The slopes of the points are computed below
How to determine the slopes of the pointsThe slope of any two points is then calculated using the following slope equation
Slope = (y₂ - y₁)/(x₂ - x₁)
Using the above as a guide, we have the following slopes in set 2
T. Slope = (9-5)/(10-7) = 4/316. Slope = (2-(-2))/(9-(-5)) = 2/7B. Slope = (-4-2)/(-5-(-8)) = -28. Slope = (-8-(-6))/(2-(-10)) = -1/6H. Slope = (-1-(-2))/(-4-2) = -1/63. Slope = (-7-1)/(-8-(-2)) = 4/3S. Slope = (7-9)/(-11-(-4)) = 2/75. Slope = (3-(-2))/(-3-(-4)) = 5O. Slope = (-6-(-1))/(4-5) = 514. Slope = (6-(-4))/(-7-(-2)) = -2For set 3, we have the following slope values
K. Slope = (-3-(-3))/(2-1) = 09. Slope = (-4-(-1))/(6-8) = 3/2R. Slope = (5-0)/(-3-3) = -5/61. Slope = (-5-(-6))/(-8-(-11)) = 1/3E. Slope = (-2-4)/(8-12) = 3/215. The slope is undefined U. The slope is undefined 12. Slope = (9-(-3))/(-5-(-2)) = -4O. Slope = (5-1)/(2-3) = -46. Slope = (8-8)/(7-(-3)) = 0H. Slope = (-8-(-6))/(-7-(-1)) = 1/310. Slope = (-7 - 3)/(7 - (-5)) = -5/6Read more about slope at
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5. If 3 km 500 m is subtracted from 10 km, then the result is
Answer:
The result of subtracting 3 km 500 m from 10 km is 6500 m (Or expressed in kilometers: 6.5 km).
Step-by-step explanation:
Hi,
We need to convert both measurements to the same unit (either km or meters) and then subtract:
Reminder:
1 km = 1000 m
=> 10 km = 10 * 1000 = 10000 m
=> 3 km 500 m = 3 * 1000 + 500 = 3500 m
Now we can subtract:
10000 m - 3500 m = 6500 m
The result of subtracting 3 km 500 m from 10 km is 6500 m (Or expressed in kilometers: 6.5 km).
Good luck!
Q.10. Jack sells toy cars on a website. The web site fee is $30. Jack sells toy cars for $4 each.
Which inequality Jack should use to determine how many toy cars, c, he must sell to make
a profit of at least $50?
A 34c ≤50
B 34c ≥ 50
C 4c-30 ≥ 50
D 4c+30 ≥ 50
Answer:
Let's break down the cost and revenue for Jack's toy car sales:
The cost to Jack is the website fee of $30.
The revenue for Jack is the number of toy cars he sells (c) multiplied by the selling price of each toy car, which is $4 per toy car.
To make a profit of at least $50, Jack's revenue must be at least $80 ($30 website fee + $50 profit). Therefore, we can set up the following inequality:
4c - 30 ≥ 50
Solving for c, we get:
4c ≥ 80
c ≥ 20
So, Jack must sell at least 20 toy cars to make a profit of at least $50. The correct answer is option B: 34c ≥ 50.
Answer:
B
Step-by-step explanation:
34c < 50 = 136 (136 is greater than 50 wrong sign) x
B 34c > 50 = 136 (136 is greater than right sign)
C 4c-30 > 50 = -14 > 50 (wrong)
D 4c + 30 > 50 = 46 > 50 ( 46 is not greater than 50)
39.6% of consumers believe that cash will be obsolete in the next 20 years. Assume that 6 consumers are randomly selected. Find the probability that fewer than 3 of the selected consumers believe that cash will be obsolete in the next 20 years.
The probability that fewer than 3 of the selected consumers believe that cash will be obsolete in the next 20 years IS 0.528.
The binomial probability:The binomial probability formula is used to calculate the probability of getting exactly k successes in n independent trials, where each trial has only two possible outcomes (success or failure) and the probability of success is denoted as p. The formula is:
[tex]P(X=k) = C(n,k)\times p^k\times(1-p)^{(n-k)[/tex]Here we have
39.6% of consumers believe that cash will be obsolete in the next 20 years.
