The slope of the tangent line is:
a = (df(x1)/dx)
The slope of the normal one is:
a' = -1/(df(x1)/dx)
How to find the slope of the tangent line?For any function y = f(x), we define the slope of the tangent line at the point x as the derivative evaluated in x.
So if we want to find the slope of the tangent line at the point (x1, y1), we just need to differentiate and evaluate in x1, then the slope will be given by:
df(x1)/dx
And the normal slope is the slope of the perpendicular line, two slopes are perpendicular if the product is -1, then:
a*(df(x1)/dx) = -1
a = -1/(df(x1)/dx)
Where df/dx reffers to the derivative of f(x).
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why does area and perimeter change in different ways
Answer:
Step-by-step explanation:
Area and perimeter are both measurements used to describe geometric shapes, but they are fundamentally different concepts and therefore change in different ways.The perimeter of a shape is the distance around the outside of the shape. It is a measure of the total length of the boundaries or sides of the shape. Perimeter depends on the length of each side of the shape, and if one or more sides change in length, the perimeter will change accordingly. For example, if you take a square and double the length of one of its sides, the perimeter will double as well.On the other hand, the area of a shape is the measure of the surface enclosed by the shape. It is a measure of the amount of space inside the shape. The area depends on the length and width of the shape, and if one or both of these dimensions change, the area will change accordingly. For example, if you take a square and double the length of one of its sides, the area will increase by a factor of four.In summary, the perimeter of a shape depends on the length of its sides, while the area of a shape depends on its length and width. Therefore, changes to the length of a side will affect the perimeter, but not necessarily the area, while changes to the length or width will affect the area, but not necessarily the perimeter.
Find the measure of angle A.
60x
O 60°
O 30°
O 23°
O 37°
30x
A
Answer:
Step-by-step explanation:
sum of angles in a triangle=180º
90+60x+30x=180
90+90x=180
90(1+x)=180
1+x=2
x=1
angle A=30º
Write an explicit formula that represents the sequence defined by the following recursive formula:
The explicit formula for the sequence defined by the recursive formula a₁ = 150 and aₙ = -1/5 aₙ₋₁ is aₙ = 150 [tex](-1/5)^{(n-1)[/tex].
To find the explicit formula that represents the sequence defined by the given recursive formula, we need to find a pattern in the sequence and express it using a formula.
The first term in the sequence is a₁ = 150. To find the second term, we use the recursive formula: a₂ = -1/5 a₁ = -1/5(150) = -30. To find the third term, we use the recursive formula again: a₃ = -1/5 a₂ = -1/5(-30) = 6.
We can continue this process to find the fourth term: a₄ = -1/5 a₃ = -1/5(6) = -6/5, and so on.
By observing the pattern, we notice that each term is obtained by multiplying the previous term by -1/5. Therefore, the explicit formula for the sequence can be written as:
aₙ = 150 [tex](-1/5)^{(n-1)[/tex]
This formula gives the value of any term in the sequence based on its position n. It can be used to find any term in the sequence without having to recursively calculate all the previous terms.
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I need help please geometry not my strong suit
The image point of (-7, -8) after the sequence of transformations is given as follows:
(-4.5, -4).
How to obtain the coordinates of the image point?The original coordinates are given as follows:
(-7, -8)
The first transformation is a dilation with a scale factor of 1/2, meaning that each coordinate is multiplied by 1/2, hence:
(-3.5, -4).
The second transformation is a translation of one unit left, meaning that one is subtracted from the y-coordinate, thus the image point after the sequence of transformations is given as follows:
(-4.5, -4).
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Two animals are experiencing major events in their life cycles.
Animal 1: A panther is a group of cells that are dividing within the mother.
Animal 2: A pelican has hatched from an egg.
Are these animals at the same stage in their life cycle, or different stages, and why?(20 points)
The same stage. Both the panther and the pelican are embryos.
The same stage. Both the panther and the pelican are adults.
Different stages. The panther is an embryo and the pelican is an infant.
Different stages. The panther is an egg and the pelican is an adult.
The two animals are at different stages in their life cycle. Hence option C: Different stages. The panther is an embryo and the pelican is an infant.
What is the life cycles?The two creatures are at distinct points of their developmental process. The panther, denoted as Animal 1, is characterized as a cluster of cells undergoing division within its maternal host. This is one that then shows that the panther is at a very early stage of growth, and that it is in embryonic phase.
The pelican, is one that is also known as Animal 2, that has successfully hatched from its egg, telling us the conclusion of its embryonic phase and the start of the post-embryonic phase.
