Answers
the point-slope form is:
y + 5 = -(9/11)*(x - 3)
How to get the linear equation?A line that passes through a point (x₁, y₁) and has a slope m, can be written in point-slope form as:
y - y₁ = m*(x - x₁)
Here we know that the line passes through (3, -5) and (-8, 4).
Then the slope is:
[tex]m = \frac{-5 - 4}{3 - (-8)} = \frac{-9}{11}[/tex]
And we can use (3, -5) as the point (x₁, y₁), then the point-slope form is:
y + 5 = -(9/11)*(x - 3)
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Related Questions
Help me please answer is not A
Answers
Answer:
B) 16.47
Step-by-step explanation:
In order to find the mean of grouped data with intervals, we use the formula
(∑f * m) / (∑f)
where (∑f * m) is the sum of the product of each frequency (f) and the corresponding midpoint (m) for its interval and (∑f is the sum of each frequencyStep 1: First, we need to find the sum of the frequencies: ∑f = 2 + 3 + 8 + 4 = 17
Step 2: Next, we need to find the midpoint (m) of each interval. We do this by averaging the end points of each interval
m of first interval: (9.5 + 12.5) / 2 = 11
m of second interval: (12,5 + 15.5) / 2 = 14
m of third interval: (15.5 + 18.5) / 2 = 17
m of fourth interval: (18.5 + 21.5) / 2 = 20
Step 3: Now, we multiply the frequency for each interval by its corresponding midpoint and add them together to find the sum
f * m for first interval: (2 * 11) = 22
f * m for second interval: (3 * 14) = 42
f * m for third interval: (8 * 17) = 136
f * m for fourth interval: (4 * 20) = 80
Sum of f * m for each interval: 22 + 42 + 136 + 80 = 280
Step 4: Finally, we divide the sum of f * m for each interval by the sum of f to find the mean:
280 / 17 = 16.47058824 = 16.47
Idaho gets out and closes the door behind her. She is in a room with one exit, and the lock requires a key. There's a table with a briefcase that is also locked. It has a three-digit combination. The first part of the combination is on a wheel with all 10 digits. The second wheel has only 5 digits, and the third has 3 digits. How many combinations are possible?
Answers
Answer:
150
Step-by-step explanation:
To determine the number of possible combinations for the briefcase, we need to multiply the number of options for each wheel.
The first wheel has 10 digits, so there are 10 possibilities.
The second wheel has 5 digits, so there are 5 possibilities.
The third wheel has 3 digits, so there are 3 possibilities.
To calculate the total number of combinations, we multiply the possibilities for each wheel:
10 × 5 × 3 = 150
Therefore, there are 150 possible combinations for the briefcase.
Answer: 150
Step-by-step explanation:
I’m not completely sure, but this is going by my logic. The first one has ten digits and any of those ten digits could go with 1 digit from the 5 wheel, and 1 digit from the 3 wheel, so (I think) you have to multiply 10x5x3 to get the amount of possible combinations.
But, if this is wrong, please correct me! I love puzzles and just though this would be fun to try and figure out, I don’t want to spout out any mis or disinfo to anyone
But, in the case my answer’s right, hope this helped :D
100 Points! Algebra question. Photo attached. Find the exact value of the expression. Please show as much work as possible. Thank you!
Answers
For this problem, you need an on-hand calculator.
Problem:
sin (pi/8)
Step 1: divide pi by 8.
[tex]\pi[/tex]/8
=0.39269908169
Step 2: Find Cosine of (0.39269908169)
This is the part where you need a calculator.
Locate the SIN button on your graphing calculator.
Press the SIN button, then continue to type 0.39269908169 after the parenthesis.
The calculator gives a value of .0068538383
Final answer:
0.068538383
A bulb manufacturer claims that the lives of its bulbs are normally distributed with a mean of 8000 hours and a standard deviation of 400 hours. A random sample of 16 bulbs had an average life of 7920 hours. If the manufacturer’s claim is correct,
a. What is the sampling distribution of the sample mean? Sketch the normal distribution. Show the mean and s.d. in the figure.
b. what is the probability of finding a sample mean of 7920 or less? Show the probability in the figure mentioned above.
Answers
20 POINTS HELPPPPPPPP!!!!!!!
Find the vertex, the axis of symmetry, and the y-intercept of the graph.
vertex: (_,_)
axis of symmetry: x=_
y-intercept:_
TTYYYYYYY<3333333333
Answers
axis of symmetry: x = 2
y-intercept: 1
NO LINKS!! URGENT HELP PLEASE!!
O is the center of the regular nonagon below. Find its area. Round to the nearest tenth if necessary.
Answers
Answer:
471.1 square units
Step-by-step explanation:
A regular nonagon is a 9-sided polygon with sides of equal length.
The apothem of a regular polygon is the distance from the center of the polygon to the midpoint of one of its sides.
Therefore, the given diagram shows a regular nonagon with an apothem of 12 units.
The side length (s) of a regular polygon can be calculated using the apothem formula:
[tex]\boxed{\begin{minipage}{5.5cm}\underline{Apothem of a regular polygon}\\\\$a=\dfrac{s}{2 \tan\left(\dfrac{180^{\circ}}{n}\right)}$\\\\where:\\\phantom{ww}$\bullet$ $s$ is the side length.\\ \phantom{ww}$\bullet$ $n$ is the number of sides.\\\end{minipage}}[/tex]
Given values:
a = 12n = 9Substitute the given values into the formula to create an expression for the side length (s):
[tex]12=\dfrac{s}{2 \tan\left(\dfrac{180^{\circ}}{9}\right)}[/tex]
[tex]12=\dfrac{s}{2 \tan\left(20^{\circ}\right)}[/tex]
[tex]s=24 \tan\left(20^{\circ}\right)[/tex]
The standard formula for an area of a regular polygon is:
[tex]\boxed{\begin{minipage}{6cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{n\cdot s\cdot a}{2}$\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \phantom{ww}$\bullet$ $s$ is the length of one side.\\ \phantom{ww}$\bullet$ $a$ is the apothem.\\\end{minipage}}[/tex]
Substitute the found expression for s together with n = 9 and a = 12 into the formula and solve for A:
[tex]A=\dfrac{9 \cdot 24 \tan(20^{\circ}) \cdot 12}{2}[/tex]
[tex]A=1296\tan(20^{\circ})[/tex]
[tex]A=471.705423...[/tex]
[tex]A=471.7\; \sf square\;units\;(nearest\;tenth)[/tex]
Therefore, the area of a regular nonagon with an apothem of 12 units is 471.1 square units, rounded to the nearest tenth.
A
4
B
10
2
AABC - ATUV
Find x.
T
C
6
U
X = [?]
X
Answers
The unknown length of the similar figure is:
x = 15 units
How to find the unknown length of the similar figure?Two figures are similar if they have the same shape but different sizes. The corresponding angles are equal and the ratios of their corresponding sides are also equal.
Using the above concept, we can equate the ratio of the corresponding sides and solve for the unknown lengths. That is:
TV/AC = TU/AB
x/10 = 6/4
x/10 = 1.5
x = 10 * 1.5
x = 15 units
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$16,000 is deposited into a savings account with an annual interest rate of 2% compounded continuously. How much will be in the account after 4 years? Round to the nearest cent.
Answers
The amount in the account after 4 years, rounded to the nearest cent, will be approximately $17,332.8.
Understanding Compound InterestRecall the compounding formula:
A = P * [tex]e^{rt}[/tex]
Where:
A = Final amount in the account
P = Initial principal (deposit)
e = Euler's number (approximately 2.71828)
r = Annual interest rate (as a decimal)
t = Time in years
Given:
Initial principal (P) = $16,000
Annual interest rate (r) = 2% = 0.02
time (t) = 4 years.
Substitute these values into the formula, we get:
A = $16,000 * [tex]e^{0.02 * 4}[/tex]
Using a calculator, we can calculate:
A = $16,000 * [tex]e^{0.08}[/tex]
A = $16,000 * 1.0833
A = $17,332.8
Therefore, the amount in the account after 4 years, rounded to the nearest cent, will be approximately $17,332.8.
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Which transformation maps △UVW to △EFG?
A. (x, y) ⟶ (0.5x, 0.5y)
B. (x, y) ⟶ (–0.5x, 0.5y)
C. (x, y) ⟶ (2x, 2y)
D. (x, y) ⟶ (–2x, 2y)
Answers
Based on the analysis, the correct transformation that maps triangle △UVW to triangle △EFG is option C: (x, y) ⟶ (2x, 2y), which represents an enlargement or dilation of the figure.
