The equation of the tangent line to the curve when y = -1 is y = -4x - 1.
To find the equations of all tangent lines to the curve when y = -1, we can use the definition of a tangent line, which is a line that touches a curve at a single point and has the same slope as the curve at that point.
To find the slope of the curve at a given point, we can use the slope formula:
slope = (y₂ - y₁) / (x₂ - x₁)
In this case, we can set y₁ = -1 and y₂ = -1 + h, where h is a small positive number, and find the corresponding value of x₂ by substituting these values into the equation x - x²y - 2y² = 0. This will give us the slope of the curve at the point (x, -1).
Substituting these values into the equation, we get:
x - x²(-1) - 2(-1 + h)² = 0
Expanding the second term and rearranging, we get:
x - x² + 2(1 - 2h + h²) = 0
This simplifies to:
x - x² + 2 - 4h + 2h² = 0
This can be rewritten as:
x - x² + 2h² - 4h + 2 = 0
To find the slope of the curve at the point (x, -1), we can take the derivative of this equation with respect to x and evaluate it at x = x and h = 0:
slope = (2h² - 4h)'|h=0
= 0 - 4
= -4
Now that we have the slope of the curve at the point (x, -1), we can use the point-slope form of a linear equation to find the equation of the tangent line:
y - (-1) = -4(x - x)
y + 1 = -4x
y = -4x - 1
Therefore, when y = -1, the equation of the tangent line to the curve is y = -4x - 1.
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Answer:
-------------------
Step-by-step explanation:
i need help pls and explain how it would help alot thjanks
Answer:
neither are functions
Step-by-step explanation:
For a relation to be a function each value of the input x must map to exactly one unique value in the output y
(1)
This relation is not a function since
7 → 2 and 5 → 2
Two different values of x have the same output , thus not a function
(2)
This relation is not a function since
3 → 10 and 3 → 8
Two different values of x have the same output, thus not a function
Answer:
Step-by-step explanation:
neither are functions
In triangle TSP, TS=SP=10 cm, TP= 12 cm. Find three heights of triangle TSP
pls answer quickly I will give brainliest to fastest answer
Answer:
Plot each graph on the same coordinate system.
TSP
TP=12cm
T
Step-by-step explanation:
help with example 4!!! first answer gets brainliest
Answer:
Assuming angle 1 is 75º.
1 -> 75
2 -> 105
3 -> 75
4 -> 105
5 -> 75
6 -> 105
7 -> 75
8 -> 105
On the Dell River, a boat will pass the Colby drawbridge and then the Wave drawbridge. Rename each of the two drawbridge opening times. There are 60 minutes in an hour so use 60 as a common denominator. Then rename each opening time using another common denominator. Explain how you found your answers
Because we know that the common denominator is 60 then 3/4 of an hour is 45mins then 1/6 of an hour is 10.
Given,
In the question:
There are 60 minutes in an hour so use 60 as a common denominator. Then rename each opening time using another common denominator.
Explain how you found your answer.
Now, According to the question:
There are 60 min in an hour
and, 60 as a common denominator.
So, 45/60 and 10/60
Explanation: Because we know that the common denominator is 60 then 3/4 of an hour is 45mins then 1/6 of an hour is 10.
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Omar is constructing equilateral triangle ABC. Using a compass and a straightedge, he need to copy AB to
form the other two sides of the triangle. He sets the compass width to AB and draws two arcs from A as shown.
Points A and B with identical construction marks as parts of a circle with center point A.
After plotting point C, he will draw three line segments to connect points A, B, and C. What steps should he follow to plot point C?
Without changing the compass width, draw an arc from B to intersect the other arc, and plot point C.
Without changing the compass width, draw an arc from B, and plot point C on the new arc.
Increase the compass width, draw an arc from B to intersect the other arc, and plot point C.
Increase the compass width, draw an arc from B, and plot point C on the new arc.
An equilateral triangle is a triangle that has three equal-length sides, commonly referred to as a "regular" triangle.
What is the equilateral triangle?When all three sides of a triangle are equal, the triangle is said to be equilateral. The third side is likewise equal in this unique instance of an isosceles triangle. A triangle with the sides AB, BC, and CA is equilateral.An equilateral triangle is a triangle whose three sides are all the same length, also referred to as a "regular" triangle. An isosceles triangle with three equal sides is called an equilateral triangle. It is a special case of an isosceles triangle.An equilateral triangle in geometry is a triangle whose sides are all of the same length. Since the three sides are equal, the three angles that are opposite the equal sides are also equal.Find the attachment answer
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which exspression shows 50+30 written as a product of two ffactors
Hey, sorry if I mixed up some words I had just broke my wrist yesterday...
