There are 2 tangent lines that pass through the point
[tex]y=\frac{1}{(-1+\sqrt{3)^2} } (x-1)+2[/tex]
and
[tex]y=\frac{1}{(-1-\sqrt{3)^2} } (x-1)+2[/tex]
Explanation:
Given:
[tex]y=\frac{x}{x+1}[/tex]
The point-slope form of the equation of a line tells us that the form of the tangent lines must be:
[tex]y=m(x-1)+2[/tex] [tex][1][/tex]
For the lines to be tangent to the curve, we must substitute the first derivative of the curve for [tex]m[/tex]:
[tex]\frac{dy}{dx} =\frac{d(x)}{dx}(x+1)-x^\frac{d(x+1)}{dx} \\ \\[/tex]
[tex]\frac{dy}{dx} =\frac{x+1-x}{(x+1)^2}[/tex]
[tex]\frac{dy}{dx}= \frac{1}{(x+1)^2}[/tex]
[tex]m=\frac{1}{(x+1)^2}[/tex] [tex][2][/tex]
Substitute equation [2] into equation [1]:
[tex]y=\frac{x-1}{(x+1)^2}+2[/tex] [tex][1.1][/tex]
Because the line must touch the curve, we may substitute [tex]y=\frac{x}{x+1}:[/tex]
[tex]\frac{x}{x+1}=\frac{x-1}{(x+1)^2}+2[/tex]
Solve for x:
[tex]x(x+1)=(x-1)+2(x+1)^2[/tex]
[tex]x^2+x=x-1+2x^2+4x+2[/tex]
[tex]x^2+4x+1[/tex]
[tex]x\frac{-4±\sqrt{4^2-4(1)(1)} }{2(1)}[/tex]
[tex]x=-2[/tex] ± [tex]\sqrt{3}[/tex]
[tex]x=-2[/tex] ± [tex]\sqrt{3}[/tex] [tex]and[/tex] [tex]x=-2-\sqrt{3}[/tex]
There are 2 tangent lines.
[tex]y=\frac{1}{(-1+\sqrt{3)^2} } (x-1)+2[/tex]
and
[tex]y=\frac{1}{(-1-\sqrt{3)^2} } (x-1)+2[/tex]
How many 150 ml bottles can be filled with 6 litres/
Answer:
40 bottles
Step-by-step explanation:
6liters=6000ml so I do 6000/150=40.Therfore 40 bottle of 150ml can fill a bottle wth 6 literes
AND SORRY FOR BAD GRAMMAR BUT I HOPE IT HELPS!!
Identify any transformations that are used in each image below.
Reflections - how many lines of symmetry and what specific type: vertical (y-axis), horizontal (x-axis), diagonal (y=x or y=-x)
Rotations - of which order or how many degrees/angle of rotation
a. Reflectional symmetry only. The mirror line is vertical along the center of the sunglasses. The left half mirrors over this line to get the right half, and vice versa. There isn't any rotational symmetry because we can't rotate the glasses (some angle between 0 and 360 exclusive of both endpoints) to have the image be the same as the preimage.
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b. Rotational symmetry only. The puzzle can be rotated 90 degrees and the before and after image will be the exact same. There isn't any reflectional symmetry here.
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c. Reflectional symmetry and rotational symmetry. Effectively a combination of parts a) and b). We have a horizontal line of symmetry to go with a vertical one. The angle of rotation is 180 degrees.
----------------------
d. Reflectional symmetry and rotational symmetry. Similar to part c). This time the angle of rotation is 360/3 = 120 degrees. There are 3 lines of symmetry and they all pass through a vertex of the triangle, and the symmetry lines are perpendicular to the opposite side.
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e. Reflectional symmetry and rotational symmetry. We can rotate 180 degrees and not change the image. There are two lines of symmetry which pass through the center, one line is horizontal and the other vertical.
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f. Rotational symmetry only. We don't have reflectional symmetry due to the smaller petals not matching up when reflections happen. But we can rotate the figure 120 degrees the same way we can with figure d.
I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER
x + 30 = 2x (since angleA = angle D, due to congruency between the two triangles.)
30 = 2x - x
30 = x
hope it helps...!!!
which is bigger 2m or 275cm
Answer:
275.
Step-by-step explanation:
If you convert 2m into CM you get 200.
If you convert 275 cm into M you get 2.75. So 275cm is bigger.
This figure represents a platform on a stage. The stage crew needs to paint it black. One gallon of paint will cover 40 square yards.
How many full gallons of paint does the crew need to buy in order to paint the entire platform?
Enter your answer in the box.
gallons
Answer:
14
Step-by-step explanation:
I took the test.
Answer:
14
Step-by-step explanation: I took the test
Can you please help
Answer:
1/12 inches
Step-by-step explanation:
1/2 = 6/12
then:
7/12 - 1/2
is equivalent to:
7/12 - 6/12 = (7-6)/12
= 1/12
To find the time it will take for a train
to travel from Springfield to Franklin,
d
where d
use the expression s,
represents distance and s represents
speed.
