The rate of change of the function over the interval [ 4, 8 ] will be 6.
What is the rate of change of the function?
The rate of change function represents the rate at which one quantity changes in relation to another. Simply put, the rate of change is the difference between the amount of change in one item and the comparable amount of change in another.
Given function:-
F(x) = x² - 6x + 10The formula for calculating the rate of change will be given as:-
[tex]ROC = \dfrac{F(x_2)-F(x_1)}{x_2-x_1}[/tex]
We have x₁ = 4 and x₂ = 8 given in the question
F(x₂) = x²₂ - 6x₂ + 10 = (8)² - ( 6 x 8 ) + 10 =
F(x₂) = 64 - 48 + 10
F(x₂) = 26
F(x₁) = x²₁ - 6x₁ + 10 = (4)² - ( 6 x 4 ) + 10 =
F(x₁) = 16 - 24 + 10
F(x₁) = 2
[tex]ROC = \dfrac{F(x_2)-F(x_1)}{x_2-x_1}[/tex]
[tex]ROC = \dfrac{26 -2}{8-4}=\dfrac{24}{4}=6[/tex]
Therefore the rate of change of the function over the interval [ 4, 8 ] will be 6.
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The changes in account balances for Elder Company for 2021 are as follows:
Assets $ 480,000 debit
Common stock 250,000 credit
Liabilities 160,000 credit
Paid-in capital—excess of par 30,000 credit
Assuming the only changes in retained earnings in 2021 were for net income and a $50,000 dividend, what was net income for 2021?
The changes in account balances for Elder Company for 2021 are net income will be $160000
We have given debt common stock = $680000
Credit liabilities = 350000
Credit paid in capital = 190000
And an excess of par 30,000 credit Assuming the only changes in retained earnings
So 680000 = 350000+190000+30000+ retained earning
What is the net income?Net income is an entity's income minus the cost of goods sold, expenses, depreciation and amortization, interest, and taxes for an accounting period.
So retained earning = $110000
Dividend paid = $50000
So Net income = dividend paid + retained earning
Net income = $110000+$50000
Net income = $160000
So option (c) will be the correct answer.
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why f is not differentiable at x = 0 , where f(x) is x ^1/3
Therefore the f is continuous on R , i.e. real numbers and f is not differentiable at 0 ,Option A and D is the correct answer.
What is a Function ?A function is a mathematical statement which find relation between independent variable and dependent variable.
It always comes with a defined range and domain.
It is given that :
[tex]\rm f(x) = x^{1/3}\\\\LHD (at\; x = 0) = RHD (at \; x = 0)\\\\\= \lim_{x\rightarrow 0}\dfrac{f(x)-f(0)}{x-0}\\\\=\lim_{h\rightarrow 0}\dfrac{f(0-h)-f(0)}{0-h-0}[/tex]
[tex]=\lim_{h\rightarrow 0}\dfrac{f(0-h)-f(0)}{0-h-0} \\\\= \lim_{h\rightarrow 0}\dfrac{(-h)^{1/3}}{-h}\\\\\lim_{h\rightarrow 0}\dfrac{(-1)^{1/3}(h)^{1/3}}{-1*h}\\\\\lim_{h\rightarrow 0} (-1)^{-2/3}h^{-2/3}[/tex]
if we substitute h = 0 ,
Here, LHD and RHD does not exist at x = 0 So, f(x) is not differentiable at x = 0 .
Therefore the f is continuous on R , i.e. real numbers
and f is not differentiable at 0
Option A and D is the correct answer.
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Identify a transformation of the function f(x) = x by observing the equation of the function g(x) = x − 90.
The transformation of a function may involve any change. The transformation of the function is Right shift by 90 units.
How does the transformation of a function happen?The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs) etc.
If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units:
y=f(x+c) (same output, but c units earlier)
Right shift by c units:
y=f(x-c)(same output, but c units late)
Vertical shift:
Up by d units: y = f(x) + d
Down by d units: y = f(x) - d
Stretching:
Vertical stretch by a factor k: [tex]y = k \times f(x)[/tex]
Horizontal stretch by a factor k: [tex]y = f\left(\dfrac{x}{k}\right)[/tex]
Since the function is transformed from f(x)=x to g(x)=x-90, therefore, the transformation of the function is Right shift by 90 units.
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A certain field is a rectangle with a perimeter of 1030 feet. The length is 181 feet more than the width. Find the width and length of the rectangular field.