Now, 50 Can be written as five, multiplied by 30 can be written as three multiplied by 10. So 50 unless 30 that's equal to five, multiplied by 10 plus three, multiplied by 10. here 10 is a common factor. So this equals 10 multiplied by the sum of five and three.
Alex made a $4000 down payment on a car. The total cost of the car was $11000. He made 40 equal monthly payments to pay the car in full. How much did Alex pay per month? Define a variable, write an equation, and solve.
Answer: Alex Paid $175 for 40 months
Step-by-step explanation:
$4000 = y-int or b
$11000 = y
40 months = x
Slope - intercept form : Y=mx+b
We are solving for m which is the slope (How much Alex Paid per month)
11000=m(40)+4000
11000=40m+4000
7000=40m
7000/40
m=175
Please say the transformations it would take to get ABCD TO A’B’C’D’
The sequence of transformations that can generate the transformed image are the reflection of the quadrilateral across the y - axis, followed by the graph transformation (x - 2, y - 0). At the end, image is reduced by a scale factor of [k].
What is Graph transformation?Graph transformation is the process by which an existing graph, or graphed equation, is modified to produce a variation of the proceeding graph.
Given is a quadrilateral ABCD and its transformed form.
The following transformations are done to obtain the transformed image -
The quadrilateral ABCD is reflected across the y - axis.The following transformation → (x - 2, y - 0) is applied to the image.Then, the image is reduced by a scale factor of [k] which is less than one.Therefore, the sequence of transformations that can generate the transformed image are the reflection of the quadrilateral across the y - axis, followed by the graph transformation (x - 2, y - 0). At the end, image is reduced by a scale factor of [k].
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In it's first four games, a netball team scores an average of 31 points per game. After the fifth game, the average for the first five games is 30. How many points did the team score in the fifth game?
The score of the netball team in 5th game is 26.
What is average?A number that is calculated by adding quantities together and then dividing the total by the number of quantities is called average.
Given that, a team scored average 31 points in first four game, and then 30 points average in first five game.
Score in 4 games = 4x31 = 124
Score in 5 games = 5x30 = 150
Score in 5th game = 150-124 = 26
Hence, The score of the netball team in the 5th game is 26.
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I need help with this question been stuck on it for a while
The correct options are B and C, or 3x-21 and -3x21, since the inequality sign must be "flipped," or reversed, whenever you multiply or divide both sides of the inequality.
What is inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other. An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.
Here,
Anytime you multiply or divide both sides of the inequality, you must “flip” or change the direction of the inequality sign. This means that if you had a less than sign <, it would become a greater than sign >.
x≤-7
3x≥-21
-3x≤21
The correct options are B and C that is 3x≥-21 and -3x≤21 because anytime you multiply or divide both sides of the inequality, you must “flip” or change the direction of the inequality sign.
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Find the coordinate using the subtraction method
-2x+9y=-9
-3x+5y=12
The co-ordinates will be(x,y) by the given equation the co-ordinates (9,1).
How to co-ordinate using subtraction method?
The technique of subtracting one vector's coordinates from another vector's coordinates is known as vector subtraction.Addition is represented by travelling up the -axis and to the right on the -axis. Subtraction is represented by going left and down the -axis. Since we are travelling below, we can deduct from our coordinate point, and since we are heading rightward, we can add to it.So, the given equations are
-2x+9y=-9 ⇒ (i)
-3x+5y=12 ⇒ (ii)
(i) * 5 ⇒ -10x + 45y = -45
(ii) * 9 ⇒ -27x + 45y = 108
⇒ 17x = 153
x = 9
Now, substitute x=9 in equation (i)
-2(9) + 9y = -9
-18 + 9y = -9
9y = -9 + 18
y = 9/9
y = 1
Hence, the co-ordinates will be(x,y) by the given equation the co-ordinates (9,1).
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which of the following are possible rational roots of the polynomial function
check all that apply
F(x)=2x^2-3x+7
a.+_2
b.+_1/2
c.+_1
d.+_1/7
e.+_7
help me
±1/2, ±1, ±7 are the possible rational roots of the polynomial function.
