The line y = - (1 / 3) · x + 4 is a equation perpendicular to line y = 3 · x + 7.
How to derive the equation of a line perpendicular to another line
Algebraically speaking, lines are described by the following equation:
y = m · x + b
Where:
m - Slopeb - y-Interceptx - Independent variable.y - Dependent variable.And two lines are perpendicular to each other if the product of their slopes is equal to:
m · m' = - 1
Where:
m - Slope of the original line.m' - Slope of the perpendicular line.Now we proceed to determine the equation of the perpendicular line. First, write the slope of the original line:
m = 3
Second, calculate the slope of the perpendicular line:
m' = - 1 / 3
Third, find the y-intercept:
b = y - m' · x
b = 0 - (- 1 / 3) · 12
b = 4
Fourth, write the resulting equation of the line:
y = - (1 / 3) · x + 4
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rose curves are characterized by equations of the form r=acos(ntheta) or r=asin(ntheta), a=/0. inf n=/0 is even, the rose has ____ petals; if n=/ -1 is odd, the rose has ___ petals
Rose curves are characterized by equations of the form r = a cos (nθ) or r = a sin (nθ), a ≠ 0. If n ≠ 0 is even, the rose has 2n petals; if n ≠ ± 1 is odd, the rose has n petals.
This means that the number of petals of a rose curve depends on the value of n in the equation. If n is even, the number of petals is 2n, and if n is odd, the number of petals is n.
The value of a determines the size of the rose curve. If a is large, the curve will be large, and if a is small, the curve will be small. The cosine or sine function determines the shape of the rose curve.
The cosine function results in a rose curve that is symmetrical about the x-axis, while the sine function results in a rose curve that is symmetrical about the y-axis.
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--The given question is incomplete; the complete question is
"Complete the sentence below.
Rose curves are characterized by equations of the form r = a cos (nθ) or r = a sin (nθ), a ≠ 0. If n ≠ 0 is even, the rose has___ petals; if n ≠ ± 1 is odd, the rose has____ petals."--
use the component method of vector addition to find the resultant of the following three vectors: a = 56 km, east b = 11 km, 22° south of east c = 88 km, 44° west of south
Using the component method of vector addition, the resultant of the given three vectors is 63.803 km at an angle of -86.6° from the positive x-axis.
We must divide each vector into its x- and y-components in order to use the component method to obtain the resultant of the given vectors.
The resultant vector can then be obtained by adding the x- and y-components together.
Vector a = 56 km, east
The x-component of vector a = 56 km
The y-component of vector a = 0 km
Vector b = 11 km, 22° south of east
To find the x-component, we can use trigonometry:
x-component = 11 km * cos(22°) = 10.213 km
To find the y-component, we can use trigonometry:
y-component = 11 km * sin(22°) = -4.282 km
Vector c = 88 km, 44° west of south
To find the x-component, we can use trigonometry:
x-component = 88 km * sin(44°) = -61.578 km
To find the y-component, we can use trigonometry:
y-component = 88 km * cos(44°) = -59.229 km
x-component: 56 km + 10.213 km + (-61.578 km) = 4.635 km (east is positive)
y-component: 0 km + (-4.282 km) + (-59.229 km) = -63.511 km (north is positive)
Resultant = sqrt((4.635 km)^2 + (-63.511 km)^2) ≈ 63.803 km
The direction of the resultant vector can be found using the inverse tangent function:
angle = atan(-63.511 km / 4.635 km) ≈ -86.6°
Thus, the resultant vector is approximately 63.803 km at an angle of -86.6° from the positive x-axis.
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Which equations correctly relate distance rate and time?
d=rt
d/r=t
t+r=d
dr=t
r=d/t
d+=r
Answer:
d=rt, d/r=t, and r=d/t
Step-by-step explanation:
d=rt is a correct option, so we can use this to solve for others
if you isolate t, d/r=t is also correct
isolate r to get r=d/t
Determine the value(s) of the variable for which the expression is undefined.
1)-
5
x-10
A)x= 10, x=-5
12
4)=
2)
Write the rational expression in lowest terms.