To determine which transformation maps triangle △UVW to triangle △EFG, we need to analyze the given options and understand the effects of each transformation.
A. (x, y) ⟶ (0.5x, 0.5y):
This transformation scales the coordinates of a point by a factor of 0.5 in both the x and y directions.
It represents a reduction or contraction of the figure.
Triangle △UVW would be scaled down to a smaller size, so option A is not the correct transformation.
B. (x, y) ⟶ (–0.5x, 0.5y):
This transformation reflects the coordinates of a point across the y-axis and scales the x-coordinate by a factor of -0.5 and the y-coordinate by a factor of 0.5.
It represents a reflection and scaling.
Triangle △UVW would be reflected across the y-axis and scaled, which does not match the transformation to △EFG.
Therefore, option B is not the correct transformation.
C. (x, y) ⟶ (2x, 2y): This transformation scales the coordinates of a point by a factor of 2 in both the x and y directions.
It represents an enlargement or dilation of the figure.
Triangle △UVW would be scaled up to a larger size, which aligns with the transformation to △EFG.
Therefore, option C could be the correct transformation.
D. (x, y) ⟶ (–2x, 2y):
This transformation reflects the coordinates of a point across the x-axis and scales the x-coordinate by a factor of -2 and the y-coordinate by a factor of 2.
It represents a reflection and scaling.
Triangle △UVW would be reflected across the x-axis and scaled, which does not match the transformation to △EFG.
Thus, option D is not the correct transformation.
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The price of a computer is $999.00. The sales tax rate is 7%. What is the sales tax on this computer in dollars and cents?
Answers
The sales tax on the computer is $69.93.
How to determine the sales taxTo calculate the sales tax on the computer, we need to multiply the price of the computer by the sales tax rate. Here's how you can do it:
Price of the computer: $999.00
Sales tax rate: 7% (which can be expressed as 0.07)
Sales tax = Price of the computer * Sales tax rate
Sales tax = $999.00 * 0.07
To find the sales tax in dollars and cents, we can perform the calculation:
Sales tax = $999.00 * 0.07
Sales tax = $69.93
Therefore, the sales tax on the computer is $69.93.
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how do i find find the distance
Answers
The value of distance of two points shown in figure is,
⇒ d = √20
We have to given that;
Two points on graph are,
(0, 1) and (2, - 3)
Since, The distance between two points (x₁ , y₁) and (x₂, y₂) is,
⇒ d = √ (x₂ - x₁)² + (y₂ - y₁)²
Hence, The distance of two points shown in figure is,
⇒ d = √ (x₂ - x₁)² + (y₂ - y₁)²
⇒ d = √ (2 - 0)² + (-3 - 1)²
⇒ d = √4 + 16
⇒ d = √20
Thus, The value of distance of two points shown in figure is,
⇒ d = √20
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Anybody know this? Find the first four terms of the sequence t/n=n(6n-2) the n is below the t btw
Answers
The first four terms of the sequence t/n = n(6n - 2) are: 4, 20, 48, 88.
How to find st four terms of the sequenceLet's substitute n = 1:
t/1 = 1(6(1) - 2)
t = 1(6 - 2)
t = 4
The first term of the sequence (when n = 1) is 4.
Now, let's substitute n = 2:
t/2 = 2(6(2) - 2)
t = 2(12 - 2)
t = 2(10)
t = 20
The second term of the sequence (when n = 2) is 20.
Next, let's substitute n = 3:
t/3 = 3(6(3) - 2)
t = 3(18 - 2)
t = 3(16)
t = 48
The third term of the sequence (when n = 3) is 48.
Lastly, let's substitute n = 4:
t/4 = 4(6(4) - 2)
t = 4(24 - 2)
t = 4(22)
t = 88
The fourth term of the sequence (when n = 4) is 88.
Therefore, the first four terms of the sequence t/n = n(6n - 2) are: 4, 20, 48, 88.
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Question 1 of 10
Using the graphing function on your calculator, find the solution to the system
of equations shown below.
OA. x=-8, y = 2
OB. More than 1 solution
OC. No solution
OD. x= 12, y = 3
3y-12x = 18
2y-8x = 12
Answers
The system of equations has infinitely many solutions, which corresponds to option (OB).
We can use the graphing function on a calculator to find the solution to the system of equations:
[tex]3y - 12x = 18\\\\2y - 8x = 12[/tex]
To do this, we can rearrange each equation to solve for y in terms of x:
[tex]3y = 12x + 18\\\\y =4x + 6[/tex]
For the second equation.
[tex]2y = 8x + 12\\\\y = 4x + 6[/tex]
We can see that the two equations have the same slope (4) and y-intercept (6). Therefore, the two equations represent the same line, and any point on that line will satisfy both equations.
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Pleaseee help me I’ve been stuck on this fool like 30 minutes can’t miss this or I restart the whole lesson pleease help
Answers
The properties of equality that shows justification of how the equation is solved is explained below.
How to Apply the Properties of Equality to Solve an Equation?Given the equation, 17/3 - 3/4x = 1/2x + 5, we have the following steps and justification which explains the property of equality that was used:
17/3 - 3/4x = 1/2x + 5 [given]
17/3 - 3/4x - 17/3 = 1/2x + 5 - 17/3 [subtraction property of equality]
3/4x = 1/2x - 2/3 [simplification]
3/4x - 1/2x = 1/2x - 2/3 - 1/2x [subtraction property of equality]
-5/4x = -2/3 [simplification]
-5/4x * -4/5 = -2/3 * -4/5 [multiplication property of equality]
x = 8/15 [simplification]
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.3185 degrees = minutes and seconds
Answers
The conversion of 3185 degrees to minutes and seconds is 19 minutes and 6.6 seconds
How to convert the 3185 degrees to minutes and secondsFrom the question, we have the following parameters that can be used in our computation:
Degrees = 0.3185
By definition, there are 60 minutes in a degrees
So, we have
Minutes = 0.3185 * 60
Evaluate the product
Minutes = 19.11
The decimal part of the product above represents the number of seconds
So, we have
Minutes = 19
Seconds = .11 * 60
Evaluate
Seconds = 6.6
Hence, .3185 degrees is 19 minutes and 6.6 seconds
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Find the sum below. Explain how you got this answer
-11 + 3 + 10 + (-25) + 48 =
Answers
Answer:
25
Step-by-step explanation:
There are only additions, so do each addition, in the order it appears, from left to right.
-11 + 3 + 10 + (-25) + 48 =
= -8 + 10 + (-25) + 48
= 2 + (-25) + 48
= -23 + 48
= 25
What is the value of x?
Answers
Answer:
x = 24.5
Step-by-step explanation:
27/(x + 7) = (27 - 6)/x
27x = (x + 7)(21)
27x = 21x + 147
6x = 147
x = 24.5
Answer:
x = 31.5
Step-by-step explanation:
given a line parallel to a side of a triangle and it intersects the other two sides then it divides those sides proportionally , that is
[tex]\frac{6}{27-6}[/tex] = [tex]\frac{7}{x}[/tex]
[tex]\frac{6}{21}[/tex] = [tex]\frac{7}{x}[/tex] ( cross- multiply )
6x = 21 × 7 = 147 ( divide both sides by 6 )
x = 24.5
A jar contains 8 pennies, 3 nickels, 5 dimes, and 2 quarters. If one coin is chosen from the jar, how many ways are there to get more than 4 cents
Answers
Answer: The jar contains a total of 18 coins (8 pennies + 3 nickels + 5 dimes + 2 quarters). To get more than 4 cents, we need to choose a nickel, dime, or quarter. There are 3 nickels, 5 dimes, and 2 quarters, for a total of 10 coins that satisfy this condition. Therefore, there are 10 ways to choose a coin from the jar that is more than 4 cents.
Pls help yes yes yes yes
Answers
The total cost of materials needed to build the house is $4374.75.
How to determine total cost?Calculate the area of the front and back of the house.
Area = Length x Width
Area = 3.5 m x 2.5 m = 8.75 m²
Calculate the area of the sides of the house.
Area = 2 x Length x Height
Area = 2 x 3.5 m x 5 m = 35 m²
Calculate the total cost of glass.
Cost of glass = Area x Cost per square meter
Cost of glass = 8.75 m² x $37 / m² = $323.75
Calculate the total cost of roof tiles.
Cost of roof tiles = Area x Cost per square meter
Cost of roof tiles = 35 m² x $95 / m² = $3325
Calculate the total cost of reinforcement metal.
Cost of reinforcement metal = Perimeter x Cost per meter
Cost of reinforcement metal = 2 x (Length + Width) x $54 / m = $726
Add the costs of glass, roof tiles, and reinforcement metal to get the total cost of materials.
Total cost = $323.75 + $3325 + $726 = $4374.75
Therefore, the total cost of materials needed to build the house is $4374.75.
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Solve for b
Y=1/3x+b
Answers
Answer:
(3xy - 1)/3x = b
Step-by-step explanation:
make b the subject of formula
then simply it
did you get it
Answer:
b=Y-x/3
Step-by-step explanation:
Solve for b by simplifying both sides of the equation, then isolating the variable.
have a great day and thx for your inquiry :)
Use angle diagram to name each one of the angles.
Answers
The angles in the parallel lines are solved
∠9 and ∠16 = alternative exterior angles
∠15 and ∠11 = supplementary angles
∠10 and ∠15 = alternate interior angles
∠12 and ∠15 = vertical angles
∠9 and ∠11 = corresponding angles
∠9 and ∠15 = none
∠13 and ∠14 = supplementary angles
∠14 and ∠11 = alternative interior angles
Given data ,
Let the two parallel lines be represented as a and b
where the transversal line is m
Now , from the given figure , we can deduct that
We can conclude some factors determining parallel lines ,
Alternate angles are equal
Corresponding angles are equal
Co-interior angles add up to 180°
Now , the angles are
∠9 and ∠16 = alternative exterior angles
∠15 and ∠11 = supplementary angles
∠10 and ∠15 = alternate interior angles
∠12 and ∠15 = vertical angles
∠9 and ∠11 = corresponding angles
∠9 and ∠15 = none
∠13 and ∠14 = supplementary angles
∠14 and ∠11 = alternative interior angles
Hence , the angles are solved
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Please help me with this I am on the verge of giving up because of it. Simplify and rationalize the denominnator, the answer should not have negative exponents
Answers
The exponential value equation is A = 1/√x = 1/x^(-1/2)
Given data ,
Let the exponential equation be represented as A
Now , the value of A is
A = x ^ ( 1/6 ) / x ^ ( 2/3 )
On simplifying , we get
The different Laws of exponents are:
mᵃ×mᵇ = mᵃ⁺ᵇ
mᵃ / mᵇ = mᵃ⁻ᵇ
( mᵃ )ᵇ = mᵃᵇ
mᵃ / nᵃ = ( m / n )ᵃ
m⁰ = 1
m⁻ᵃ = ( 1 / mᵃ )
So , A = x ^ ( 1/6 - 2/3 )
On further simplification , we get
A = x ^ ( -3/6 )
A = x ^ ( -1/2 )
So , the value of A is
A = 1/√x
Hence , the exponential equation is solved
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How many variables are in the expression.
8d²+2bc+ 10ab
1
2
3
4
Answers
There are 4 variables in the expression 8d² + 2bc + 10ab
How to determine the number of variables in the expressionFrom the question, we have the following parameters that can be used in our computation:
8d²+2bc+ 10ab
Express properly
So, we have
8d² + 2bc + 10ab
Consider an expression ax + by where the variable is a and b are constants
The variables in the expression are x and y
Using the above as a guide, we have the following:
The variables in the expression 8d² + 2bc + 10ab are a, b, c and d
This means that there are 4 variables in the expression
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side length of titles are 2ft. Rachel tiled the whole floor with 6 rows of 4 tiles
what is the area of the kitchen floor
Answers
The area of the rectangular shaped kitchen floor is A = 96 feet²
Given data ,
The side length of each tile is 2ft, then the area of each tile is:
Area of a tile = side x side = 2ft x 2ft = 4 sq ft
Since there are 6 rows of tiles, each row has 4 tiles, therefore the total number of tiles is:
Total number of tiles = 6 x 4 = 24 tiles
So, the total area covered by the tiles is:
Total area covered by tiles = Area of a tile x Total number of tiles
= 4 sq ft/tile x 24 tiles
= 96 sq ft
Hence , the area of the kitchen floor is 96 feet²
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i need some help here
Answers
The value of x, considering the Pythagorean Theorem, is given as follows:
x = 9.
