The equation of the line that passes through (-2,1) and is perpendicular to y = -5x² is y = -10x + 21
The equation of a line is a mathematical representation of the relationship between its x and y values.
In this case, we are given a line that passes through the point (-2,1) and is perpendicular to y = -5x².
To find the equation of this line, we first need to find the slope of the line that is perpendicular to y = -5x².
The slope of a line can be found by finding the derivative of the original equation.
In this case, the derivative of
=> y = -5x² is -10x,
which gives us the slope of -10x.
Since we know that the line passing through (-2,1) is perpendicular to
y = -5x²,
we can use the point-slope form of the equation of a line.
The point-slope form of the equation is given by
=> y - y1 = m(x - x1),
where m is the slope and (x1, y1) is a point on the line.
Plugging in the values, we have
=> y - 1 = -10(x + 2).
We can simplify this equation further by distributing the -10 and combining like terms.
This gives us
=> y - 1 = -10x - 20,
which we can then rearrange to get
=> y = -10x + 21.
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it costs johnny $15 a month plus $1.50 per song to download music. this situation is represented by the expression 1.5x 15, where x is the number of songs downloaded. how much will it cost johnny to download 10 songs?
The cost of downloading 10 songs for Johnny is $30.
The cost of downloading music for Johnny can be represented by the expression 1.5x + 15, where x is the number of songs downloaded. To find the cost of downloading 10 songs, we can plug in x = 10 into the expression:
1.5 * 10 + 15 = 15 + 15 = 30
So, it will cost Johnny $30 to download 10 songs. This expression represents the total cost as the sum of a $30 $30 ($15 monthly fee) and a variable cost ($1.50 per song fee).
The fixed cost remains constant regardless of the number of songs downloaded, while the variable cost increases as more songs are downloaded.
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How do you find the image under a linear transformation?
To calculate the kernel, locate the vector subspace in which the homogeneous implicit equations result from the linear transformation formula's component parts being equal to zero.
What is linear transformation?A function from one vector space to another that respects the underlying (linear) structure of each vector space is called a linear transformation.
A linear operator, or map, is another name for a linear transformation.
The zero transformation and identity transformation are two significant illustrations of linear transformations.
An illustration of a linear transformation is the zero transformation, which is denoted by T(x)=(0) for every x.
Also linear is the identity transformation denoted by T(x)=(x).
Find the vector subspace in which the implicit equations are the homogeneous equations produced when the components of the linear transformation formula are equal to zero in order to compute the kernel.
This is the same as finding the null space of the linear transformation matrix.
Therefore, to calculate the kernel, locate the vector subspace in which the homogeneous implicit equations result from the linear transformation formula's component parts being equal to zero.
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For the vectors u = (-4,-1) and v= (1,3), express u as the sum u=p+n, where p is parallel to v and n is orthogonal to v. + 7 21 33 11 u=p+n= 10 10 10 10
For the given vectors the sum of u is (-44/10,-6/10).
Vectors are mathematical objects that have both magnitude and direction.
The projection of u onto v is equal to the dot product of u and the unit vector of v divided by the magnitude of v.
The unit vector of v can be found by dividing v by its magnitude. Once we have the unit vector, we can multiply it by the dot product and add it to the initial point of v to find p.
Since u = (-4,-1) and v = (1,3), the magnitude of v is √(1^2 + 3^2) = √10 and the unit vector of v is (1/√10, 3/√10).
The dot product of u and the unit vector of v is
=> (-4)(1/√10) + (-1)(3/√10)
=> -4/√10 - 3/√10.
Thus,
=> p = (-4/√10 - 3/√10)(1/√10, 3/√10) + (1,3)
=> p = (-4/10 - 3/10, -1/10 + 3/10) + (1,3)
=> p = (7/10 + 3/10, 2/10 + 3/10) = (10/10, 5/10).
To find n vector, we subtract p from u.
Finally,
=> n = u - p = (-4,-1) - (10/10, 5/10)
=> (-4 - 10/10, -1 - 5/10) = (-44/10,-6/10).
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Evaluate x + 2x - 4 if x = −4.
12
A.
B. 4
C. -8
D. -28
Answer:
C. - 8
Step-by-step explanation:
substitute - 4 for x value
-4 + (2×-4) - (-4)
= -4 + (-8) + 4
= -12 +4
= -8
In the graph, polygons JKLM and YXWZ are congruent.