8z³
3)
20z6
15
12-4
C)
A).
A)
A) Never undefined-any real number may be substituted for y
B) 15
C) -2, 2
D) 4
+ 5y - 36
1²-16
y + 9
y-4
8
20z³
B)x= -10
5y-36
16
C)x=10
B) 23⁹
2
99-3333
B) cannot simplify
D)
y+9
y+4
D) x=5
D) 2535
1)
3)
4)
Whole page pls
The lowest term of rational expression is 4z⁶/3
What is rational expression?
A rational expression is simply a quotient of two polynomials. Or in other words, it is a fraction whose numerator and denominator are polynomials.
Rational expressions look like fractions that have variables in their denominators (and often numerators too). For example, x 2 x + 3 \dfrac{x^2}{x+3} x+3x2 start fraction, x, squared, divided by, x, plus, 3, end fraction is a rational expression.
To write a rational expression in lowest terms, we must first find all common factors (constants, variables, or polynomials) or the numerator and the denominator. Thus, we must factor the numerator and the denominator. Once the numerator and the denominator have been factored, cross out any common factors.
A) The expression is undefined when x=10 or x=-5 because the denominator would be equal to zero, which is undefined in mathematics.
B) The rational expression 8z³/20z⁶ can be simplified to 2z³/5z⁶. The expression can be further simplified by dividing both the numerator and denominator by z³, giving us 2/5z³.
C) The expression 12-4/5y-36 is undefined when y=-9 or y=4 because the denominator would be equal to zero, which is undefined in mathematics.
D) The expression (99-3333)/2535 cannot be simplified as the numerator and denominator are prime numbers and cannot be further reduced.
So, the answer is:
A) x=10, x=-5
B) 2/5z³
C) y=-9, y=4
D) cannot simplify
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An electronic scale in an automated filling operation stops the manufacturing line after three underweight packages are detected. Suppose that the probability of an underweight package is 0.001 and each fill is independent. a. What is the average number of fills before the line is stopped? b. What is the standard deviation of the number of fills before the line is stopped?
The average number of fills before the line is stopped is 1000 and the standard deviation is 31.62. This means that over many repetitions of the automated filling operation, the number of fills before the line is stopped will tend to be around 1000, with most values falling within 31.62 units of 1000
An electronic scale in an automated filling operation is a device used to measure the weight of packages filled with a certain product. The purpose of the scale is to ensure that each package is filled with the correct amount of product. In this case, the scale stops the manufacturing line after three underweight packages are detected.
a. The average number of fills before the line is stopped can be calculated using the formula for the expected value. The expected value is the average outcome of a random process over many repetitions. In this case, the random process is the number of fills before the line is stopped. The expected value can be calculated as follows: E(x) = 1/p, where p is the probability of an underweight package. Plugging in the value of p = 0.001, we get E(x) = 1/0.001 = 1000. So, the average number of fills before the line is stopped is 1000.
b. The standard deviation of the number of fills before the line is stopped can be calculated using the formula for the standard deviation of a Poisson distribution. The Poisson distribution is a discrete probability distribution that is used to model the number of events in a fixed interval of time or space. In this case, the events are underweight packages. The standard deviation can be calculated as follows: σ = √(λ), where λ is the expected value. Plugging in the value of λ = 1000, we get σ = √(1000) = 31.62. So, the standard deviation of the number of fills before the line is stopped is 31.62.
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Reflect the point (13, 8). across the y-axis. What is the result?
The image of the point after the reflection across the y-axis is:
(-13, 8)
What is the image of the point after the reflection?Remember that for a general point (x, y), a reflection across the y-axis just changes the sign of the x-component, so the new point will be:
(-x, y)
Here we want to apply this reflection to (13, 8), using the rule above, we can see that the new coordinates after the reflection are:
(-13, 8)
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El papa de Carlos compró 5 películas por $250 si solo comprara 2 películas ?cuanto pagaría?
(a) estimate the area under the graph of f(x)=55−x2 from x=−2 to x=4 using three approximating rectangles and right endpoints.
By splitting the range into three equal pieces and approximating the area under the graph using rectangles with right endpoints, the area under the graph of f(x) from x=-2 to x=4 is calculated.