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Which best demonstrates the way consumers and producers influence each other in the free-market system? O assembly line Circular-flow model downward spiral O flow chart
Answer:
The best choice is:
Circular-flow model
The circular-flow model demonstrates how consumer demand and production supply influence each other in a market economy. Some key points:
• Consumers demand goods and services by spending money (aggregate demand). This drives production.
• Producers supply goods and services to meet demand (aggregate supply). But supply depends on and influences demand.
• There is a continuous flow and feedback loop between consumers, producers, and the money/resources flowing between them.
The circular-flow model highlights this interconnectedness and interdependence. It shows how consumer spending drives production, which in turn enables more consumer spending, and so on. Changes in demand, supply, spending or consumption ripple through the economy.
The other choices do not accurately represent this relationship:
• Assembly line - Focuses on supply-side production process, not the demand-supply feedback loop.
• Downward spiral - Implies a negative, self-defeating cycle rather than the mutually supporting feedback in the circular-flow model.
• Flow chart - Too generic. A flow chart could represent any process, not specifically the demand-supply relationship.
So in summary, the circular-flow model is the best choice as it demonstrates the way consumer demand and producer supply interact with and influence each other in a free market system. The circular flow of money, resources, supply and demand relies on this interconnection.
Does this help explain the circular-flow model and why it is the best choice? Let me know if you have any other questions!
Step-by-step explanation:
Find the 8th term of the geometric sequence 10, 50, 250,...
The 8th term of the sequence is 781, 250.
We have geometric sequence 10, 50, 250,...
First term= 10
Common ratio = 50/10 = 5
So, the 8th term of sequence is
= 10 x [tex]r^{8-1[/tex]
= 10 x [tex]r^7[/tex]
= 10 x [tex](5)^7[/tex]
= 10 x 5 x 5 x 5 x 5 x5 x 5 x 5
= 10 x 78125
= 781, 250
Thus, the 8th term of the sequence is 781, 250.
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Needing help finding this answer!
Answer:
78.947%
Step-by-step explanation:
It says A OR B, so:
5/19 + 6/19 + 4/19
11/19 + 4/19
15/19 = approx. 0.78947 = 78.947%
Maggie bought 50 lbs of clay for her art projects. She used 15.6 lbs to make a sculpture, and 0.84 lbs for each mug. How many mugs did Maggie make if she had 19.28 lbs of clay left over? Solve on paper. Then check your work on Zearn.
The number of mugs that Maggie made with the left over clay that she had would be = 23 mugs
How to calculate the quantity of mug made by Maggie?The total quantity of clay that Maggie bought = 50lbs
The quantity she used for sculpture = 15.6lbs
The quantity of clay she used for mug = 0.84 lbs
The quantity of clay left = 19.28 lbs
If 0.84 = 1 mug
19.28 = X
make X the subject of formula:
X = 19.28/0.84
= 23 mugs
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A carnival game has 160 rubber ducks floating in a pool. The person playing the game takes out one duck and looks at it.
If there’s a red mark on the bottom of the duck, the person wins a small prize.
If there’s a blue mark on the bottom of the duck, the person wins a large prize.
Many ducks do not have a mark.
After 50 people have played the game, only 3 of them have won a small prize, and none of them have won a large prize.
Estimate the number of the 160 ducks that you think have blue marks.
The estimated number of the 160 ducks that have blue marks would be 5 ducks.
How to estimate the number ?Assuming none of the 50 people have received a considerable reward, it is probable that winning a small prize bears higher odds than claiming a more substantial one. Estimating, the probability of achieving a large prize may be considered half as likely to succeed as obtaining a smaller sum:
P ( large prize ) :
= 0.5 x P(small prize)
= 0.5 x 0.06 = 0.03
Number of ducks with blue marks (large prize):
= ( total number of ducks ) x P( large prize )
= 160 x 0.03
= 4.8
= 5 ducks
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Arianna says that the graphs of both of these functions will grow at the same cale s
she correct? Why or why not?
She is correct They grow at the same rate because
She is not correct. The graph of grows at a faster tale
than the graph of g because each value is mutplied by 4
There is not exgh intymaton to to which graph will
grow at a fasheerale
She is not correct The graph of g grows at a faster ale
than the graph of because & greater than 2
37
Answer:She is not correct The graph of g grows at a faster rate
than the graph of because 8 greater than 2
Step-by-step explanation:
Using PEMDAS, the exponents are done first.
8^3 = 512
4*2^3 = 32
This works for every number that X can be, 3 was just an example.
