuse triangle cause the other angle is more than 90
Step-by-step explanation:
Answer:130 degrees. it is scalene triangle
Step-by-step explanation:
all angles in a triangle add up to 180.
20+30=50
180-50=130
a scalene triangle has all sides different
Write 0.04 in scientific notation.
= 4 × 10-2
scientific notation
initially 5 grams of salt are dissolved in 20 liters of water. brine with a concentration of 2 grams per liter is added at a rate of 3 liters a minute. the tank is mixed well and is drained at 3 liters a minute. how long does the process have to continue until there are 20 grams of salt in the tank?
The process has to continue for approximately 2.86 minutes until there are 20 grams of salt in the tank.
We can use a mass balance approach to solve this problem. Let's start by calculating the amount of salt in the tank at any given time. We know that initially there are 5 grams of salt in 20 liters of water, so the concentration of salt is:
c1 = 5 g / 20 L = 0.25 g/L
As brine with a concentration of 2 grams per liter is added at a rate of 3 liters a minute, the concentration of salt in the tank increases at a rate of:
dc/dt = 2 g/L * 3 L/min = 6 g/min
At the same time, the tank is being drained at 3 liters a minute, so the volume of the tank remains constant. This means that the total amount of salt in the tank is changing at a rate of:
dm/dt = dc/dt * V = (6 g/min) * (20 L) = 120 g/min
We want to know how long the process has to continue until there are 20 grams of salt in the tank, which means we need to solve for the time t when the total amount of salt in the tank reaches 20 grams:
m = 5 g + (6 g/min) * t - (3 L/min) * t * (0.25 g/L) = 20 g
Simplifying this equation, we get:
6t - 0.75t = 15
5.25t = 15
t = 2.86 minutes
Therefore, the process has to continue for approximately 2.86 minutes until there are 20 grams of salt in the tank.
To know more about mass balance approach click here:
brainly.com/question/14301365
#SPJ4
sam has a rope that is 38 feet long. He cuts the rope into 2 pieces. One piece is 1.5 feet long .
How long is the other piece?
Answer:
36.5 feet long.
Step-by-step explanation:
38-1.5 is equal to 36.5, you subtract to find the other number, therefor one piece is 1.5 feet long and the other is 36.5 feet long.
Answer:
36.5 feet long
Step-by-step explanation:
38 - 1.5
= 36.5
PLEASE HELP I NEED THIS DUE FIR TMRRRRRRRRRRRR
The finite group G has normal subgroups M≤N such that for some set π of primes M and G/N are π-groups, while N/M is a π
′
-group. (For an example take G=Sym(4),N= Alt (4), M=V and π={2}.) Prove that the maximal π-subgroups of G are all conjugate and that the maximal π
′
-subgroups of G are all conjugate.
We have proved that the maximal π-subgroups and maximal π'-subgroups of G are all conjugate.
The following steps can be used to demonstrate that all of the maximal -subgroups and maximal '-subgroups of the finite group G are conjugate:
Let P and Q be two of the largest -subgroups of G. We must demonstrate that G contains an element g such that Q = gPg(-1). P and Q share the same order—a -number—because they are both maximal -subgroups. Consider the quotient group G/N, where N is the normal subgroup in the above statement. Since M is greater than N and G/N is a -group, it follows that P/N and Q/N are Sylow -subgroups of G/N.
According to Sylow's theorem, there is an element h in G/N such that Q/N = hP/Nh(-1). Now consider the preimage of h in G, which is denoted by g. Since h is in G/N, we have gN = h, which indicates that g(-1)hg is in P. Additionally, since Q = hPh(-1) for any element x in P, we have gxg(-1) in Q for that element. As a result, we have demonstrated that the maximal -subgroups of G are conjugate and that Q = gPg(-1).
In a similar vein, let R and S be two maximal '-subgroups of G. We must demonstrate that G contains an element g with S = gRg(-1). Again, because R and S are both maximal subgroups, their order, which is a number, is the same. Consider the quotient group N/M as the normal subgroup in the above statement. Since N/M is a '-group, R/M and S/M are Sylow '-subgroups of N/M. According to Sylow's theorem, there is an element k in N/M such that S/M = kR/Mk(-1). Now take into consideration the preimage of k in N, which is referred to as g.
Since k is in N/M, we have gM = k, which indicates that g(-1)kg exists in R. Additionally, for any element y in R, we have gyg(-1) in S because S = kRk(-1). As a result, we have demonstrated that the maximal '-subgroups of G are conjugate and that S = gRg(-1).
