Identify the equation that is parallel to :
y = 1/3 x -12
Group of answer choices
A. y = -1/3x -10
B. y =-3x +2
C. y = 3x +2
D. y = 1/3x -10
Answers
Answer:
D
Step-by-step explanation:
This problem can be solved without doing any math, due to the fact that parallel lines will have identical slopes. This means that choice D is the correct answer.
To check this, consider graphing both equations either on a graphing calculator or on the internet.
Related Questions
A rectangle initially has dimensions 6 cm by 7 cm. All sides begin increasing in length at a rate of 3 cm/s. At what rate is the area of the rectangle increasing after 23 s?
Answers
Answer:
The area of the rectangle is increasing at a rate of 54 cm2/s.
Step-by-step explanation:
Factor the expression completely. 4 x + 6
Answers
Answer:
It's.
.
.
.
Step-by-step explanation:
2(2x +3).
.
.
.
.
.
.
Answer:
2(2x+3)
Step-by-step explanation:
g An employee joined a company in 2017 with a starting salary of $50,000. Every year, the employee receives a raise of $1,000 plus 5% of the salary of the previous year. (a). Set up a recurrence relation for the salary of the emplyee n years after 2017. A recurrence relation of a sequence is an equation that express a subscript n using one or more of previous terms. (b). What will be the salary of the employee in 2025
Answers
Answer:
a) s[n] = 1.05s[n-1] +1000; s[0] = 50,000
b) $83,421.88
c) s[n] = 70000·1.05^n -20000
Step-by-step explanation:
a) Let s[n] represents the employee's salary in dollars n years after 2017. The salary in 2017 is given as $50,000, so ...
s[0] = 50000 . . . . the recursion relation initial condition
The next year, the salary is multiplied by 1.05 and 1000 is added:
s[1] = 1.05·s[0] +1000
This pattern repeats, so the recursion relation is ...
s[n] = 1.05·s[n-1] +1000
__
c) It is convenient to find a formula for the salary before trying to compute the salary 8 years on. So, we work part (c) before part (b).
The base salary gets multiplied by 1.05 each year, so can be described by the exponential function ...
base salary after n years = 50,000·1.05^n
The add-on to the raise becomes a geometric sequence whose common ratio is 1.05. The sum can be described by the formula for the sum of such a sequence:
sum = a1(r^n -1)/(r -1) . . . . . (see note below)
sum of add-ons = 1000(1.05^n -1)/(1.05 -1) = 20000(1.05^n -1)
So, the total salary after n years is ...
s[n] = 50000·1.05^n + 20000(1.05^n -1)
The exponential terms can be combined, so we have the explicit formula ...
s[n] = 70000·1.05^n -20000
__
b) The year 2025 is 8 years after 2017, so we want to find s[8].
s[8] = 70000·1.05^8 -20000 = 70000·1.4774554 -20000
= 103,421.88 -20000 = 83,421.88
In 2025, the employee's salary will be $83,421.88.
_____
Note on the sum of the add-ons
A geometric sequence starts with term a1 and gets multiplied by a ratio r to make the next term: a2=r·a1; a3=r²·a1, ....
The sum of such a geometric sequence has the formula
Sn = a1·(r^n -1)/(r -1)
Here, the sequence starts in year 1 with a1=1000 and has a common ratio r=1.05. The denominator of the sum is r-1 = 0.05 = 1/20, so the sum can be written as
Sn = 20000·(1.05^n -1).
A que tasa De interes Simple un
Capital de $150,000 Produce
Un monto de $280,000 en un tiempo de 9 meses
Answers
The simple interest rate that would lead to an amount of $ 280, 000 being produced in 9 months is 116 % .
How to find the simple interest rate ?First, find the amount that is being made per month on the amount invested:
= ( 280, 000 - 150, 000 ) / 9 months
= 130, 000 / 9 months
= $ 14, 444
The monthly simple interest rate is :
= 14, 444 / 150, 000
= 9. 63 %
For the year, this amount is :
= 9. 63 % x 12 months
= 116 %
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For the functions f(x)=−7x+3 and g(x)=3x2−4x−1, find (f⋅g)(x) and (f⋅g)(1).
Answers
Answer:
Find f(g(x)) f(x)=7x-8 , g(x)=3x-2. f(x)=7x−8 f ( x ) = 7 x - 8 , g(x)=3x−2 g ( x ) = 3 x - 2. Step 1. Set up the composite result function. f(g(x)) f ( g ...
please mark me as a brainalist
The point (4, 16) is on the graph of f(x) = 2^x. Determine the coordinates of this point under the following transformations.
f(x) = 2^4x: ____________
Answers
The coordinate of the image after the transformation is (4, 65536)
How to determine the coordinate of the image?From the question, the coordinate of the point is given as
(4, 16)
From the question, the equation of the function is given as
f(x) = 2^x
When the function is transformed. we have the equation of the transformed function to be given as
f(x) = 2^4x65536
So, we substitute 4 for in the equation f(x) = 2^4x
So, we have
f(4) = 2^(4 x 4)
Evaluate the products
f(4) = 2^16
Evaluate the exponent
f(4) = 65536
So, we have (4, 65536)
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What is the range of the function? f(x)=3^x−1−2
Answers
The range of the equation f(x) = 3ˣ ⁻ ¹ - 2 is y > -2
Calculating the range of the equation?From the question, we have the following parameters that can be used in our computation:
f(x) = 3ˣ ⁻ ¹ - 2
The above equation is an exponential function
The rule of an exponential function is that
The domain is the set of all real numbersHowever, the range is always greater than the constant termIn this case, it is -2
So, the range is y > -2
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NO LINKS!! URGENT HELP NEEDED!! SHOW WORK PLEASE!!!
