The correct answers are option 1, Option 3 and option 4 which are:-
2(x² + 6x + 9) = 3 + 18
2(x² + 6x) = 3
x+3 = ±√21/√2
What is a quadratic equation?The polynomial having a degree of two or the maximum power of the variable in a polynomial will be 2 is defined as the quadratic equation and it will cut two intercepts on the graph at the x-axis.
We will check all three options one by one:-
2(x² + 6x + 9) = 3 + 18
2x² + 12x + 18 = 3 + 18
2x² + 12x -3 = 0
We are getting the original equation so it is correct.
2(x² + 6x) = 3
2x² + 12x = 3
2x² + 12x - 3 = 0
This is also right.
x+3 = ±√21/√2
Squaring on both the sides:-
( x + 3 )² = 21 / 2
x² + 6x + 9 = 21 / 2
2x² + 12x + 18 = 21
2x² + 12x = 21 - 18
2x² + 12x -3 = 0
This is also right
Therefore the correct answers are option 1, Option 3 and option 4 which are:-
2(x² + 6x + 9) = 3 + 18
2(x² + 6x) = 3
x+3 = ±√21/√2
To know more about quadratic equations follow
https://brainly.com/question/1214333
#SPJ1
Answer:
A, C, D
A: 2(x2 + 6x + 9) = 3 + 18
C: 2(x2 + 6x) = 3
D: x + 3 = Plus or minus StartRoot StartFraction 21 Over 2 EndFraction EndRoot
Step-by-step explanation:
Got 100% on quiz
If f(x) = sin(x) and g(x) = sin(2x), then the derivative of f(x) + g(x) is
The derivative of f(x) + g(x) is cosx+2cos2x
Derivative : In mathematical calculus, the derivative is the rate of change of a function at a instant point.
Derivative of a function is denoted by dy/dx, where derivative of y is happening with respect to x.
We have to add f(x) and g(x), then differentiate the whole addition with respect to x.
Given that, f(x) = sin(x) & g(x) = sin(2x)
So, f(x) + g(x) = sin(x) + sin(2x)
Now, differentiating with respect to x we get,
(f(x)+g(x))' = d/dx(sinx) + d/dx(sin 2x)
= cosx+2cos2x
Derivative of f(x) + g(x) = cosx+2cos2x
Learn more about derivative here :
https://brainly.com/question/23819325
#SPJ10
Between every pair of distinct points, there is a positive unique number called the ??? , which can be determined as the ??? of the corresponding real numbers of the two points.
The positive number between every pair of distinct points is known as the distance and it can be found as the absolute value of the difference between the corresponding real numbers.
How is the distance found?The distance represents the space between a pair of distinct points. This is called the distance postulate.
In order to find the distance, you would need to solve for the absolute value of the difference between the real numbers that are at the two points.
Find out more on the distance postulate at https://brainly.com/question/24748568.
#SPJ1
Answer:
The positive number between every pair of distinct points is known as the distance and it can be found as the absolute value of the difference between the corresponding real numbers.
Step-by-step explanation:
Identify the category to which the following statement belongs: Brandon has two weeks to decide on the topic of his research paper.
O Not important - Not Urgent
O Not Important - Urgent
O Important - Not Urgent
O Important-Urgent
Answer:
Important- not urgent
Step-by-step explanation:
The research paper is important but since Brandon has two weeks to decide it is not urgent.
Simplest form of ratio 25g:3kg
Answer:
look at the picture.
Step-by-step explanation:
look at the picture.
Two cars leave Chicago to go to a town in that suit up north. One car is traveling 13 mph faster in it arrived in four hours the other car took five hours to get there find the speed of each car
The speeds of the two cars will be 52 mph and 64 mph.
How to find the speed of an object?If the object is going linearly, and at constant speed, then the speed of that object is given by the distance it traveled to the time it took to travel that distance.
If the object traveled D distance in T units time, then that object's speed is S = D/T
Two cars leave Chicago to go to a town in that suit up north.