Step-by-step explanation:
the perimeter is
2×length + 2×width = 1030 ft
length + width = 515 ft
length = width + 181
now we use that in the first equation :
(width + 181) + width = 515
2×width + 181 = 515
2×width = 334
width = 167 ft
because of
length = width + 181
length = 167 + 181 = 348 ft
The width and length of the rectangular field are 165.5 ft and 346.5 ft respectively.
Concept: Perimeter is the sum of the length of all sides of a figure/solid.
Given: Length = 181+width
Let width be equal to 'width' ft
Perimeter= 1030 feet
In a rectangle there are 2 length and 2 width so the perimeter of a rectangle is equal to 2*(181+ width) + 2width = 362 + 2width + 2 width = ⇒362 + 4width =1030 ft
4width = 662 ( on transposing)
width= 165.5 ft
length= 181+ 165.5 ft
length = 346.5 ft
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What is the reason for statement 7 in the given proof? A. definition of midpoint B. definition of slope C. Parallel lines have equal slopes. D. using point-slope formula
The reason is using point slope formula.
The photo attached given below:
what is point slope formula?The equation of a straight line in the form y − y1 = m(x − x1) where m is the slope of the line and (x1, y1) are the coordinates of a given point on the line — compare slope-intercept form.
Now, we have to find the slope of AE, BF and CD.
We have to done this with help of coordinates.
So, we have to use point slope formula to find the slope of AE, BF and CD.
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Liz earns a salary of $2,200 per month, plus a commission of 5% of her sales. She wants to earn at least
$2,500 this month. Enter an inequality to find amounts of sales that will meet her goal.your
variable represents. Enter the commission rate as a decimal.
Answer:
2200 + 0.5x >= 2500
Step-by-step explanation:
x is the amount of sales
A single card is drawn from each of two decks of 52 cards. What is the probability of getting a heart from the first deck and then a diamond on the second deck?
The probability of getting a heart from the first deck and then a diamond on the second deck will be 6.25%.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
The probability of getting a heart from the first deck = 13/52.
And the probability of getting a diamond from the second deck = 13/52.
So, The probability of getting a heart from the first deck and then a diamond on the second deck will be,
Probability = (13/52) × (13/52) = 0.0625 = 6.25%
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Ohm's law states that the current (I) in amps equals the voltage (E) in volts divided by the resistance (R) in ohms. If you connect a 2 megohm resistor (2× 10^6 ohms) across a 2.4 kilovolt voltage source (2.4×10^3 volts),what would be the current in amps?
Ohm's law states that the current (I) in amps equals the voltage (E) in volts divided by the resistance (R) in ohms. The current in the amp is 1.2 × 10⁻³.
What is Ohm's Law?Ohm's law states that the current (I) in amps equals the voltage (E) in volts divided by the resistance (R) in ohms.
The current in amps = (2.4×10³ volts)/(2× 10⁶ ohms)
= 1.2 × 10⁻³ amp
Hence, the current in the amp is 1.2 × 10⁻³.
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What is the perimeter in units ?
Answer:
12 + [tex]4\sqrt{5}[/tex] approximates to 20.944
Step-by-step explanation:
VU - 8 units
UW - 4 units
VW - [tex]\sqrt{64+16} = \sqrt{80} =4\sqrt{5}[/tex]
12 + 4sqrt(5)
Answer:
6 (2 + √5) units
Step-by-step explanation:
Finding the length of the 3rd side :
*Applying Pythagorean Theorem*
VW² = 4² + 8²VW² = 16 + 64VW = √80VW = 6√5The perimeter :
4 + 8 + 6√512 + 6√56 (2 + √5) unitsCells B1, C1, and D1 contain the values Seat1Row1, Seat2Row1, and Seat3Row1. If cells B1, C1, and D1 were selected, and autofill
used to fill E1, F1, and G1, what would be the auto-filled values?
Seat1Row2, Seat2Row2, Seat3Row2
Seat 2Row2, Seat3Row3, Seat4Row4
Seat 1Row1, Seat2Row2, Seat3Row2
Seat 2Row2, Seat3Row2, Seat4Row2
In the event that cells B1, C1, and D1 were highlighted and then used to fill E1, F1, and G1, the values we would see are A. Seat1Row2, Seat2Row2, Seat3Row2.
What values would be in E1, F1, and G1?When using a spreadsheet, you can autofill succeeding cells if you highlight the preceding ones and then drag the cursor.
If Seat1Row1, Seat2Row1, and Seat3Row1 are in the cells B1, C1, and D1, then the spreadsheet would take note of the "1s" at the end of the values.
When it is then used to autofill the next cells, it would make this a 2 such that we see Seat1Row2, Seat2Row2, Seat3Row2.
If cells H1, I1, and J1 are filled, we would then see Seat1Row3, Seat2Row3, Seat3Row3.
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Which of the following is the conjugate of the expression below when x>-2?
6+√x+2
OA. 6+√x+2
B. 6-√x-2
C. 6-√√x+2
D. 6+√x-2
graph g(x) = -8|x| +1
Answer:
look the attachment in the above
A rectangle has a side length of three and two sevenths centimeters and a side width of 4 centimeters. What is the area of the rectangle?ten and six sevenths cm2
thirteen and one seventh cm2
thirteen and five sevenths cm2
fifteen and one seventh cm2
The area of the rectangle is thirteen and one seventh cm2
What is the area of the rectangle?A rectangle is a four-sided object that has two widths and two lengths. The sum of angles in a rectangle is 360 degrees.
Area of a rectangle = length x width
3 2/7 x 4
23/7 x 4 = 92 / 7 = 13 1/7 cm²
We conclude that the area of the rectangle is (13 + 1/7) cm²
How to get the area of the rectangle?
For a rectangle of length L and width W, the area is:
A = L*W
Here we know that:
L = (3 + 2/7)cm
W = 4cm
Then the area is:
A = (3 + 2/7)cm*4cm = (12 + 8/7)cm² = (13 + 1/7) cm²
We conclude that the area of the rectangle is (13 + 1/7) cm²
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Question 1
Kapoor Corporation uses the following activity rates from its activity-based costing to assign overhead costs to products.
Activity Cost Pools Activity Rate
Setting up batches $86.50 per batch
Assembling products $4.63 per assembly hour
Processing customer orders $52.16 per customer order
Data concerning two products appear below:
Product J00A Product S06U
Number of batches 34 43
Number of assembly hours 105 812
Number of customer orders 17 32
Required:
a. How much overhead cost would be assigned to Product J00A using the company's activity-based costing system?
b. How much overhead cost would be assigned to Product S06U using the company's activity-based costing system?
Overhead Cost:
There are some expenses incurred at the time of manufacturing of products and services that are not directly attributable to the finished products. These expenses are known as manufacturing overheads or indirect expenses.
The overhead cost would be assigned to Product J00A using the company's activity-based costing system is $4313.87.
How to calculate the cost?The overhead cost that would be assigned to Product J00A using the company's activity-based costing system will be:
= ($86.50 × 34) + ($4.63 × 105) + ($52.16 × 17)
= $2941 + $486.15 + $886.72
= $4313.87
The overhead cost would be assigned to Product S06U using the company's activity-based costing system will be:
= ($86.50 × 43) + ($4.63 × 812) + ($52.16 × 32)
= $3719.50 + $3759.56 + $1669.12
= $9148.18
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Vector g is shown below.
Vector h is parallel to g, in the same direction and
half as long.
Work out h as a column vector.
9
Answer:
h = [tex]\left[\begin{array}{ccc}5\\1\\\end{array}\right][/tex]
Step-by-step explanation:
g = [tex]\left[\begin{array}{ccc}10\\2\\\end{array}\right][/tex] , then
h = [tex]\frac{1}{2}[/tex] [tex]\left[\begin{array}{ccc}10\\2\\\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}5\\1\\\end{array}\right][/tex]
What is the product?
(3a²b7)(5a³b³)
O 8a5b15
O 8a6b56
O 15a³b¹5
O 15a5b56
Answer:
15a^5 b^10
Step-by-step explanation:
The product is 15a⁵b¹⁰.
What is an exponent?Exponentiation is one of the mathematics operations.
Let mᵃ, where m and a are the real numbers.
And m is multiplied by a times to itself.
So, a is the exponent of m.
When multiplying two terms with the same base, you add the exponents. Therefore:
(3a²b⁷)(5a³b³) = 3 x 5 x a⁵ x b ¹⁰
= 15a⁵b¹⁰.
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HELP pls. Which statement correctly demonstrates using limits to determine a vertical asymptote of
Answer:
Step-by-step explanation:
Difficult one. Need help with work shown.