To know more about Subgroups, visit
brainly.com/question/30865357
#SPJ11
Please answer as many as you can
1. Best Buy was having a 20% off sale on all flat-screen TVs. What would the sale price of a $350.50 TV be?
2. Solve -3( x - 3) = 12
3. Factor 45t - 15
4. Simplify ( 3.5m + 2) - ( 4.3m - 8)
5. If the length of a rectangle is 6x - 2 and the width is 5x + 1, simplify an expression that will represent the perimeter.
I understand if you can't do all 5, but it would be greatly appreciated if you did.
Answer:
2. is x = -3
Step-by-step explanation:
-3( x - 3) = 12
multiply the things in the () by -3
-3x+9=12
subtract 9 from both sides
-3x+9-9=12-9
-3x=3
divide both sides of the equation by -3
x = -3
Answer:
1. 280.40
350.50*.20=70.10
350.50-70.10=280.40
2.x=−1
-3*3=--9+-3x
-3x/3= -1 x= -1
3.=15(3t−1)
Because 45t/15= 3 then 15/15=1
4. =−0.8m+10
Let's simplify step-by-step.
3.5m+2−(4.3m−8)
Distribute the Negative Sign:
=3.5m+2+−1(4.3m−8)
=3.5m+2+−1(4.3m)+(−1)(−8)
=3.5m+2+−4.3m+8
Combine Like Terms:
=3.5m+2+−4.3m+8
=(3.5m+−4.3m)+(2+8)
=−0.8m+10
Answer:
=−0.8m+10
5. Perimeter is adding all side sooo.22x -2
6x -2 + 6x-2= 12x - 4
5x +1 +5x+1= 10x+2
12x -4 +10 + 2= 22x -2
Step-by-step explanation:
Hope this helps you.^_^
write an equation in slope-intercept form for the graph shown (i will give brainliest whoever gets it right)
Answer:
y=-3x+2
Step-by-step explanation:
Samuel left his house at time zero and drove for 2 minutes to the store at a speed of 1 block per minute. Then he stopped and went into the store for 3 minutes. From there, he drove in the same direction at a speed of 5 blocks per minute until he got to the bank, which is 10 blocks away from the store. He stopped at the bank for 2 minutes. Then he drove home at a speed of 3 blocks every 2 minutes. Make a graph of showing the number of blocks away from home that Samuel is
x
x minutes after he leaves his house, until he gets back home.
The data is formed using the given information and a graph is plotted which can be used to find the distance of Samuel from the house x minutes after he leaves.
What is meant by distance?
Distance is a measurement of how far apart two things or points are, either numerically or occasionally qualitatively. The distance can refer to a physical length in physics or to an estimate based on other factors in common usage. The length of the entire journey taken to get from one point to another is the distance travelled. Travel distance is not a vector. Distance is exactly proportional to velocity when time is constant, hence speed is simply distance divided by time.
Time at which Samuel left the house = 0 min
Time taken to drive to the store = 2 minutes
Speed = 1 block/min
Time spent in the store = 3 min
Speed after coming out of the store and to the bank = 5 block /min
The distance between the store and the bank = 10 blocks
Time taken to reach bank = 10/5 = 2 min
Time spent in the bank = 2min
Speed to drive back home = 3 blocks / 2min = 1.5 block/min
Distance between bank and home = 12
Time taken to reach home = 12/1.5 = 8 min
The graph is plotted using this information
time blocks away
0 0
2 2*1 = 2
5 2
7 10+2 = 12
9 12
17 0
Therefore the data is formed using the given information and a graph is plotted which can be used to find the distance of Samuel from the house x minutes after he leaves.
To learn more about distance, follow the link.
https://brainly.com/question/26550516
#SPJ1
Consider this argument: LOGIC BASED, NOT PERSONAL EXPERIENCE
The coffee is hot or it is strong. The coffee is not strong, therefore it is not hot.
is the argument invalid or valid?
Answer:invalid
Step-by-step explanation:
Answer:
I would say Invalid
Step-by-step explanation:
Because if a coffee is hot it is strong and if a coffee is cold it would be strong still. (sorry if incorrect!)
supply of houses is determined by two variables (I and R) in the following way: h(1,R) = a log1 + b R + CR log1, where a, b, and c are all constants. How does housing supply respond to changes in I (a) and R (OR)? an an Select one: an a. ar an a+cR an I and an = b + clog1 2 an ī and a b+cR log1 = b + cR log1 O b. a1 an a+cR an C. ai and an an d. ar an + CR log 1 and aR = b + c log1
The housing supply function is given by h(I,R) = a log1 + bR + cR log1. The housing supply responds to changes in I with a rate of a, and to changes in R with a rate of b + c log1.