Area = (55 - (-2)^2) + (55 - (1)^2) + (55 - (4)^2) = 55 + 9 + 1 = 65
By splitting the interval into three equal pieces and approximating the area under the graph using rectangles with right endpoints, the area under the graph of
f(x)=55x2 from x=2 to x=4
is calculated. We begin by calculating the area of the rectangle whose right endpoint is at
x = -2. F(-2)
provides the height of this rectangle, which is equal to
55 - (-2)2 = 55 + 4 = 59.
The rectangle's width is
(4 - (-2))/3 = 6/3 = 2.
The area of this rectangle is therefore 59 x 2 = 118. The area of the rectangle with x = 1 as its right terminus can also be determined in a similar manner. This rectangle has a height of f(1), which equals
55 - (1)2 = 55 - 1 = 54.
The rectangle's width is
(4 - (-2))/3 = 6/3 = 2
The area of this rectangle is therefore 54 x 2 = 108. f(4), which equals 55 - (4)2 = 55 - 16 = 39, gives the area of the rectangle with x = 4 as the right endpoint. The rectangle's width is
(4 - (-2))/3 = 6/3 = 2.
The area of this rectangle is therefore 39 x 2 = 78. The sum of the areas of the three rectangles, which equals 118 + 108 + 78 = 304, represents the total area under the graph.
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GROWTH An old oak tree is 1012 inches tall. A younger oak tree near it is 98 inches tall. About how many orders of magnitude as tall is the old oak tree?
Based on the information given, the old oak tree is 1 order of magnitude or ten times bigger in comparison to the younger oak tree.
How to calculate the orders of magnitude?In mathematics and related areas, the orders of magnitude compare two items or variables using 10 as a reference. In this way, if the value is 10 times bigger than another the order of magnitude is 1 (one zero), but if one value is 100 times bigger then the order of magnitude is 2(100 or 2 zeros).
What is the order of magnitude?1012 / 92 = 11 which means the order of magnitude is 1
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x+y=3 2x+2y=6 how do i solve this using substitution
Answer:
X = 0
Y = 3
Step-by-step explanation:
To solve using substitution, you would solve one equation and substitute it into the other to get that x or y value, then you would use that found value on any original equation.
x+y=3 2x+2y=6
Using the first equation, if we subtract x
y = -x+3
Lets put this into the second equation
2x + 2y = 6
2x + 2(-x+3) = 6
2x + 2x + 6 = 6
4x = 0
x = 0
Now that we have X, we can plug it into any original equation. let's do the first cause it's easier
x+y=3
0+y=3
y=3
We can use the other too
2x+2y=6
2(0)+2y=6
0+2y=6
y=3
For each of the following English expressions, determine whether the expression properly expresses a proposition. 1. Mike likes beer. 2. Meter momma dogface to the banana patch. 3. Where is the bathroom? 4. An isosceles right triangle has two interior angles that are 45 degrees each and one interior angle that is 90 degrees. 5. Do you want another beer? 6. Two plus two equals five. 7. Yes, I would like a beer. 8. Porkchop Sandwiches! 9. George Washington was not the first president of the United States. 10. If I fitz then I sitz. (assume that this non-standard spelling is okay)
the second, third, sixth, eighth, and tenth expressions did not properly express propositions because they cannot be proven true or false.
1. Yes
2. No
3. No
4. Yes
5. Yes
6. No
7. Yes
8. No
9. Yes
10. No
Propositions are statements that can be either true or false. Of the ten expressions provided, seven of them properly expressed propositions. The first expression, "Mike likes beer," is a proposition because it is a statement that can be proven true or false. The fourth expression, "An isosceles right triangle has two interior angles that are 45 degrees each and one interior angle that is 90 degrees," is also a proposition because it is a statement that can be proven true or false. The fifth expression, "Do you want another beer?," is a proposition because it is asking a question that can be answered with either a yes or a no. The ninth expression, "George Washington was not the first president of the United States," is a proposition because it is a statement that can be proven true or false. However, the second, third, sixth, eighth, and tenth expressions did not properly express propositions because they cannot be proven true or false.