The transformation that maps polygons JKLM into polygon YXWZ is
A. a rotation 90 deg clockwise about the origin, then a reflection across the x-axis and a translation by (5, 6)How to map the transformationUsing point M as reference (0, -6)
The transformation rule for reflection 90 deg clockwise is (x, y) → (y, -x)
M (0 -6) → M' (-6, 0)
Reflection across the x-axis (x, y) → (x, -y)
M' (-6, 0) → M'' (-6, 0)
Translation by (5, 6) (x, y) → (x + 5, y + 6)
M'' (-6, 0) → M''' (-6 + 5, 0 + 6) = M'' (-1, 6)
M''' = Z (-1, 6)
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Nelda baked two kinds of pasta in pans. Each pan was the same size. She sliced one pan of pasta into 4 equal pieces. She sliced the other pan into 10 equal pieces. How can the pans of pasta now be sliced so that both pans have the same-sized pieces? If Nelda has served 5 pieces from 1 pan so far, what fraction of 1 pan has she served?
The pans must be sliced in the following way:
Slice the first pan in 10 slices.Slice the second pan in 4 slices.B) 5 pieces are equivalent to the fraction 1/8 of the pan.
How can the pans of pasta now be sliced so that both pans have the same-sized pieces?The number of pieces in each pan will be equal to the product between the numbers of slices (assuming that the sets of slices are perpendicular)
So, if she wants to have pieces of the same size, she needs to:
Slice the first pan in 10 slices.
Slice the second pan in 4 slices.
Now both of these will have:
10*4 = 40 pieces.
B) There are 40 pieces in each pan, so if she served 5, the fraction is:
5/40 = 1/8
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Is it possible to form a triangle with side lengths 3, 4, and 5? if so, will it be scalene, isosceles, or equilateral?.
Answer:
yesscalenehope this helps :)
What is the measure of the exterior angle at D when AD¯¯¯¯¯¯is extended?
Answer:
117
Step-by-step explanation:
B=D=63
=>the exterior angle at D = 180-63
find the area of the region that is bounded above by the curve f(x)=(x 8)2 and the line g(x)=−x−2 and bounded below by the x-axis.
The area of the region bounded by f(x)=(x-8)^2, g(x)=-x-2 and the x-axis is the definite integral of f(x)-g(x) from -2 to 8.
The area of the region bounded by f(x)=(x-8)^2, g(x)=-x-2 and the x-axis is given by the definite integral of f(x)-g(x) from -2 to 8. First, expand f(x) and g(x) to get f(x)=x^2-16x+64 and g(x)=-x-2. Then, subtract g(x) from f(x) to get f(x)-g(x)=x^2-16x+66. This is the equation of the area of the region. To calculate the area, use the definite integral of f(x)-g(x) from -2 to 8. This is equivalent to the integral from -2 to 8 of x^2-16x+66 dx. After integrating, the area is given by the expression (x^3/3)-8x^2+66x from -2 to 8, which is equal to 1176/3 units^2. Therefore, the area of the region bounded by f(x), g(x) and the x-axis is 1176/3 units^2.
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The freezing point of water is 0^\circ\text{C}0
Answer:
For the first question:
A) -9.7 > -18.2
For the second:
A) The temperature is warmer in Minnesota than South Dakota.
Step-by-step explanation:
Hope it helps! =D
Which is equivalent to 64 superscript one-fourth
Answer:
Below
Step-by-step explanation:
this is the same as [tex]\sqrt[4]{64}[/tex] and is [tex]\sqrt[4]{16*4}[/tex] and this equals 2 [tex]\sqrt[4]{4}[/tex]
(Need help asap) Richie and Saul are conducting a survey on the most popular board games played by students at their high school. Richie interviews 25 boys from grades 9 through 12 and concludes that card games are the most popular among high school students. Saul speaks with 20 students, including girls and boys, from grades 9 through 12 and concludes that word games are the most popular among high school students. Whose generalization is valid? Why?
Answer: I’d say that Saul’s generalization is more valid because even though he interviewed less people, he interviewed girls as well as boys, and Richie only interviewed the boys.
Answer:Given that Saul spoke with both boys and females, his generalization is accurate
Step-by-step explanation:?A generalization is a kind of abstraction where the general traits of specific cases are articulated as overarching concepts or claims. Generalizations presuppose a domain or collection of elements, as well as one or more shared characteristics.Why is being general useful?Generalization is the capacity to do an action, engage in an activity, or display a behavior in a variety of situations, with a variety of people, and at a variety of times. Our ability to complete routine tasks in a variety of contexts and settings is due to the fact that we have "generalized" the necessary skills.