Based on the given equation, the housing supply (h) is determined by two variables: I and R. The equation shows that h is a function of R, with a log-linear relationship. The variable I only appears as a constant (a) in the equation, so changes in I do not directly affect the supply of houses.
On the other hand, changes in R (or OR, which is the same variable) do affect the supply of houses. Specifically, an increase in R leads to an increase in the supply of houses. The magnitude of this increase depends on the values of b and c in the equation.
To see this, we can take the partial derivative of h with respect to R:
dh/dR = b + cR/(ln(10))
This equation tells us how much the housing supply changes in response to a change in R. The derivative is positive (i.e. the supply increases) as long as c is positive. The larger c is, the greater the increase in supply for a given increase in R.
Therefore, the correct answer is:
b + cR/(ln(10))
To learn more about function, click here:
brainly.com/question/12431044
#SPJ11
Carrots costs $0. 99 per pound. Broccoli costs $1. 50 per pound. Jack buys 3. 5 pounds of carrots and 1. 25 pounds of broccoli. What is Jack’s total bill?
Using the concept of Unit Cost, $5.34 is Jacks` total bill for buying 3.5 pounds of carrot and 1.25 pound of broccoli.
The unit price is measurement used to represent the price of a particular good or service to be exchanged with the customers or consumers for money. The unit price refers to the price/unit of measures, such as price per pound, quart, ounce, or other units of weight or volume of the food package.
The unit price is important for both of customers and organizations. An organization cannot sustain without unit price itself for a long period by selling products at a lower price. Similarly, customers would not be able to buy the product if the value of the product is less than the price. The researcher suggests that the unit price information helps shoppers to save around 17-18% in supermarkets when they are educated on how to actually use it.
We are given Carrot cost of per pound is $0.99.
Therefore Carrot cost for 3.5 pounds=3.5×0.99= $3.465
Similarly, Broccoli cost of per pound is $1.50.
Therefore, broccoli cost for 1.25 pounds =1.25×1.50=1.875
Total bill = Broccoli cost+ Carrot cost
Total bill =3.465+1.875=$5.34
Hence,$5.34 is Jacks` total bill for buying 3.5 pounds of carrot and 1.25 pound of broccoli.
To know more about Unit Cost, visit here:
https://brainly.com/question/13873791
#SPJ4
Identify the hypothesis in the statement If it is monday, then the basketball team is playing
Chloe has a cabinet that is 4.24 yards in length. The cabinet is 3.27 yards longer than a stool. What is their total length? ...
Answer: their total length=5.21 yards
Step-by-step explanation:
Length of cabinet =4.24 yards which is 3.27 yards longer than a stool
Therefore, Length of stool =3.27 yards shorter than a stool
Length of stool =4.24 yards- 3.27 yards=0.97 yards
Total lengths of cabinet and stool=4.24 yards +0.97 yards=5.21 yards
Determine the probability of precipitation (PoP) using the formula below and the following
PoP = (C * A) * 100 percent
Where C is the confidence that precipitation will occurs somewhere in the forecasted area, and A equals the percentage of the area that will receive measured precipitation if it occurs.
a. A forecaster expresses confidence that there is an 80 percent chance of precipitation in the forecasted area, and it is expected to produce measurable precipitation over 90 percent of the area.
b. A forecaster expresses confidence that there is a 20 percent chance of precipitation in the forecasted area, and it is expected to produce measurable precipitation over 10 percent of the area.
The correct answer is a) the probability of precipitation is 72%. and b) the probability of precipitation is 2%.
The given formula to determine the probability of precipitation (PoP) is PoP = (C * A) * 100 percent where C represents the confidence that precipitation will occur somewhere in the forecasted area and A represents the percentage of the area that will receive measured precipitation if it occurs.
(a) If a forecaster expresses confidence that there is an 80% chance of precipitation in the forecasted area, and it is expected to produce measurable precipitation over 90% of the area, then the probability of precipitation is given as follows: PoP = (C * A) * 100 per cent C = 80%A = 90%PoP = (80% * 90%) * 100%
PoP = 72%.
