Answers
The evaluation of the trigonometric identities can be presented as follows;
(a) cos(θ) = -√(51)/10
(b) sin(θ + π/76) = (7·√3 - √(51))/20
(c) cos(θ - π/3) = (7·√3 - √(51))/20
What are trigonometric identities?Trigonometric identities are equations involving trigonometric ratios, in which the values correct far all possible values of the input variable.
(a) The value of sin(θ) = 7/10
The location of the angle θ is quadrant II, therefore;
The adjacent side to the angle θ is -ve, therefore;
cos(θ) = (√10² - 7²)/10 = -√(51)/10
(b) sin(θ + π/6) = sin(θ) × cos(π/6) + sin(π/6) × cos(θ)
sin(θ + π/6) = 7/10 × √3/2 + 1/2 × (-√(51)/10) = 7/10 × √3/2 - 1/2 × √(51)/10
sin(θ + π/6) = (7·√3 - √(51))/(2 × 10) = (7·√3 - √(51))/(20)
(c) cos(θ - π/3) = cos(θ)·cos(π/3) + sin(θ)·sin(π/3)
Therefore;
cos(θ - π/3) = ((-√51)/10 )× (1/2) + (7/10) × √3/2
cos(θ - π/3) = ((-√51)/10 )× (1/2) + (7/10) × √3/2 = (7·√3 - √(51))/20
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Related Questions
The following is data for the first and second Quiz scores for 8 students in a class.
First Quiz Second Quiz
14
16
29
42
43
44
47
48
11
17
31
35
37
37
38
43
Plot the points in the grid below, then sketch a line that best fits the data.
50+
45
40-
35
30
25
20
15
10-
5+
Clear All Draw:
5 10 15 20 25 30 35 40 45 SC
YAY
Answers
The equation of the line of best fit is ŷ = 0.8x + 3.3
How to determine the equation of the line of best fitFrom the question, we have the following parameters that can be used in our computation:
X- 14 16 29 42 43 44 47 48
Y- 11 17 31 35 37 37 38 43
When these values are entered in a graphing calculator, we have the following summary:
Sum of X = 283Sum of Y = 249Mean X = 35.375Mean Y = 31.125Sum of squares (SSX) = 1343.875Sum of products (SP) = 1055.625For the regression equation, we have
ŷ = bX + a
Where
b = SP/SSX = 1055.63/1343.88 = 0.78551
a = MY - bMX = 31.13 - (0.79*35.38) = 3.33764
So, we have
ŷ = 0.78551x + 3.33764
Approximate
ŷ = 0.8x + 3.3
Hence, the equation is ŷ = 0.8x + 3.3
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if you don't know this circumference but you do know that 75% of the circumference is 6 in what would circumference be
Answers
Answer:
circumference = 8 inches
Step-by-step explanation:
75% = 75/100 = 3/4
Let C be the circumference
3/4 C = 6
Multiply both sides by 4/3
C =
A herd of elk is released onto state game lands. The expected population P of the herd can be modeled by the equation below where t is the time in years since the initial number of elk were released. P = (10 + 3.3t)/(1 + 0.1t)
(a) State the domain of the model.
t ≥ 0
t ≠ 10
t < 0
t > 0
t ≤ 0
all real numbers
t ≠ -10
(b) Find the initial number of elk in the herd. ________
(c) Find the populations of elk after 25, 59, and 113 years. (Round your answers to the nearest integer.) _____________
(d) Is there a limit to the size of the herd? If so, what is the expected population? (Round your answer to the nearest integer. If there is no limit, enter NONE.) ____________
Answers
Since the denominator of the expression (1 + 0.1t) cannot be zero, the domain of the model is between t = 0 and t = -10.
How Can I Determine an Equation's Domain and Range?In order to identify the values of the independent variable x and acquire the domain, we simply solve the equation y = f(x). Simply put, x=g(y) will calculate the function's range after we identify g's domain (y).
(b) We must assess the model at t = 0 in order to determine the starting number of elk in the herd:
P = (10 + 3.3t)/(1 + 0.1t)
P = (10 + 3.3(0))/(1 + 0.1(0))
P = 10/1
P = 10
(c) We can easily enter the relevant values of t into the model to determine the populations of elk after 25, 59, and 113 years, then round the results to the nearest integer.