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Help me please I need help
Answer:
Step-by-step explanation:
v + 7/8 = 2/8
v = -5/8
let f(x)=∫x1sin(t)tdt. find the indicated derivative.
The function F(x) has a derivative f'(x) = sin(x) - xcos (x). This is accomplished by employing the chain rule and the basic calculus theorem.
The calculus fundamental theorem can be used to derive the derivative of f(x).
Let x1sin(t)dt equal F(x). The fundamental theorem of calculus states that F'(x) = sin (x).
Let g(x) now equal x. The chain rule then states that f'(x) = g' (x) F'(x)= g'(x)sin(x)=cos (x).
Therefore, f'(x) = sin(x) - xcos is the derivative of f(x) (x).
F(x) has a derivative f'(x) = sin(x) - xcos (x). Applying the chain rule and the calculus's fundamental theorem will get this result. The integrand assessed at the integral's upper limit is equivalent to the derivative of a definite integral, according to the calculus fundamental theorem. According to the chain rule, the derivative of a function made up of two functions is equal to the sum of the derivatives of the inner and outer functions. The inner function in this instance is sin(t), while the outer function is x. Thus, by using the chain rule and the fundamental theorem of calculus, we can determine that f'(x) = sin(x) - xcos (x)
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Given (x – 7)2 = 36, select the values of x.
a. x = 13
b. x = 1
c. x = –29
d. x = 42
The value of x for the expression (x – 7)² = 36 is 13. The correct option is A.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the expression is (x – 7)² = 36. The value of x will be calculated as:-
(x – 7)² = 36
(x – 7) = √36
(x - 7) = 6
x = 13
Hence, the value of x for the expression (x – 7)² = 36 is 13. The correct option is A.
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b) The average of 9 numbers is 23. If the average of first five numbers is 20 and
that of last five numbers is 25, what is the fifth number?
NEXT QUESTION:
c) The average age of a husband and wife was 23 years at the time of their
marriage. After 10 years, they have now a daughter of 6 years, what is he
average age of the family at present?
Answer:
b)
Step-by-step explanation:
As here it's stated that average of first 9 numbers is 23
so,
sum of 9 numbers = 9×23 = 207
Average of first 5 numbers is 20
so,
Sum of first 5 numbers = 5×20 = 100
Sum of remaining numbers = 207-100 = 107
Average of last five numbers = 25
So,
Sum of last five numbers = 5×25 = 125
Fifth Number = Sum of last five numbers- Sum of remaining numbers
= 125 - 107 = 18
A 1800 kg car with the brakes applied comes to a stop in 7.90 s. During these 7.90s the force of friction slowing down the car is 2800 N. What is the change in momentum of the car?
The change in momentum is 22120Ns
What is change in momentum ?The change in momentum (Δp ) is defined as the change in the product of an object's mass and velocity. A force is required to change the momentum of an object. This applied force can increase or decrease the momentum or even change the object's direction.
Therefore the change in momentum = Final momentum - initial momentum
i.e mv -mu
where m is the mass
v is the final velocity
u is the initial velocity
The change of momentum is also called impulse. impulse is the product of the force and the time in applying it.
Change in momentum = force × time
= 2800× 7.90
= 22120 Ns
Therefore the change in momentum of the car is 22120Ns
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Find M∠ABD.
ABC= 30*
CBD= 45*
use the washer method to determine the volume of the solid formed when the region bounded by y=12x2, y=0, and x=2 is rotated about the line y=3.
The volume of the solid can be calculated by integrating the area of the cross section over the entire height of the solid.
The washer method is a way to calculate the volume of a solid that is created when a region is rotated about a certain line.
Here you find the area of this cross section, and multiply it by the circumference of a circle with the same radius as the cross section.
To use the washer method to find the volume of the solid created when the region bounded by
=> y = 12x², y=0, and x=2 is rotated about the line y=3,
we first need to find the cross section of the solid at different heights along the line of rotation.
To do this, we need to find the points where the plane perpendicular to the line of rotation intersects the original region. This is done by finding where the equation of the plane and the equation of the original region intersect.