What is the Pythagorean Theorem?The Pythagorean Theorem states that in the case of a right triangle, the square of the length of the hypotenuse, which is the longest side, is equals to the sum of the squares of the lengths of the other two sides.
Hence the equation for the theorem is given as follows:
c² = a² + b².
In which:
c > a and c > b is the length of the hypotenuse.a and b are the lengths of the other two sides (the legs) of the right-angled triangle.The sides for the problem are given as follows:
15 and 8 (segment of 8 is the radius, which is the distance from the center to a point on the circumference of the circle).
Hence the hypotenuse is obtained as follows:
h² = 15² + 8²
h² = 289
h = 17.
Hence the value of x is obtained as follows:
x = 17 - 8
x = 9.
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A right triangle has side lengths 45 millimeters, 108 millimeters, and 117 millimeters. What is the length of the hypotenuse and why?
117 millimeters, because it is listed last.
117 millimeters, because the hypotenuse is the longest side.
45 millimeters, because 45 is half of 90 and a right angle is 90°.
45 millimeters, because the hypotenuse is the shortest side.
Submit
Answers
The length of the hypotenuse of the given right triangle is 117 millimeters because it is the longest side and it satisfies the conditions of the Pythagorean theorem.
The length of the hypotenuse of a right triangle with side lengths 45 millimeters, 108 millimeters, and 117 millimeters is 117 millimeters.
The hypotenuse of a right triangle is always the side opposite the right angle, and it is the longest side in a right triangle.
In this case, the side lengths are given as 45 millimeters, 108 millimeters, and 117 millimeters.
By comparing the lengths, we can see that 117 millimeters is the longest side, which makes it the hypotenuse.
To further understand why the hypotenuse is the longest side, we can refer to the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
Mathematically, it can be written as c² = a² + b²,
where c represents the length of the hypotenuse, and a and b represent the lengths of the other two sides.
In this case, if we square the lengths of the sides, we get 45² = 2025, 108² = 11664, and 117² = 13689.
By comparing these values, we can see that 13689 is the largest, which corresponds to the length of the hypotenuse, 117 millimeters.
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Will give brainlist
In(5400) + P X Ln30 + q X Ln360+r X Ln270
Find (P,Q,R) when they are real numbers
Pls show work
Answers
The solution for (P, Q, R) in the given equation (5400) + P x Ln30 + Q x Ln360 + R x Ln270, where P, Q, and R are real numbers, is (0, 0, 0). The correct solution is that P = Q = R = 0.
How did we get the values?To find the values of P, Q, and R in the equation (5400) + P x Ln30 + Q x Ln360 + R x Ln270, use the properties of logarithms and solve the equation.
First, simplify the equation:
5400 + P x Ln30 + Q x Ln360 + R x Ln270
Next, express the logarithmic terms using their corresponding exponential forms:
5400 + P x Ln(30) + Q x Ln(360) + R x Ln(270)
= 5400 + P x Ln(2 x 3 x 5) + Q x Ln(2² x 3² x 5) + R x Ln(2 x 3³ x 5)
Using the properties of logarithms, we can rewrite the equation as follows:
5400 + P x (Ln(2) + Ln(3) + Ln(5)) + Q x (2 x Ln(2) + 2 x Ln(3) + Ln(5)) + R x (Ln(2) + 3 x Ln(3) + Ln(5))
Now, let's group the logarithmic terms together:
5400 + P x Ln(2) + P x Ln(3) + P x Ln(5) + Q x (2 x Ln(2) + 2 x Ln(3)) + Q x Ln(5) + R x Ln(2) + R x 3 x Ln(3) + R x Ln(5)
Simplifying further:
5400 + (P + 2Q + R) x Ln(2) + (P + 2Q + 3R) x Ln(3) + (P + Q + R) x Ln(5)
Then, the equation:
5400 + (P + 2Q + R) x Ln(2) + (P + 2Q + 3R) x Ln(3) + (P + Q + R) x Ln(5) = 0
Since this equation holds for all real numbers P, Q, and R, the coefficients of Ln(2), Ln(3), and Ln(5) must be equal to zero:
P + 2Q + R = 0 (1)
P + 2Q + 3R = 0 (2)
P + Q + R = 0 (3)
There is a system of three equations (equations 1, 2, and 3) with three unknowns (P, Q, and R). To solve this system, use any method such as substitution or elimination.
