Answers
Computing the limit directly:
\(\displaystyle\lim_{h\to0}\frac{f(2+h)-f(2)}h=\lim_{h\to0}\frac{((2+h)^2+(2+h)+1)-7}h\\\displaystyle=\lim_{h\to0}\frac{5h+h^2}h\\=\displaystyle\lim_{h\to0}(5+h)=\boxed{5}\)
Alternatively, you can recognize the limit as being equivalent the derivative of f(x) at x = 2, in which case differentiating and plugging in 2 gives
f'(x) = 2x + 1 => f' (2) = 5
Related Questions
How is the sum expressed in sigma notation?
22 + 27 + 32 + 37 + 42 + 47
Enter your answer by filling in the boxes.
the sum from i is equal to 1 to blank of open paren close paren$$
Answers
The sum of the arithmetic sequence is S = 207 and the summation notation is S = ∑i=1 to 6 ( 5n + 17 )
What is Arithmetic Progression?An arithmetic progression is a sequence of numbers in which each term is derived from the preceding term by adding or subtracting a fixed number called the common difference "d"
The general form of an Arithmetic Progression is a, a + d, a + 2d, a + 3d and so on. Thus nth term of an AP series is Tn = a + (n - 1) d, where Tₙ = nth term and a = first term. Here d = common difference = Tₙ - Tₙ₋₁
Sum of first n terms of an AP: Sₙ = ( n/2 ) [ 2a + ( n- 1 ) d ]
Given data ,
Let the arithmetic sequence be represented as A
Now , the value of A is
A = 22 + 27 + 32 + 37 + 42 + 47
The number of terms n = 6
So , the value of i ranges from 1 to 6
Now , the summation is represented as ∑i=1 to 6 ( 5n + 17)
when n = 1
S₁ = 5 ( 1 ) + 17 = 22
when n = 2
S₂ = 22 + 5 ( 2 ) + 17
S₂ = 22 + 27
when n = 3
S₃ = 22 + 27 + 5 ( 3 ) + 17
S₃ = 22 + 27 + 32
Hence , the sum of the arithmetic sequence is S = 207
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the equations are
A. y=5/3 x -5
B. y=3/5 x -5
C. y=5/3 x +5
D. y=3/5 x +5
Answers
Y₂ = 10
X₁ = 6
X₂ = 9
slope = Δy ÷ Δx
slope = 10-5 ÷ 9-6
Slope = ⁵/₃
y-y₁ = m (x-x₁)
y-5 = ⁵/₃ (x-6)
y-5 = ⁵/₃x -10
y = ⁵/₃ x -10 + 5
y= 5/3 x - 5
Option A
Answer:
A
Step-by-step explanation:
Which of the following polynomials is in standard form?
SHESH Tecaci
ہے
te
O A. F(x) = 5x + 2x³ - x² - 3
OB. F(x) = -3+5x - x² + 2x³
O c. F(x) = -3 - x² + 2x³ + 5x
O D. F(x) = 2x³ - x² + 5x − 3
-
Answers
F(x) = 2x³ - x² + 5x − 3 is the polynomial that is in standard form. Thus, option D is correct.
What is polynomial?Algebraic expressions called polynomials can include exponents that are multiplied, divided, or added. Different types of polynomials exist. specifically, monomial, binomial, and trinomial. A polynomial with only one term is referred to as a monomial. A polynomial with two unlike terms is referred to as a binomial. An algebraic expression with three terms is known as a trinomial.
Monomials - The term "monomial" refers to algebraic expressions with a single term. In other words, it is an expression that includes any number of similar terms. Hence the name "Bi"nomial," binomials are algebraic expressions with two unlike terms. Trinomials - Trinomials are algebraic expressions with three dissimilar terms, hence the name "Tri"nomial.
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A sample of 51 observations will be taken from a process (an infinite population). The population proportion equals .85. The probability that the sample proportion will be between .9115 and .946 is _____.
Answers
Answer:
0.0819
Step-by-step explanation:
What is the place value of 2 in 369.425
Answers
Answer:
The two is in the hundredths place
Step-by-step explanation:
369.425
hundreds tens ones. tenths hundredths thousandths
3 6 9 . 4 2 5
The two is in the hundredths place
Answer:
The place value of 2 in 369.425 is hundredths.
The number 369.425 is a decimal number. It has a whole number part (369) and a decimal part (0.425). The decimal part is divided into tenths, hundredths, thousandths, and so on. The 2 is in the hundredths place.
Step-by-step explanation:
If f(x) = 4x – 8 and g(x) = 5x + 6, find (f - g)(x).
Answers
Answer:
(f - g)(x) = -x - 14
Step-by-step explanation:
Step 1: Plug in equations
4x - 8 - (5x + 6)
Step 2; Distribute negative
4x - 8 - 5x - 6
Step 3: Combine like terms
-x - 14
Answer:
-x-14
Step-by-step explanation:
Hope this helps
50 POINTS JUST PLS HELP ME
London borrowed $12,900 from a lender that charged simple interest at a rate of 2.56% for 7 years.
What is the amount of interest London paid at the end of the loan
Answers
Answer:
2311.68 dollars
Step-by-step explanation:
12 900 * 7 * .0256 =
London paid interest of $2311.68 at the end of the loan.
What is simple interest?Simple interest is interest that is only calculated on the initial sum (the "principal") borrowed or deposited.
The basic simple interest formula looks like this:
Simple Interest = Principal Amount × Interest Rate × Time
Given,
Principal amount = $12900
Rate of interest = 2.56%
Time = 7 years
Simple interest = Principal amount × Rate of interest × Time
= ($12900 × 2.56 × 7)/100
= ($33024 × 7)/100
= $231168/100
Simple interest = $2311.68
Hence, $2311.68 is amount of interest London paid at the end of the loan.
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The vertices of a rectangle in the coordinate plane are located at (4, -3), (4,5), (-5,5), and (-5, -3).
Answers
Use the slope formula to find the slope
Answers
The slope of line: 1. m= 6 , 2. m= -6 , 3. m= 2.5, 4. m= .5
The slope of the line :
In Mathematics, a slope of a line is the change in y coordinate with respect to the change in x coordinate.
The net change in the y-coordinate is represented by Δy and the net change in the x-coordinate is represented by Δx.
Hence, the change in y-coordinate with respect to the change in x-coordinate is given by,
m = change in y/change in x = Δy/Δx
Where “m” is the slope of a line.
Tan θ = Δy/Δx can also represent the slope of the line
So, tan θ to be the slope of a line.
Generally, the slope of a line gives the measure of its steepness and direction. The slope of a straight line between two points says (x1,y1) and (x2,y2) can be easily determined by finding the difference between the coordinates of the points. The letter ‘ m’ usually represents the slope.
If P(x1,y1) and Q(x2,y2) are the two points on a straight line, then the slope formula is given by:
Slope,
m = Change in y-coordinates/Change in x-coordinates
m = (y2 – y1)/(x2 – x1)
Therefore, based on the above formula, we can easily calculate the slope of a line between two points.
In other terms, the slope of a line between two points is also said to be the rise of the line from one point to another (along the y-axis) over the run (along the x-axis). Therefore,
Slope, m = Rise/Run
1.
(-1,-1) & (0,5)
m = (y2 – y1)/(x2 – x1)
m = (5 – (-1)) /(0– (-1))
m = (5 +1)/(0 +1)
m = (6)/(1)
m = 6
2.
(3,5) & (4,-1)
m = (-1 – 5)/(4 – 3)
m = (-6)/(1)
m = -6
3.
(2,1) & (4,6)
m = (6 – 1)/(4 – 2)
m = (5)/(2)
m = 2.5
4.
(-5,-2) & (3,2)
m = (2 – (-2))/(3 – (-5))
m = (2 +2/(3 +5)
m = (4)/(8)
m = (2/(4)
m = (1)/(2)
m = 0.5
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Pls help I’ll mark brainliest!!
Answers
Answer:
Answer is explained in the photo
Genesis is older than Dylan. Their ages are consecutive integers. Find Genesis's age if
the product of their ages is 110.
(ill give brainliest )
Answers
Answer:
Dylan is 10 years old, and Genesis is 11.
Step-by-step explanation:
If Genesis and Dylan's age are consecutive integers, and Genesis is older, we can represent their ages as:
Dylan's age: x
Genesis' age: x+1
This would mean Genesis is a year older than Dylan.
The product of their ages is 110.
We can write an equation:
x×(x+1)=110
x²+x=110 (Distribute x)
x²+x-110=0 (Move 110 to the other side)
You can solve this by the quadratic equation, by factoring or by completing the square
I'll solve it by the quadratic equation:
We must first find the coefficients a, b and c, and then plug it into the formula.
\(x = \frac{ - 1 + - \sqrt{ {1}^{2} - 4 \times 1 \times - 110} }{2 \times 1} \\ x = \frac{ - 1 + - \sqrt{1 + 440} }{2} \\ x = \frac{ - 1 + - 21}{2} \)
Since we have a ± symbol, we get 2 real solutions, x1 and x2.
x=-1±21/2
x1=-1+21/2
x1=20/2
x1=10
x2=-1-21/2
x2=-22/2
x2=-11
Since their age can't be negative, x2 can't be a solution, so Dylan's age must be 10, and Genesis' age must be 11.