Let p be the probability that a consumer believes that cash will be obsolete
=> p = 39.6% or 0.396.
Then, the probability that a consumer does not believe that cash will be obsolete is q = 1 - p = 0.604.
We need to find the probability that less than 3 of the selected consumers believe that cash will be obsolete.
P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)
Using the binomial probability formula, we have:
[tex]P(X = k) = C(n,k) \times p^k\times q^{(n-k)[/tex]
=> P(X = 0) = C(6, 0) × (0.396)⁰ × (0.604)⁶ = 0.048
=> P(X = 1) = C(6, 1) × (0.396)¹ × (0.604)⁵ = 0.18
=> P(X = 1) = C(6, 2) × (0.396)² × (0.604)⁴ = 0.3
P(X < 3) = 0.048 + 0.18 + 0.3 = 0.528
Therefore,
The probability that fewer than 3 of the selected consumers believe that cash will be obsolete in the next 20 years IS 0.528.
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1. When you accrue interest, what does that mean?
A. monetary value is added to your account.
B. You get discounts off your monthly charges.
C. People want to be involved in your account.
D. You have to pay extra.
When you accrue interest, it means that A. monetary value is added to your account.
What is accruing interest?Accruing interest means computing, determining or adding the interest amount due on the principal (sometimes on the principal and accumulated interest) fora period.
When a person accrues interest, it does not mean that they get discounts off their monthly charges or have to pay extra. It does not mean that people want to be involved in your account.
Thus, when a person accrues interest, it involves adding additional monetary value to the account.
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The sides length 4, 6, 9 can be used to form the size of a triangle
The triangle will have a perimeter of 19 units.
What is a perimeter?Triangle perimeter: The circumference of any two-dimensional figure is referred to as its perimeter. By adding the lengths of the sides, we can determine the perimeter of any closed shape. You will first learn what the perimeter is in this article.
For a triangle, the perimeter is the sum of all the sides of the triangle. To calculate the perimeter add all the sides of the triangle as below,
Perimeter = 4 + 6 + 9
Perimeter = 19 units
Therefore, the perimeter of the triangle is 19 units.
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The complete question is given below.
The sides lengths 4, 6, and 9 can be used to form the size of a triangle. Find the perimeter of the triangle.
Suppose a company has fixed costs of $49,400 and variable cost per unit of
4
9
x + 222 dollars,
where x is the total number of units produced. Suppose further that the selling price of its product is
2148 −
5
9
x dollars per unit.
(a) Find the break-even points. (Enter your answers as a comma-separated list.)
x =
(b) Find the maximum revenue. (Round your answer to the nearest cent.)
$
(c) Form the profit function P(x) from the cost and revenue functions.
Find maximum profit.
$
(d) What price will maximize the profit? (Round your answer to the nearest cent.)
$
(a) The break-even points are approximately 1,581 and 2,809 units produced.
(b) The maximum revenue is approximately $2,088,931.47.
(c) P(x) = -5/9x² + 919x - 49,400
(d) The price that will maximize the profit is approximately $1,829.17 per unit.
What is the algebraic equations?An algebraic expression is when we use numbers and words in solving a particular mathematical question.
(a) To find the break-even points, we need to find the values of x at which the total revenue equals the total cost. The total revenue is the product of the selling price and the number of units sold, while the total cost is the sum of the fixed cost and the variable cost per unit multiplied by the number of units sold. Thus, we have:
Total revenue = Selling price × Number of units sold = (2148 - 5/9x)x
Total cost = Fixed cost + Variable cost per unit × Number of units sold = 49,400 + (49x/9 + 222)x
Setting the total revenue equal to the total cost, we get:
2148x - 5/9x² = 49,400 + (49x/9 + 222)x
Multiplying both sides by 9, we get:
19332x - 5x² = 445,110
Simplifying, we get:
5x²- 19332x + 445,110 = 0
Using the quadratic formula, we get:
x = (19332 ± sqrt(19332² - 4(5)(445,110))) / (2(5))
x ≈ 2808.6 or x ≈ 1581.4
Hence, the break-even points are approximately 1,581 and 2,809 units produced.
(b) The revenue function is given by:
R(x) = (2148 - 5/9x)x
To find the maximum revenue, we can take the derivative of the revenue function with respect to x, set it equal to zero, and solve for x:
R'(x) = 2148 - 10/9x = 0
x = 19332/10 ≈ 1933.2
Substituting this value of x into the revenue function, we get:
R(1933.2) ≈ $2,088,931.47
Hence, the maximum revenue is approximately $2,088,931.47.
(c) The profit function P(x) is given by:
P(x) = R(x) - C(x) = (2148 - 5/9x)x - (49,400 + (49x/9 + 222)x)
Simplifying, we get:
P(x) = -5/9x² + 919x - 49,400
(d) To find the maximum profit, we can take the derivative of the profit function with respect to x, set it equal to zero, and solve for x:
P'(x) = -10/9x + 919 = 0
x = 8265
Substituting this value of x into the profit function, we get:
P(8265) ≈ $1,077,927.78
Therefore, the maximum profit is approximately $1,077,927.78.
To find the price that will maximize the profit, we need to substitute the value of x into the selling price function:
Selling price = 2148 - 5/9x = 2148 - 5/9(8265) ≈ $1,829.17
Hence, the price that will maximize the profit is approximately $1,829.17 per unit.
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Mary cart worth purchased a four piece lugar set for 750 she made a down payment of 15% and was charged 6% interest find the total installment price and the monthly payments if she payed it off in 8 months
Mary's monthly payments will be approximately $117.50.
What is the instalment price?The total instalment price is the price of the furniture plus the interest charged. Since Mary made a down payment of 15%, the amount that is subject to interest is 85% of the total price. Therefore:
Total price = (100% / 85%) * $750 = $882.35
The interest charged is 6% of the total price over the 8-month payment period. Therefore:
Interest charged = 6% * $882.35 * (8 / 12) = $35.29
The total installment price is the sum of the total price and the interest charged:
Total installment price = $882.35 + $35.29 = $917.64
To find the monthly payments, we can use the formula for the present value of an annuity:
Payment = [tex]\mathrm{PV \times (r / (1 - (1 + r)^{(-n)}))}[/tex]
where PV is the present value (total installment price), r is the interest rate per month (6% / 12 = 0.005), and n is the number of payments (8).
Substituting the values:
Payment = $917.64 × (0.005 / [tex](1 - (1 + 0.005)^{(-8)}[/tex] ≈ $117.50
Therefore, Mary's monthly payments will be approximately $117.50.
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Every year Marla collects
acorns. If she collects 1,378
acorns each year for 7
years, how many acorns will
she have?
Answer:
9,646
Step-by-step explanation:
1378 acorns x 7 years = 9,646 acorns
Mary goes to the store to buy Pokémon cards for her sister Cloey’s birthday. She has $4,032 and Pokémon card packs cost $4 each. How many Pokémon cards can she buy?
Answer:
To determine how many Pokémon cards Mary can buy, we need to divide the amount of money she has by the cost per card:
$4,032 ÷ $4 = 1,008
Mary can buy 1,008 Pokémon cards.
Find dz/dt using chain rule
Using the chain rule, the value for dz/dt is obtained as [tex]dz/dt = 2(2t + (4 - t^2)e^{(4-t^2)}) ((1 - t)e^{(4-t^2)})[/tex].
What is chain rule?
The chain rule is the formula used to determine the derivative of a composite function, such as cos 2x, log 2x, etc. Another name for it is the composite function rule. Only composite functions are subject to the chain rule.
To find dz/dt using the chain rule, we need to differentiate each term of z with respect to t, then multiply by the derivative of the inner function with respect to t.