Next, we find the area of the cross section and multiply it by the circumference of a circle with the same radius.
Finally, we add up all of these washer volumes to find the total volume of the solid.
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What do I put in the boxes??!!
The value of 845 divided by 3 will be 281 R 2.
How to calculate the expressionAn expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator. Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc.
In this case, 845 divided by 3 will be:
= 845 / 3
= 281 2/3
Therefore, 845 ÷ 3 = 281 R 2.
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[WILL GIVE BRAINLIEST HELPPP!!]
Determine the value of x.
Answer: 14.46
Step-by-step explanation:
sin 56 = 12/x
0.83 = 12/x
0.83x = 12
x = 12/0.83
x = 14.46
Answer: 14.475
Step-by-step explanation:
Since we are given the angle 56°, this means that the other angle is 34°. We are given the side 12 this means that x, or the hypotenuse, is 14.475.
The hypotenuse is c, b is 12, and a is the side with the 90° angle.
What we do is c = a/sin(a) = b / sin(56°)
Thank you need answer soon as possible
The y-intercept of f(x) = 4^x is f(0) = 4^0 = 1. This means that the graph of f(x) intersects the y-axis at the point (0, 1).
What is the difference between intercept and asymptotes?
The intercept of a function is a point where the graph of the function intersects a coordinate axis. For example, in the case of a function f(x), the x-intercept is a point (a, 0) where the function takes on the value of 0 for some value of x=a. The y-intercept is a point (0, b) where the function takes on the value of b for x=0.An asymptote, on the other hand, is a line that the graph of a function approaches but never touches. There are two types of asymptotes: horizontal and vertical. A horizontal asymptote occurs when the graph of a function approaches a horizontal line as x approaches positive or negative infinity. A vertical asymptote occurs when the graph approaches a vertical line, either from the positive or negative direction, as x approaches a certain value (which may or may not be finite).So, the main difference between an intercept and an asymptote is that an intercept is a specific point where the graph intersects a coordinate axis, while an asymptote is a line that the graph approaches but never touches.The y-intercept of f(x) = 4^x is f(0) = 4^0 = 1. This means that the graph of f(x) intersects the y-axis at the point (0, 1).
The graph of f(x) = 4^x does not have any horizontal asymptotes, since the value of 4^x approaches infinity as x approaches infinity, and approaches 0 as x approaches negative infinity.
The range of f(x) = 4^x is all positive real numbers, since for any positive real number y, there exists a real number x such that 4^x = y.
In contrast, the graph of g(x) = -4^x would have a y-intercept of g(0) = -4^0 = -1. The graph would approach negative infinity as x approaches positive infinity and approach positive infinity as x approaches negative infinity. The range of g(x) = -4^x would be all negative real numbers.
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a group of students is asked if they travel to school by car c) work out the mean number of students in each car
Answer:
wow this is highschool
Step-by-step explanation:
I'm still in ms so I can't help sozz
Answer: 1.75
Step-by-step explanation:
Add the number of cars (3+4+1) which would give you 8.
Then multiply the number of students in one car by the the number of cars in each row (1x3, 2x4, 3x1) which would give you 3, 8 and 3.
Then you add all 3 numbers together to give you 14.
You then do 14/8 which would give you 1.75
please please helppppp
Answer:
D
Step-by-step explanation:
Yes... Is D................
HELP ME PLSS!?!?
In the mall you receive a coupon for $5 off of a pair of jeans when you arrive at the store you find that all jeans are 25% off
.let x represent the original cost of the jeans
.the function f(x)=x-5 represents the cost of the jeans if you use the coupon
.the function g(x)=0.25x represents the cost of the jeans if you apply the store discount of 25% first
Write a function: H(x) that represents how much you would pay if you use the mall coupon that followed by applying the discount from the store??
The price of the jeans will be $27 if you apply the function composition h(x). The price of the jeans will be $30 if you apply the composition j(x). Because it is less expensive.
what is function?The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found.
