The equation 4x²+8xy+ky²-9 = 0 will have a pair of straight lines when k = 0.
What is an auxiliary equation?An equation obtained from the standard form of a linear differential equation by replacing the right member by zero.
Given that, an equation having a pair of straight line 4x²+8xy+ky²-9 = 0
The auxiliary equation of a line is given by, ax²+2hxy+by²+2gx+2fy+c = 0
or, abc-2fgh-af²-bg²-ch²= 0
Comparing with the given equation,
a = 4, h = 4, b = k, g = 0, f = 0 and c = -9
4k(-9)+0-0-0+9(4)² = 0
36k = 144
k = 4
Hence, The equation 4x²+8xy+ky²-9 = 0 will have a pair of straight lines when k = 0.
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Use both the first and second derivative tests to show that f(x) = 3x2 − 6x + 1 has a relative minimum at x=1.
Step-by-step explanation:
Given: f(x) = 3x^2 − 6x + 1. x ∈ (-∞, ∞)
now differentiating f(x) w.r.t. x we get
f'(x) = 6x-6
equating it 0 we get
x = 1, which is a critical point
Now using second derivative test to check relative maxima or minima
f''(x) = 6 >0
⇒ x=1 is a relative minima.
also, x=1 f(1) = 3-6+1 = -2
A bus traveled 330 miles between two cities. If the bus traveled for 6 hours, how
many miles did the bus travel per hour?
Answer:
55 miles per hour
Step-by-step explanation:
.......ur welcome.......
330÷6=55
we divide the amount of miles by the time it took the bust to travel
A bus traveled 330 miles between two cities. If the bus traveled for 6 hours,, The bus will travel approximately 55 miles per hour.
To determine the number of miles the bus traveled per hour, we need to divide the total distance traveled by the time taken.
Given:
Total distance traveled = 330 miles
Time taken = 6 hours
To find the miles per hour, we divide the total distance traveled by the time taken:
Miles per hour = Total distance traveled / Time taken
Miles per hour = 330 miles / 6 hours
Miles per hour ≈ 55 miles per hour
Therefore, the bus traveled approximately 55 miles per hour.
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Full Question
A bus traveled 330 miles between two cities. If the bus traveled for 6 hours, how many miles did the bus travel per hour?
(No graph Needed)
Christine biked 36 miles in 6 hours. What is her average speed in miles per hour? Please answer
Answer:
6 mph
Step-by-step explanation:
36 divided by 6
Answer:
6 mph
Step-by-step explanation:
To find his average speed for each mile per hour, you start by dividing with the miles by the hours:
[tex]36\div6=6[/tex]
If you multiply 6 by 6, you'll get 36.
6 is your final answer!
Which of the following is a numerical expression that involves addition?
x + 5
3 + 5
5x
6 – x
Answer:
a i think im sorry if wrong
Any helpers pls ?will give brainliest
Answer:
26
Step-by-step explanation:
when x is 0, y = 26
also y = mx+b where b is the y intercept b is 26
Answer:
26
Step-by-step explanation:
x=0
f(0)=-3x+26=-3*0+26=26
a line has a slope of 1 and 1 and a y-intercept of -15. what is its equation in slope intercept 6
Answer:
y = x -15
Step-by-step explanation:
Evaluate the following using
powers of ten rules.
10/652.3
Please help will mark brainliest:)
Answer:
65.23
Step-by-step explanation:
We divide the inside number by the outside number. We can first right this problem as 652.3/10. Using power of ten rules we can move the decimal point one to the left. Making the answer 65.23
(0,0); y = 4/5x+7 help me
Answer:
(-8.75, 7)
Step-by-step explanation:
I hope this helped.
The following sequence is arithmetic. Fill in the missing terms.
12 , ? , ? , ? , 18, ? ...
Answer:
12,13.5,15,16.5,18,19.5
Step-by-step explanation:
just add 1.5
Kim bought four bottles of water and 2 candy bars at a snack shack. Steve bought one bottle of water and 7 candy bars from the same snack shack. A bottle of water cost $1.25 and all candy bars are the same price. If Kim and Steve spent the same amount of money, how much does one candy bar cost?
$0.70
$0.75
$1.25
$1.33
Answer:A
Step-by-step explanation:
1 bottle is 1.50
4*1.50=5
5+1.25= the total
5divided by 7=0.70
Double check your work I’m not sure if I’m right!
Which statement below accurately describes the data in the table?
A)
More than 75% of the students prefer Alternative or Hip Hop music.
B)
40% of students prefer Hip Hop.
C)
The mode of the data is Alternative Music,
D)
More than 25% of students prefer Country or Rock Music.
Answer:
The answer is A:More than 75% of the students prefer Alternative or Hip Hop music.
Step-by-step explanation:
Help plz ASAP for 20pts
Answer:
Not sure if this is correct but this is what I found.
area of sector=74.84
radius = 8
angle of sector=?
74.84=1/2×8²×angle of sector
74.84=32 × angle of sector
74.84/32= angle of sector
2.33875=angle of sector
Step-by-step explanation:
Sorry if it is incorrect.
Need ASAP will give brainliest!