Please help me geometry too hard
The value of distance between two points on graph is,
⇒ d = √32 units
We have to given that;
The coordinates of two points are,
⇒ (9, - 4) and (5, -8)
We know that;
The distance between two points (x₁ , y₁) and (x₂, y₂) is,
⇒ d = √ (x₂ - x₁)² + (y₂ - y₁)²
Hence, The value of distance between two points on graph is,
⇒ d = √ (x₂ - x₁)² + (y₂ - y₁)²
⇒ d = √ (5 - 9)² + (- 8 - (-4))²
⇒ d = √ 16 + 16
⇒ d = √32
Thus, The value of distance between two points on graph is,
⇒ d = √32 units
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A total of $8000 is invested: part at 6% and the remainder at 10%
. How much is invested at each rate if the annual interest is $760
The requried, $1000 is invested at 6%, and $7000 is invested at 10%
Let x be the amount invested at 6%, and y be the amount invested at 10%. We know that x + y = $8000 since the total amount invested is $8000.
We also know that the annual interest earned on the 6% investment is 0.06x, and the annual interest earned on the 10% investment is 0.1y. The total annual interest earned is given as $760.
So we have the system of equations:
x + y = 8000 (1)
0.06x + 0.1y = 760 (2)
We can use either substitution or elimination to solve for x and y. Here, we'll use elimination. Multiplying equation 1 by 0.06, we get:
0.06x + 0.06y = 480 (3)
0.1y - 0.06y = 0.04y = 280
y = $7000.
Substituting y = $7000 into equation 1, we get:
x + $7000 = $8000
So x = $1000.
Therefore, $1000 is invested at 6%, and $7000 is invested at 10%.
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A poll showed that 53.2% of Americans say they believe that statistics teachers know the true meaning of life. What is the probability of randomly selecting someone who does not believe that statistics teachers know the true meaning of life. Round to 3 decimal places.
The probability that a statistics teachers do not know the true meaning of life is 46.8%
What is the probability of someone who does not believeFrom the question, we have the following parameters that can be used in our computation:
53.2% of Americans say they believe that statistics teachers know the true meaning of life.
This means that
P(Believe) = 53.2%
For the required probability, we have
P(Not believe) = 1 - P(Believe)
So, we have
P(Not believe) = 1 - 53.2%
Evaluate
P(Not believe) = 46.8%
Hence, the probability that a statistics teachers do not know the true meaning of life is 46.8%
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The box and whisker blot below represent some data set. Which is the maximum value of the data?
The maximum value of the data = 64
We know that in the box and whisker plot with the left end of the whisker represents the minimum value of the data and the right end of the whisker represents the maximum value.
From the attached box and whisker plot, we can observe that between two numbers on the number line there are 5 equal units.
So, the value of each unit length = 4 unit
Here, the left end of the whisker has value 8 and the right end of the whisker has value 64
This means that the meaximum value = 64
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The group thought there was enough food for all 5 group members to complete the trip, with each person getting the required 5600 calories per day. However, they discover that they are missing 28,000 calories. Using the map, create a plan for the rest of the trip that includes taking as many group members as possible to the South Pole, while sending the rest of the group members directly back to base camp. Remember that each person must have 5,600 calories of food per day until he or she gets back to base camp.
Be sure to explain how you came up with your plan. Include all work necessary to support your answer.
Please answer as soon as possible due in an hour. Thank you.
The plan would be to send 2 group members back to base camp with enough food to sustain them for 5 days, while the remaining 3 members continue to receive 5,600 calories per day from the remaining food supply to complete the journey to the South Pole.
To create a plan for the rest of the trip, we need to consider the total number of days it will take for the group to return to base camp from their current location, and the number of group members who can be taken to the South Pole given the remaining food supply.
Given that the group is missing 28,000 calories, we can calculate the number of days of food that are missing by dividing 28,000 by the daily requirement of 5,600 calories per person. This gives us 5 days of missing food. Therefore, the group has enough food for 5 people to continue to receive 5,600 calories per day for 5 days, but not for all 5 members to continue for the entire trip.
To maximize the number of group members who can continue to the South Pole, we can send two members back to base camp immediately with enough food to sustain them for 5 days (2 people x 5 days x 5,600 calories/day = 56,000 calories). This will leave us with 3 group members who can continue to receive 5,600 calories per day for the remaining journey.
Assuming the trip back to base camp takes the same amount of time as the trip to the current location, we can estimate that the total trip duration will be around 20 days. Therefore, the remaining 3 group members will need a total of 20 days x 3 people x 5,600 calories per day = 336,000 calories.
Given the remaining food supply of 28,000 calories, we have a total of 364,000 calories available (28,000 missing calories + 336,000 required calories). Therefore, the 3 remaining group members can continue to receive their required daily calorie intake and complete the journey to the South Pole.