Find the time if the train travels
at a speed of 79
miles per
hour.
Your answer is incorrect
In the past year, Charmaine watched 28 movies that she thought were very good. She watched 80 movies over the whole year of the movies she watched,
what percentage did she think were very good?
0
?
Find all solutions to the equation
in the interval [0, 2π). Enter the
solutions in increasing order.
cos 2x = cos x
X = [?],
Remember: cos 20 = cos²0 - sin²0
Can y’all help me pls
Answer:
The change in expected height for every one additional centimeter of femur length.
Step-by-step explanation:
The slope represents how the value along the y axis is affected by the value along the x axis. So if x = femur length and y = expected height,
the slope is how the expected height is affected by the femur length.
Use the picture attached!!
How many lines of symmetry does the picture have?
A.
1
B.
3
C.
0
D.
2
Answer:
The Correct Answer is C.0.
Hope it hepls you Czn!
Please Mark me as Brainleast!!!!!!!!
I can buy a $1000 bond for $950. I get $50 / year and it matures in 20 years. What interest rate am I earning?
The interest rate you are earning on a bond that has a face value of $1000, a price of $950 and a coupon of $50 is 5.42%
What is the interest rate?The interest rate is the rate of return on the bond given its face value, coupon payments and price.
Interest rate can be determined using a financial calculator:
Cash flow in year 0 = -950 Cash flow in year 1 to 20 = 50 Cash flow in year 20 = 1000Interest rate = 5.42%
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What value of x makes the
equation true? Write your
answer in the box below,
-1/4x-12=x+3
Answer:
[tex]x = -12[/tex]
Step-by-step explanation:
Step 1: Add 1/4x to both sides
[tex]-\frac{1}{4}x - 12 = x + 3[/tex]
[tex]-12 - \frac{1}{4}x + \frac{1}{4}x = x + 3 + \frac{1}{4}x[/tex]
[tex]-12 = \frac{5}{4}x + 3[/tex]
Step 2: Subtract 3 from both sides
[tex]-12 - 3 = \frac{5}{4}x + 3 - 3[/tex]
[tex]-15 = \frac{5}{4}x[/tex]
Step 3: Multiply both sides by 4/5
[tex]-15*\frac{4}{5}=\frac{5}{4}x * \frac{4}{5}[/tex]
[tex]-12 = x[/tex]
Answer: [tex]x = -12[/tex]
Vector Vector C D. has an initial point of (–7, 2, 8) and a terminal point of (0, 7, 3). Vector Vector E F. has an initial point of (4, 1, –2) and a terminal point of (6, –2, –3). What is the component form of vector Vector C D minus vector E F.?
LeftAngleBracket negative 5, negative 8, 4 RightAngleBracket.
LeftAngleBracket 5, 8, negative 4 RightAngleBracket.
LeftAngleBracket 9, 2, negative 6 RightAngleBracket.
LeftAngleBracket negative 9, negative 2, 6 RightAngleBracket.
A vector is a quantity in physics that has both magnitude and direction. The component form of Vector CD minus vector EF is <5, 8, -4>.
What is a vector?A vector is a quantity in physics that has both magnitude and direction. It is often represented by an arrow whose length is proportionate to the magnitude of the quantity and whose direction is the same as that of the quantity.
The value of the Vector CD can be written as,
[tex]|\vec{CD}| = (0+7)\hat i+(7-2)\hat j+(3-8)\hat k = 7\hat i+5\hat j-5\hat k[/tex]
The value of the Vector EF can be written as,
[tex]|\vec{EF}| = (6-4)\hat i+(-2-(-1))\hat j+(-3-(-2))\hat k = 2\hat i-3\hat j-5\hat k[/tex]
Now, the component form of Vector CD minus vector EF can be written as,
[tex]\vec{CD} - \vec{EF} = < (7-2) , (5-(-3)) , (-5-(-1)) > = < 5,8,-4 >[/tex]
Hence, the component form of Vector CD minus vector EF is <5, 8, -4>.
Learn more about Vector:
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Edgar and June ate 75% of a pizza. If the pizza had 12 slices, how many slices did they eat
Answer:
9
Step-by-step explanation:
100% = 12
12/4= 3
25%=3
3+3+3=25%+25%=25%= 75%
daniel wants to build a sandbox that has a perimeter of 20.5 feet . The length is 5.25
76. 30 students at a sports event are
wearing purple. This is 40% of the
students at the event. How many
students are at the event?
