Given :
A curve : 3x² - 2xy + y² = 11
To Find :
The slope of the line tangent to the curve 3x^2-2xy+y^2=11 at the point (1, -2).
Solution :
Differentiating given curve w.r.t x is :
6x - ( 2y + 2xy' ) + 2yy' = 11
Putting the point ( 1, -2) in above equation, we get :
6 - ( 2(-2) + 2y' ) - 4y' = 11
6 - ( -4 + 2y' ) - 4y' = 11
10 - 6y' = 11
6y' = -1
[tex]y' =\dfrac{-1}{6}[/tex]
Therefore, the slope of the line tangent to the given point is [tex]y' =\dfrac{-1}{6}[/tex] .
Answer:
5/3
Step-by-step explanation:
The previous explanation was incorrect because they forgot to differentiate the other side of the equation (11), which would actually become 0, and make the answer 5/3
PLEASE SOMEONE HELP ME SOLVE THIS!!!
A leaking pond loses 12 gallon of water in 23 hours How many gallons of water will it lose in 31 hours
Answer:
The volume of water the pond will lose in 31 hours is 17.71 gallons.
Step-by-step explanation:
Given;
Rate of water leakage, R = 12 gallon of water in 23 hours
[tex]R = \frac{12 \ gallons}{23 \ hours}[/tex]
In 31 hours the volume of water leaked is calculated as;
[tex]V = \frac{12 \ gallons}{21 \ hours} \times 31 \ hours\\\\V = 17.71 \ gallons[/tex]
Therefore, the volume of water the pond will lose in 31 hours is 17.71 gallons.
For the second quarter of 2015, Apple sold 61.0 million iPhones. This represented a year- over-year increase of 40%. What were the sales for iPhone for the same quarter in the previous year (rounded to the nearest 10,000)?
Answer:
It sold 43.57 iPhones for the same quarter in the previous year.
Step-by-step explanation:
It sold 61.0 million iPhone, which is an increase of 40% over the value of the previous year x.
This can be interpreted as:
61 million is 140% = 1.4 of the previous year amount, that is, x. So
[tex]1.4x = 61[/tex]
[tex]x = \frac{61}{1.4}[/tex]
[tex]x = 43.57[/tex]
It sold 43.57 iPhones for the same quarter in the previous year.
A $450 washing machine is on sale for 15% off.
What is the discount?
What is the sale price?
What is the total price including the 7% sales tax
Answer:
67.5=discount
382.5= Sale Price
Total=409.27
Step-by-step explanation:
450/100=4.5
4.5*15=67.5
67.5=discount
450-67.5
382.5= Sale Price
382.5(1.07)
Total=409.275
Find the value of x in the triangle shown
Answer:
5
Step-by-step explanation:
you need to use the Pythagorean theorem
a^2+b^2=c^2
a&b=sides
c=hypotonuse
plug the side values into the equation
4^2+3^2=c^2
16+9=c^2
25=c^2
you have to square root 25 to find c itself
c=5
Answer : would be 5
Because a triangle that has a sequence of the number 3 & 4, or 3 & 5, or 4 & 5 will always consider of the number 3,4 and 5.
Also if te triangle did consist of different numbers the Pythagorean theorem ( a^2 + b^2 = c^2 ) can be use.
So in this case it’ll be 3^2 + 4^2 = c^2
9 + 16 = c^2
25 = c^ 2
Then we square root both sides and the answe will be : 5 = c
correct answer only!!!
Answer:
yea I'm not sure but maybe 40
A line graph does NOT:
a.
show trends clearly
c.
use percentages to display data
b.
allow viewers to make predictions about data
d.
show specific values of data
Answer:
show trends clearly. that's the answer
PLS HELP ME FIND THE MEASURE OF THE ANGLE TY I APPRECIATE YOUR TIME& HELP <333
Answer:
I think its 90 degrees.
Step-by-step explanation:
Its a right angle
Answer:
180
Step-by-step explanation:
52 + 90 = 142
180-142=38
YXZ =180
(I'm going off based on what I was taught)
1. Jiyoung spent $82 at Uniqlo on shirts and shorts. She lost the receipt but knows that the shirts are
$11 each, and the shorts were $9 each. If Jiyoung bought 5 shirts, how many shorts did she buy?
2. Normally, Bath and Body Works sells scented lotions for $9 each. During the holidays, they have a
special deal: $15 for 3 lotions. If Angela buys 6 lotions, how much money would she save if she paid
for the holiday special instead of the regular price?
3. Game cards go for $3 for 10 cards. If Angelina spent $18 on cards, how many cards does she have
in total?
4. Liana has Apple music, which costs $17 each month. One month, she buys 8 songs for $2 each. How
much money did she spend on her Apple music account that month?
