To find the value of f(2), we need to use the equation of the normal to the curve at the point (2,-1). We know that the normal to the curve is perpendicular to the tangent at that point.
From the given equation of the normal, we can determine the slope of the tangent line, which is -1/2.
Now we can use the point-slope form of a line to find the equation of the tangent line to the curve at (2,-1): y + 1 = (-1/2)(x - 2).
To solve for f(2), we need to find the y-coordinate of the point on the curve that lies on this tangent line. We can substitute x=2 into the equation of the tangent line to find the y-coordinate: y + 1 = (-1/2)(2 - 2) => y = -1.
Therefore, f(2) = -1.
Choose the correct graph of the function
|y=-
1
√x-2-3
The correct graph of the function [tex]y=-1\sqrt{x-2-3}[/tex] is attached as picture below.
How can we graph a function?To graph a function, we need to first determine the domain and range of the function. The domain is the set of all possible input values for the function, while the range is the set of all possible output values. Once we have determined the domain and range, we can plot the points on a graph.
To plot the graph, we can choose a set of values for the independent variable (usually denoted as x) and use the function to find the corresponding values of the dependent variable (usually denoted as y). We can then plot these points on the graph and connect them to create a curve that represents the function.
Graph using the end point and a few selected points.
x y
2 − 3
3 −4
4 −4.41
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Eleni rents a car on two separate occasions. The first time she pays $180 for 3 days and 150km
The average cost per day is $90 and the average cost per km is $0.655.
To calculate the average cost per day, we need to first calculate the total cost of renting the car for both occasions and divide it by the total number of days.
The total cost of renting the car for both occasions is $180 + $180 = $360. The total number of days is 4 (2 days for each occasion).
Therefore, the average cost per day is $360 ÷ 4 = $90.
To calculate the average cost per km, we need to first calculate the total cost of renting the car for both occasions and divide it by the total number of kilometers driven.
The total cost of renting the car for both occasions is $180 + $180 = $360. The total number of kilometers driven is 550km (150km for the first occasion + 400km for the second occasion).
Therefore, the average cost per km is $360 ÷ 550km ≈ $0.655.
Correct question is " Eleni rents a car on two separate occasions. The first time, she paid $180 for 2 days and 150km. The next time, she paid $180 for 2 days and 400km. What is the average cost per day? What is the average cost per km?"
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Suppose a jar contains 7 red marbles and 18 blue marbles. If you reach in the jar and pull out 2 marbles at random at the same time, find the probability that both are red.
Answer:
63
Step-by-step explanation:
we divided 18÷2=9
and we multiply 9×7=63
Answer:
[tex]p(a) = \frac{7}{100} [/tex]
Step-by-step explanation:
Given:
7 red marbles
18 blue marbles
Total number of marbles: 7 + 18 = 25
All outcomes:
[tex]n = \frac{25 \times 24}{2 \times 1} = 300[/tex]
25 × 24, because the first marble can be pulled out in 25 ways, and the second marble - in 24 ways, since the first one has already been pulled out.We divide by the factorial of 2, because the order does not matter how we pull out the marblesLet's name the event A:
A - "both marbles are red"
Event's A favorable outcomes:
[tex]m(a) = \frac{7 \times 6}{2 \times 1} = 21[/tex]
7 × 6, because we only need to pull the red marbles out, so there are 7 ways to pull out the 1st marble and 6 ways for the 2nd one to be pulled out (the order doesn't matter)[tex]p(a) = \frac{m(a)}{n} = \frac{21}{300} = \frac{7}{100} [/tex]
In which survey was a parameter reported? Select two answers.
Answer: would be great if you could give the options of the questions?
3) Dados los siguientes 35 números:
2,2,2,2,2,4,4,4, 4, 6, 6,6, 6, 6, 4, 4, 4, 4, 8, 8, 8, 6, 6, 6, 6, 6, 10, 10, 10, 8, 8, 8, 10, 10 y 10
3.1) Calcule la mediana con la lista de los datos.
3.2) Calcule la media y mediana realizando una tabla de frecuencias.