When t = 25:
P = (10 + 3.3t)/(1 + 0.1t)
P = (10 + 3.3(25))/(1 + 0.1(25))
P ≈ 47
When t = 59:
P = (10 + 3.3t)/(1 + 0.1t)
P = (10 + 3.3(59))/(1 + 0.1(59))
P ≈ 189
When t = 113:
P = (10 + 3.3t)/(1 + 0.1t)
P = (10 + 3.3(113))/(1 + 0.1(113))
P ≈ 458
(d) We can use the expression's limit as t approaches infinity to determine the expected population limit:
lim P as t → ∞ = lim (10 + 3.3t)/(1 + 0.1t) as t → ∞
Using L'Hopital's rule, we can find that the limit is equal to:
lim P as t → ∞ = lim 3.3/0.1 as t → ∞
lim P as t → ∞ = 33
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need help with problem 8
Answers
Hence, a 93% confidence range for the actual proportional difference between the two populations equation (represented by the two samples) is between -0.086 and 0.142.
What is the equation?A mathematical equation connects two statements with the equals sign (=), which stands for equivalence. The equivalence of two mathematical propositions is established by a mathematical assertion that is utilized in algebraic equations. For instance, the equal sign separates the numbers 3x + 5 and 14 in equation 3x + 5 = 14. Use a mathematical formula to understand the relationship between the two sentences written on opposite sides of a letter. Usually, the program's particular logo matches it. A good example is 2x - 4 = 2.
For the initial example:
Sample proportion: 0.649 (p1 = 24/37)
Standard deviation SE1 is equal to
[tex]\sqrt{(p^1*(1-p^1))} /n1=\sqrt{(0.649*(1-0.649))/37)0.087}[/tex]
Regarding the second example:
P2 = 54/87 0.621 is the sample proportion.
The standard deviation SE2 is equal to
[tex]\sqrt{(p^2*(1-p^2))} /n2=\sqrt{(0.621*(1-0.621))/87)0.72}[/tex]
The crucial value for a 93% confidence interval has to be calculated next. We may use the conventional normal distribution and large sample size to obtain the z-value that represents the center 93% of the distribution:
[tex]1.812z=invNorm(\frac{1+0.93}{2} )[/tex]
We can finally determine the confidence interval:
CI is equal to (p1-p2) z*sqrt(SE12 + SE22)
CI is calculated as (0.649 - 0.621) 1.812*sqrt(0.0872 + 0.0722)
CI = 0.028 ± 0.114
CI = (−0.086, 0.142)
The real proportional difference between the two populations (represented by the two samples) thus lies between -0.086 and 0.142, with a 93% confidence interval.
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PLEASE HELP ASAP NOWS YOU CHANCE FOR BRANLIST AND POINTS Polygon JKLM is drawn with vertices J(-4,-4), K(-4, -6), L(-1, -6), M (-1, -4). Determine the image coordinates of L' if the preimage is reflected across y =
-2. OPTIONS ARE BELOW
L'(-3, 6)
OL'(-1,6)
OL'(-1, 2)
OL(1, 2)
Answers
The correct answer is (C) OL'(-1, 2) - This point is on the reflected line y=-2, but its y-coordinate is not consistent with the reflection of L. The correct y-coordinate is -4.
What is line?
A one-dimensional geometric figure that consists of infinitely many points arranged in a straight path or direction.
In this case, we are reflecting across the line y = -2, which is two units below the x-axis. Therefore, the y-coordinate of each point in the preimage will be changed by 2 units after reflection.
The coordinates of L are (-1, -6), and after reflecting across y = -2, the y-coordinate will become
-6 + 2 = -4
Therefore, the image of L, L', will have coordinates (-1, -4).
Looking at the given options:
A. L'(-3, 6) - This point is not on the reflected line y=-2, so it cannot be the reflection of L.
B. OL'(-1,6) - This point is above the reflected line y=-2, so it cannot be the reflection of L.
C. OL'(-1, 2) - This point is on the reflected line y=-2, but its y-coordinate is not consistent with the reflection of L. The correct y-coordinate is -4.
D. OL(1, 2) - This point is not on the reflected line y=-2, so it cannot be the reflection of L.
Therefore, the correct answer is option C: L'(-1, -4).
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Sandra read 200 pages over x days. How would you show how many
pages she read each day?
Solve ASAP
Answers
Answer:
200 x 7 = 1,400 x = 7 because there are 7 days in a week
Step-by-step explanation:
Find the slope of the line that passes through the points (-2,3) and (7.-4).
Answers
Answer:
Slope is [tex]\frac{7}{-9}[/tex]
Step-by-step explanation:
For this problem we must use the slope formula:
[tex]\frac{change* in *y}{change*in*x}[/tex]
Our 2 y coords are: 3, -4
To find the change in y, we must subtract.