First, we have -
x = 2t
Taking the derivative with respect to t, we get -
dx/dt = 2
Next, we have -
y = 4 - t²
Taking the derivative with respect to t, we get -
dy/dt = -2t
Using the chain rule, we have -
[tex]dz/dt = (x + y)e^y \times (\frac{dx}{dt} + \frac{dy}{dt}e^y)[/tex]
Substituting x and y into this equation, we get -
[tex]dz/dt = (2t + (4-t^2))e^{(4-t^2)} \times ((2 - 2t) e^{(4-t^2)})[/tex]
Simplifying this expression, we get -
[tex]dz/dt = 2(2t + (4 - t^2)e^{(4-t^2)}) ((1 - t)e^{(4-t^2)})[/tex]
Therefore, the value is obtained as [tex]dz/dt = 2(2t + (4 - t^2)e^{(4-t^2)}) ((1 - t)e^{(4-t^2)})[/tex].
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EASY MATH POINTS!
Answer from the screenshot below :)
The domain and range for the mapping diagram are given as follows:
Domain: {-9, -0.5, 1, 2.1, 6}.Range: {-7, 1, 6, 20, 154}.The diagram represents a function, as each value of the input is mapped to a single value of the output.
How to obtain the domain and the range of the diagram?The concepts for the domain and the range of the diagram are defined as follows:
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Convert 14ft3 to fluid ounces. Round to the nearest hundredth if necessary. First fill in the blanks on the left hand side with two of the ratios given. Then write the answer.
14 ft³ is equal to 104,720 fluid ounces.
What is Unit of Measurement?A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.
We have to convert 14 ft³ to fluid ounces
we need to use the conversion factor: 1 ft³ = 7,480 fluid ounces
Multiplying both sides by 14, we get:
14 ft³ = 14 x 7,480 fluid ounces
= 104,720 fluid ounces
Therefore, 14 ft³ is equal to 104,720 fluid ounces.
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Jake gets to a party at to'dock having alredy baned off 25 calories throughout his normal day. After dancing at the party. he checked! and burned off 85 total for the day by 9o'clock.
The calories burned per hour is 30 calories per hour
How to determine the calories burned per hourFrom the question, we have the following parameters that can be used in our computation:
Calories at 7 = 25 calories
Calories at 9 = 85 calories
Using the above as a guide, we have the following:
Rate = Difference in calories/Difference in time
Substitute the known values in the above equation, so, we have the following representation
Rate = (85 - 25)/(9 - 7)
Evaluate
Rate = 30
Hence, the rate is 30 calories per hour
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Find the area of this composite shape. Include correct units
Answer:
A = 273 m^2
Step-by-step explanation:
We have two shapes:
One Triangle and One Rectangle
Area of Triangle: A = 1/2*B*H
Area of Rectangle: A = L*W
Area of Triangle:
A = 1/2 * 6 * 7
A = 3 * 7
A = 21 m^2
Area of Rectangle:
A = 18 * 14
A = 252 m^2
Now add Area of Triangle and Area of Rectangle to get the whole area of the shape.
A = 21 + 252 = 273 m^2
find the measure of gpy
The value of ∠ GPY, given the angle measures on the figure, can be found to be 118 °
How to find the angle ?The angles ∠ GPY and ∠ KPR are congruent, which means that they are the same.
The angle ∠ GPY can therefore be found by equating both angles to themselves:
8 p + 94 = 5 p + 103
Collect like terms ;
8 p - 5 p = 103 - 94
3 p = 9
p = 9 / 3
p = 3
The value of ∠ GPY is therefore :
= 5 ( 3 ) + 103
= 15 + 103
= 118 °
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Kabir has three fuel containers. One has a capacity of 7 litres,
one has a capacity of 4 litres and one has a capacity of 3 litres.
The 7 litre container is full, the other two containers are empty.
None of the containers has a measurement scale.
How can Kabir transfer the fuel so that two of the containers contain
a volume of 2 litres each, and the other contains a volume of 3 litres,
vithout having to estimate?
The solution is, the capacity of the largest container that can fill the tanks an exact number of times is, 44 litres.
What is CGF?In mathematics, the greatest common divisor of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers. For two integers x, y, the greatest common divisor of x and y is denoted {\displaystyle \gcd}.
here, we have,
We subtract the remainders from the amounts.