Answer:
3.1) Para calcular la mediana de la lista de datos, primero debemos ordenarlos de menor a mayor:
2, 2, 2, 2, 2, 4, 4, 4, 4, 4, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6, 8, 8, 8, 8, 8, 10, 10, 10, 10, 10, 10
Como la lista tiene un número impar de elementos (35), la mediana es el valor central de la lista, es decir, el elemento en la posición 18. En este caso, el valor de la mediana es 6.
3.2) Para calcular la media y la mediana mediante una tabla de frecuencias, primero debemos determinar las frecuencias de cada valor en la lista:
Valor Frecuencia
2 5
4 8
6 9
8 5
10 8
La media se calcula sumando todos los valores y dividiendo entre el número total de elementos:
media = (25 + 48 + 69 + 85 + 10*8) / 35 = 5.8
Para calcular la mediana, primero debemos determinar el valor que ocupa la posición central de la lista. Como el número total de elementos es impar, ese valor es el que ocupa la posición (n+1)/2, donde n es el número total de elementos. En este caso, ese valor es el que ocupa la posición (35+1)/2 = 18.
Luego, debemos encontrar el valor que ocupa la posición 18 contando los valores de la tabla de frecuencias. Podemos hacer esto sumando las frecuencias hasta alcanzar o superar la posición 18:
Valor Frecuencia Frec. Acumulada
2 5 5
4 8 13
6 9 22
8 5 27
10 8 35
Como la posición 18 está dentro del intervalo correspondiente al valor 6, la mediana es 6.
Find the area and the circumference of a circle with a radius of 2km. Write your answers in terms of pi, and be sure to include the correct units in your answers.
The area and the circumference of the circle would be 4π square kilometers and 4π kilometers respectively.
Area and circumference of a circleThe area of a circle with a radius r is given by:
A = πr^2The circumference of a circle with a radius r is given by:
C = 2πr.Given that the radius of the circle is 2km, we can substitute r = 2 into these formulas to find the area and circumference:
Area = πr^2 = π(2km)^2 = 4π km^2Circumference = 2πr = 2π(2km) = 4π kmIn other words, the area and the circumference of the circle are 4π square kilometers and 4π kilometers respectively.
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1. In a city where the sales tax rate is 12%, how much sales
tax will be charged on a purchase of $30.00?
A. $0.12
B. $0.25
C. $0.36
D. $1.20
E. $3.60
Answer: $3.60
Step-by-step explanation: $30(Item Purchased)x0.12(Sales Tax)=$3.60(Sales Tax Rate for a 12% Sales Tax State.)
4(1 +6p)
U need to simplify the expressions what would be the answer
Aldrin bought 5 pencils and 7 notebooks. A notebook cost 10. 80 more than a pencil write an algebraic equation showing that the total amount of the school supplies bought is210. 00
Answer:
5x + 7(x + 10.80) = 210.00
Step-by-step explanation:
Let x be the cost of a pencil in dollars. Then, the cost of a notebook is 10.80 dollars more, which is x + 10.80 dollars.
Aldrin bought 5 pencils and 7 notebooks, so the total cost is:
5x + 7(x + 10.80) = 210.00
Simplifying and solving for x, we have:
5x + 7x + 75.60 = 210.00
12x = 134.40
x = 11.20
Therefore, a pencil costs 11.20 dollars and a notebook costs 10.80 dollars more, which is 22.00 dollars.
We can check that the total cost of 5 pencils and 7 notebooks at these prices is indeed 210.00 dollars:
5 pencils * 11.20 dollars/pencil + 7 notebooks * 22.00 dollars/notebook = 56.00 dollars + 154.00 dollars = 210.00 dollars
Curious about people's recycling behaviors, Sandra put on some gloves and sifted through some recycling and trash bins. She kept count of the plastic type of each bottle and which bottles are properly dispensed.
What is the probability that a randomly selected bottle is correctly placed AND is a Plastic #4 bottle?
show all steps
The probability that a randomly selected bottle is correctly placed AND is a Plastic #4 bottle is: P(Correctly placed and Plastic #4) = 15/100 = 0.15 is 15% chance.
