The difference quotient of f(t) is: (6 - 2h - 4t)
And when h tends to zero is (6 - 4t)
How to get the difference quotient?
Here we have the function:
f(t) = (2t)(3 - t)
Expanding the function we get:
f(t) = 6t - 2t^2
Now we want to get the difference quotient, which is:
(f(t+h) - f(t))/h
Replacing our function there, we will get:
( 6*(t + h) - 2*(t + h)^2 - 6*t + 2*t^2)/h
Now we can simplify the numerator to get:
(6*t + 6*h - 2t^2 - 2h^2 - 4*t*h - 6t + 2t^2)/h
(6h - 2h^2 - 4th)/h
Now divide by h so we get:
(6 - 2h - 4t)
Now, remember that in the difference quotient we need to take the limit when h tends to zero, in that limit we will get:
(6 - 4t)
That is the difference quotient of the function f(t).
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Consider the given right triangle if A=20 and b =20 then
If anyone could please answer the following questions!! (photo is below)
Answer:
Natural Numbers:
1 , 17 , 24.0
Whole Numbers:
0 , 1 , 17 , 24.0
Integers:
-775 , -54.3 , -12
Rational Numbers:
0.5 , 24.0 , 3/4 , 2 5/8
Write an explicit formula for each sequence. Then generate the first five terms. a₁ = 10, r=-1
The explicit formula for the nth term is a(n) = 10 . (-1)ⁿ⁻¹, while the first five terms are 10, -10, 10, -10, 10
In a geometric sequence, the next term is obtained by multiplying the previous term by a common ratio, usually denoted as r.
The general formula of the nth term of a geometric sequence is:
a(n) = a₁ . r^(n-1)
Here a₁ refers to the first term and r to the ratio.
In the problem, the given parameters are:
a₁ = 10, r = -1
Substitute these into the general formula, we get:
a(n) = 10 . (-1)ⁿ⁻¹
Notice that
(-1)ⁿ⁻¹ = -1 if n-1 is an odd number, or if n is an even number
(-1)ⁿ⁻¹ = 1 if n-1 is an even number, or if n is an odd number
Therefore, the first five terms are: 10, -10, 10, -10, 10
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Find the factor pairs for the number.
24
Answer:(1, 24), (2, 12), (3, 8), and (4, 6).
Step-by-step explanation:a pair of numbers when multipled you get 24.
Determine whether each sequence is arithmetic, geometric, or neither. Then find the tenth term. -12,-5,2,9,16, . . . .
The sequence -12,-5,2,9,16, . . . .. is an arithmetic sequence and its 10th term is a(10) = 65
To determine whether a sequence is an arithmetic or geometric one, we need to check the relation between two consecutive terms.
In an arithmetic sequence, the nth term is obtained by adding the (n-1)th term with a constant, called a common difference (d).The given sequence is:
-12,-5,2,9,16, . . . .
In this sequence:
a(1) = -12
a(2) = -5
a(3) = 2
a(4) = 9
and so on.
Notice that:
a(2) - a(1) = -5 - (-12) = 7
a(3) - a(2) = 2 - (-5) = 7
a(4) - a(3) = 9 - 2 = 7
Since each consecutive terms have common difference, then, the given sequence is an arithmetic sequence. Furthermore, the common difference, d = 7.
The formula for the nth term in an arithmetic sequence is given by:
a(n) = a(1) + (n - 1) . d
Substitute n = 10, d = 7, and a(1) = -12
a(10) = -12 + (12 - 1) . 7
a(10) = -12 + 77 = 65
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I need some help please:(
The average sale price (online) for a certain brand of professional mountain bike is approximately normally distributed with a mean of $4,200 and a standard deviation of $250.
Find the 30th percentile of this distribution.
According to the question, for the average sale price the given parameters are mean as $4200 and standard deviation as $250.
As per normal distribution, the standard formula is as written below:
[tex]z = \frac{value - mean}{SD}[/tex]
And through normal distribution, the value of z = -0.52 which gives the area of the left bounded.