447 - 7 = 440
577 - 5 = 572
669 - 9 = 660
Now we need the GCF of 440, 572, 660
440 = 2³ × 5 × 11
572 = 2² × 11 × 13
660 = 2² × 3 × 5 × 11
GCF = 2² × 11 = 44
The greatest common factor is 44.
Answer: 44
Check:
447/44 = 10 reminder 7
577/44 = 13 remainder 5
669/44 = 15 remainder 9
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Sketch the graph of f by hand and use your sketch to find the absolute and local maximum and minimum values of f. (If an answer does not exist, enter DNE.) f(t) = 5 cos t, −3/2 ≤ t ≤ 3/2
Therefore , the solution of the given problem of graph comes out to be the graph is a symmetric wave that oscillates between 5 and 5.
A graph is what?Mathematicians use graphs to logically chart or illustrate claims rather than values in an interesting visual way. Usually, a graph point shows the connection between two or more objects. A graph is a particular kind of non-linear railway assembly composed of nodes and lines. The nodes, also known as the borders, should be joined together with glue. The node numbers in this network included 1, 2, 3, and 5, while the edge numbers included 1, 2, 3, and 4, along with (2.5), (3.5), (4.5), but also (4.5). (4.5).
Here,
Plotting a few important spots will help us later when we sketch the graph of f(t) = 5 cos(t).
Since the function has a phase of 2, we can concentrate on the range from 3/2 to 3/2. We possess
=> f(−3/2) = 5 cos(−3/2) ≈ 4.515
=> f(−π) = 5 cos(−π) = −5
=> f(−1/2) = 5 cos(−1/2) ≈ 4.045
=> f(0) = 5 cos(0) = 5
=> f(1/2) = 5 cos(1/2) ≈ 4.045
=> f(π) = 5 cos(π) = −5
=> f(3/2) = 5 cos(3/2) ≈ 4.515
Using these coordinates, we can create the following f(t) graph:
With maximum positions at t = /2 and t = /2, and minimum points at t = 3/2, t = 1/2, t = 1/2, and t = 3/2,
the graph is a symmetric wave that oscillates between 5 and 5.
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Can someone please help me with this math problem, ASAP?
The equation rewritten as a function of x is
[tex]y \ln \left(-2 x+x^2+2 y \right)=\ln (x)[/tex]
What is a mathematical function?Generally, In the field of mathematics, an assignment of one element from set Y to each and every element in set X is the definition of a function. This particular set, X, is referred to as the function's domain, and this particular set, Y, is referred to as the function's codomain.
Historically, functions have been seen as an idealization of the way in which one variable relies on another variable. Wikipedia
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PLS I BEG YALL TO GUVE ME THE CORRECT ANSWER
The x intercept is (2, 0) and the y intercept is (0, 8)
What is an intercept?x-intercept and y-intercept are the two main intercepts. The line's x-intercept and y-intercept are located where the line crosses the x and y axes, respectively.
As per the given data:
The function is [tex]f(x) = -3^x + 9[/tex].
For the x intercept, f(x) = 0:
[tex]0 = -3^x + 9\\3^x = 9\\x = 2[/tex]
The x intercept is 2.
For the y intercept, x = 0:
[tex]y = -3^0 + 9\\y = -1 + 9\\y = 8[/tex]
The y intercept is 8.
Hence, The x intercept is (2, 0) and the y intercept is (0, 8)
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Emails arrive randomly on Oliver's computer at an average rate of 1.46 per hour. Stating a necessary assumption, find the probability that between 9.00am and 11.30am Oliver receives: (i) no emails
The probability that Oliver will receive no emails in between 9.00am and 11.30am is 2.599%.
What is Poisson Distribution?Poisson Distribution is defined as a discrete distribution which measures the likelihood of happening an event in a certain period of time.
The formula for Poisson distribution is,
P(x) = (e^(-λ) λˣ) / x!
Given that,
Average rate of arrival of emails in an hour = 1.46 per hour
Between 9.00 am and 11.30 am, there are 2.5 hours.