What is probability?
To find the probability that a randomly selected bottle is correctly placed AND is a Plastic #4 bottle, we need to divide the number of bottles that meet both conditions by the total number of bottles.
Let's say Sandra examined 100 bottles, and 60 of them were properly placed, and 25 of them were Plastic #4 bottles, and 15 of those Plastic #4 bottles were also properly placed.
Then, the number of bottles that meet both conditions is 15, and the total number of bottles is 100. Therefore, the probability that a randomly selected bottle is correctly placed AND is a Plastic #4 bottle is:
P(Correctly placed and Plastic #4) = 15/100 = 0.15
So, there is a 15% chance that a randomly selected bottle is both correctly placed and a Plastic #4 bottle.
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Complete question is: Curious about people's recycling behaviors, Sandra put on some gloves and sifted through some recycling and trash bins. She kept count of the plastic type of each bottle and which bottles are properly dispensed. The probability that a randomly selected bottle is correctly placed AND is a Plastic #4 bottle is: P(Correctly placed and Plastic #4) = 15/100 = 0.15 is 15% chance.
A rectangle is drawn so the width is 7 inches longer than the height . If the rectangle’s diagonal measurement is 34 inches, find the height
Answer:
To solve this problem, we can use the Pythagorean theorem, which relates the sides of a right triangle. Let's call the height "h" and the width "w". Then we have: w = h + 7 (since the width is 7 inches longer than the height) We also know that the diagonal measurement is 34 inches, so we can use the Pythagorean theorem to relate the height, width, and diagonal: h^2 + w^2 = d^2 Substituting the values we have: h^2 + (h+7)^2 = 34^2 Expanding and simplifying: 2h^2 + 14h - 795 = 0 Now we can solve for h using the quadratic formula: h = (-14 ± sqrt(14^2 - 4(2)(-795))) / (
Can anyone help? Look at image below
Linear Scale Factor:
1) Enlargement. Scale Factor = 18/6 = 3
2) Reduction. Scale factor = 6/12 = 1/2
The side of a square floor tile is measured to be 12 inches, with a possible error of 1/32 inch. Use differentials to approximate the possible propagated error in computing the
area of the square.
±
in²
Answer:
Step-by-step explanation:
r=12 in
dr=±32
A=πr²
dA=2 πr×dr=2π×12×1/32=3π/4
Possible error in computing the area=3π/4 ~square~inches.
Triangle PQR is drawn with coordinates P(0,2), Q(0, 5), R(1, 4). Determine the translation direction and number of units if R'(-7, 4)
A. 8 units down
B. 8 units up
C. 8 units to the right
D. 8 units to the left
the correct answer is (D) 8 units to the left. To find the translation direction and number of units, we need to find the vector that takes us from point R to point R'.
Vector RR' can be found by subtracting the coordinates of R from the coordinates of R':
RR' = R' - R = (-7, 4) - (1, 4) = (-8, 0)
This means that the translation moves 8 units to the left, since the x-coordinate of the vector is negative.
To determine the translation direction and number of units required to move R to R', we need to first find the distance between the x-coordinates of R and R'. We can do this by subtracting the x-coordinate of R from the x-coordinate of R': -7 - 1 = -8.
This tells us that we need to move R' 8 units to the left to get to R. However, the question is asking for the translation required to move R to R', not the other way around. Therefore, we need to reverse the direction and say that we need to move R 8 units to the right to get to R'.
We can confirm this by checking the y-coordinates of R and R'. We see that they are both 4, which means there is no vertical translation required. Therefore, the answer is C. 8 units to the right.
Therefore , the correct answer is (D) 8 units to the left.