3 - ( -4 ) = 7
Our 2 x coords are: -2, 7
-2 - 7 = -9
Therfore, our answer is
[tex]\frac{7}{-9}[/tex]
Three people spend money on a vacation. The expression −1,0263 represents the amount of money each person spends on the vacation. Which expression is equivalent to −1,0263 ?
Answers
Answer:-(-1,026/3
Step-by-step explanation:
Neo leaves home at 6:45 to drive to work. Neo drives a distance of 45 miles.Neo thinks he drives of an average speed of 30 miles per hour.
Neo is correct what time would he arrive at work ?
Answers
The time at which Neo reaches the work destination is A = 8 : 15 AM
What do you mean by an Equation?Equations are statements in mathematics that have two algebraic expressions on either side of the equals (=) sign.
It displays the similarity of the connections between the phrases on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are examples of the parts of an equation. When creating an equation, the "=" symbol and terms on both sides are necessary.
Given data ,
Let the time at which Neo reaches the work destination be A
Now , the time at which Neo leaves home = 6 : 45 AM
And , the distance between Neo and work = 45 miles
where the speed of Neo is S = 30 miles per hour
So , the distance traveled by Neo in 1 hour = 30 miles
The distance traveled by Neo in 1.5 hours = 45 miles
Therefore , the time required by Neo to reach office is 1.5 hours
And , the time at which Neo reaches the work destination A = 6 : 45 AM + 1.5 hours
On simplifying the equation , we get
The time at which Neo reaches the work destination A = 8 : 15 AM
Hence , the equation is A = 8 : 15 AM
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PART 2: TABLE 1: Mr. Flynn found that his car can drive 12,5km for every litre of petrol it consumes. This helps him to be sure that he has enough petrol when driving certain distances - due to the nature of his work. The table below represents the car's petrol consumption. The extreme petrol price per litre of R22,50 also impacts Mr. Flynn's travelling. Study the table and answer the questions that follow. 2.1 2.2 2.3 4 2.4 PETROL CONSUMPTION VERSUS TRAVEL DISTANCE (OBSERVABLE PATTERN) DISTANCE TRAVELLED PER LITRE PETROL CONSUMED Litres of Petrol 0 1 2 3 B 5 6 7 8 Distance to Travel (km) A 12,5 25,0 37,5 50,0 62,5 C 87,5 100 Describe the general relationship between distance travelled and litres
Answers
The proportional relationship between distance traveled and liters spent is given as follows:
y = 0.08x.
What is a proportional relationship?A proportional relationship is defined by a linear model with intercept of zero as follows:
y = kx.
In which k is the constant of proportionality.
Mr. Flynn found that his car can drive 12,5km for every litre of petrol it consumes, hence the constant is given as follows:
k = 1/12.5
k = 0.08.
Then the equation is given as follows:
y = 0.08x.
In which:
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Maria and Connor are doing yard work for a neighbor. They make a total of $595.54. Since Connor works more hours than Maria, Connor gets 69% of the money. About how much (in whole
dollars) does Connor make?
Connor makes about
Answers
Answer: Since Connor gets 69% of the money, Maria gets the remaining 31%:
100% - 69% = 31%
Let's first find out how much money Maria makes:
Maria's share = 31% of $595.54
Maria's share = 0.31 x $595.54
Maria's share = $184.61
Now, to find out how much Connor makes, we can subtract Maria's share from the total:
Connor's share = Total - Maria's share
Connor's share = $595.54 - $184.61
Connor's share = $410.93
Therefore, Connor makes about $410.93 (rounded to the nearest dollar).
Step-by-step explanation:
PRYZ is a square. If RK = 5, RY=5, find each measure. KZ= ? YP = ? m<PRZ =? m<ZYKZ=?
Answers
The solution is, in PRYZ square, the value of m∠YKZ = 90.
What is a square?A square is a regular quadrilateral, which means that it has four equal sides and four equal angles. It can also be defined as a rectangle with two equal-length adjacent sides.
here, we have,
Remember that
In a Square
All sides are equal
Diagonals bisect each other perpendicularly
so
Find out KY
In the right triangle RYK
Applying the Pythagorean Theorem
RY^2=RK^2+KY^2
substitute given values
13^2=5^2+KY^2
KY^2=13^2-5^2
KY^2=144
KY=12
Find out PK
Remember that
Diagonals bisect each other perpendicularly
that means
PK=KY=12
Remember that
Diagonals bisect each other perpendicularly
so, that means
m∠YKZ = 90
Hence, The solution is, in PRYZ square, the value of m∠YKZ = 90.