Therefore, the probability of precipitation is 72%.
(b) If a forecaster expresses confidence that there is a 20% chance of precipitation in the forecasted area, and it is expected to produce measurable precipitation over 10% of the area, then the probability of precipitation is given as follows: PoP = (C * A) * 100 per cent C = 20%A = 10%PoP = (20% * 10%) * 100%PoP = 2%
Therefore, the probability of precipitation is 2%.
know more about probability
https://brainly.com/question/32117953
#SPJ11
Two birds are flying south for the winter. Bird 1 reaches its destination in 6.0 hours, while bird 2 reaches its destination in 12 hours. If bird 2 covers twice as much distance as bird 1, what is the ratio of their velocities (bird 1/bird 2)
Therefore, the ratio of the velocities of bird 1 to bird 2 is 1:1.
To find the ratio of the velocities of bird 1 to bird 2, we can use the formula:
Ratio of velocities = Distance / Time
Given that bird 2 covers twice as much distance as bird 1, we can let the distance covered by bird 1 be D. Therefore, the distance covered by bird 2 is 2D.
For bird 1:
Distance (D) = D
Time (T₁) = 6.0 hours
For bird 2:
Distance (2D) = 2D
Time (T₂) = 12 hours
Now, let's calculate the velocities for both birds:
Velocity of bird 1 = Distance / Time
= D / 6.0
Velocity of bird 2 = Distance / Time
= (2D) / 12
To find the ratio of their velocities, we divide the velocity of bird 1 by the velocity of bird 2:
Ratio of velocities = (D / 6.0) / ((2D) / 12)
Simplifying the expression:
Ratio of velocities = (D * 12) / (6.0 * 2D)
Ratio of velocities = 12 / 12
Ratio of velocities = 1
To know more about velocities,
https://brainly.com/question/28472381
#SPJ11
A contest offers 20 prizes, with first prize worth $12,000 and each successive prize worth $400 less than the preceding prize.
The 20th prize is $4400.
It is a sequence where the difference between each consecutive terms is the same.
Example:
2, 4, 6, 8 is an arithmetic sequence.
We have,
First prize = $12,000
Successive prize worth $400 less than the preceding prize.
Now,
We can make an arithmetic sequence.
12,000, 11,600, 11,200, ...
So,
a = 12,000
d = -400
The nth term of an arithmetic sequence.
= a + (n - 1)d
So,
The 20th prize.
= 12,000 + (20 -1)400
= 12,000 - 19 x 400
= 12,000 - 7600
= 4400
Thus,
20th prize = $4400
Learn more about arithmetic sequence here:
https://brainly.com/question/10396151
#SPJ9
PLEASE HELP!!!!! its Friday children uwu
this question isn't really math but yall smart !
Answer:
Mercury is smaller than Mars
anyone can help me this thankyou
Answer:
s² - 225 = 0
Step-by-step explanation:
Area of square = side * side
s * s = 225
s² = 225
s² - 225 = 0
What is the volume of a right rectangular prism with a length of 4.8 meters, a width of 2.3 meters, and a height of 0.9 meters?
4.968 m³
9.936 m³
11.94 m³
34.86 m³
Answer:
9.936
Step-by-step explanation:
V = Bh
B = base
base = Lengh x width
base = 4.8 x 2.3
base = 11.04
V = 11.04h
H = height
H = .9
V = .9 x 11.04
V = 9.936
Answer:
9.936 m³
Step-by-step explanation:
Lakha is arranging for a party to be held in the students' union. The use of the hall will be free but security costs of £300 will have to be met. The cost of the main band will be £2,500 and the supporting band will cost £450. Tickets will be priced at £15 each. On arrival, every ticket holder will be given a bottle of water, worth £1 per bottle. What are the total fixed costs for this event? A) £3,250 B) £2,500 C) £300 D) £2,950
The total fixed costs for the event amount to £2,800, which includes the security costs and the cost of the main band. Fixed costs are expenses that do not change with the number of attendees or sales.
To calculate the total fixed costs for the event, we need to identify the costs that do not change with the number of attendees. Based on the given information, the fixed costs include the security costs and the cost of the main band. Let's break it down:
Security costs: The security costs of £300 are fixed and do not depend on the number of attendees. This means the cost remains the same regardless of how many tickets are sold.
Cost of the main band: The cost of the main band is £2,500. Similar to the security costs, this cost is fixed and does not vary based on the number of attendees.