If you first use the coupon and then utilize the shop discount, the price of the jeans is represented by the function h(x). The combination of the functions f(x) and g may be used to calculate the function h(x) (x). If you first apply the shop discount and then utilize the coupon, the cost of the jeans is represented by the function j(x). The combination of the functions g(x) and f may be used to calculate the function j(x) (x).
The price of the jeans will be $27 if you apply the composition h(x). The price of the jeans will be $30 if you apply the composition j(x). Because it is less expensive, the composition h(x) will provide you a bigger discount.
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when people call into tv contest shows to vote, such as american idol or dancing with the stars, they are an example of a population. a probability sample. a nonprobability sample. a representative sample.
When people call into tv contest shows to vote, such as american idol or dancing with the stars, they are an example of a. non probability sample
ABOUT PROBABILITY SAMPLINGIn general, the probability sampling is the most common sampling technique for studies of public opinion, election polls, and other studies where the results will be applied to a wider population. Therefore, in this case it must provide information that the research methods carried out must represent the wider population.
Probability sampling can also be interpreted as a sampling method that uses some form of random selection. To be able to get the random selection method, a researcher must prepare several processes or procedures to be able to ensure that different units are in the population and have the same probability of being selected.
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Drag the tiles to the correct boxes to complete the pairs.
Based on given equations, using factorization, A = (x-4)(x+4), B = 8x³ + 12x² + 6x + 1, C = 4x² + 12xy + 9y², D = x³ + 8y³
The left-hand side of the equation is a perfect square, so we can use the factorization method to complete the square to get a binomial squared.
What does an equation in math mean?Algebraically speaking, an equation is a statement that shows the equality of two mathematical expressions. For instance, the two equations 3x + 5 and 14, which are separated by the 'equal' sign, make up the equation 3x + 5 = 14.
A) x² - 16 =
x² - 16 = (x² - 16) + 16 - 16 = (x-4)(x+4)
So, x² - 16 = (x-4)(x+4)
B) (2x+1)³ =
We can use the binomial theorem to expand the cube:
(2x+1)³ = (2x)³ + 3(2x)² × 1 + 3(2x)×1² + 1³
= 8x³ + 12x² + 6x + 1
so, (2x+1)³ = 8x³ + 12x² + 6x + 1
C) (2x+3y)² =
We can use the binomial theorem to expand the square:
(2x+3y)² = (2x)² + 22 x 3y + (3y)²
= 4x² + 12xy + 9y²
so, (2x+3y)² = 4x² + 12xy + 9y²
D) x³ + 8y³ =
The left-hand side of the equation is not a perfect cube, so we cannot use the factorization method to complete the cube. The equation is already in the simplest form, so we don't have to do any further manipulation.
x³ + 8y³ = x³ + 8y³
So the given equation is already in the simplest form.
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Which of the following polygons are quadrilaterals? Select all that apply.
an f1,v random variable can be thought of as the square of what kind of random variable
The type of random variable is continuous
The term called variable in math is known as a quantity that may change within the context of a mathematical problem or experiment.
Here we know that the f1,v random variable can be thought of as the square.
Here the term random variable is known as a set of possible values from a random experiment and the domain of a random variable is called sample space
As we all know that random variables are classified into discrete and continuous variables.
Here the main difference between the two categories is the type of possible values that each variable can take.
The value of the function is continuous one.
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Use the long division method to find the result when x³ + 3x² + 5x + 6 is divided
by x + 2.
i hate deltamath.
[tex](x + 2)x( {x }^{2} + x + 3)[/tex]
Compare the rates of change of the following items
y = 0.25 +2
a line with y-intercept (0, 2) which
passes through the point (2.6)
A The rate of change of item I is greater than the rate of change of item I
B. The rate of change of item I is equal to the rate of change of item I
C. The rate of change of item ill is greater than the rate of change of item
Answer:
The rate of change of a linear function is its slope, which is the coefficient of the x-term in the equation.
Item I: y = 0.25x + 2
The slope of this line is 0.25.
Item II: y = 2
This is a horizontal line with zero slope, so it has a rate of change of 0.
The slope of Item I is greater than the slope of Item II, therefore option C is correct: "The rate of change of item I is greater than the rate of change of item II".
Step-by-step explanation:
