Over what domain interval is the graph of f(x)=(x-3)^2 increasing?
Answers
The increasing interval of a function can be founded by taking the derivative of the function and then calculating where the derivative is possitive.
We have the function:
\(f(x)=(x-3)^2\)The derivative, by the chain rule is:
\(f^{\prime}(x)=2(x-3)\)Now we need to find the interval where the derivative is possitive. Let's find the root:
\(\begin{gathered} 0=2(x-3) \\ 0=x-3 \\ x=3 \end{gathered}\)The derivative is 0 when x = 3. Now lets evaluate the derivative in a number greater than 3, if it's possitive, the increasing interval will be (3,∞) If it's negative, the interval will be (-∞, 3)
Let's evaluate for x = 4:
\(f^{\prime}(4)=2(4-3)=2\)Then, the increasing interval is (3,∞)
Related Questions
Prove that "If α is an ordinal and β ∈ α, then β is an ordinal" ?
Answers
If α is an ordinal and β ∈ α, then β satisfies all three properties of an ordinal. Therefore, β is also an ordinal.
To prove the statement "If α is an ordinal and β ∈ α, then β is an ordinal," we need to demonstrate that if α is an ordinal and β is an element of α, then β satisfies the three properties of an ordinal:
Well-Ordering: Every element of β is strictly well-ordered by the membership relation ∈. This property holds because α is an ordinal and satisfies the well-ordering property, and β being an element of α inherits this property.
Transitivity: For any two elements γ and δ in β, if γ ∈ δ and δ ∈ β, then γ ∈ β. Since β is an element of α and α is transitive, the transitivity property carries over to β.
Trichotomy: For any two elements γ and δ in β, either γ ∈ δ, δ ∈ γ, or γ = δ. Again, this property is inherited from α, as β is an element of α.
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A ramp is designed with the profile of a right triangle.
The measure of one acute angle is 2 times the measure
of the other acute angle. Find the measure of each
acute angle.
Answers
The measure of each acute angle \(30^{0}\)
What is the acute angle?Angles that are less than 90° are considered acute, and a protractor can be used to measure these angles. Acute, Obtuse, Right, Straight, Reflex, and Full Rotation are the names of the basic angles. Two rays are joined at their ends to create the geometric shape known as an angle. Typically, angles are expressed in terms of degrees. A triangle that has each angle less than 90 degrees is said to be acute.Triangles are not sharp even when one of their angles is 90 degrees. The fact that all angles (60°) in an equilateral triangle are less than 90° ensures that it is always sharp.If you need to see the algebra, the acute angles in a right triangle are complementary, adding to 90 degrees:
x + 2x = 90
3x = 90
x = 30
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PLEASE HELP!!! Jeanie is 21 years old. She opens an account that pays 3.9% interest compounded monthly. She
sets a goal of saving $10,000 by the time she is 24 years old. How much must she deposit each
month?
Answers
Answer:
$11,170
Step-by-step explanation:
First you convert the percentage to decimal form out of 100 (which you divide)
3.9%/100 = 0.039
A = P(1 + rt)
A = 10000(1 + 0.039 * 3) ( * = multiplication)
I = $11,170 - 10,000 = $1,170
Which you should get $1,170.00 or $1,170 (which is pretty much the same thing)
Hope this helps!
please help !!!! urgent
Answers
Answer:
\(P(x) = 16x - 100 - 0.1x^2\)
Step-by-step explanation:
Given
\(R(x) = 46x\)
\(C(x) = 100 +30x +0.1x^2\)
Required
Determine the profit function
This is calculated as follows:
\(P(x) = R(x)- C(x)\)
Substitute values for R(x) and C(x)
\(P(x) = 46x - (100 + 30x + 0.1x^2)\)
Open bracket
\(P(x) = 46x - 100 - 30x - 0.1x^2\)
Collect like terms
\(P(x) = 46x - 30x - 100 - 0.1x^2\)
\(P(x) = 16x - 100 - 0.1x^2\)
helpppp please im so close
Answers
Answer:
7.5
Step-by-step explanation:each line is 5
Answer:
B. -7.25
Step-by-step explanation:
On a number line, if there is one bar between 1 and 2, that bar is 1.5. If there are 3 bars between 1 and 2, the three bars from left to right are 1.25, 1.5, and 1.75. Using this knowledge, your answer would be -7.25. A picture is attached for further clarity.
18 pounds for 9 dollars what is it in unit rate
Answers
Answer:
0.5
Step-by-step explanation:
9 dollars divided by 18lbs.
9/18 = 0.5
$0.50/lbs
This is accounting. Please answer
Answers
All answers are mentioned below.
Describe balance sheet?A balance sheet is a financial statement that provides a snapshot of a company's financial position at a specific point in time. It presents the company's assets, liabilities, and equity, and shows how these are financed. The balance sheet follows the accounting equation, which states that the total assets must equal the sum of liabilities and equity.
(a) Trading, Profit & Loss and Profit & Loss Appropriation Account for the year ended December 31, 1996
Trading Account
$
Sales (51,550 - 5,550 + 5,385) 51,385
Less: Cost of Goods Sold
Opening Stock 5,550
Add: Purchases 29,525
35,075
Less: Closing Stock 5,385
Cost of Goods Sold 29,690
Gross Profit 21,695
Profit & Loss Account
$
Gross Profit 21,695
Less: Expenses
Carriage Inward 100
Discount Allowed 1,000
Wages & Salaries 17,650
Motor Vehicle Repairs 5,850
Telephones 350
Rent & Rates 1,800
Advertising 2,750
Carriage Outward 1,000
Bank Charges 550
Depreciation
Land & Building (30,000/50 years) 600
Motor Vehicle (20% x 20,000) 4,000
34,550
Net Loss (12,855)
Profit & Loss Appropriation Account
$
Net Loss (12,855)
Add: Interest on Capital (5% x $90,000) 4,500
(8,355)
To be shared equally between Knox and Cox
Knox (4,178)
Cox (4,178)
Additional Salary for Cox (5,000)
Carried Forward (13,356)
(b) Partners' Current Account
Knox Cox
$ $
To Opening Balance 8,185 4,400
By Share of Net Loss (4,178) (4,178)
By Interest on Capital 2,500 2,000
By Drawings (1,200) (500)
By Salary 0 (5,000)
To Closing Balance 5,307 (3,278)
(c) Balance Sheet as at December 31, 1996
Fixed Assets
Land & Building (100,000 - 30,000) 70,000
Motor Vehicles (20,000 - 4,000) 16,000
86,000
Current Assets
Stock 5,385
Debtors 7,250
Bank 3,200
Cash 510
16,345
Current Liabilities
Creditors (7,650)
Net Current Assets 8,695
94,695
Less: Partners' Capital and Current Accounts
Knox Capital (50,000 + 5,307) 55,307
Cox Capital (40,000 - 3,278) 36,722
92,029
2,666
Notes:
Depreciation of Land and Building: 30,000/50 years = 600 per year
Depreciation of Motor Vehicles: 20% x 20,000 = 4,000
Interest on Capital: Knox - 5% x 50,000 = 2,500, Cox - 5% x 40,000 = 2,000
Interest on Drawings: Knox - 10% x 1,200 = 120, Cox - 10% x 500 = 50
Additional Salary for Cox is treated as an expense and charged to the Profit & Loss Account.
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(a) Trading, Profit & Loss and Profit for the year ended December 31, 1996 is mentioned below. (b) Knox Cox, Opening Balance 8,185 4,400, respectively.(c) Interest on Drawings: Knox - 10% x 1,200 = 120, Cox - 10% x 500 = 50
Describe balance sheet?A balance sheet is a financial statement that provides a snapshot of a company's financial position at a specific point in time. It presents the company's assets, liabilities, and equity, and shows how these are financed. The balance sheet follows the accounting equation, which states that the total assets must equal the sum of liabilities and equity.