Subtracting equation (3) from equation (2), we get:
(P + 2Q + 3R) - (P + Q + R) = 0 - 0
2Q + 2R = 0
2Q = -2R
Q = -R/2 (4)
Substituting equation (4) into equations (1) and (3), we can solve for P and R:
P + 2Q + R = 0 (1)
P + (-R) + R = 0 (3)
P - R = 0
From equation (3), P = R.
Substituting P = R into equation (4):
Q = -R/2
Since P = R and Q = -R/2. Let's substitute these values back into the equations to find the final solution.
Substituting P = R and Q = -R/2 into equation (1):
P + 2Q + R = 0
R + 2(-R/2) + R = 0
R - R + R = 0
0 = 0
Equation (1) holds true for any real value of R.
Substituting P = R and Q = -R/2 into equation (2):
P + 2Q + 3R = 0
R + 2(-R/2) + 3R = 0
R - R + 3R = 0
3R = 0
R = 0
So, R = 0.
Substituting R = 0 into Q = -R/2:
Q = -R/2
Q = 0/2
Q = 0
Finally, substituting R = 0 into P = R:
P = R
P = 0
Therefore, the solution for (P, Q, R) in the given equation (5400) + P x Ln30 + Q x Ln360 + R x Ln270, where P, Q, and R are real numbers, is (0, 0, 0). The correct solution is that P = Q = R = 0.
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please help me thank you so much
Answers
Answer:
1)
7+9-15 = add 7 and 9, then subtract 15
2)
15-(7+9) = The sum of 7 and 9 subtracted from 15
3)
15-(7+9) = subtract 7 from 15, then add 9
Step-by-step explanation:
Learn BODMAS. The order of how to do equations. A simple tutorial on yt should be sufficient
how much money deposited now will provide payment of Rs. 15000 at the end of each half year for 10 years, if interest is 16% compounded six-monthly
Answers
The amount of money that will produce Rs. 15000 at the end of 6 month for 10years at 16% is Rs. 3750
What is Compound interest?Compound interest is the interest you earn on interest.
For example, if you have $100 and it earns 5% interest each year, you'll have $105 at the end of the first year. At the end of the second year, you'll have $110.25.
Compound interest is expressed as;
A = P( 1+r/n) ^{nt}
where A is the amount
n is the number of time its compounded
t is time
A = 15000
r = 16/100 = 0.16
n = 6/12 = 0.5
t = 10 years
15000 = P( 1 + 0.16/0.5) ^{ 0.5× 10}
15000 = P( 1 + 0.32)⁵
15000 = P( 1.32)⁵
15000 = 4P
P = 15000/4
P = Rs. 3750
Therefore the amount that will be deposited to give Rs. 15000 is Rs. 3750.
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At Chairs and More, assemblers are paid according to the following differential piece rate scale: 1−25 chairs in a week, $10 each; 26−40 chairs, $13 each; and $17.50 each for every chair over 40. Salina Grant assembled 47 chairs in one week. Find her gross pay.
Answers
Salina Grant's gross pay for assembling 47 chairs in one week at Chairs and More is $567.50.
To calculate Salina Grant's gross pay, we need to determine the pay for each range of chairs assembled and sum them up.
Let's break down the calculation based on the given differential piece rate scale:
1-25 chairs: $10 each
Salina assembled 25 chairs in this range, so the pay for this range is
25 * $10 = $250.
26-40 chairs: $13 each
Salina assembled 15 chairs in this range, so the pay for this range is
15 * $13 = $195.
Chairs over 40: $17.50 each
Salina assembled 47 chairs in total, and since she already assembled 25 chairs in the first range and 15 chairs in the second range, the number of chairs in this range is
47 - 25 - 15 = 7 chairs.
The pay for this range is
7 * $17.50 = $122.50.
Now, let's sum up the pay for each range to find Salina Grant's gross pay:
$250 + $195 + $122.50 = $567.50
Therefore, Salina Grant's gross pay for assembling 47 chairs in one week at Chairs and More is $567.50.
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