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please helppppppppppppppppppppp
Answer:
AB = 14 units
BC = 11 units
CD = 14 units
AD = 11 units
Step-by-step explanation:
d=√((x2-x1)²+(y2-y1)²)
AB= (-7,6)-(7,6) √((7+7)²+(6-6)²)=√((14)²+(0)²)=√(196+0)=√(196)=14
BC= (7,6)-(7,-5) √((7-7)²+(-5-6)²)=√((0)²+(-11)²)=√(0+121)=√(121)=11
CD= (7,-5)-(-7,-5) √((-7-7)²+(-5+5)²)=√((-14)²+(0)²)=√(196+0)=√(196)=14
AD= (-7,-5,)-(-7,6) √((-7+7)²+(6+5)²)=√((0)²+(11)²)=√(0+121)=√(121)=11
A portfolio has a value P(E, S), so that the value P is a function of E, the price of a Euro in Canadian dollars, and S, the level of the TSX stock index. Presently the portfolio is worth $207,000, while a Euro is $1.50 Canadian, and the index is S = 18,000. If the partial derivatives of P have values ∂P ∂E = 80,000, and ∂P ∂S = −20, what approximately will the portfolio value be if the price of a Euro goes down by 0.07 and the stock index goes down by 629?
Answer:
The new value of the portfolio would be $207,000 - $18,180 = $188,820
Step-by-step explanation:
Using the first-order partial derivatives, we can calculate the approximate change in the portfolio value due to changes in E and S using the formula:
ΔP ≈ ∂P/∂E * ΔE + ∂P/∂S * ΔS
where ΔE is the change in the price of a Euro and ΔS is the change in the TSX stock index.
Given that ∂P/∂E = 80,000 and ∂P/∂S = -20, and the changes ΔE = -0.07 and ΔS = -629, we can plug in the values and get:
ΔP ≈ 80,000 * (-0.07) + (-20) * (-629)
≈ -5,600 - 12,580
≈ -18,180
Therefore, the portfolio value is expected to decrease by approximately $18,180 if the price of a Euro goes down by $0.07 and the TSX stock index goes down by 629 points. The new value of the portfolio would be $207,000 - $18,180 = $188,820.
so what do i do when is multiply a improper and a proper fraction
Answer:
Multiply the numerators first together then multiply the denominators together.
Step-by-step explanation:
example 1/2(4/2) =4/4 = 1
Let A ={1, 2, 3, 4, 5}, and let R be the relation on A given by
R= {(x, y): x y and x is prime)
i. List the elements of R
ii. Give matrix representation of R
iii. Give di-graph of R.
iv. Check whether R is reflexive, symmetric, transitive, equivalence, anti-symmetric,
asymmetric and irreflexive with reasons.
Asymmetric: Since, for instance, (2,3) is in R but (3,2) is not, R is not asymmetric. No element in A is connected to itself under R, making R irreflexive.
describe range.The collection of output values that such a function of relation can produce is referred to as the range in mathematics. It is the distinction between the largest or smallest values within an ensemble of data or a collection of all conceivable function or relation output values.
In other terms, it is the range of possible values for a variable. For instance, the range is 21 - 3 = 18 if the integers are 3, 7, 12, 15, and 21. The set of all value of y which may be produced by a function f(x) for the given subject area of x values is known as the range.
given
We will now examine the many characteristics of the relation R:
As no element in A is connected to itself under R, R is not reflexive. For instance, R does not support (2,2).
R is not symmetric since, for instance, (3,2) is not in R yet (2,3) is.
R is transitive because, for instance, the existence of (2,3) and (3,5) in R entails the existence of (2,5) in R.
Equivalence: As R is not reflexive or symmetric, it is not an equivalence relation.
Asymmetric: Since, for instance, (2,3) is in R but (3,2) is not, R is not asymmetric. No element in A is connected to itself under R, making R irreflexive.
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Vary the plane of intersection, and note all the types of cross sections you observe. In the table, describe the shape of the cross section formed when a particular plane passes through the pyramid.
Answer:
Cross Sections
In this task, you will use cross section flyer, an online tool, to investigate the cross sections of cones, cylinders, pyramids, and prisms by passing different planes through such objects.
For each part of this task, you will select a three-dimensional object from the list of shapes in the bottom-left corner of the screen. A three-dimensional view of the object appears on the left, and the two-dimensional cross section formed by the intersection of the object with the chosen plane appears on the right. The bottom-right controls allow you to rotate and move the plane of intersection. By varying the intersecting plane, you can change the resulting cross section.