Now, substitute the values in the given expression, we get:
[tex]-0.52=\frac{x-4200}{250}[/tex]
Now the calculated value of 'x' = $4070.
To calculate the 30 percent of the mountain bike, the sale price will be $4068.90.
Therefore, the 30th percentile of the distribution is $4068.90.
What is normal distribution?
The normal distribution play a vital role in statistics. It measured the data which occurred very frequently and it is close to the mean value of the data. And it is of bell shaped.
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Find each sum.
6+(-6)
GRIDDED RESPONSE Triangle A B C is congruent to ΔH I. The vertices of \triangle A B C are A(-1,2), B(0,3) and C(2,-2) . What is the measure of side HI?
The measures of HI will be 11.8 units under the Corresponding parts of the congruent triangles (CPCT) condition.
What is the definition of a triangle?A triangle is a three-sided polygon with three edges.It is a basic geometric shape.Triangle ABC is a three-vertical triangle with the letters A, B, and C.In Euclidean geometry, any three non-collinear points define a unique triangle and, by extension, a unique plane.So,
The formula sides of the triangle: √(x₂−x₁)²+(y₂−y₁)²
Filling the values in the formula, we obtain:
= √(0-(-1))²+(3−2)²= 11.8 unitsThen, the side of the triangle will be: 11.8 units
Since ΔABC is congruent to ΔHJI, then, the measure of HI will also be 11.8 units under the CPCT condition.Therefore, the measures of HI will be 11.8 units under the Corresponding parts of the congruent triangles (CPCT) condition.
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A large western state consists of 4825 million acres of land. approximately 75% of this land is federally owned. find the number of acres that are not federally owned.
Answer:
1206.5 acres
Step-by-step explanation:
tatle acres=4825m
%of not federally owned =100%-75%=25%
[tex]( \frac{25}{100} ) \times 4825[/tex]
=1206.5 acres
Which of the following is the correct solution to the linear inequality shown
below?
y<2/3x+1
Answer:
3x+1
Step-by-step explanation:
Is 2 5/8 a rational number??
Answer:
2×5/8 which is 5/4 which is a rational number because denominator is not 0
Step-by-step explanation:
Hope it helps you
Answer:
yes it is
Step-by-step explanation:
rational numbers are numbers that can be expressed in the form of ratio. for example
[tex] \frac{85}{5} [/tex]
=
85:5
Write an explicit and a recursive formula for each sequence. 27,15,3,-9,-21, . . . . . .
an=a1+d(n−1) is the explicit and a recursive formula for each sequence .
What is sequence?An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6.
Arithmetic sequences are sequences containing these patterns. The distance between succeeding terms in an arithmetic series is always the same. The difference between consecutive words is always two, hence the sequence 3, 5, 7, 9... is arithmetic.
An explicit formula that states a = d (n - 1) + c, where d is the common difference between succeeding words, and c = a1, can be used to establish an arithmetic sequence.
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The interior angle measure of a regular polygon is given. Identify the polygon.
108
The regular polygon with an interior angle of measure 108° is a pentagon.
A regular polygon is a polygon that has equal side lengths and equal interior angle measures.
Interior angle of a polygon is the angle inside it that is formed by two adjacent sides. The number of interior angles formed inside a polygon is the same as the number of its sides. Meanwhile, the sum of all the interior angles of any polygon is constant to that polygon and depends on the number of sides.
sum = 180(n - 2)
Using this formula,
sum = 180(n - 2)
where n = number of sides of the polygon = number of interior angles
sum = measure of interior angle x n
108n = 180(n - 2)
108n = 180n - 360
180n - 108n = 360
72n = 360
n = 5
If the polygon has 5 sides and 5 interior angles, then the regular polygon is a pentagon.
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a machine operator can program machine #1 to produce 100 parts per hour, but the machine requires 2 hours of service each day when it is not operating. machine #2 can produce only 80 parts per hour, but only requires 30 minutes of service each day. which machine is more productive in an eight hour work day?