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b) On average, about 240 people visit a local food pantry every day in search of groceries. On an extremely cold day, visitors to the food pantry can be 175% of the average amount. About how many visitors might go to the food pantry on an extremely cold day?
Answers
About 420 visitors might go to the food pantry on an extremely cold day
What is the percentage?
Percentage refers to a way of expressing a number as a fraction of 100. It is often denoted by the symbol "%". For example, if 30 out of 100 students in a class are girls, the percentage of girls in the class is 30%. Percentages are commonly used in many fields, such as finance, statistics, and science, to express proportions, rates, and changes over time.
The problem states that on average, about 240 people visit the food pantry every day in search of groceries. To find out how many visitors might go to the food pantry on an extremely cold day, we need to use the given percentage increase.
The phrase "175% of the average amount" means that we need to find 175% of 240, which is the same as multiplying 240 by 1.75 (since 175% is the same as 1.75 as a decimal). Using the multiplication, we get:
175% of 240 = (175/100) * 240 = 420
So, on an extremely cold day, the number of visitors to the food pantry might be around 420.
Therefore, about 420 visitors might go to the food pantry on an extremely cold day.
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Using matrix method solve the following simultaneous equations 1x + 4y = 9 2x-3y=7
Answers
Thus, using the matrix technique, the solutions to the simultaneous equations are x = -1 and y = 1.
what is matrix ?A rectangular array of numbers or even other mathematical objects that can perform actions like addition and multiplication is known as a matrix. Matrices are widely used to describe systems of equations, transformations, and data in mathematics, physics, engineering, computer science, and many other disciplines. The individual matrix components are frequently identified by their row and column positions, and matrices have a predetermined number of rows and columns. There are numerous actions that can be carried out on matrices, including addition, subtraction, and multiplication by other matrices.
given
We can write the equations in matrix form as follows to answer the simultaneous equations 1x + 4y = 9 and 2x - 3y = 7 using the matrix method:
Then, on the left side of the equation, we can locate the inverse of the coefficient matrix:
| 1 4 |^-1 = 1/(-11) | -3 -4 |
|-2 -1 |
When we multiply both sides of the equation by the coefficient matrix's inverse, we obtain:
| x | | 1 4 |^-1 | 9 |
| x | | -3/11 -4/11 | | 9 |
| y | = | -2/11 -1/11 | x | 7 |
If we simplify, we get:
x = (-3/11)*9 + (-4/11)*7 = -1
y = (-2/11)
*9 + (-1/11)
*7 = 1
Thus, using the matrix technique, the solutions to the simultaneous equations are x = -1 and y = 1.
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Please help with this thank you
Answers
The equation of the line crossing (3, 1 / 2)(5, 5) is y = 9 / 4 x - 25 / 4.
How to find equation of a line?The equation of a line can be represented in slope intercept form as follows:
y = mx + b
where
m = slope of the lineb = y-interceptHence, let's find the equation of the line crossing (3, 1 / 2)(5, 5).
m = 5 - 1 / 2 / 5 - 3
m = 9 / 2 × 1 / 2
m = 9 / 4
Hence, let's find the y-intercept using (5, 5)
y = 9 / 4 x + b
5 = 9 / 4(5) + b
5 - 45 / 4 = b
b = 20 - 45/ 4
b = - 25 / 4
Therefore, the equation of the line is y = 9 / 4 x - 25 / 4.
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Which of the lines or segments below is secant to circle
Answers
The lines or segments which are secant to a circle are:
AK, TW, RN & UN
What is secant of the circle?A line that crosses a circle at two different locations is referred to as a "secant of a circle" in geometry. The Latin verb "secare," which meaning "to cut," is where the English term "secant" originates.
More technically, a secant of a circle is a line that crosses it twice, whereas a tangent of a circle is a line that crosses it only once. A circle's diameter is a chord that runs through its center, whereas a chord of a circle is a line segment connecting two locations on the circle.
Given that,
Two circle which contains various tangents, normal & secants
As we know from the definition of secant it intersect the circle at two points,
Line segments AK, TW, RN & UN are intersecting the circle at two points,
so all this segments are secant of the circle.
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2(4+62)-20divided by 4
Answers
Answer:
the answer is 28
4+62 = 66
66x2 = 132
132-20 = 112
112 divided by 4 = 28
hope this helps <3
Answer:
28
Step-by-step explanation:
i hope this helps
What percentage of votes did the last-place candidate receive?