What is the standard form of (2,7) ; m =-4 ??
-Exploring Linear Equations in Two Variables
Answer:
4x + y = 15
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here m = - 4 , then
y = - 4x + c ← is the partial equation
to find c substitute (2, 7 ) into the partial equation
7 = - 4(2) + c = - 8 + c ( add 8 to both sides )
15 = c
y = - 4x + 15
the equation of a line in standard form is
Ax + By = C ( A is a positive integer and B, C are integers )
then
y = - 4x + 15 ( add 4x to both sides )
4x + y = 15 ← in standard form
Describe the pattern that you see. In your description, include the shapes that create the pattern. You can also mention colors. What is the first term (how does the pattern start)? How does the pattern change with each term? What would the next term in the sequence (pattern) be?
The value of a computer is $1200. It loses 20% of its value every year. How much will the computer be worth after 4 years?
Answer:
After 4 years, the computer will be worth approximately $576. Since the computer loses 20% of its value each year, the total amount lost after 4 years is 80%. This means that the computer's original value of $1200 will be reduced to $576.
Step-by-step explanation:
Find the following partial derivatives: Jif f(x,y) = 5000 10x 40y 3x2y5 Jif f(x,y) = Ty + T2xy
The first three terms are all 0 since they are constants. The last term is [tex]15x2y4[/tex]. Therefore, the partial derivative of J with respect to y is [tex]40 + 15x2y4.[/tex]
Partial Derivative of J with Respect to[tex]x: 50 - 6x2y5[/tex]
Partial Derivative of J with Respect to[tex]y: 40 + 15x2y4[/tex]
To find the partial derivatives of J with respect to x and y, we need to use the chain rule. The partial derivative of J with respect to x is the derivative of 5000 with respect to x plus the derivative of 10x with respect to x plus the derivative of 40y with respect to x plus the derivative of [tex]3x2y5[/tex] with respect to x. The first three terms are all 0 since they are constants. The last term is [tex]6x2y5[/tex]. Therefore, the partial derivative of J with respect to x is [tex]50 - 6x2y5[/tex]. The partial derivative of J with respect to y is the derivative of 5000 with respect to y plus the derivative of 10x with respect to y plus the derivative of 40y with respect to y plus the derivative of [tex]3x2y5[/tex] with respect to y. The first three terms are all 0 since they are constants. The last term is [tex]15x2y4.[/tex]Therefore, the partial derivative of J with respect to y is [tex]40 + 15x2y4[/tex].
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Amanda is using wire to construct a triangle for an art project. She has 4 inches of blue eirr and 8 inches of green wire. Amanda is going to buy some purple wire for the third side of her triangle. She needs to buy enough wire to make a triangle, but does not want to have any wire let over. What is the least amount and the greatest amount of purple wire she could buy?
Amana could buy more than ___ inches but less than ___ inches of purple wire.
Amanda could buy more than 4 inches but less than 8 inches of purple wire to make triangle.
For Amanda to make a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
Therefore, the minimum amount of purple wire she could buy would be the sum of the lengths of the blue and green wires (4 inches + 8 inches = 12 inches), minus the length of the longest side (which is 8 inches), so 12 inches - 8 inches = 4 inches.
The maximum amount of purple wire she could buy would be the sum of the lengths of the two shorter sides (4 inches + 4 inches = 8 inches).
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let u and a . is u in the plane in spanned by the columns of a why or why not
u in the plane is not spanned by the columns of A.
If u in the plane in spanned by the columns of A, then u can be obtained by the linear combination of the columns of A. That is
(4, -1, 4) = x(2, 0, 1) + y(5, 1, 2) + z(-1, -1, 0)
In matrix form we get
[tex]\left[\begin{array}{ccc}2&5&-1\\0&1&-1\\1&2&0\end{array}\right]\left[\begin{array}{c}x&y&z\end{array}\right] = \left[\begin{array}{c}4&-1&4\end{array}\right][/tex]
Determinant of matrix A is
= 2*1*0 + 5*-1*1 + -1*0*2 - -1*1*1 - 5*0*0 - 2*-1*2
= 0 - 5 + 0 + 1 + 0 + 4
= 0
Determinant of matrix A is 0, thus no solutions exist.
So u cannot be spanned by columns of A.
--The question is incomplete, answering to the question below--
"Let u = [tex]\left[\begin{array}{c}4&-1&4\end{array}\right][/tex] and A = [tex]\left[\begin{array}{ccc}2&5&-1\\0&1&-1\\1&2&0\end{array}\right][/tex] . Is u in the plane is spanned by the columns of A? why or why not?"