If a machine operator can program machine #1 to produce 100 parts per hour, but the machine requires 2 hours of service each day when it is not operating and machine #2 can produce only 80 parts per hour, but only requires 30 minutes of service each day, then both the machines are equal in productivity in an eight hour work day.
To determine which machine is more productive in an eight hour work day, an algebraic expression can be used.
x = y ( 8 hours - s )
Here, x = to the parts produced in an eight hour work day
y = parts produced per hour
s = service hours
Thus, the parts produced by both the machines in an eight hours work day can be calculated using this algebraic expression as follows,
For Machine #1:
y = 100 and s = 2
x = 100 ( 6 )
x = 600
Machine #2:
y = 80 and s = 0.5
x = 80 ( 8 - 0.5 )
x = 80 ( 7.5 )
x = 600
Hence, both machines are equally productive in an eight hour work day.
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Compare √180 and 102/8 using <, >, or =.
Answer:
the answer is √180>102/8
e function.
f(x)= -x²
Find f(-1)
Answer:
f(-1) = -1
Step-by-step explanation:
f(x) = -x^2
Let x = -1
f(-1) = - ( -1) ^2
= -1
How are tables of values like pictorial representation? How are they different?
Answer: The difference is that the pictorial representation is usually used to visualize the pattern, whether the tabular form is an organized form of data used to show the relation between inputs and outputs (usually using numerical representation).
Step-by-step explanation:
Which of the following definitions pertaining to Solving Linear Equations are incorrect? Check all that apply.
Equivalent equations are two or more equations that have the same solution.
An algebraic expression is a mathematical sentence connecting one statement to another statement with an equal sign (=).
An algebraic equation is a mathematical sentence connecting one expression to another expression with an equal sign (=).
To solve an equation means to isolating the variable on the left hand side of the equal sign.
The solution to an equation is the value, or values, that makes the equation true.
To solve an equation means to "undo" all the operations of the equation, leaving the variable by itself on one side. This in known as isolating the variable.
The two incorrect definitions are:
"An algebraic expression is a mathematical sentence connecting one statement to another statement with an equal sign (=)."
"To solve an equation means to isolating the variable on the left hand side of the equal sign."
Which definitions are incorrect?Here we have some definitions pertaining to solving linear equations, and we need to identify which ones are incorrect.
The first incorrect definition is:
"An algebraic expression is a mathematical sentence connecting one statement to another statement with an equal sign (=)."
The sentences that have an equal sign are called equations, algebraic expression is more general than that.
The second incorrect definition is:
"To solve an equation means to isolating the variable on the left hand side of the equal sign."
It is true that you need to isolate the variable, but it does not matter in which side of the sign you do that.
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The width of a rectangle is 8 units less than the length. The area of the rectangle is 9 units. What is the length, in units, of the rectangle?
The length of the given rectangle is 9.
According to the statement
We have to find that the length of the rectangle.
So, For this purpose, we know that the
A rectangle is a type of quadrilateral, whose opposite sides are equal and parallel.
From the given information:
The width of a rectangle is 8 units less than the length. The area of the rectangle is 9 units
Then
Let the Length of the rectangle = x
Let the width of the rectangle = x-8
Area of the rectangle = L*B
Then
L*B = 9
x(x-8) = 9
x^2 -8x -9 = 0
x^2 -9x + 1x -9 = 0
x(x-9) +(x-9) = 0
(x+1) (x-9) = 0
here x = -1 and then x = 9.
Here neglect x = -1 then
Length of the rectangle is 9
Let the width of the rectangle is 1.
So, The length of the given rectangle is 9.
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Find the scale factor used to dilate quadrilateral LOVE, L (0,-7), O (5,-4), V (1,-5), E (3, -1) to L'O'V'E', L' (0, -21), O' (15, -12), V' (3, -15), E' (9,-3).