Average rate of arrival of emails in 2.5 hours = 2.5 × 1.46
= 3.65
So, λ = 3.65
x = 0 (since no emails.)
P(0) = (e^(-3.65) (3.65)⁰) / 0!
= e^(-3.65)
= 0.02599
= 2.599%
Hence the probability is 2.599%.
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Please help me with this math question!
Step-by-step explanation:
To write the expression (-4-7i)+(-1-4i) in a+bi form, we need to simplify the expression by adding the real parts and the imaginary parts separately.
(-4-7i)+(-1-4i) = -4 - 1 - 7i - 4i = -5 - 11i
Therefore, (-4-7i)+(-1-4i) can be written in a+bi form as -5 - 11i.
Answer:
a= -24
b= 23
Step-by-step explanation:
(-4-7i)(-1-4i)
4+16i+7i-28
-24i+23i
An architect designs a rectangular flower garden such that the width is exactly two-thirds of the length. If 320 ft of antique picket fencing are to be used to enclose the garden for the length and width of the garden.
Answer:
The length of the garden would be 480 ft and the width would be 320 ft.
Step-by-step explanation:
In rectangle ABCD
triangle ABE is equilateral
triangle CDE is isosceles, with CE = DE
Work out the size of angle x.
Your final answer must say, x =
The value of x in the given arrangement of equilateral triangle and isosceles triangle is 88°
What is an angle ?An angle is a mathematical term, which we can define, when two straight lines or rays meet at a common endpoint. The common point is called the vertex of an angle. The word angle comes from a Latin word named ‘angulus,’.
Given that,
A arrangement which contains,
one equilateral triangle ABE &
one isosceles triangle CDE
It is known that sum of all the angles in each direction is 180°.
ΔAEB is equilateral triangle,
so angle will be of 60°
∠AEB = 60°
And in isosceles triangle,
∠EDC = ∠ECD
∠ADC = 90°
∠ADC = ∠ADE + ∠EDC
90° = 62° + ∠EDC
∠EDC = 28° = ∠ECD
It is known that sum of all the interior angles of the triangle is 180°.
∠EDC + ∠ECD + ∠DEC = 180°
28° + 28° + ∠DEC = 180°
∠DEC = 124°
Now sum of all the angles around point E is 360°
∠AED + ∠DEC + ∠BEC + ∠AEB = 360°
x + 124° + x + 60° = 360°
2x = 176°
x = 88°
Hence, the value of x is 88°
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Mr. Gaspar wants to store a 12-foot-long pipe
in a tool closet. The closet has the shape of a
right rectangular prism with the dimensions
shown. Will the pipe fit? Show your work.
The longest pipe can fit in the prism is 11.7 ft, so, 12 ft long pipe does not fit.
What is the Pythagoras theorem?The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle. According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.
From the given figure,
By considering base of the prism, we get
c²=6²+6²
c²=72
c=6√2 ft
Now, d²=c²+8²
d²=72+64
d²=136
d=√136
d= 11.7 ft
Hence, the longest pipe can fit in the prism is 11.7 ft, so, 12 ft long pipe does not fit.
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Your teacher has requested that two rows of strips be placed around the entire room what is the total length of strips that is required
The Length of wooden strip based on the information is 106 cm.
How to calculate the lengthThe perimeter of a shape is simply the total length of the boundary that the shape has. It should be noted that in this case, it's gotten by adding all the length that the shape has.
Length of wooden strip = Perimeter of a rectangular table.
= 2(Length+Breadth)
= 2(32+21)
= 2(53)
= 106 cm
Length of wooden strip is 106 cm.
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What is the length of the wooden strip required to frame a photograph of length and breadth 32 cm and 21 cm respectively?
what is the value of the x-coordinate of point A
The value of the x-coordinate of point A is -0.342
What is the value of the x-coordinate?If we measure the angle from the x-axis, we will get:
angle = 90° + 20° = 110°
Now remember that the rectangular coordinates are for a point with radius R and defined by an angle a are given by the expressions below:
x = R*cos(a)
y =R*sin(a)
Where in this case we can see that we have an unit circel, thus, R = 1, and a is the angle, in this case 110° as we saw above.