Answer:
the length of the fence = 420 ft
The total area = 8000 ft²
Step-by-step explanation:
the fence has the same length as the perimeter of the rectangle
then
the length of the fence = 2×(160+50) = 420 ft
………………………………………………………………
The total area enclosed by the fencing = the area of the rectangle
Then
The total area = 160×50 = 8000 ft²
Answer:
see explanation
Step-by-step explanation:
the perimeter (P) of a rectangle is calculated as
P = 2(length + width)
= 2(160 + 50)
= 2 × 210
= 420 ft ← amount of fencing needed
the area (A) of a rectangle is calculated as
A = length × width = 160 × 50 = 8000 ft²
Please Hurry !!!!!!!A line has a slope of -4/5. Which ordered pairs could be points on a line that is perpendicular to this line? Select two options.
(–2, 0) and (2, 5)
(–4, 5) and (4, –5)
(–3, 4) and (2, 0)
(1, –1) and (6, –5)
(2, –1) and (10, 9)
Answer:
(–2, 0) and (2, 5)
(2, –1) and (10, 9)
Step-by-step explanation:
1. Find the slope of the what is considered perpendicular to -4/5. To do this, we simply use the reciprocal and multiply it by -1. Therefore, a perpendicular line would have a slope of 5/4.
2. Next, we can plug each of the ordered pairs into [tex]\frac{y2-y1}{x2-x1}[/tex] to see whether or not they have a slope of 5/4. We must do this to all of the ordered pairs until we find 2. Keep in mind that coordinates give you (x, y) in that order, so don't get the x's and y's confused. Additionally, it does not matter which coordinate goes first, just make sure that you get y2 and x2 from the same coordinate, and y1 and x1 from the same coordinate.
[tex]\frac{0-5}{-2-2}=\frac{-5}{-4}=\frac{5}{4}[/tex] The first answer![tex]\frac{5-(-5)}{-4-4}=\frac{0}{-8}[/tex] Not an answer[tex]\frac{4-0}{-3-2}=\frac{4}{-5}[/tex] Not an answer[tex]\frac{-1-(-5)}{1-6} =\frac{4}{-5}[/tex] Not an answer[tex]\frac{-1-9}{2-10} =\frac{-10}{-8}= \frac{5}{4}[/tex] The second answer!Okay last question, I’ll mark brainliest whoever gets it correct first
Answer:
Angle ABC = 112°
Step-by-step explanation:
THAT IS CORRECT TRUST ME
According to the graph, what is the factorization of x² - 5x+6?
OA. (x-3)(x+2)
OB. (x+3)(x-2)
OC. (x+3)(x+2)
OD. (x-3)(x-2)
y xẻ 5Xtộ
Answer:
OD.(x-3)(x-2)
Step-by-step explanation:
we need two numbers (negative ir positive) that multiply to get 6 abd add to get -5.
so its OD
as -3×-2=6
and -3+-2=-5
A car travels 18 mile in 213 minutes. What is its speed in terms of miles per minute?
Answer:
[tex]\textsf {0.08 miles per minute}[/tex]
Step-by-step explanation:
[tex]\textsf {Speed = Distance (Miles) / Time (Minute) }[/tex]
[tex]\textsf {Speed = 18 miles / 213 minutes }[/tex]
[tex]\textsf {Speed = 0.08 miles per minute }[/tex]
Answer:
The speed in miles per minute is 0.0845 mpm.
Step-by-step explanation:
The explanation above clearly states that a car travel a distance of 18 miles in a time of 213 minutes . And it is asking for speed in miles per minute. Keep this in mind that the symbol for miles per minute is mpm. Speed formula is distance ÷ time.
Speed = Distance ÷ Time
Speed = 18 m / 213 min
18 divided by 213 = 0.0845
speed = 0.0845 mpm
Therefore the speed in miles per minute is 0.0845 mpm.
Find the value of x which satisfies the following equation.
log2(x−1)+log2(x+5)=4
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: x = 3[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: log_{2}(x - 1) log_{2}(x + 5) = 4[/tex]
[tex]\qquad \tt \rightarrow \: log_{2} \{(x - 1)(x + 5) \} = 4[/tex]
[ log (x) + log (y) = log (xy) ]
[tex]\qquad \tt \rightarrow \: ( x - 1)(x + 5) = {2}^{4} [/tex]
[tex]\qquad \tt \rightarrow \: {x}^{2} + 5x - x - 5 = 16[/tex]
[tex]\qquad \tt \rightarrow \: {x}^{2} + 4x - 5 - 16 = 0[/tex]
[tex]\qquad \tt \rightarrow \: {x}^{2} + 4x -21 = 0[/tex]
[tex]\qquad \tt \rightarrow \: {x}^{2} + 7x - 3x - 21 = 0[/tex]
[tex]\qquad \tt \rightarrow \: x(x + 7) - 3(x + 7) = 0[/tex]
[tex]\qquad \tt \rightarrow \: (x + 7)(x - 3) = 0[/tex]
[tex]\qquad \tt \rightarrow \: x = - 7 \: \: or \: \: x = 3[/tex]
The only possible value of x is 3, since we can't operate logarithm with a negative integer in it.