(a) Trading, Profit & Loss and Profit & Loss Appropriation Account for the year ended December 31, 1996
Trading Account
$
Sales (51,550 - 5,550 + 5,385) 51,385
Less: Cost of Goods Sold
Opening Stock 5,550
Add: Purchases 29,525
35,075
Less: Closing Stock 5,385
Cost of Goods Sold 29,690
Gross Profit 21,695
Profit & Loss Account
$
Gross Profit 21,695
Less: Expenses
Carriage Inward 100
Discount Allowed 1,000
Wages & Salaries 17,650
Motor Vehicle Repairs 5,850
Telephones 350
Rent & Rates 1,800
Advertising 2,750
Carriage Outward 1,000
Bank Charges 550
Depreciation
Land & Building (30,000/50 years) 600
Motor Vehicle (20% x 20,000) 4,000
34,550
Net Loss (12,855)
Profit & Loss Appropriation Account
Net Loss (12,855)
Add: Interest on Capital (5% x $90,000) 4,500
(8,355)
To be shared equally between Knox and Cox
Knox (4,178)
Cox (4,178)
Additional Salary for Cox (5,000)
Carried Forward (13,356)
(b) Partners' Current Account
Knox Cox
$ $
To Opening Balance 8,185 4,400
By Share of Net Loss (4,178) (4,178)
By Interest on Capital 2,500 2,000
By Drawings (1,200) (500)
By Salary 0 (5,000)
To Closing Balance 5,307 (3,278)
(c) Balance Sheet as at December 31, 1996
Fixed Assets
Land & Building (100,000 - 30,000) 70,000
Motor Vehicles (20,000 - 4,000) 16,000
86,000
Current Assets
Stock 5,385
Debtors 7,250
Bank 3,200
Cash 510
16,345
Current Liabilities
Creditors (7,650)
Net Current Assets 8,695
94,695
Less: Partners' Capital and Current Accounts
Knox Capital (50,000 + 5,307) 55,307
Cox Capital (40,000 - 3,278) 36,722
92,029
2,666
Notes:
Depreciation of Land and Building: 30,000/50 years = 600 per year
Depreciation of Motor Vehicles: 20% x 20,000 = 4,000
Interest on Capital: Knox - 5% x 50,000 = 2,500, Cox - 5% x 40,000 = 2,000
Interest on Drawings: Knox - 10% x 1,200 = 120, Cox - 10% x 500 = 50
Additional Salary for Cox is treated as an expense and charged to the Profit & Loss Account.
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please help!!! if i don’t get this test right then i fail and i really can’t ! i’ll mark brainlyist ! pleasee
anyone
Answers
Answer:
208 cubic units
Step-by-step explanation:
The composite figure in the picture is composed of a triangular prism and a rectangular prism, both which can be calculated by the base * height formula.
First, let’s calculate the volume of the triangular prism:
The base is the area of the triangle base, which is dc/2, or 4*3/2, which is 6. Next, multiply the area of the base by the height “b”: 6 * 8 = 48.
Now, let’s calculate the volume of the rectangular prism:
The base is the rectangular base’s area, which is a*c, or 5*4, which is 20. Next multiply the base by the height “b”: 20 * 8 = 160
Now, add up the volumes of the rectangular and triangular prisms:
160 + 48 = 208 cubic units
Help! I’ll reward brainest its pretty easy
Answers
Answer:
$5250
Step-by-step explanation:
multiply the cost by the number of people
Answer:
The answer is 5250
Step-by-step explanation:
Add 20 plus ten which is thirty then multiply that buy 175 which is 5250$
What is the value of
(x3 x 7y÷)(10.6+5.4)for x=2 and y=6?
Answers
Step-by-step explanation:
Hope you can correct you question
step by step 6x + 3y = 12
Answers
Answer:
x=4-y/2
Step-by-step explanation:
subtract 3y from both sides
simplify
divide both sides by 6
0.000549 in scientific notation
Answers
Answer: 5.49 × 10-4
Step-by-step explanation:
When you move the decimal over move it over to the right by 4 units.
When you move right it is (-) negative. So you get 5.49 x 10-4.
please help me solve this
Answers
The area of triangle EFG is given as follows:
A = 18.63 square units.
How to obtain the area of a triangle?The area of a rectangle of base b and height h is given by half the multiplication of dimensions, according to the formula presented as follows:
A = 0.5bh
The base is given by segment EF as follows:
\(EF = \sqrt{(9 - 4)^2 + (-7 -(-9))^2}\)
EF = 5.4.
The midpoint of EF is given as follows:
M(6.5, -8).
The height is given by the segment MG as follows:
\(MG = \sqrt{(6.5 - 3)^2 + (-2 - (-8))^2}\)
MG = 6.9.
Hence the area is given as follows:
A = 0.5bh
A = 0.5 x 5.4 x 6.9
A = 18.63 square units.
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To go to the theater you would pay $8.00 for each ticket you purchase. Which answer choice correctly represents the algebraic expression for the cost of t tickets?
A. 8t
B. 8 + t
C. 8 – t
D.