5. A gardener uses 4 plots of land to plant 5 fruit trees each. On each of the fruit trees, there are 3
pieces of fruit. If the gardener picks 17 fruits in total, how many pieces of fruit are there left on the
land?
6. Alisha is composing a pop song. Her song has 6 half notes, which have 2 beats each, and 12 whole
notes, which have 4 beats each. Alisha gives her song to a composer, who divides the notes into
groups of 4. How many groups are there in total?
7. The Harry Potter book series has 7 books. Each book has around 400 pages each. If it takes Irwin 1
month to finish 200 pages, how many months will it take Irwin to finish the entire book series?
8. Most movies are around 2 hours long. Martin spends a full day watching 4 movies. During winter
break, he has a whole week to watch movies. If he needs to add 2 hours each day for lunch and
dinner, how many hours has Martin wasted watching movies and eating?
9. Johinder can type 30 words a minute. He spends 4 hours typing a book. If divides his book into 20
chapters, how many words are in each chapter?
10. There are 12 students in a 4
th grade class. Mr. Erwin needs is printing math packets for the class and
needs one for himself as well. Each math packet has 6 pages, and Mr. Erwin also needs an extra page
for his answers. How many pages does he need to print out in total?
11. On a chessboard, two team have 16 pieces each. Half of the pieces are pawns, and they are all
destroyed. If 2 knights are also destroyed, how many pieces are left in play?
12. Azita has 24 coworkers. She is going to buy donuts for them. Dunkin Donuts sells donuts in boxes
of 6. She buys 9 boxes of donuts. After everyone else eats 2 donuts, how many are left for Azita?
13. Ursula buys 300 ounces of beef from the supermarket. She splits the beef into 6 groups and makes
meatballs with them. If she makes 25 meatballs with each group, how much does each meatball
weigh?
ANSWER ALL OF THIS FFOR ME PLS WITH EXAMPLES
The amount of money Karen will have in her savings account after 15 weeks can be determined using the expression below:
d + 15x
where d represents the dollar amount currently in the account, and x represents the dollar amount Karen will add to the account each week.
If Karen currently has $20 in the account and adds $3 to it each week, how much should Karen have in the account after 15 weeks?
A)S38
B) $65
C) S105
D) $303
HELP URGENT PLEASEEEEE
Answer:cccc
Step-by-step explanation:
ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc should be right
First you want to make sure they are the same measurement.
Therefore we need to make ft into inches
4 ft = 4 x 12 = 48 inches
48 in to 6 in
48/6 to 6/6
8 in to 1 in
C would be the correct answer
A map of the United States is drawn to a scale of 1 in. = 400 mi. If San Francisco and Salt Lake City are 900 miles apart, how far apart will they be on the map?
Answer:
2.25 inches
Step-by-step explanation:
400+400 is 800 then 1/4 is .25 so that would make it 100 out of the 400 add that to 800 = 900 so its 2.25 inches
Question
Express the inequality -2 8 using interval notation.
Provide your answer below:
B FEEDBACK
MORE INSTRUCTIO
Content attribution
Answer:
(-2, 8)
Step-by-step explanation:
To express any given inequality, note the following:
✔️< or > means the end value or the beginning value referred to is not included.
✔️ ≤ or ≥ indicates that the end of beginning value is included.
✔️ "( )" when used in writing an inequality in interval notation means an end or beginning value is not included.
✔️. "[ ]" means the end or beginning value is included.
Now let's express -2 < x < 8 using interval notation.
✅The beginning value is -2, which is < x. This means -2 is not included. Therefore, we would start our interval notation by stating this as: "(-2"
✅The end value is 8. x < 8. The "<" sign means 8 is not included. Thus, this statement would be expressed in interval notation as "8)"
✔️Combining both together, the inequality is experessed in interval notation as (-2, 8)
What is ____ of the x-intercept is
The
always zero.
A . X-coordinate
B. Y-coordinate
The x-intercept is Y-coordinate always zero which is the correct answer that would be an option (B).
What is a graph?A graph can be defined as a pictorial representation or a diagram that represents data or values.
What is x-Intercept?The x-intercept is defined as an intercept that is located at the x-axis of the plane, is the location or coordinate from where the line crosses
The general form of the linear equation, where m and b are constants, is written as y = mx + b. . As a result, the value of the y-coordinate in the corresponding linear equation will always be zero when it crosses the x-axis.
The y-coordinate for the x-intercept and the x-coordinate for the y-intercept are both zero. Another name for the x-intercept is the horizontal intercept.
Therefore, the x-intercept is Y-coordinate always zero which is the correct answer that would be an option (B).