[tex]\qquad \tt \rightarrow \: x = 3[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
An arithmetic sequence is shown in the graph.
What is the equation for the nth term of the arithmetic sequence?
an = –3 + 5(n – 1)
an = –3 + 5(n + 1)
an = –3 – 5n
an = –3 + 5n
Answer:
an= -3+5(n-1)
Step-by-step explanation:
Try writing out the terms and finding a pattern. In this case, inserting any plotted x-value into the sequence -3+5(n-1) produces the correct y-value.
Answer:
A.) an = -3 + 5(n - 1)
Explanation:
Given: (1, -3), (2, 2), (3, 7), (4, 12), (5, 17)
Arithmetic Series: a + (n - 1)d
['a' is first term, 'n' determines term position, 'd' is common difference]
Determine the following:
a = -3d = second term - first term = 2 - (-3) = 5Putting into equation:
-3 + (n - 1)5-3 + 5(n - 1)Y=3x-7 complete the missing value in the solution to the equation (1,
Answer: (1, -4) or y = -4
Step-by-step explanation:
Given:
y = 3x - 7
Plug in the value of 1 for x - given to us by "(1, ?)
y = 3x - 7
y = 3(1) - 7
Multiply:
y = 3 - 7
Subtract:
y = -4
y = -4
-11-(-5)
————-
2x3
is an example of
A. a numerical equation
B. a numerical expression
C. an algebraic expression
D. an algebraic equation
Answer:
B.a numerical expression
GUYS PLEASE HELP WITH THIS PLEASE
Examine how sounds of music are related to trigonometric functions.
What does change of amplitude do? How about frequency?
Using graphs and equations, represent multiple transformations explaining their relevancy to the sound wave
The sounds of music are related to trigonometric functions because trigonometry is used in measuring the level of the pitch of a sound wave or musical note.
How is trigonometry used in sound?It should be noted trigonometry is important for measuring pitch level. The notes are measured in Hertz.
A sound wave's amplitude relates to the change in the pressure that's caused by the wave measured at a specific location.
The sound is perceived as louder when the amplitude increases.
Pieces of music often have repetitive choruses or bars, similar to patterns. In mathematics, we look for patterns to interpret and predict the unknown. Music uses the same techniques. If you look at a piece of music, artists look at the notes they see to find the rare (high or low) and uncommon notes.
In this way, the notes are related. Relationships are important in mathematics and create an interesting link between music and mathematics.
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Solve −x+5≤4 or 2x+3≥−1 and write the solution in interval notation.
Answer:
Step-by-step explanation:
[tex]\left \{ {{-x+5\leq 4} \atop {2x+3\geq -1}} \right.[/tex] ⇒ [tex]x\geq 1\\2x\geq 4\\x\geq -2[/tex]
or
[tex]x \geq -2\\(-2,+ { \infty} )[/tex] (Answer)
What expression is equivalent to ten square root five
The expression 10√5 can be written as √500 because √(10×10) = 10 option (A) √500 is correct.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have an expression:
= 10√5
We can write the above equation:
= √(10×10×5)
Because √(10×10) = 10
= √(100×5)
= √500
Thus, the expression 10√5 can be written as √500 because √(10×10) = 10 option (A) √500 is correct.
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Discrete Math please help
Considering the given operations, the discrete sets are given as follows:
A = {1,3,5,6,7,8,9}.B = {2,3,6,9,10}.What is operation A - B?It is the operation of elements that are in set A but not in set B, hence, since A - B = {1, 5, 7, 8}, we have that:
A = {1,5,7,8}
What is operation B - A?It is the operation of elements that are in set B but not in set A, hence, since B - A = {2,10}, we have that:
B = {2,10}
What is the intersection operation?It contains the elements that are in both sets, hence, since [tex](A \cap B) = \{3,6,9\}[/tex], we have that the sets are completed as follows:
A = {1,3,5,6,7,8,9}.B = {2,3,6,9,10}.More can be learned about discrete math at https://brainly.com/question/13309484
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