Answer:
7142213126 LOVE
Step-by-step explanation:
i dont no what i am doing this answer is wrong
If Zb= 85° and Ze = 115°, then Zc is
Answer:
∠ c = 30°
Step-by-step explanation:
the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
∠ e is an exterior angle of the triangle , then
∠ b + ∠ c = ∠ e , that is
85° + ∠ c = 115° ( subtract 85° from both sides )
∠ c = 30°
The triangles are similar. Find the value of x.
First triangle:
Width: 3
Length: 17
Second triangle:
Width: x
Length: 102
Answer:
Step-by-step explanation:
I would say the width is 18 because the scale factor is 6
102/17= 6
3*6=18
Use the order of operations to simplify each expression.
5[(2+5) / ]
Simplification of the given expression 5[(2+5) /35 ] using the order of operation PEDMAS is equal to 1.
As given in the question,
Given expression is 5[(2+5) /35 ]
Simplify the given expression using the order of operation PEDMAS,
5[(2+5) /35 ]
= 5[ 7/35]
= 5 [ 1/5]
=1
Therefore, simplification of the given expression 5[(2+5) /35 ] using the order of operation PEDMAS is equal to 1.
The complete question is :
Use the order of operations to simplify each expression.
5[(2+5) /35 ]
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y=-|x|
where does that go on a graph ?
Record remainder.
2.
44) 6,668
Steps
Answer:
24.
Step-by-step explanation:
44)6668(151
44
226
220
68
44
24 <-------- Remainder
An ant carries food at a speed of 1 centimeter/second. How long will it take an ant to carry a cookie crumb a distance of 500 centimeters?
The total time taken by the ant to take cookie crumb from the kitchen table to an anthill is 83.33 minutes.
What is the linear system?
It is a system of an equation in which the highest power of the variable is always 1. A one-dimension figure that has no width. It is a combination of infinite points side by side.
Given
An ant carries food at a speed of 1 cm/s.
The kitchen table to an anthill, a distance of 50 m.
We know the relation between speed and time.
Time=distance/speed.
Speed = 1 cm per second = 0.6 m per minute
Distance = 50 m
Then total time taken will be
=50/0.6
=83.33
Thus, the total time taken by the ant to take cookie crumb from the kitchen table to an anthill is 83.33 minutes.
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ASAP. Please help me with this question. ASAP Please
Answer:
y=x
z=110
d=3cm
A glide reflection includes both a reflection and a (rotation, translation).
Translation, rotations are not involved in a glide reflection.
How is a glide reflection created?
There is a mirror line in every reflection. A glide reflection is a mirror reflection that is followed by a parallel translation to the mirror. Every glide reflection has a translation distance and mirror line.
A glide reflection is made up of what two transformations?
A glide reflection is made up of a translation and a reflection in which the translation and the reflection are parallel to each other or the direction of the translation. A gliding reflection has opposite isometry and is -commutative.The translation of a glide reflection?
The composition of transformations is a glide reflection. In a glide reflection, the figure is first translated before being reflected over a line.
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What is the y -coordinate of the y -intercept of the line?
The y-intercept of the equation of a line in general form is:(0, -c/b) or -c/b
The y-intercept is the point where the graph intersects the y-axis. To graph, any function that is of the form y = f(x) finding the intercepts is really important. There are two types of intercepts that a function can have. They are the x-intercept and the y-intercept. An intercept of a function is a point where the graph of the function cuts the axis.
The y-intercept of a function is a point where its graph would meet the y-axis. The x-coordinate of any point on the y-axis is 0 and we use this fact to derive the formula to find the y-intercept. i.e., the y-intercept of a function is of the form (0, y).
The equation of a straight line in general form is ax+by+c=0. For the y-intercept, we substitute x=0 and solve it for y.
a(0)+ by + c =0
by + c =0
y = - c/b
Thus, the y-intercept of the equation of a line in general form is:(0, -c/b) or -c/b
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