Learn more about the x-intercept here:
https://brainly.com/question/14180189
#SPJ6
The top speeds for a sample of five new automobiles are listed below. Calculate the standard deviation of the speeds. Round to four decimal places. 170, 160, 130, 165, 125
Answer:
20.92
Step-by-step explanation:
Given the data:
X : 170, 160, 130, 165, 125
Standard deviation (s) :
s = √Σ((X - m)² / n)
m = mean
n = sample size
Mean , m = Σx/n
m = (170 + 160 + 130 + 165 + 125) / 5
m = 750/5
m = 150
((X - m)² / n - 1)
[(170-150)^2 + (160-150)^2 + (130-150)^2 + (165-150)^2 + (125-150)^2] / (5-1)
= 1750 / 4
= 437.5
s = √437.5
s = 20.9165
s = 20.92
If James randomly chooses his ride in the morning and in the evening, what is the probability that he'll take the same mode of transportation twice?
Answer:
10.89 percent chance
Step-by-step explanation:
if there are 3 choices that means he has a 33 percent chance to choose any ride
Answer:
1/3
Step-by-step explanation:
Drag the tiles to the correct boxes to complete the pairs.
Match each division expression to its quotient,
Answer:
1/3, 1, 3/25, 1/2, 36/49
Step-by-step explanation:
When dividing fractions you flip the second fraction and multiply across
Answer:
1 = 1/3 2 = 1 3 = 3/25 4 = 1/2 5 = 36/49
Step-by-step explanation:
Is zero a positive or negative number?
Answer:
Zero is a neutral number.
Because zero is neither positive nor negative.
Find x & y so that quadrilateral is a parallelogram. (Look at image) please help!!
Answer:
y = 2 and x = -3
Step-by-step explanation:
we know that opposite sides of a parallelogram are equal so
7y + 3 = 12y - 7
12y - 7y = 3 + 7
5y = 10
y = 10 / 5
y = 2
Now
-6x = -4x + 6
-6x + 4x = 6
-2x = 6
x = 6 / - 2
x = - 3
Hope it will help :)❤
A circle railroad crossing sign has diameter of 30inches which measurement is closest to the area of the sign in square inches
the price of a pair of shoes increases from $50 to $64. What is the percent increase. Please Help, god bless
Answer:
Step 1: Calculate the change by subtracting old cost ($50) from the new cost ($64)
Step 2: Divide that change by the old cost ($50). You will get a decimal number
Step 3: Convert the decimal number to a percentage by multiplying by 100%
Step-by-step explanation:
Try this first
What is the answer to this specific question please and thank you
Which of the following equations is equivalent to 4 x + 6 = 1 ?
Answer:
x=-5/4
Step-by-step explanation:
4x+6=1
4x=1-6
4x=-5
x=-5/4
Find the missing exponent
Answer:
the missing exponet is 72
Step-by-step explanation:
you do that because you do 18 times 4
When flipping a coin once and rolling a six-sided die,
what is the probability of the coin landing on heads and rolling a multiple of three?
Answer:
Explanation: When you flip a coin there are two possible outcomes (heads or tails) and when you roll a die there are six outcomes(1 to 6). Putting these together means you have a total of 2×6=12 outcomes.
Natalia paid $38.95 for three medium-sized pizzas and a salad. If Natalia paid $11.98 for the salad, how much did each pizza cost?
Find the value of each variable. What are x and y ?
Answer:
Step-by-step explanation:
since 105 + z is a straight line we know it equals 180 so we can use this equation
180 = 105 + z
simplify
75 = z
the since we know that all quadrilaterals equal 360 degrees we can add our two given number and z then subtract from 360:
102 + 85 + 75
= 262
now subtract
360 - 262
= 98
y = 98
hope this helps <3
Write the equation in standard form
using factoring.
f(x) = (x + 2)(x + 1)
Answer:
f(x)=x^2+3x+2
Step-by-step explanation:
A rental car company charges $75 per day to rent a car and $0.05 for every mile driven. Serenity wants to rent a car, knowing that:
She plans to drive 500 miles.
She has at most $340 to spend.
Write and solve an inequality which can be used to determine
x
x, the number of days Serenity can afford to rent while staying within her budget.
Answer:
Inequality:75x+25_<340
x<_4.2
Step-by-step explanation:
The other guy seemed like a butt. Its okay sometimes we miss something in class and need help. THATS OKAY! Welp hoped this helped. I got this straight from delta so this IS correct. lol no butts its correct!! Hope this helped! ^_~
an hour before Showtime only 160 people are seated for a recital according to ticket sales 95% of the people have yet to arrive how many tickets were sold for the recital
Answer:
answer is 152
Step-by-step explanation:
this is an ratio proportion question