Hope this helps, and let me know if you need help with another method to solve this problem!
Use transformation of f(x) = 1/x or f(x) = 1/x^2 to graph the rational function
Answers
Explanation:
First, we need to identify the graph of f(x) = 1/x
So, the graph of f(x) is:
Then, if h(x) = f(x) - c, we can say that h(x) has the same graph of f(x) but it is shifted c units down.
Therefore, the graph of f(x) = 1/x - 3 is the same graph of f(x) = 1/x but 3 units down. So, the graph of f(x) = 1/x - 3 is:
I think I have the right answer but I would still like to be 100% sure that I understand i also have to show my work
Answers
To solve this inequality, we can proceed as follows:
First: multiply both sides of the inequality by 9:
\(9\cdot\frac{x}{9}\leq9\cdot1\Rightarrow x\leq9\)Then, the answer is x <= 9. In interval notation, we have that the answer is:
(-infinity, 9 ]. Or graphically:
2 x 2
3
Write in its simplest form
Answers
Answer:
\( \frac{2}{3} \times 2 \\ = \frac{4}{3} \)
omitir
Step-by-step explanation:
_________________
4. Levi bought two Rescue Bots for $7.50 each and three DVDs for $5.25
each. How much money did he spend? *
A. $12.75
B. $25.50
C. $30.75
D. $39.38
Answers
Answer:
A. 7.50+5.25= 12.75........
Answer:
C.
Step-by-step explanation:
Two bots 7.50 each
Three DVDs 5.25 each
2 x 7.50 = 15
3 x 5.25 = 15.75
15 + 15.75 = 30.75
$30.75
Plz Help!
Will Give Brainliest!!!
Rectangle ABCDABCDA, B, C, D is graphed in the coordinate plane. The following are the vertices of the rectangle: A(2, -3),A(2,−3),A, left parenthesis, 2, comma, minus, 3, right parenthesis, comma B(4, -3)B(4,−3)B, left parenthesis, 4, comma, minus, 3, right parenthesis, C(4, 5)C(4,5)C, left parenthesis, 4, comma, 5, right parenthesis, and D(2, 5)D(2,5)D, left parenthesis, 2, comma, 5, right parenthesis.
What is the perimeter of rectangle ABCDABCDA, B, C, D?
units
Answers
Answer:
28
Step-by-step explanation:
2×8. scayzd hduebdu uduenì jd
Answer:
the answer is 20
Step-by-step explanation:
because, kahan
Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.
A business owner wants to have the front window of his store painted and is considering two artists for the job. John has quoted a flat rate of $88 for the job. Zachary's quote is $5 per hour, plus $78 to cover the cost of materials. Depending on how long it takes Zachary to paint the window, these two could end up charging the same amount. How long would Zachary have to take? How much would it cost?
If the job takes Zachary hours, the cost would be $ with either artist.
Answers
John's quote: y = 88
Zachary's quote: y = 5x + 78
We want to find the value of x where John's quote and Zachary's quote are equal, so we can set the two expressions for y equal to each other and solve for x:
88 = 5x + 78
Subtract 78 from both sides:
10 = 5x
Divide by 5:
x = 2
So Zachary would have to take 2 hours to charge the same amount as John's flat rate of $88.
To find how much it would cost, we can substitute x = 2 into Zachary's quote:
y = 5x + 78
y = 5(2) + 78
y = 10 + 78
y = 88
So if the job takes Zachary 2 hours, the cost would be $88 with either artist.
For breakfast, Mr. Hill bought a cup of coffee for $1.39 and a bagel for $1.85. What was his total cost?
Answers
Answer:
$3.24
Step-by-step explanation:
Cost for the coffee + Cost for the bagel
$1.39 + $1.85
$3.24
1
mayor que
Que tanto es menor o
la suma de 4 노
Y
5 8
42
Answers
ANSI’s bought 3 1/2 yards of ribbon she had 2 feet 10 inches of ribbon left after trimming some curtains how many inches did she used to trim the curtains
Answers
With the help of conversion units, we know that 56 inches of ribbon was used in the curtains.
What is a conversion unit?If you want to change the units of a measured quantity without changing the value, you can do so by using a conversion factor, which is an expression representing the relationship between the units. A conversion ratio (or unit factor), if the numerator and denominator have the same value represented in various units, always equals one (1).So, inches of ribbon Ansi used in curtains:
1 yard = 36 inches
Now,
3½6+1/25/22.5Now, 2.5 yards in inches:
2.5 × 36 = 90 inchesNow, 1 foot = 12 inches.
Then, 2 feet and 10 inches:2 × 12 + 1024 + 1034 inchesInches of ribbon used:
90 - 34 = 56 inchesTherefore, with the help of conversion units, we know that 56 inches of ribbon was used in the curtains.