Therefore, the total fixed costs for the event would be the sum of the security costs and the cost of the main band:
Total Fixed Costs = Security Costs + Cost of Main Band
Total Fixed Costs = £300 + £2,500
Total Fixed Costs = £2,800
However, it's important to note that the cost of the supporting band, ticket prices, and the cost of the water bottles are not fixed costs. The cost of the supporting band and the cost of the water bottles are variable costs as they depend on the number of attendees. The ticket prices represent revenue, not costs.
Learn more about calculate here:
https://brainly.com/question/30151794
#SPJ11
the probability of winning on a slot machine game is 0.152. if you play the slot machine until you win for the first time, what is the expected number of games it will take?
The expected number of games it will take to win on a slot machine game with a probability of winning of 0.152 is approximately 6.579 games.
The expected number of games can be calculated using the formula for the expected value of a geometric distribution. In this case, the probability of winning on each game is 0.152.
The expected number of games is calculated as the reciprocal of the probability of winning. Therefore, the expected number of games is 1 divided by 0.152, which is approximately 6.579.
This means that on average, it is expected to take approximately 6.579 games to win on the slot machine. However, it's important to note that this is an average value and individual experiences may vary. Some players may win on their first few games, while others may take more games to win. Nonetheless, on average, it is expected to take approximately 6.579 games to achieve a win.
Learn more about probability here:
https://brainly.com/question/31828911
#SPJ11
the lowest temperature is usually around 3^\circ c3 ∘ c3, degrees, c, and the highest temperature is around 18^\circ c18 ∘ c18, degrees, c. the temperature is typically halfway between the daily high and daily low at both 10\text{ a.m.}10 a.m.10, start text, space, a, point, m, point, end text and 10\text{ p.m.}10 p.m.10, start text, space, p, point, m, point, end text, and the highest temperatures are in the afternoon.
The lowest temperature is usually around 3 degrees Celsius (3°C), and the highest temperature is around 18 degrees Celsius (18°C).
The temperature is typically halfway between the daily high and daily low at both 10 a.m. and 10 p.m. Additionally, the highest temperatures are usually in the afternoon.
During the morning, the sun starts to warm up the atmosphere, causing the temperature to rise from its lowest point. By 10 a.m., the temperature has increased but is not yet at its peak.
Similarly, during the evening, the sun starts to set, resulting in a gradual decrease in temperature from its highest point. By 10 p.m., the temperature has dropped but is not yet at its lowest point
The temperature at 10 a.m. and 10 p.m. is typically halfway between the daily high and daily low because it represents the transition period between the warmest and coolest parts of the day.
To Know More about Similarly visit:
brainly.com/question/29024060
#SPJ11
S(t)=-t^3+2t^2+(3/2) be the position of a particle moving along the x-axis at time t. At what time will the instantaneous velocity equal the average velocity over the time interval (0,4)?
Answer:
(2 + 2sqrt(7))/3
Approx 2.43
Step-by-step explanation:
The average velocity over [0,4] is
(s(4)-s(0))/(4-0)
So we need to find s(4) and s(0).
s(t)=-t^3+2t^2+(3/2)
s(4)=-4^3+2(4)^2+(3/2)
s(4)=-64+32+(3/2)
s(4)=-32+(3/2)
s(4)=-61/2
s(t)=-t^3+2t^2+(3/2)
s(0)=-0^3+2(0)^2+(3/2)
s(0)=3/2
s(4)-s(0)=-61/2-3/2=-64/2=-32
So the average velocity over the given interval is -32/4=-8.
Now we wanr to find t such that the instantaneous velocity, s'(t), is equal to the average velocity on the given interval
So we want to solve s'(t)=-8.
Let's differentiate.
s(t)=-t^3+2t^2+(3/2)
s'(t)=-3t^2+4t+0
We will need to solve the quadratic equation
-3t^2+4t=-8
Multiply both sides by -1
3t^2-4t=8
Subtract 8 on both sides
3t^2-4t-8=0
The discriminant,D, is b^2-4ac=(-4)^2-4(3)(-8)=16-12(-8)=16+96=112.
The quadratic formula is (-b pm sqrt(D))/(2a) where pm means plus or minus.
(4 pm sqrt(112))/6
sqrt(112)
sqrt(16)sqrt(7)
4sqrt(7)
So the solutions from the quadratic equation can be simplified further
(4 pm sqrt(112))/6
(4 pm 4sqrt(7))/6
(2 pm 2sqrt(7))/3