Answer:
c
Step-by-step explanation:
hiiii
the surface area 5cm x 14cm x 6cm
please help me solve for x and find missing side lengths and angle measures,,
Answer: 90
Step-by-step explanatio
Answer:
the angle measure for angles T and V would be 127 because they are on opposite locations from each other. the angles S and U would 53 because T and U are coplemantery angles (180 degrees) so you subtract. 180-127 to get 53. To find x, on angle S, we simply subtract 1 from 53 (53-1) and divide the answer by 2. To find the lengths of the sides, put them next to each other and separet
them by an equal sign. subtract 3y from both sides of the equation and add 5 to both sides of the equation to get 3y=12. then divide 12 by 3 to get 4 so y=4. Then, simply replace the y with a 4 and solve the equations of the sides.
which property is BEST to use when combining 3/5 + 1/4 + 2/5? A) distributive property B) identity property of addition C) additive inverse property D) commutative property of addition
Answer:
D Community property of addition
Step-by-step explanation:
Answer:
d
Step-by-step explanation:
Youll thank me later!
Answer:
Step-by-step explanation:
thx
prove the identity. 25 points + brainliest to whoever explains/shows work.
Answer:
Truth
Step-by-step explanation:
sin (2x)/sin (x) - cos (2x)/ cos (x) = sec (x)
If you look at sin (2x) cos (x)/ sin - cos (2x) sin (x)/ cos (x) sin (x) =
sin (2x) cos (x) - cos (2x) sin (x)/ sin (x) cos (x) = sec (x) yes still equals sec (x)
Alex records the running time—the number of minutes a movie lasts from start to finish—of 50 popular movies. The distribution of times, in minutes, is displayed in the histogram below.
Answer:
You forgot to attach the question and the histogram.
Is your question “the interval containing the most movies” ? If yes, then the answer is :
Interval 90-100 minutes
Step-by-step explanation:
A histogram is a chart that is used to represent data in form of bars.
Like every other chart, it consists of both the x and y axis. The y axis contains the frequency or percentage of occurrences while the x axis contains the range or intervals.
To determine the interval with the most occurrences, that is the interval containing most movies, we look for the bar with the most height. The bar that is tallest amongst others has the most movies in its running time.
From the attached histogram, the interval containing the most movies is the 90- 100 minutes interval.
This simply means that from Alex’s record, out of the 50 popular movies, more movies run with the 90-100 minutes interval.
PS: view the attached histogram
Answer:
There are two problems like this, one involving median and the shape.
Here are your answers for both.
Shape is skewed right, this is because it decreases towards the right, like a hill. (C)
Extra info/this part isnt right: It would be skewed left but it isn't because it is not decreasing towards the left like a hill.
The median is between the interval 90-100, because it looks to be the typical number. (A)
Paul's house has an area of 1,650 square feet. He plans to add another room on to his house. The new rectangular addition will have dimensions 12 feet by 15 feet. What is the area of the house after the new room has been added?
PLEASE HELP
Answer:
1,830 sq. ft.
Step-by-step explanation:
12 x 15= _180_
1,650 + 180=_1,830__
which one should I be picking?
Answer:
x = 9
Step-by-step explanation:
Given a segment joining the midpoints of 2 sides of a triangle, then
the segment is half the length of the 3rd side , that is
3x = 0.5 × 54 = 27 ( divide both sides by 3 )
x = 9
Can someone help me solve? Simplify each expression show work
Ms. Seith had 4 7/12 boxes of jelly beans but she ate 2 1/12 of the jelly beans on her way to school. How many jelly beans were left in the box when she arrived at school?
Answer:
ur mom
Step-by-step explanation:
O0O
i need help asap PLEaSSSSSSSSAE
Answer:
c
Step-by-step explanation:
For A-D, choose Yes or No to indicate whether the situation can be represented by a negative number.
A. A student answered a 5-point question correctly.
B. Mila lost 30 points answering a question incorrectly.
C. A dog loses 13 pounds.
D. The average temperature in a city last month was 68°F.
OYes No
OYes No
OYes No
OYes No
Answer:
A. NO
B. YES
C: YES
D: NO
Step-by-step explanation:
In 2010, the population of a city was 124,000. From 2010 to 2015, the population
grew by 5%. From 2015 to 2020, it fell by 4%. To the nearest 100 people, what was
the population in 2020?
Answer:
is 125,000
Step-by-step explanation:
Lorenzo reads at a rate of 45 words per minute. If he reads at a constant rate, how many words can he read in 6 minutes?
Answer:
270
Step-by-step explanation:
45 * 6 = 270
11. A rate written as 80 miles per hour is an example of a
(2 points)
A.Ratio
B.Equivalent Ratio
C.Unit Rate
please help me i am begging you. its one question. I WILL GIVE BRAINLIEST!!!!!
Answer:
3og -5 “times (x)” 3
Step-by-step explanation:
(3og minus 5) times 3
I don’t have time to explain but I hope this helps, I’m in a rush rn I got to do something
Sue invested $2400 at a 3% simple interest rate for 18 months. How much did she earn on her investment after the 18 months?
Answer:
sinple interest= principle*rate*time/100
SI= 2400*3*1.5/100
SI= 108
AMOUNT= SI + PRICIOLE
AMOUNT= 108+2400
AMOUNT= 2508
{ I converted 18 months to 1.5 years}