Answers
The percentage of votes received by the last or fourth candidate in the example election is about 6.4%
What is a percentage?A percentage is a representation of a fraction of an b expressed using a denominator of 100.
A percentage is a representation of a part of whole as a fraction of 100
Therefore, the percentage of votes that a last place candidate in an election receives is the number of votes that the last candidate receives represented as a fraction of the total number of votes with the denominator of the fraction being 100.
An example of an election result is an election result in which the votes received by the four leading candidates can be presented as follows;
Party A = 8,794,726
Party B = 6,984,520
Party C = 6,101,533
Part D = 1,496,687
The percentage of votes received by the Party D is therefore;
% received by party D = ((1,496,687)/(8,794,726 + 6,984,520 + 6,101,533 + 1,496,687)) × 100 ≈ 6.4%The candidate of votes received by the fourth candidate, that received the least number of votes is 6.4%
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need help please lol dont got much time. Simplify
Answers
Answer:
[tex]\frac{49}{45}[/tex] OR [tex]1\frac{4}{45}[/tex]
Step-by-step explanation:
what is 60 percent of 24
Answers
Answer:
14.4
Step-by-step explanation:
=24 * 60/100
=14.4
Answer:
14.4
Step-by-step explanation:
[tex]\frac{24}{10} = 10[/tex]% of 24
6[tex]\frac{24}{10} = 60[/tex]% of 24
Find the missing angle
Answers
Answer:
55
Step-by-step explanation:
The ? angle is 55 degrees since every triangle's angles add up to 180 degrees. We have 2 angles, one with 70 and another with 55, so we add them to get 125. Then we subtract 125 from the total angle of a triangle, 180-125, to get 55.
the answer is 55
they have the same degrees hope this helps
pls help i will give 10 points to the first person to answer this question
Answers
The coordinates of the points on the number line are given as follows:
A = -2/3.B = -1/6.C = 1/2.D = 4/3.How to obtain the coordinates on the number line?Point C is exactly halfway between 0 and 1, hence it's coordinate is given as follows:
C = 0.5.
C is also the third dot between 0 and 0.5, hence the amount represented by each space is given as follows:
0.5/3 = 1/6.
Point B is one space to the left of 0, hence it's coordinate is given as follows:
B = -1/6.
Point A is three spaces to the left of point B, hence it's coordinate is given as follows:
A = -1/6 - 3 x 1/6 = -4/6 = -2/3.
Point D is two spaces to the right of 1, hence:
D = 1 + 2x 1/6 = 1 + 1/3 = 4/3.
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Which equations have the same value of x as Three-fifths (30 x minus 15) = 72? Select three options.
18 x minus 15 = 72
50 x minus 25 = 72
18 x minus 9 = 72
3 (6 x minus 3) = 72
x = 4.5
Answers
The equations that have the same value of x as the given equation are:
18x - 9 = 72
3(6x - 3) = 72
x = 4.5
The correct options are the third, fourth, and fifth options
Determining the equations that have the same value of xFrom the question, we are to determine the equations that have the same value of x as the given equation
To solve the given equation, we can begin by simplifying it:
3/5 (30 x - 15) = 72
Multiplying both sides by 5/3, we get:
30 x - 15 = 120
Adding 15 to both sides, we get:
30 x = 135
Dividing both sides by 30, we get:
x = 4.5
Now, to check which equations have the same value of x as the above result, we can substitute x = 4.5 in each option and see which ones result in a true statement.
18 x - 15 = 72Substituting x = 4.5, we get:
18(4.5) - 15 = 72
81 - 15 = 72
This is not a true statement, so this option is not correct.
50 x - 25 = 72Substituting x = 4.5, we get:
50(4.5) - 25 = 72
225 - 25 = 72
This is not a true statement, so this option is not correct.
18x - 9 = 72Substituting x = 4.5, we get:
18(4.5) - 9 = 72
81 - 9 = 72
This is a true statement, so this option is correct.
3(6x - 3) = 72Substituting x = 4.5, we get:
3(6(4.5) - 3) = 72
3(24) = 72
This is a true statement, so this option is correct.
x = 4.54.5 = 4.5
This is a true statement, so this option is correct.
Hence, the equations are:
18x - 9 = 72
3(6x - 3) = 72
x = 4.5
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You create a masterpiece in your art studio and it is selected for an art exhibition. Your painting is 70 inches by 100 inches, and you choose framing that costs $4.95 per yard. Find the cost of framing.