One car is traveling 13 mph faster in it arrived in four hours the other car took five hours to get there.
Let the distance traveled by both cars is x.
Speed of the first car = x/5
Speed of the second car = x/4
So, the equation form will be
x/5 + 13 = x/4
(65 + x )/ 5 = x /4
4(65 +x ) = 5x
260 + 4x =5x
x = 260
Speed of the first car = x/5 = 52mph
Speed of the second car = 52 + 13 = 65 mph
The speeds of the two cars will be 52 mph and 64 mph.
Learn more about speed;
https://brainly.com/question/1988783
#SPJ1
4. During a camping trip, a group went one-third of the total distance by boat, 10km by foot and One-sixth of it by riding horses. Find the total distance of the trip. Plss answer thiissss
Answer:
20 km
Step-by-step explanation:
So 1/3 = 2/6
2/6 = distance traveled by boat + 1/6 traveled by riding horses = 3/6 = 1/2
Meaning the 10 km by foot left is the other half
find an equation equivalent to (x-2)^2 + (y + 2)^2 = 8 in polar coordinates
The circle equation in polar coordinates is:
[tex]r - 4*cos(\theta) + 4*sin(\theta) = 0[/tex]
How to change the coordinates of the circle equation?
Here we have the circle equation:
[tex](x - 2)^2 + (y + 2)^2 = 8[/tex]
First, we expand it to:
[tex]x^2 - 4x + 4 + y^2 + 4y + 4 = 8[/tex]
Now we can rewrite it as:
[tex]x^2 + y^2 -4x + 4y + 4 + 4 = 8\\\\x^2 + y^2 - 4x + 4y = 0[/tex]
Remember that:
[tex]x^2 + y^2 = r^2\\\\x = r*cos(\theta)\\y = r*sin(\theta)[/tex]
Replacing that, we get:
[tex]x^2 + y^2 - 4x + 4y = 0\\\\r^2 - 4r*cos(\theta) + 4r*sin(\theta) = 0[/tex]
That is the equation in polar form.
Now, because we can discard the solution r = 0, we can divide both sides by r to get:
[tex]r - 4*cos(\theta) + 4*sin(\theta) = 0[/tex]
To simplify it.
If you want to learn more about polar coordinates:
https://brainly.com/question/14965899
#SPJ1
The planet Earth is about 193,000,000 miles away from the sun, and the speed of light is approximately 1.86 × 10 5 miles per second. Which expression could you use to figure out how many seconds it takes the light from the sun to reach Earth?
Answer:
Speed of light 186000 miles/second.
it takes 500 seconds (approx 8 minutes) for light from the sun to reach Earth.
Step-by-step explanation:
Earth travels around the sun in a slightly oval-shaped orbit, known as an ellipse. Therefore, the planet's distance from the sun changes throughout the year.
However, the average distance from Earth to the sun is about 93 million miles (150 million kilometres). Scientists also call this distance one astronomical unit (AU).
A universe is a big place, and sometimes researchers use astronomical units to communicate how far celestial objects are separated from one another. For example, Jupiter orbits about 5 AU from the sun.
The distance between the earth and the sun d= velocity of light × time taken to reach light from the sun to earth
Distance from Earth to Sun=93000000 miles.
Speed of light = 186000 miles/second.
=> [tex]\frac{93000,000}{186000}[/tex]
=> 500 seconds.
=> 8.333 minutes
it takes 500 seconds (approx 8 minutes) for light from the sun to reach Earth.
Read to know more about:
https://brainly.com/question/24144885?referrer=searchResults
#SPJ10
This table represents a proportional relationship between x and y.
x 0.2 0.4 0.6 0.8
y 0.25 0.5 0.75 1.0
What is the constant of proportionality?
Enter your answer as a decimal in the box.
Answer:
x
Step-by-step explanation:
I got it right.........
Which expression is equivalent to...
Step-by-step explanation:
hope you can understand
need help with this question for geometry
Answer:
[tex]31[/tex]
Step-by-step explanation:
It's 31 degrees, I hope it is the right answer
The table shows the probabilities of certain prizes in a restaurant’s contest where the first 100 customers are winners.
A 2-column table with 6 rows. The first column is labeled prize with entries 1 dollar drink, 5 dollar meal, 5 dollar gift card, 10 dollar gift card, 20 dollar gift card, 100 dollar gift card. The second column is labeled number of prizes with entries 44, 25, 16, 10, 5, 1.
How does the $100 gift card affect the measure of center of the data?
It increases the mean value of the prizes.
It decreases the mean value of the prizes.
It increases the median value of the prizes.
It decreases the median value of the prizes.
A mean is an arithmetic average of a set of observations. The correct option is A.
What is Mean?A mean is an arithmetic average of a set of observations. it is given by the formula,
Mean = (Sum of observations)/Number of observations
Since the median is the middle value of the given data set, therefore, the median will not be changed for the given data set. But since the mean is the arithmetic average, therefore, the $100 gift will increase the mean value of the prizes.
Hence, the correct option is A.
Learn more about Mean:
https://brainly.com/question/16967035
#SPJ1
Answer:
this is the anwser
this
The sum of two numbers is ten. One number is twenty less than four times the other. Find the numbers
Answer:
6 and 4
Step-by-step explanation:
Let one number be x.
Then another will be : 4x - 20
In accordance with the question;
x + 4x - 20 = 10
5x = 10 + 20
x = 30/5
= 6
x = 6
4x - 20 = 4×6 - 20 = 4
So, the numbers are 6 and 4.
Ella wants to buy a home. The maximum loan she can get from the bank is $445,000
If Ella has $55,000 available to make a down payment, what is the highest valued home she can purchase?
Ella can buy a house worth $5 million
What is a Loan ?Loan is the amount of money borrowed from a bank or any other person , The amount has to be returned back with a Interest.
It is given that
The maximum loan Ella can get from the bank is $445,000
Ella has $55,000 available to make the down payment.
The highest value home that she can purchase is the sum of money she has and the maximum amount of money she can get from the bank.
It is given by
$445,000 + $55,000
$500,000
Therefore Ella can buy a house worth $5 million
To know more about Loan
https://brainly.com/question/11794123
#SPJ1
if A={4,7,10,13,17} and B={3,5,7,9}, then which of the following statements is true
A U B= {7}
B c A
B c B
Answer:
good questing it is something
Step-by-step explanation:
1-1-2- --3--1234-3
3-4
Q-
-4
-24
-4
-
q 43-
43-
3 4-3
4-
4-4
- answer is 2def not cap i need 5 poinnts i gues
Assume the domain of the function is {1,2,3,...}. Determine the theta notation for the function f(n)=7n^2+4n+2
We have that O(n²) is the theta notation for 7n² + 4n + 2.
Let's give big-Oh a formal definition:
O(g(n)) = {the set of all f such that 0 [tex]\leq[/tex] f(n) [tex]\leq[/tex] cg(n) for any n >= n₀ fulfilling positive constants c and n₀}
To show this
We need to find c and n₀ such that:
7n² + 4n + 2 <= cn² for all n >= n₀ .
Divide both sides by n², getting:
7 + 4/n + 2/(n²) <= c for all n >= n₀ .
If we choose n₀ equal to 1, then we need a value of c such that:
7 + 4 + 2 <= c
We can set c equal to 13. Now we have:
7n² + 4n + 2 <= 13n² for all n >= 1 .
Hence, 7n² + 4n + 2=O(n²)
Learn more about Big-Oh notation here-
brainly.com/question/14438669
#SPJ10
Help please
charles has $2.90 in coins. if he only has dimes and quarters and a total of 17 coins, how many quarts does he have?