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What is meant by linear algebra?
Answer:
Step-by-step explanation:
a branch of mathematics that is concerned with mathematical structures closed under the operations of addition and scalar multiplication and that includes the theory of systems of linear equations, matrices, determinants, vector spaces, and linear transformations.
What is 1 gallon equal to in Litres?
1 gallon equal to 3.785411784 liter.
What is gallon?The gallon is a unit of volume in imperial units and United States customary units. Three different versions are in current use:
The imperial gallon (imp gal), defined as 4.54609 litres, which is or was used in the United Kingdom, Ireland, Canada, Australia, New Zealand and some Caribbean countries.
The US gallon (US gal), defined as 3.785411784 L, (231 cubic inches) which is used in the US and some latin American and Caribbean countries.
The US dry gallon ("usdrygal"), defined as 1/8 US bushel (exactly 4.4.0388377086 L)
By using the above formula to convert US gallons to litres.
Solution: Inserting the value of a gallon in the above formula we will get:
Litre =1×3.785411784 =3.785411784
Hence 1 gallons are equal to 3.785411784 liter.
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What does a Right-Skewed Histogram Mean?
A right-skewed histogram has a peak that is left of center and a more gradual tapering to the right side of the graph. This is a unimodal data set, with the mode closer to the left of the graph and smaller than either the mean or the median.
Define Right-Skewed Histogram?A right-skewed histogram is one in which the majority of the data falls to the right of the graph's peak.The mean, median, and mode of a right-skewed histogram have a definite relationship, which can be written as mean > median > mode.The right side of a right-skewed distribution is longer than the left. Positive skew is another name for right skew. Skewness can be thought of as tails. A distribution's tail is the long, tapering end of the distribution.A "skewed right" distribution has the tail on the right side. Right skewed: The mean is greater than the median. Left skewed: The mean is less than the median.To learn more about Right-Skewed Histogram refer to:
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What is 15kg in lbs ?
Answer: 15kg is equivalent to 33.0693 or 33, for short.
Step-by-step explanation:
33.0693 kilograms, or 33, are equal to 15 kilograms.
How many kg means 1 pound?A pound is about equivalent to 0.45359237 kilograms. By dividing the specified pound value by 0.45359237, one can convert a pound to kilograms. Remember that 1 kg equals 2.2046 lbs when converting weights.
The weight of a kilogram (kg) is said to be 2.2 times that of a pound. Thus, 2.26 pounds are equal to one kilogram of mass. In light of this, we shall now examine some of the primary variations between the pound and the kilogram. A pound is an imperial unit used to measure bulk or weight.
A weight of 500 pounds exceeds a weight of 200 kilograms because 227 kilograms is greater than 200 kilograms.
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Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
The sum of the angle measures of a polygon with s sides is
2 and 340( degrees). Find s.
The sum of the angle measures of a polygon with s sides can be calculated using the formula:
(s - 2) * 180 degrees
We can use this formula to solve for s:
2 = (s - 2) * 180
Dividing both sides by 180:
2 / 180 = (s - 2)
Solving for s:
s = 2 + 2 / 180 = 2 + 1 / 90 = 2 + 1 / 90 * 180 / 180 = 2 + 2 / 3
So the number of sides of the polygon is s = 2 + 2 / 3 = 4 2/3.
Since a polygon must have a whole number of sides, s cannot be a fraction, which means this answer is not a valid solution for the number of sides of a polygon. I don't think the problem as stated does not have a valid solution.
what is the linear regression equation? (round your answers to three decimal places.) estimated tip amount
The linear regression equation for estimating tip amount is y = 0.174x + 1.971, where x is the total bill amount and y is the estimated tip amount.
First, collect data by having participants record the total bill amount and the amount of tip they gave.Next, calculate the linear regression equation by plotting the data points on a scatter plot and fitting a line of best fit.Once the line of best fit has been determined, calculate the equation of the line using the slope-intercept form.Finally, round the values of the equation to three decimal places, and the linear regression equation for estimating tip amount is y = 0.174x + 1.971, where x is the total bill amount and y is the estimated tip amount.Learn more about linear regression equation: https://brainly.com/question/25987747
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Can anyone solve 21x>5y+49x>2y>2-28x>2y?