What is the rational root theorem?The rational root theorem, also known as the rational root test, is an algebraic theorem that states that for a polynomial equation in one variable with integer coefficients to have a solution (root) that is a rational number, both the constant term (the term without a variable) and the leading coefficient (the coefficient of the highest power) must be divisible by the fraction's denominator.
An anXn+ an− 1xn − 1 + … + a1x1 + a0 = 0 is a polynomial equation in one variable (x), where a0, a1,..., and an are regular integers. Therefore, q must divide a and p must divide a0 for a polynomial equation to have a rational solution, p/q.
It is given in the question,
F(x)=2x^2-3x+7
Here, p is a 7-fold factor.
p, thus, might have a value of 1, -1, 7, or -7.
and q is a two-fold factor.
Thus, q might have a value of 1, -1, 2, or -2.
Hence, ±1/2, ±1, ±7 are the possible rational roots of the polynomial function.
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Below are two parallel lines with a third line intersecting them.
x =
136
find the equation of a line passing through points (-9,8) (-18,12)
Answer: -4/9
Step-by-step explanation:
12 - 8 / -18 - (-9)
4 / -18 + 9
4 / -9
- 4/9
The figure shows two parallel lines cut by a transversal what is the value of x
The value of.x will be 20 and the angles will each have a value of 90 degrees.
What are angles?When two rays are linked at their ends, they create an angle in geometry. The sides or arms of the angle are what are known as these rays.
When two lines meet at a point, an angle is created.
An "angle" is the measurement of the "opening" between these two rays. It is symbolized by the character. The circularity or rotation of an angle is often measured in degrees and radians.
Angles are a common occurrence in daily life.
Angles are used by engineers and architects to create highways, structures, and sports venues.
Hence, The value of.x will be 20 and the angles will each have a value of 90 degrees.
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Express the radical using the imaginary unit, i.
Express your answer in simplified form.
+√-16 = ±
For each value of u, determine whether it is a solution to 9u-7≥65.
which point is not on the graph of 5x+6y=-42
The slope is m = RISE / RUN, and the change in y is frequently referred to as "RISE."
Step-by-step explanation:[tex]5*x-6*y-(42)=0[/tex]
Tiger understands that this is a straight line equation. Typically, this equation is expressed as y=mx+b (or "y=mx+c" in the UK).
A straight line drawn using the Cartesian coordinate system has the formula "y=mx+b," where "y" denotes the vertical axis and "x" denotes the horizontal axis.
In this equation, y represents how high the line rises, x represents how far it travels along, m represents the slope or gradient, or how steep the line is, and b represents the Y-intercept, or the point at which the line crosses the Y axis.
The X, Y, and slope are collectively referred to as the line properties. We will now plot the line 5x-6y-42 = 0 and determine its characteristics.
x = 0 the value of y is 7/-1 so this line "cuts" the y axis at y=-7.00000
y-intercept = 42/-6 = 7/-1 = -7.00000
y = 0 the value of x is 42/5 Our line therefore "cuts" the x axis at x= 8.40000
x-intercept = 42/5 = 8.40000
Slope = 1.667/2.000 = 0.833 x-intercept = 42/5 = 8.40000 y-intercept = 42/-6 = 7/-1 = -7.00000To learn more about 5x+6y=-42 refer to:
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In art, what is the difference between symmetry and balance?
This should probably go in the ART section of Brainly, it may be confusing to people like me, who only have math on here :]
Balance is the use of even elements in a work of art, while symmetry is a type of balance, where parts of the image are mirrored.
Hope this helps,
:]
a restaurant wants to gather data about a new dish by giving out free samples and asking for feedback. who should the restaurant give samples to? 1 point all diners diners who are willing to pay for the samples 80% of diners diners who spend the most money on their meal
The correct option regarding who should the restaurant give samples to generate a representative sample is given as follows:
All diners diners who are willing to pay for the samples.
What is sampling?Sampling is a technique for when a group of elements from a population is taken to represent the entire population.
This group of elements has to be representative of the entire population, as to lead to correct conclusions.
In this problem, all the dinners who are willing to pay for the samples should be sampled, as if they are willing to pay, it means that they are interested in the new dish, hence their opinions should be considered as it would improve the restaurant's revenue with the new dish.
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A work ladder can extend to 8 meters. How many centimeters is that? How many kilometers is that? Use 1000 m) unit analysis to solve this conversion problem (1 km ==
Answer:
8m = 800cm
8m = 0.008km
Step-by-step explanation:
1 kilometer is 1000 meters
1 meter is 100 centimeters
You'd only have to multiply in the first one:
[tex]8 \times 100 = 800[/tex]
8m = 800cm
Remember that when multiplying by 100 you only have to add zeros.