Answer:
8
Step-by-step explanation:
8*25=2.00
2.00+.90=2.90
help fast please
i have no idea what to do in math so i need help
Answer:
see the attachment photo!
Mr Tong had some money. After giving $1300 to each 5 of his children, he had $450 left. How much money did he have at first
Answer:
Step-by-step explanation:
money given to children=1300x5
=6500
total money =6500+450
=6950
[tex]3.135x 789[/tex]
Answer:
Step-by-step explanation:
Use the parabola tool to graph the quadratic function f(x)=−(x−3)(x+1).
Graph the parabola by first plotting its vertex and then plotting a second point on the parabola.
The parabola has roots at x=3 and x=-1, so its vertex is halfway between those points, at x=1, and so the y-coordinate of the vertex is -(1-3)(1+1)=4.
Another point that lies on the parabola is (-1, 0).
Question
A company is considering producing some new Gameboy electronic games. Based on past records, management believes that there is a 70 percent chance that each of these will be successful and a 30 percent chance of failure. Market research may be used to revise these probabilities. In the past, the successful products were predicted to be successful based on market research 90 percent of the time. However, for products that failed, the market research predicted these would be successes 20 percent of the time. If market research is performed for a new product, what is the probability that the results indicate a successful market for the product and the product is actually not successful?
The probability that the results indicate a successful market for the product and the product is actually not successful is P=0.77.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
Events are given:
S: success
F: failure
MS: market research forecast a success
MF: market research forecast a failure
we have given:
P(S)=0.70
P(F)=0.30
P(S | MS)=0.90
P(F | MS)=0.20
we can derive that P(F | MF)=0.80.
We also can conclude that P(S | MF)=0.10.
We can calculate the probability of having a forecast of a failure,
[tex]P(MF | F) =\dfrac{ P(F | MF)P(F)}{ P(F | MF)P(F) + P(S | MS)P(S) }[/tex]
P (MF | F) = 0.24 / 0.31
P (MF | F) = 0.77
The probability that the results indicate a successful market for the product and the product is actually not successful is P=0.77.
Learn more about probability here;
https://brainly.com/question/11234923
#SPJ1
Cory drinks water from a bottle during a bike ride. The average amount of water, in
ounces, in his water bottle can be represented by the equation y = -8x+32, where y is the amount of water remaining after x hours. Based on the equation, what amount of water, in ounces, will remain in the bottle after Cory rides for 2 1/2 hours?
The amount of water will remain in the bottle after Cory rides for 2 1/2 hours will be;
⇒ y = 12 ounces
What is Equation of line?
The equation of line in point-slope form passing through the points (x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
The average amount of water, in ounces, in his water bottle can be represented by the equation,
⇒ y = - 8x + 32
Where, y is the amount of water remaining after x hours.
Now,
Since, The average amount of water, in ounces, in his water bottle can be represented by the equation,
⇒ y = - 8x + 32
Hence, The amount of water will remain in the bottle after Cory rides for 2 1/2 hours is,
Substitute x = 2 1/2 in above equation,
⇒ y = - 8 × 2 1/2 + 32
⇒ y = - 8 × 5/2 + 32
⇒ y = - 20 + 32
⇒ y = 12 ounces
Thus, The amount of water will remain in the bottle after Cory rides for 2 1/2 hours is,
⇒ y = 12 ounces
Learn more about the equation of line visit:
https://brainly.com/question/18831322
#SPJ2
please i need this fast
Answer:
the second option
Step-by-step explanation:
UV and AB are at a right Angie to reach other.
and
UV is parallel to ZY
Vikram drinks 6/10 of a litter of water after gym class and 33/100 of a litter of juice with his lunch Vikram says he drank a total of 39 hundredths of a litter. use the drop-down menus to explain why Vikram is not correct?
Answer: Vikram is not incorrect because he found the sum by adding the numerators and denominators
Step-by-step explanation: The first blank doesn't have a word so I answer it
Part B
Assume the statement is true for n=k. Prove that it must be true for n=k+1, therefore proving it true for all natural
numbers, n.
Hint: Since the total number of dots increases by n each time, prove that d (k) + (k+1)=d (k+ 1).
The inductive step is assuming that the statement is true for some n = k , where k is one of the values we want to prove the statement for, it shows that it is also true for n = k+1.
How to carry out Mathematical Induction?Suppose we have the statement 3n > 4n for all positive integers n.
Now, the statement above is false when n = 1 , since 3 is less than 4. However, it will be true for all other positive integers.
In that case, we can still prove this statement by induction for all integers n ≥ 2 .
Thus, the inductive step is assuming that the statement is true for some n = k , where k is one of the values we want to prove the statement for, it shows that it is also true for n = k+1.
Read more about Mathematical Induction at; https://brainly.com/question/24672369
#SPJ1
How do you write
f(x)=-5x^2-100x+8
in vertex form?
Find the equation of the line that
is perpendicular to y = -8x + 2
and contains the point (-4,1).
Answer:
Step-by-step explanation:
slope of line ⊥ to y=-8x+2
is -1/-8=1/8
eq. of line with slope 1/8 thro' (-4,1) is
y-1=1/8 (x+4)
8y-8=x+4
8y=x+4+8
8y=x+12
y=1/8 x+12/8
or
y=1/8 x+3/2
a teacher promised a movie day to the class that did better, on average, on their test. The box plot shows the results of the test
The question is incomplete. The complete question is
A teacher promised a movie day to the class that did better, on average, on their test. The box plot shown in the below-mentioned figure shows the results of the test.
Which class should get the reward, and why?
- The 2nd-period class should get the reward. They have the highest score, a perfect 100.
- The 2nd-period class should get the reward. They have a higher median.
- The 4th-period class should get the reward. Though the medians are the same, the first and third quartiles are higher, so the students did better on average than in the 2nd-period class.
- The 4th-period class should get the reward. Their lowest score is an outlier and should be thrown out.
The box plot shown in the question provides the information that
In 2nd period the minimum of the data is 77, first quartile is 78, median of the data is 89, third quartile is 92 and the maximum of the data is 100.
Hence, the mean of the results of 2nd period is
[tex]\frac{77+78+89+92+100}{5}=87.2[/tex]
In 2nd period the minimum of the data is 72, first quartile is 83, median of the data is 89, third quartile is 96 and the maximum of the data is 98.
Hence, the mean of the results of the 4th period is
[tex]\frac{72+83+89+96+98}{5}=87.6[/tex]
Hence, obviously, the 4th period is having more mean.
Moreover, we can observe that if more of the marks are on the higher side the average will automatically be more. Hence, as the first and the third quartiles are more on the 4th-period, so the average marks for the 4th period must be better.
So, just by observing the box plot, we can give the statement that "The 4th-period class should get the reward. Though the medians are the same, the first and third quartiles are higher, so the students did better on average than in the 2nd-period class. "
Therefore, the 4th-period class should get the reward. Though the medians are the same, the first and third quartiles are higher, so the students did better on average than in the 2nd-period class.
Learn more about box plots here-
brainly.com/question/1523909
#SPJ10
Determine the x and y intercepts of the equation y = -3x + 4.
Select one:
O a. y-int y = 4 and x-int x = 4/3
O b. y-int y = 4/3 and x-int x = 4
O c. y-int y = 4 and No x-int
O d. No y-int and x-int x =4/3
Answer:
O c. y-int y = 4 and No x-int
Step-by-step explanation:
In the slope-intercept equation y = -3x + 4, only slope and y-intercept are displayed as it is in slope-intercept format which is y = mx + b; m being the slope and b being the y-intercept.
There is no x-intercept present in a slope-intercept equation.
But due to the 4 being in the place of the y-intercept is the y-intercept of the graph and line depicted off this linear equation (slope-intercept equation).
Hence, the answer is C. Y-intercept = 4 and No x-intercept.