Answers
The algebraic expression that correctly represents the cost of t tickets is 8t , the correct option is (a) .
In the question ,
it is given that
the cost of 1 ticket for the theater is = $8.00
let the number of ticket be = t
so , the cost for t tickets = (cost of 1 ticket ) × ( number of tickets )
Substituting the values of number of tickets and cost of 1 ticket ,
we get ,
cost for t tickets = 8 × t
= 8t
Therefore , The algebraic expression that correctly represents the cost of t tickets is 8t .
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In 20 years Charles will be three times as old as he is now.Now how old is he?
Answers
Answer:
The answer is 50
Step-by-step explanation:
20x3=50
The highway fuel economy of a 2016 Lexus RX 350 FWD 6-cylinder 3.5-L automatic 5-speed using premium fuel is a normally distributed random variable with a mean of μ = 26.50 mpg and a standard deviation of σ = 3.25 mpg.
(a) What is the standard error of X¯¯¯
, the mean from a random sample of 25 fill-ups by one driver? (Round your answer to 4 decimal places.)
Answers
The standard error represents the average deviation of the sample means from the true population mean. Rounding this value to four decimal places, the standard error of X¯¯¯ is approximtely 0.6500 mpg.
A smaller standard error indicates that the sample means are more likely to be close to the population mean.To calculate the standard error of X¯¯¯, the mean from a random sample of 25 fill-ups by one driver, we can use the formula:
Standard Error (SE) = σ / sqrt(n),
where σ is the standard deviation and n is the sample size.
In this case, the standard deviation (σ) is given as 3.25 mpg, and the sample size (n) is 25.
Plugging in these values into the formula, we have:
SE = 3.25 / sqrt(25).
Calculating the square root of 25, we get:
SE = 3.25 / 5.
Performing the division, we find:
SE ≈ 0.65.
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Which angle is NOT coterminal with 110 degrees
-250degrees
480degrees
-110 degrees
830 degrees
Answers
What is the answer to these questions?
Answers
Answer:
The answer to the first question is: 9 4/21
The answer to the second question is: B.) 24 14/27
I hope this helps you! :D
What is the slope of the line segment that passes through
points (1,3) and (5, 13)?
Answers
Answer: 5/2
Step-by-step explanation:
slope equation: (y2-y1)/(x2-x1)
13-3/5-1 = 10/4 or 5/2
Answer:
2.5
Step-by-step explanation:
Gradient (slope) =
\(m = \frac{y2 - y1}{x2 - x1} = \frac{13 - 3}{5 - 1} = \frac{10}{4} = 2 \frac{1}{2} \)
Where is the first error or skipped step in this proof?
The reason of statement ___ is not correct because ___
Answers
The reason of statement step 3 is not correct because the sum of angles equals an angle must be shown first by using the angle addition postulate.
What is the Angle Addition Postulate?In Mathematics and Geometry, the Angle Addition Postulate states that the measure of an angle formed by two (2) angles that are placed side by side to each other is equal to the sum of the measures of the two (2) angles.
This ultimately implies that, the Angle Addition Postulate can be used to determine the measurement of a missing angle in a geometric figure or it can be used for calculating an angle that is formed by two (2) or more angles.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
4.
X =
x
16
60°
_____y=_
-
y
Answers
Answer: what the hell the happened
Step-by-step explanation:
At 8:00 A.M., the temperature is 53 °F. At 11:00 A.M., it is 69 °F.
What is the average change in temperature per hour?
A.) 5.3 F
B.) 40.7 F
C.) 61.0 F
D.)16.0 F
E.) 8.0 F
Answers
what are the answers? thank you.
Answers
Answer:
176.78cm squared,23.57cm,Step-by-step explanation:
inorder to solve the area of the shaded area;°/360ñRsquared
arc length you use ;°/360ñD
What would need to be used to show the triangles are congruent by AAS?
A: Nothing as the triangles can not be proved congruent by AAS.
B: Angles are congruent by vertical
angles.
C: Sides are congruent by the
reflexive property.
D: Angles are congruent by the
reflexive property.
Answers
Triangles are shown to be congruent by the statement that "Angles are congruent by vertical angles."
What is the congruent triangle?Triangles are said to be congruent if, under a correspondence, two of a triangle's sides and the angle that connects them are equal to two of another triangle's sides and the angle that connects them.