For km, as it is bigger than m you have to divide by 1000, when dividing this time you only have to carry an imaginary point starting from right to left, the amount of zeros there are:
[tex]8. \\ .8 \\ .08 \\ .008 \\ 8 \div 1000 = .008[/tex]
8m = 0.008km
If you run out of numbers when carrying the point, just add zeros.
A box has length of 6 feet width of 7 feet and a height of 4 inches
Answer: 168in^3
Step-by-step explanation:
6 x 7 x 4 = 168
What is the range of the function f(x) = -2(x+1)-2, when the domain is {-5, 0, 5}?
A {-5,0,5}
B {-11,-1,9}
C {-14,-4,6}
D {-10, 0, 10}
Answer: D
Step-by-step explanation:
To find the range, substitute each element in the domain into the function.
[tex]f(-5)=-2(-5+1)-2=-10\\\\f(0)=-2(0+1)-2=0\\\\f(5)=-2(5+1)-2=10[/tex]
Which is g(x)? In this question
The equation of the transformed function is (c) g(x) = 4(1/3x)²
How to describe the transformation from the parent function?From the question, we have the following function that can be used in our computation:
f(x) = x²
g(x) = horizontally shrunk of f(x) by a factor 1/3 and vertical stretch by a factor of 4
The above equations implies that, we have the transformation to be:
Horizontally shrunk of f(x)Vertical stretch by a factor of 4Mathematically, this can be represented as
g(x) = 4f(1/3x)
Substitute the known values in the above equation, so, we have the following representation
g(x) = 4(1/3x)²
Hence, the transformed function si g(x) = 4(1/3x)²
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Solve this problem and explain how you did it. Hurry, it's due by Sunday at 11:59 pm!
Answer: m<a 57 degrees
Step-by-step explanation:
All of the angles are the same and equal, so all angles are 57 degrees. Including m<a
What is the equation of this line? Graph of a line passing through the origin and the point begin ordered pair 4 comma negative 1 end ordered pair
Answer:
y = - [tex]\frac{1}{4}[/tex] x
Step-by-step explanation:
the equation of a line passing through the origin is
y = mx ( m is the slope )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (4, - 1) ← 2 points on the line
m = [tex]\frac{-1-0}{4-0}[/tex] = [tex]\frac{-1}{4}[/tex] = - [tex]\frac{1}{4}[/tex]
y = - [tex]\frac{1}{4}[/tex] x ← equation of line
HELP ME ASAP!!!!!!!!
Answer:
The lie is #3
Step-by-step explanation:
The only way to solve this is by testing each equation to see if it's true. Remember that dividing powers with the same base, in this case b, means you're just subtracting the exponents.
Substituting 5 for y in #1 gives us the equation [tex]\frac{b^9}{b^5}=b^4[/tex]. This is the same as saying [tex]b^9^-^5=b^4[/tex], which is true.
Substituting 7 for z and 2 for x in #2 gives us [tex]\frac{b^7}{b^2}=b^5[/tex]. Like we did for the first one, this is the same as [tex]b^7^-^2=b^5[/tex], which is also true.
That means that #3 is a lie, but substituting 2 for x anyway gives us [tex]\frac{b^8}{b^2}=b^8[/tex], or [tex]b^8^-^2=b^8[/tex]. This is not a true statement, and x would have to equal 0 for this to be true.
question is attached
Answer:
56
Step-by-step explanation:
Top line:
100% - 80% = 20%
20% of 60 = 0.2 × 60 = 12
Small piece on top is 12.
Second line:
Small piece is 12.
100% - 60% = 40%
Small piece is also 40%.
40% of x = 12
0.4x = 12
x = 12/0.4
x = 30
The entire second line is 30.
60% of 30 = 0.6 × 30 = 18
60% of second line is 18.
Third line:
30% of third line = 18
100% - 30% = 70%
30/18 = 70/x
30x = 18 × 70
x = 42
Larger part of third line is 42.
Fourth line:
75% of 4th line is 42.
100/x = 75/42
75x = 100 × 42
x = 56
Answer: 56
what is 1-1/3 pls help me
Answer:
2/3
Step-by-step explanation:
1-1/3 is the same that 3/3 - 1/3
3/3 - 1/3 = 2/3