Answer:
Step-by-step explanation:
i cant but someone can habha
Cada una de las gaseosas se va a repartir en seis vasos
Gaseosa grande 3 335,9cm3 y la gaseosa pequeña 1 550,
De la gaseosa grande quedaran _________ cm3
De la gaseosa pequeña quedaran _________ cm3
De la botella _______ quedarán mas liquido.
Answer:4
Step-by-step explanation:
4
Answer:
4
Step-by-step explanation:
The output y and input x of a device are related by y = x + 1. 4x3. (a) Find the values of the output for steady-state operation at the two operating points xo = 1 and xo = 2. (b) Obtain a linearized model for both operating points and compare them
The values of the output for steady-state operation at the two operating points xo = 1 and xo = 2 are y(1)=2.4, y(2)=13.2, and the linearized model for both operating points is y(x)=2.4+5.2(x-1), y(1)=2.4 y(2)= 7.6
The given equation is y=x+1.4x³.
The values of the output for steady-state operation are:
Now substitute Xo=1 and Xo=2 in given equation:
y(1)=1+1.4(1)³.
y(1)=2.4
y(2)=2+1.4(2)³.
y(2)=13.2
The formula for linearization is:
[tex]y(x)=y(1)+\frac{dy}{dx} |_x_=_1.(x-1)[/tex]
The first derivative of the formula evaluated at x = 1 is:
[tex]\frac{dy}{dx} |_x_=_1=1+4.2(1)^2\\\\\frac{dy}{dx} |_x_=_1=5.2[/tex]
The linearized model is:
y(x)=2.4+5.2.(x-1)
The output at x = 2 is presented below:
y(x)=2.4+5.2.(2-1)
y(2)=7.6
The linearized model offers reasonable approximations for small intervals.
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The day has come! It is time for you to buy your first car. At the car lot, you find the very car you have always wanted and it costs $4,100 after all taxes and fees. Since you have little credit history, your interest rate will be 10.50%. But good news—you are still able to get a car loan!
What will the loan balance be after 3 months if the interest is compounded monthly and you pay $88.13 each month?
According to the information, it can be inferred that the balance after 3 months is that we have made interest payments for $107.6 of interest and $264.39.
How to calculate the balance of interest and car loan payments?To calculate the payment balance for the car loan we must take into account the following information:
interest rate 10.50%Each mother we will pay $88.13Total loan $4,100According to the above, we must find how much the interest is equal to:
4,100 / 100 * 100.50 = 430.5So, we must divide the result in the 12 months of the year
430.5 / 12 = 35.8and later multiply it by the three months that are being asked.
35.8 * 3 = 107.4Additionally, we must calculate how much the installment payment would be.
88.13 * 3 = 264.39So we would pay 371.79 for the 3 months.
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Which angle has a vertex on the center of the circle and sides that are radii of that circle?
Answer:
central angle
Step-by-step explanation:
an angle with a vertex on the center of a circle and slides that are radii of that circle is called a central angle
Central angle has a vertex on the center of the circle and sides that are radii of that circle .
What does central angle mean?
A right angle, which has sides that are the radii of the circle, and a vertex that is at the center of the circle Given that it intercepts an arc with a length equal to the circle's radius, a central angle has radian measure [Math Processing Error].
Where can I find the center angle?
The angle that the arc at the center of a circle occupies is known as the central angle. The arms of the angle are created by the radius vectors. The formula for calculating a central angle is: Central Angle = Arc length(AB) / Radius(OA) = (s 360°) / 2r, where s denotes the length of the arc and r denotes the radius of the circle.
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A triangle ha a 60 degree angle, and the two adjacent ide are 12 and 12 root 3. Find the radiu of a circle with the ame vertex a a center, if the arc inide the triangle divide it into two region of equal area
The radius of the circle with the same vertex is 6 and the height of the triangle is 10.39 and the area of the triangle is 62.34.
Since the arc divides the triangle into two regions of equal area, it follows that half of the circle's area is equal to the area of the triangle. The area of a triangle with sides 12 and 12√3 and a 60-degree angle can be found using the formula for the area of a triangle, which is 0.5bh.
The height of the triangle can be found using trigonometry, as the sine of 60 degrees is 0.8660. Thus, the height of the triangle is 10.39 and the area of the triangle is 62.34.
Since half of the circle's area is equal to the area of the triangle, the radius of the circle can be found by taking the square root of the area of the triangle and dividing it by pi. Thus, the radius of the circle is 6.
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A triangle has a 60-degree angle, and the two adjacent ide are 12 and 12 roots 3. Find the radius of a circle with the same vertex a center, if the arc inside the triangle divides it into two regions of equal area