You can also adjust the view of the three-dimensional object by clicking and dragging anywhere inside the object window. Use the coordinate X-Y-Z axes to guide you through the views. You can verify the name of a cross section by using the Click to show identification of cross section checkbox.
A rectangular prism has a base area of 54 m square, and a volume of 702 m. What is its height?
Answer:
Therefore, the height of the rectangular prism is approximately 13 meters.
Step-by-step explanation:
Let's call the height of the rectangular prism "h". We know that the base area is 54 m², which means that the product of the length "l" and the width "w" is 54. In other words:
l × w = 54
We also know that the volume of the rectangular prism is 702 m³, which means:
l × w × h = 702
We can use the first equation to solve for one of the variables, for example:
w = 54 / l
Substituting this expression for "w" into the second equation, we get:
l × (54 / l) × h = 702
Simplifying and canceling the "l" terms, we get:
54h = 702
Dividing both sides by 54, we get:
h = 702 / 54
Simplifying this expression, we get:
h ≈ 13
Therefore, the height of the rectangular prism is approximately 13 meters.
What is the value of x?
4.
A 20
B 25
C 70°
D 90
280°
4x
Answer:
70°
Step-by-step explanation:
280°÷4x
what is x?
x=70°
: Find the ordered pair solutions for the system of equations. please help
Answer:
(-1, 2) and (4, -8)
Step-by-step explanation:
You want the ordered pairs (x, f(x)) that satisfy both equations ...
f(x) = x² -5x -4f(x) = -2xSolutionEquating the two expressions for f(x), we have ...
x² -5x -4 = -2x
x² -3x -4 = 0
(x -4)(x +1) = 0
x = 4 or -1
Corresponding values of f(x) are ...
f(x) = -2{4, -1} = {-8, 2}
Ordered pair solutions are ...
(x, f(x)) = (-1, 2) and (4, -8)
Find the 5th term of the arithmetic sequence 4x+4, -x+10, -6x+16...
Answer:
-16x+28
Step-by-step explanation:
Using the 2nd and 1st term in the sequence, we can find the change.
4x+4, -x+10. Using mental math, we can see that x decreases by 5 and 4 increases by 6. Using this, the change is -5x + 6.
The easiest way to solve this is mental math because the 5th term is very close to the last term (the 3rd).
Solving:
-6x+16 = 3rd term, so -6x+16-5x+6 = -11x+22 | -11x+22-5x+6 = -16x+28.
I need help can someone help thxxxx
Answer:
I hope this helps :)
Step-by-step explanation:
its the correct answer
Fill in table using this function rule y= -4x - 2. I'm confused on on the table of function on what they y is when x is -10
When x is -10, the value of y is 38. This means that the point (-10, 38) is on the graph of the function y = -4x - 2.
We must determine the values of x and solve for the matching value of y in order to fill in the table using the function rule y = -4x - 2. The table can then be populated with the resulting values for x and y.
An illustration table with x values ranging from -3 to 3 is shown below:
x y
-3 10
-2 6
-1 2
0 -2
1 -6
2 -10
3 -14
We may easily change x in the function rule y = -4x - 2 to -10 to find the value of y when x is -10:
y = -4(-10) (-10) - 2 \sy = 40 - 2 \sy = 38
As a result, y equals 38 when x is -10. This indicates that the point (-10, 38) is located on the y = -4x - 2 function graph.
It's vital to remember that the numbers in the table are produced by inserting various x values into the function rule, and the resulting y-values represent the corresponding locations on the function's graph. The line passing through the point on the graph of the function y = -4x - 2 has a slope of -4 and a y-intercept of -2. (-10, 38).
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Solve the simultaneous equations
X-Y=-1
2X-Y=0
Answer: X = 1, Y = 2
Step-by-step explanation:
X - Y = -1
X = Y - 1
2(Y - 1) - Y = 0
2Y - 2 - Y = 0
Y - 2 = 0
Y = 2
X - (2) = -1
X - 2 = -1
X = 2 - 1
X = 1
Please see the attachment
a) The temperature decreases at a rate of -4°C per km.
b) The temperature is 0°C at a height of 8km
At what rate does the temperature changes?Here we can see the graph of a relation between the height and the temperature.