Then the x-coordinate of point A is:
x = 1*cos(110°) = -0.342
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A law firm billed a client $3,300 for work performed in the current month. Which of the following general journal entries will the firm make to record this transaction?
Therefore , the solution of the given problem of unitary method comes out to be amount billed to the client.
An unitary method is what?To finish the job using the unitary technique, the equation from this nano section should be multiplied by two. In essence, when a wanted object is present, both the characterised by either a group and the pigment sections are omitted from the unit method. A variable fee of Inr ($1.01), for instance, would be paid for 40 pens. It's conceivable that one nation will have complete control over the strategy used to achieve this. Almost all living things have a unique trait.
Here,
$3,300 is debited from Accounts Payable - Client's Name.
Credit: $3,300 in revenue
This shows the revenue earned by the law company for the job done and records the increase in accounts receivable for the amount billed to the client.
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the ___ appears on correspondence, such as invoices and statements.
The blank in the sentence can be filled by the word "date." The date appears on correspondence, such as invoices and statements, to indicate the day on which the document was issued or created.
what is expression ?Multiplying, dividing, adding, and subtracting are all mathematical operations. As an example, consider the following expression: Expression, mathematics, and a numeric value Numbers, parameters, and functions are the components of an expression in mathematics. Using opposing words and phrases is possible. An expression, sometimes referred to as an algebraic expression, is any mathematical statement that includes variables, numbers, and a mathematical action between them. For instance, the expression 4m + 5 is made up of the expressions 4m and 5, as well as the variable m from the previous equation, all of which are separated by the mathematical symbol +.
The blank in the sentence can be filled by the word "date." The date appears on correspondence, such as invoices and statements, to indicate the day on which the document was issued or created.
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Use implicit differentiation to find an equation of the tangent line to the curve at the given point.
x2+y2=(2x2+2y2−x)2,(0,1/2)
As a result, y = -x + 1/2 is the equatiοn οf the tangent line tο the curve x² + y² = (2x² + 2y² - x)² at the pοsitiοn (0,1/2).
What is equatiοn?An equatiοn in mathematics is a claim that twο mathematical expressiοns are equivalent. An equatiοn has an equal sign, typically has οne οr mοre factοrs, and can be sοlved fοr by applying algebraic οr numerical techniques. Equatiοns are used tο represent real-wοrld phenοmena, resοlve issues, and make predictiοns in many branches οf mathematics, science, and engineering.
given:
We must first use implicit differentiatiοn tο determine the derivative οf the curve in οrder tο determine the equatiοn οf the tangent line tο the curve at the pοsitiοn (0,1/2).
By taking the derivative οf the equatiοn's twο sides with regard tο x, we arrive at:
dy/dx = 2x + 2y
(2x² + 2y²- x) * (4x - 1) (4x - 1)
When we sοlve fοr dy/dx and simplify this equatiοn, we get:
[(1 - 4x)(2x + 2y)] Equals dy/dx / [4(2x² + 2y² - x) - 2y(1 - 4x)]
The slοpe οf the tangent line at the pοint (0,1/2) can nοw be calculated by plugging in the numbers x = 0 and y = 1/2:
dy/dx = [(1 - 4(0))
(2(0) + 2(1/2))] / [4(2(0)² + 2(1/2)² - 0) - 2(1/2)(1 - 4(0))] = -1
Therefοre, the tangent line's slοpe at the pοsitiοn (0,1/2) is negative οne. We can use the pοint-slοpe fοrm οf a line tο determine the equatiοn οf the tangent line:
where (x1,y1) is the tangency pοint and m is the inclinatiοn οf the tangent line. When we enter the numbers we have, we οbtain:
y - 1/2 = -1(x - 0) (x - 0)
When we simplify this sοlutiοn, we οbtain:
y = -x + 1/2
As a result, y = -x + 1/2 is the equatiοn οf the tangent line tο the curve x² + y2 = (2x² + 2y² - x)² at the pοsitiοn (0,1/2).
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What is the rate (i.e. Slope) between these two points? (-5,0) and (0, 6) *