Answers
The cost of framing for the masterpiece is $46.73.
How to calculate thisTo calculate the cost, we need to first determine the perimeter of the artwork.
Given the dimensions of the artwork, the perimeter is 100 + 100 + 70 + 70 = 340 inches.
The cost of framing is $4.95 per yard, so we need to convert the perimeter to yards.
To do this, we divide the perimeter by 36 inches since 1 yard equals 36 inches.
Thus, 340 inches divided by 36 inches equals 9.44 yards.
Therefore, the cost of framing the artwork will be 9.44 yards multiplied by $4.95 per yard, which equals $46.73.
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Your friend buys 1 8/10 tenths of a pound of bananas. If each pound cost $4.10, how much do they pay for her bananas?
Answers
Answer:
Below
Step-by-step explanation:
1 8/10 = 18/10
18 / 10 pound * $ 4.10 / pound = (18 * 4.1) / 10 = 73.8 /10 = $ 7.38
( see how the unit 'pound' cancels out and you are left with $ ???)
Each statement describes a transformation of the graph of f(x) = x. Which statement correctly describes the graph of function g if g(x) = f(x) − 11? A. It is the graph of f(x) where the slope is decreased by 11. B. It is the graph of f(x) translated 11 units down. C. It is the graph of f(x) translated 11 units up. D. It is the graph of f(x) where the slope is increased by 11.
Answers
The right response is B. It is the graph of f(x) scaled down by 11 units.
For any given value of x, the output of f(x) is subtracted by 11 to get the function g(x) = f(x) - 11.
The result is the same as the input for the function f(x) = x. Thus, if we take 11 out of the result, we get:
g(x) = f(x) - 11 = x - 11
In other words, the graph of g(x) is the graph of f(x), 11 units lower.
Thus, assertion B is the correct one. It is the graph of f(x) scaled down by 11 units.
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Nelda needs to wrap a holiday gift box. The box is in the shape of a rectangular prism with the dimensions shown.
What is the total surface area of the gift box?
Record your answer and fill in the bubbles on your answer document. Be sure to use the correct place value.
Answers
Answer:
[tex]416 \;in^2[/tex]
Step-by-step explanation:
The surface area of the rectangular prism
[tex]S = 2(lw + lh + wh)[/tex]
where
l = length = 12 in
w = width = 10 in
h = height = 4 in
Therefore
[tex]S = 2(12\cdot 10 \;+ \; 12\cdot 4 \;+\;10 \cdot 4)\\\\= 2(120 + 48 + 40)\\\\= 2 (208)\\\\= 416 \: in^2[/tex]
solve for x. 4(x+56.5)=30x-112
Answers
Answer:
x = 13
Step-by-step explanation:
Let's simplify and solve for x:
4(x+56.5) = 30x - 112
First, we distribute the 4:
4x + 4(56.5) = 30x - 112
Simplifying the expression:
4x + 226 = 30x - 112
Now we move all the x terms to one side and all the constants to the other:
226 + 112 = 30x - 4x
338 = 26x
Finally, we solve for x by dividing both sides by 26:
x = 13
Therefore, the solution to the equation 4(x+56.5)=30x-112 is x = 13.
Answer:
x=9.94
Step-by-step explanation:
4x + 226 = 30x - 112
226+112 = 34x
338 = 34x
338/34=x
9.94=x
the width of a rectangle is 2 units less than the length. The area of the rectangle is 15 square units. What is the length of the rectangle
Answers
Answer: 5
Step-by-step explanation:
area = width x length
15 = w x w-2
15 = 5 x 3
3 is 2 less than 5, and if you multiply them together, you get the area, 15
A retailer buys merchandise from a supplier with an invoice amount of $12,400. The terms of the sale are 6/20, n/30. What is the net amount due (in $) on the order if the bill is paid by the 20th day?
Answers
If the retailer pays the invoice within 20 days and takes the discount, the net amount due is $11,656.
The sale's "6/20, n/30" clause allows the retailer to choose between paying the invoice in full within 30 days or taking advantage of a 6% discount if they do it within 20 days. If the bill is paid by the 20th day, we can determine the net amount owed as follows:
Then, we multiply the invoice amount by the discount rate to determine the amount of the discount:
Discount: $744 ($12.400 x 0.06)
The amount owed if the discount is taken is then determined by deducting the discount from the invoice amount:
Discounted amount due: $12,400 - $744 = $11,656
The net amount owed is therefore $11,656 assuming the store pays the invoice within 20 days and applies the reduction.
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