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Identify the area of a regular hexagon with side length 14in. rounded to the nearest tenth.
The area of a regular hexagon with side length 14 inches is 509.22 square inches.
Given that, a regular hexagon with side length 14 inches.
We know that, area of a regular hexagon can be calculated using A=3√3/2 a².
Here, area of a regular hexagon = 3√3/2 ×14²
= 3√3 ×98
= 509.22 square inches
Therefore, the area of a regular hexagon with side length 14 inches is 509.22 square inches.
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An ice block in the form of rectangular prism with a square base is melting at a rate of 550cm^3/min. The base length is decreasing at a rate of 1cm/min. How fast is the surface area of the ice block changning when the base length is 10cm, and height is 20cm?
The speed at which the surface area of the ice block changes when the base length is 10cm, and the height is 20cm is 180 cm^2 /min
What is the surface area of a rectangular prism?The total area or region that is covered by a rectangular prism's six faces is known as its surface area.
Solids called prisms have identical polygon bases and flat parallelogram sides. Prisms come in a variety of shapes, including triangles, squares, rectangles, pentagons, hexagons, and more.
Thus, it can be seen that the speed at which the surface area of the ice block changes when the base length is 10cm, and the height is 20cm is 180 cm^2 /min
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(X-3)/4+(x-1)/5-(x-2)/3=1
i Got u Bro! Answer:X=8x/15+77/15
:D
Rectangle WXYZ is dilated by a factor of 3 to make rectangle W'X'Y'Z. What is the perimeter of rectangle W'X'Y'Z?
The perimeter of rectangle W'X'Y'Z is 16 units
Perimeter of rectangle:he rectangle has four sides. There are two lengths and two widths in a rectangle. Therefore, the perimeter of the rectangle is twice the sum of two adjacent sides that are length and width. The formula is given by:
Perimeter of rectangle = 2(l + b)
We have :
Rectangle WXYZ will be the dilated by a scale factor of 1/2 creating rectangle W'X'Y'Z'
So, By the image:
The analysis will be the:
Rectangle of WXYZ = 2 × 4
and, The rectangle of W'X'Y'Z' = 2 × WXYZ
= 16
W'X' = 4
W'Z' = 4
Hence, The perimeter of rectangle is = 4 + 4 + 4 + 4 = 16
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The given question is incomplete, So i take the similar question :
Rectangle WXYZ will be the dilated by a scale factor of 1/2 creating rectangle W'X'Y'Z'. What is the perimeter of rectangle W'X'Y'Z?
And also to see the attachment.
Consider the following triangle.
A right triangle. The side opposite to theta is 5 meters and the side adjacent is 6 meters.
Determine the measure of the angle represented by Theta using the inverse tangent function.
a.
50.2º
b.
56.4º
c.
39.8º
d.
33.6º
Answer:
Step-by-step explanation:
tan theta=5/6
theta=tan-1(5/6)
=39.8º
the coordinate grid shows 4 locations. Each unit on the grid represents 1 city block. Jeremiah walk twice around the rectangular path connecting the four locations. how many city blocks does Jeremiah walk
From the graph, Jerimiah walks along 44 city blocks.
Hence the correct option is (D).
It is given that each unit on the grid represents 1 city block.
From the given graph we can see that
Number of city block between Restaurant and Museum = 7
Number of city blocks between Museum and Hotel = 4
Number of city blocks between Hotel and Arena = 7
Number of city blocks between Arena and Restaurant = 4
Total number of city blocks along the rectangular path = (7 + 4 + 7 + 4) = 22 city blocks.
Jerimiah walks twice around the rectangular path.
So Jerimiah walks through = 2*22 = 44 city blocks.
Hence the correct option will be (D).
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The question is incomplete. The complete question will be -
I NEED HELP WITH TTHIS PROBLEM IN STATISTICS
Answer:
Step-by-step explanation:
the median would be 9.
Noah tried to prove that
cos
(
�
)
=
sin
(
�
)
cos(θ)=sin(θ)cosine, left parenthesis, theta, right parenthesis, equals, sine, left parenthesis, theta, right parenthesis using the following diagram. His proof is not correct.
A right triangle A B C. Angle B A C is a right angle. Angle A C B is theta.
A right triangle A B C. Angle B A C is a right angle. Angle A C B is theta.
Statement Reason
1
�
∠
�
=
�
m∠B=θm, angle, B, equals, theta The acute angles in a right triangle are congruent.
2
sin
(
�
)
=
�
�
�
�
sin(θ)=
BC
AB
sine, left parenthesis, theta, right parenthesis, equals, start fraction, A, B, divided by, B, C, end fraction Definition of sine.