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Pls help ASAP if you can
Answers
Answer:
136 units²
Step-by-step explanation:
6(4)/2 = 12 (since you have two triangles you don't really have to divide and you can just write 24)5(7) + 5(7) + 6(7) = 136 units².I know no one really uses the explanations but eh.what was your favorite year of high school?
Answers
Answer:
highschool is the worst, middle school was everything <3
PRETTY PLEASE HELP ME! this is 4 a test and i’m rlly struggling :/
Answers
First we need to find the upper angle by doing 180 - 143 = 37. Because it’s a straight line.
Second we need to find angle ADC
a triangle has 180 degrees, and we have 38 and 37.
180 - (38+37) = 105
then we find what the question wants:
180 - 105 = 75 degrees
The following tables represent a function and its inverse. Compare the functions.
h(x)
h–1(x)
Which statements describe the functions? Check all that apply.
The domain of h–1(x) is the range of h(x).
The range of h–1(x) is the range of h(x).
The x-intercept of h–1(x) is the x-intercept of h(x).
The x-coordinate of the x-intercept of h–1(x) is the y-coordinate of the y-intercept of h(x).
The maximum of h(x) is the largest x-value of
h–1(x).
Answers
the 3 correct statements are:
The domain of h⁻¹(x) is the range of h(x).The maximum of h(x) is the largest x-value of h⁻¹(x).The x-coordinate of the x-intercept of h⁻¹(x) is the y-coordinate of the y-intercept of h(x).Which statements describe the functions?For a function f(x), we define the inverse function f⁻¹(x):
This means that, if for a given value of x = x₀ we have:
f(x₀) = y₀
Then:
f⁻¹(y₀) = x₀
From this, we can conclude that the domain of f(x) is the range of the inverse, and the range of f(x) is the domain of the inverse.
Then the statements that are correct are:
The domain of h⁻¹(x) is the range of h(x).The maximum of h(x) is the largest x-value of h⁻¹(x).The x-coordinate of the x-intercept of h⁻¹(x) is the y-coordinate of the y-intercept of h(x).These 3 are the 3 correct statements.
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Which graph represents the solution to (x – 3)2 + (y + 4)2 > 36?
Answers
Answer:
second choice
Step-by-step explanation:
edge
The region outside the circle is under the consideration. Then the correct option is B.
What is an equation of a circle?A circle can be characterized by its center's location and its radius's length.
Let the center of the considered circle be at the (h,k) coordinate.
Let the radius of the circle be 'r' units.
Then, the equation of that circle would be:
(x – h)² + (y – k)² = r²
The inequality equation of the graph is given below.
(x – 3)² + (y + 4)² > 36
(x – 3)² + (y + 4)² > 6²
From the equation, the radius of the circle will be 6 units and the center of the circle will be (3, –4).
The region outside the circle is under the consideration.
Then the correct option is B.
The graph is given below.
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Anthony has a backpack that is 3/5 full. Roger has a backpack that is 2/3 as full as Anthony's. How full is Roger's backpack
Answers
9/10 is the answer because 3/5 divided by 2/3 is 9/10
Which inequality is graphed below?
3x + 2y < –6
3x + 2y > –6
3x – 2y > 6
3x – 2y < 6
Answers
Answer:
3x-2y > 6
Step-by-step explanation:
3x-2y > 6
see attached figure.
5.27 + 3.5
Find the value of
7.9 - 4.36
Give your answer as a decimal.
Write down all the figures on your
calculator display.
Answers
Answer:
The value of 7.9-4.36 is 3.54
The value of 5.27 + 3.5 is 8.77
Step-by-step explanation:
SITVATION
1. Jim ordered a sports drink
and three slices of pizza for
$8.50. His friend ordered two
sports
drinks and two
slices
of pizza for
$8.00. What is the equation and solution for this word problem?
Answers
The equation is given by
a + 3b = 8.50
2a + 2b = 8
And the value of a and b is given by 1.75 and 2.25.
What is an equation and substitution method?
The substitution method is the algebraic method to solve simultaneous linear equations. As the word says, in this method, the value of one variable from one equation is substituted in the other equation.
An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values. For example, 3x + 5 = 15. There are different types of equations like linear, quadratic, cubic, etc.
Let a and b the cost of sports drink and slice of pizza.
Jim ordered one sport drink and 3 slice of pizza and it cost him 8.50.
Hence, equation become
a + 3b = 8.50
Similarly, for his friend
2a + 2b = 8
a +b = 4
Subtracting these equation we get,
2b = 4.50
b = 2.25
Substitute this value of b in any equation, we will get a = 1.75
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NEED HELP ASAP PLS AND THX