We can see that the line goes downwards from left to right, this means that as the height increases, the temperature decreases.
Notice that the horizontal squares represent 1km, while the vertical ones represent 4°C, then, the temperature is decreasing at a rate of -4°C per kilometer, your answer is correct here.
At which height is the temperature zero?
the temperature is zero at the horizontal axis, we can see that the line meets the horizontal axis at a height of 8 km, so that is the answer here.
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RQPS is rotated 180° clockwise about the origin.
10
9
8
7
6
5
R
S
P
1 2 3 4 5 6 7 8 9 10
What are the coordinates of P'?
OA. (-7,2)
B. (-2,-7)
O, C. (-7,-2)
D. (7,-2)
Step-by-step explanation:
The answer is (-2, -7)
Before rotated, the coordinates of P is (7,2)
Imagine if P is rotated 360° clockwise, it will come back to the initial place (7,2).
Now it is just rotated 180° clockwise, halfway of 360° clockwise. So the coordinates should be(-7,-2) after rotated 180° clockwise.
PLEASE. HELP. ME.
Find the measure of the missing angles.
Answer:
∠h = 61°
∠g = 119°
∠m = 59°
∠k = 121°
Step-by-step explanation:
According to the Vertical Angles Theorem, when two straight lines intersect, the opposite vertical angles are congruent.
Therefore, as angle g is opposite 119°:
⇒ ∠g = 119°
As angle k is opposite 121°:
⇒ ∠k = 121°
Angles on a straight line sum to 180°.
As angle h and 119° form a straight line:
⇒ ∠h + 119° = 180°
⇒ ∠h + 119° - 119° = 180° - 119°
⇒ ∠h = 61°
As angle m and 121° form a straight line:
⇒ ∠m + 121° = 180°
⇒ ∠m + 121° - 121° = 180° - 121°
⇒ ∠m = 59°
Answer:
see belowStep-by-step explanation:
To find:-
The values of m , k , g and h .Answer:-
From the given figure we can see that angles k and 121° are vertically opposite angles . Also we know that vertically opposite angles are equal to each other. Hence here we can say that,
[tex]\longrightarrow \boxed{ k = 121^o}\\[/tex]
Secondly, we know the the mesure of angle of a straight line is 180° . So the sum of angles on a straight line would be 180° . If two angles are present we call them linear pair . Hence here , we can see that m and 121° are linear pairs.
So that,
[tex]\longrightarrow m + 121^o = 180^o \\[/tex]
[tex]\longrightarrow m = 180^o-121^o\\[/tex]
[tex]\longrightarrow \boxed{m = 59^o } \\[/tex]
Similarly we can see that g and 119° are vertically opposite angles. Again they will be equal. So ,
[tex]\longrightarrow \boxed{g = 119^o} \\[/tex]
Again, 119° and h form linear pair.So their sum would be 180° .
[tex]\longrightarrow h + 119^o = 180^o \\[/tex]
[tex]\longrightarrow h = 180^o - 119^o\\[/tex]
[tex]\longrightarrow \boxed{ h = 61^o }\\[/tex]
These are the required values of the unknown angles.
Kaira collects data on the costs of maracas: $12.50, $13.00, $13.25, $14.25,
$14.50, $14.50, $14.50, $14.75, $15.75, $16.00, $16.50. Explain why a stem-and-leaf
plot would be an appropriate display to use to analyze and interpret the data.
The stem and leaves display the image and distribute information continuously. These charts are similar to histograms, but instead of using lines, they show numbers. It is a useful tool, especially when searching for statistical information.
The stem and leaf diagram, also known as the stem and leaf diagram, is a method of organizing data in a way that makes it easy to observe the frequency of importance of different species. A chart that shows numerical data arranged in a series. Each data value or number is divided into stems and leaves.
Rows and sheets are represented in the form of a special table in which each first digit or digit of the document value is divided by the stem and the last digit of the document in sheets. The letter is used to represent the stem and leaf, called stem and leaf values.
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