Given two triangles, Where the base of these triangles are same
And also given that the two angles are the same.
Since,
Two intersecting lines form a pair of vertical angles. The vertical angles are opposite angles with a common vertex (which is the point of intersection).
Thus, the third angle is also equal
From AAS:
AAS stands for Angle-Angle-Side. When two angles and a non-included side of a triangle are equal to the corresponding angles and sides of another triangle, then the triangles are said to be congruent
Therefore. "Angles are congruent by vertical angles" is used to show the triangles are congruent by AAS,
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Using the image below. Write the equation of the line fully simplified slope-intercept form. NO SPACES BETWEEN TERMS * just letting you know the answer is not y=-5x+2 or y=6x+2
Answers
The slope-intercept form is
\(y=mx+b\)m is the slope
b is the y-intercept
The rule of the slope of a line that passes through points (x1, y1) and (x2, y2) is
\(m=\frac{y2-y1}{x2-x1}\)From the given graph, the line passes through points (1, -4) and (0, 2)
Let (x1, y1) = (1, -4) and (x2, y2) = (0, 2)
\(\begin{gathered} m=\frac{2-(-4)}{0-1} \\ m=\frac{2+4}{-1} \\ m=\frac{6}{-1} \\ m=-6 \end{gathered}\)Substitute the value of m in the form of the equation
\(y=-6x+b\)Since the line intersects the y-axis at point (0, 2)
Then the y-intercept is 2
Then b = 2
The equation of the line is
\(y=-6x+2\)If the reliability is
r = 0.25,
the equation becomes
R(n) =
0.25n
0.75 + 0.25n
.
What percent improvement is there in the reliability when the test length is doubled?
Answers
The percentage improvement in reliability when test length is doubled is 15%
R(n) = 0.25n / (0.75 + 0.25n)
For a test length of 1substitute n = 1 into the equation :
R(n) = 0.25n / (0.75 + 0.25n)
R(1) = 0.25(1) / (0.75 + 0.25(1))
R(1) = 0.25 / 1
R(1) = 0.25
For a test length of 2when test length is doubled , n = 2
substitute n = 1 into the equation :
R(n) = 0.25n / (0.75 + 0.25n)
R(2) = 0.25(2) / (0.75 + 0.25(2))
R(2) = 0.5 / 1.25
R(2) = 0.4
Percentage improvement can be calculated thus ;
R(2)-R(1)/R(1) × 100%
(0.4-0.25)/0.25 × 100%
0.15 × 100%
=15%
Therefore, percentage improvement in reliability is 15%
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Algebraic expression for 4less then 3x
Answers
When 'x' is 5, the Algebraic expression 3x - 4 evaluates to 11.
To find the algebraic expression for "4 less than the product of 3 and some number," let's break it down step by step.
First, let's define the unknown number as 'x.' Since the problem states "the product of 3 and some number," we can express this as 3 * x or simply 3x.
Next, we want to subtract 4 from this product. The phrase "4 less than" indicates subtraction, so we subtract 4 from 3x. This can be represented as 3x - 4.
In summary, the algebraic expression for "4 less than the product of 3 and some number" is 3x - 4, where 'x' represents the unknown number.
To calculate the value of this expression for a specific value of 'x,' you substitute that value into the expression and simplify. For example, if 'x' is 5, you would substitute 5 into the expression:
3(5) - 4
This simplifies to:
15 - 4 = 11
So, when 'x' is 5, the expression 3x - 4 evaluates to 11.
In general, the algebraic expression allows us to represent a mathematical relationship between quantities using symbols and operations. By substituting specific values into the expression, we can calculate the corresponding results.
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Note the complete question:
Algebraic expression for 4 less than the product of 3 and some number
What is the algebraic expression for "4 less than the product of 3 and some number?
Please help me understand the meaning of how to calculate.
if 6x is 6, then what is the square root of 4761 x
Answers
Answer:
the answer is 69
Step-by-step explanation:
you find the square root of 4761
Answer:
its 69
Step-by-step explanation:
Show work please and thanks
Answers
In the adjoining fig.
Answers
Given info:
In the given figure,
AB and CD are two parallel lines.Transversal EF intersects AB at G and CD at H making two pairs of alternative interior angles.Now, ray HG stand on line CD
∠ M = ∠n [vert. opp. ∠s]
∠P = ∠Q [corres. ∠s axiom]