3
cos
(
�
∠
�
)
=
�
�
�
�
cos(m∠B)=
BC
AB
cosine, left parenthesis, m, angle, B, right parenthesis, equals, start fraction, A, B, divided by, B, C, end fraction Definition of cosine.
4
cos
(
�
)
=
�
�
�
�
cos(θ)=
BC
AB
cosine, left parenthesis, theta, right parenthesis, equals, start fraction, A, B, divided by, B, C, end fraction Substitution.
5
cos
(
�
)
=
sin
(
�
)
cos(θ)=sin(θ)cosine, left parenthesis, theta, right parenthesis, equals, sine, left parenthesis, theta, right parenthesis Substitution
The possible first mistake Noah made in the evaluation of the sine and cosine of the acute angles of a right triangle is that the acute angles are complementary and are not always congruent. The correct option is the option (A).
(A) Angles ∠B and ∠C are complementary, not congruent
What are complementary angles?Complementary angles are angles that when added together are equivalent to 90°
The possible two column table Noah used to attempt to prove that cos(θ) = sin(θ) obtained in a similar proof on the website can be presented as follows;
Statement [tex]{}[/tex] Reason
1 m∠B = θ [tex]{}[/tex] The acute angles in a right triangle are congruent
2 sin(θ) = AB/BC [tex]{}[/tex] Definition of sine
3 cos(m∠B) = AB/BC [tex]{}[/tex] Definition of cosine
4 cos(θ) = AB/BC [tex]{}[/tex] Substitution
5 cos(θ) = sin(θ) [tex]{}[/tex] Substitution
Part of the question is; What is the first mistake in Noah's statement used to prove that cos(θ) = sin(θ)
The first mistake is the statement and reason that angle m∠B = θ because all acute angles are congruent.
The acute angles in the right triangle are ∠B and ∠C
The sum of the acute angles in a right triangle is; ∠B + ∠C = 90°
Therefore the acute angles in a right triangle are always complementary, and not always congruent.
The correct option is therefore the option (A)
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Given that a/b=3/4 and b/c=5/6 find a:b:c Give you answer in its simplest form
Answer:
LCM of 4 and 5 is 20.
a/b = 3/4 = 15/20
b/c = 5/6 = 20/24
a:b:c = 15:20:24
19. Two angles are complementary. The larger
angle is 36 more than the smaller angle. What
is the measure of the larger angle?
Answer:
larger angle = 63°
Step-by-step explanation:
complementary angles sum to 90°
let x be the smaller angle then larger angle is x + 36 , then
x + x + 36 = 90
2x + 36 = 90 ( subtract 36 from both sides )
2x = 54 ( divide both sides by 2 )
x = 27
Then
larger angle = x + 36 = 27 + 36 = 63°
What is the sum?
X
3
2
+
x+3 x+3 " x+3
0
+
5
X+5
x+3
X+5
3x+27
Ex
x+3
Answer: 2, 2, 135, 9, 5, 35, 15, 10, 15, 15
Step-by-step explanation:
Please Help Quickly ASAP Hurry Geometry ASAP
Questions in the picture
Answer:
The answer is Area: 25.5
Step-by-step explanation:
Mr. James is teaching his students about the volume of rectangular prisms. He has various rectangular prisms with a height of 6 inches. The table shows the relationship between the base of the prism and its volume. Which equation can be used to find B, the area of the base with a volume of V?
The proportional relationship used to find B, the area of the base with a volume of V, is given as follows:
B = V/6.
What is a proportional relationship?A proportional relationship is a type of relationship between two quantities in which they maintain a constant ratio to each other.
The equation that defines the proportional relationship is given as follows:
y = kx.
In which k is the constant of proportionality, representing the increase in the output variable y when the constant variable x is increased by one.
From the table given in the image at the end of the answer, we have that the base area is a sixth of the volume, hence the equation is:
B = V/6.
Missing InformationThe table is given by the image presented at the end of the answer.
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The data table shows the numbers of eggs laid by
individual chickens in a year
What is the median number of eggs laid in a year?
A. 231
B. 229
C. 230
D. 234,6
The value of the median number of eggs laid in a year is,
⇒ 231
We have to given that;
The data table shows the numbers of eggs laid by individual chickens in a year.
Now, We can arrange it into ascending order as;
⇒ 222, 229, 229, 231, 234, 235, 262
Since, There are 7 terms
Hence, Median is,
= (7 + 1)/2
= 4th term
= 231
Thus, The value of the median number of eggs laid in a year is,
⇒ 231
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Answer:
A. 229 is correct
answer D.231 is wrong