Answer:
75 students
Step-by-step explanation:
So firstly lets make convert these words to alegbra :
30 people are 40%of the total students at the event meaning that the following equation can be made :
30 = 40% of x (x is the unknown amount of students there)
30 = 40% * x
30 = 0.4x (we can convert the precentage into a decimal by dividing by 100)
Now that we have the equation that 30 = 0.4x we can evalute it and find x :
30=0.4x
30/0.4=0.4x/0.4 (divide by 0.4 on both sides)
75=x
So thats how we get that 75 students were in the event in total.
15. Find the height of a parallelogram with an area of 41 square meters and
base 8.2 meters
Necesito saber cómo lograr el 5 y 6.
Answer:
5) 12 pieces for $36
6) 12 pieces for $36
They require the same amount of wood pieces.
Step-by-step explanation:
5)
Sandbox A: ? = 2
one side is 6, the other is 4 + ? = 6, so 6-4= ? and 6 - 4 = 2
now we add up the perimeter: 2 + 2 + 4 + 4 + 6 + 6 = 24ft total
we know that each wood piece = 2 ft so:
24 / 2 = 12 pieces of wood
each piece costs $3, so we multiply...
12 * 3 = $36 for all the wood.
____________
Sandbox B: ? = 4
one side is 6, the other is 2 + ? = 6, so 6 - 2= ? and 6 - 2 = 4
now we add up the perimeter: 2 + 2 + 4 + 4 + 6 + 6 = 24ft total
we know that each wood piece = 2 ft so:
24 / 2 = 12 pieces of wood
each piece costs $3, so we multiply...
12 * 3 = $36 for all the wood.
Use the point-slope formula to write an equation of the line that passes through (-1,-6) and (4, 1). Write the answer in slope-intercept form (if possible). h The equation of the line is
Answer:
y = 1.4x - 4.6
hope this helped :)
I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER
Answer:
a=1/2b, 2a=b
Step-by-step explanation:
Since angle a is 1/2 the size of angle b, a=1/2b and b=2a. In order to get a numeral answer, you need the number of one of the angles.
3(p-6)
Which of the expressions is equivalent to the given expression?
Part A
a) (3 * p)-6
b) (3* p)-(3 *6)
c) (3 +p) - (3 *6)
d) (3 * p)* (3-6)
Part B
Which expression is also equivalent to the given expression?
a) p-18
b)3p+6
c)3p-6
d)3p-18
what is the radius of D
6 cm
12 cm
3 cm
24 cm
Answer:
3 Is the Radius
Step-by-step explanation:
Diameter is always 2R (R for radius), as they have given us the diameter of 6 we can conclude the answer by forming a simple equations
D=2R
6=2R
3=R
what digit 7 sits in this number 714,583
Answer:
Hundred thousands place.
Answer:
In this case the number 7 would be located in the hundreds of thousands.
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Thank you so much for participate in the community of Brainly.com
I hope help you :)
Kind regards, Antonio.
1 Jack and Diane want to meet for breakfast. Jack walks 1.5 mph and Diane walks 1 mph. They started 5 miles apart from each other. How long does it take them to meet up?
anwers : jack take 3.33 hours and diane would take 5 hours
2 How far apart were they after 1 hour?
surface area of prisms need help ASAP I will give brainliest
Step-by-step explanation:
A=2πr(r+h)
A=6.28×14mm(+29mm)
A=77.92(14mm+29mm)
A=77.92×43
A=3350.56 mm
Hope it helps
KC
Solve the equation x^2+6x= -11/4
Answer:
Step-by-step explanation:
First, move the -11/4 to the other side, so the expression can equal 0.
[tex]x^2+6x+11/4=0[/tex]
To make the equation easier to work with, multiply both sides by 4, cancelling out the fraction.
[tex]4x^2+24x+11=0[/tex]
There are many ways to solve a quadratic equation (factoring, quadratic formula, completing the square).
Solving this equation by factoring is the easiest. Factoring with a leading coefficient greater than one can be difficult and there are many ways to accomplish it. The way I'm going to do it is to first find the factors of [tex]4x^2[/tex] and then the factors of 11. And then multiply across, add the middle terms (derived from multiplying) and try to make it equal 24x.
[tex]4x^2[/tex]: 24x 11:
2x 22x 11
2x 2x 1
24x (works)
I'll then take the factors diagonal. (2x+1)(2x+11)=0
So [tex]x=-\frac{1}{2}, -\frac{11}{2}[/tex]
A long-distance runner finished a race in 2.75 hours. How is the runner's time expressed
as a mixed number?
A cylinder has a height of 5 centimeters. Its volume is 62.8 cubic centimeters. What is the
radius of the cylinder?
mund your answer to the nearest hundredth
Answer: 2
Step-by-step explanation: It would have been 1.99949 but rounded to the nearest hundreth is 2 :)
What is the area of the smaller rectangle?
Answer:
64 mm^2
Step-by-step explanation:
The area of the rectangles is calculated by multiplying width and length:
for the bigger rectangle:
12*48 = 576 mm^2
for the smaller rectangle:
4*16 = 64 mm^2