6. A ladder is leaning against a building at an angle of 78 degrees with the ground. The foot of the ladder is 5 feet from the building. How high is the ladder?
7. A sledding hill is 300 yards long with a vertical drop of 27.6 yards. Find the angle of elevation between the hill and the ground at the bottom.
Answers
The diagrams are below.
===============================================
Explanation:
Problem 6
Refer to figure 1 shown below.
tan(angle) = opposite/adjacent
tan(78) = x/5
x = 5*tan(78)
x = 23.5231505473922
x = 23.52
Round this value however your teacher instructs. Make sure your calculator is in degree mode.
------------------
Problem 7
Refer to figure 2 shown below.
sin(angle) = opposite/hypotenuse
sin(theta) = 27.6/300
theta = arcsin(27.6/300)
theta = 5.2786761033211
theta = 5.28 degrees
The notation arcsin or arcsine is the same as inverse sine. On many calculators this is shown as the button \(\sin^{-1}\)
Answer:
7. \(\displaystyle 5\degree\)
6. \(\displaystyle 23,5\:yd.\)
Step-by-step explanations:
7. When drawn out, you will notise you must use the inverce cotangent trigonometric ratio:
\(\displaystyle ? = cot^{-1}\:\frac{300}{27,6}; 5,2564149414...\degree \\ \\ \boxed{5\degree \approx\:?} \\ \\ \\ OR \\ \\ \\ ? = tan^{-1}\:\frac{27,6}{300}; 5,2564149414...\degree \\ \\ \boxed{5\degree \approx\:?}\)
_______________________________________________
6. When drawn out, you will notise you must use the cotangent trigonometric ratio:
\(\displaystyle ? = \frac{5}{cot\:78}; 23,523150547... \\ \\ \boxed{23,5 \approx\:?} \\ \\ \\ OR \\ \\ \\ ? = 5tan\:78; 23,523150547... \\ \\ \boxed{23,5 \approx\:?}\)
I am joyous to assist you at any time.
Extended information on trigonometric ratios
\(\displaystyle \frac{OPPOCITE}{HYPOTENUSE} = sin\:\theta \\ \frac{ADJACENT}{HYPOTENUSE} = cos\:\theta \\ \frac{OPPOCITE}{ADJACENT} = tan\:\theta \\ \frac{HYPOTENUSE}{ADJACENT} = sec\:\theta \\ \frac{HYPOTENUSE}{OPPOCITE} = csc\:\theta \\ \frac{ADJACENT}{OPPOCITE} = cot\:\theta\)
Elena receives $95 per year in simple interest from three investments totaling $2100 . Part is invested at 3%, part at 4%, and part at 5%. There is $1000 more invested at 5% than at 4%. Find the amount invested at each rate.
The amount invested at 3% is $
the amount invested at 4% is $
and the amount invested at 5% is $
Answers
The amount invested at 3% is $400, the amount invested at 4% is $700, and the amount invested at 5% is $1000.
Let's assume the amount invested at 4% is x dollars.
According to the given information, the amount invested at 5% is $1000 more than the amount invested at 4%.
So, the amount invested at 5% is (x + $1000).
The total amount invested is the sum of the amounts invested at each rate, which is $2100.
Therefore, we can write the equation:
x + (x + $1000) + (amount invested at 3%) = $2100
Now, we can calculate the amount invested at 3%.
We subtract the sum of the amounts invested at 4% and 5% from the total investment:
(amount invested at 3%) = $2100 - (x + x + $1000) = $2100 - (2x + $1000)
Given that Elena receives $95 per year in simple interest from the investments, we can use the formula for simple interest:
Simple Interest = Principal × Interest Rate
The interest earned from the investment at 3% is (amount invested at 3%) × 0.03, the interest earned from the investment at 4% is (amount invested at 4%) × 0.04, and the interest earned from the investment at 5% is (amount invested at 5%) × 0.05.
According to the problem, the total interest earned is $95.
So we can write the equation:
(amount invested at 3%) × 0.03 + (amount invested at 4%) × 0.04 + (amount invested at 5%) × 0.05 = $95
Now we can substitute the expression for (amount invested at 3%) and solve for x.
Once we have the value of x, we can calculate the amounts invested at 3%, 4%, and 5% using the given information.
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Quadrilateral YFGT can be mapped onto quadrilateral MKNR by a translation. If TY = 2, find RM.
Answers
Based on the information given, we can conclude that RM = 2, but we cannot determine the lengths of the other sides of the quadrilaterals without further information.
Given that quadrilateral YFGT can be mapped onto quadrilateral MKNR by a translation, we can use the information to determine the length of RM.
A translation is a transformation that moves every point of a figure by the same distance and in the same direction. In this case, the translation is such that the corresponding sides of the quadrilaterals are parallel.
Since TY = 2, and the translation moves every point by the same distance, we can conclude that the distance between the corresponding points R and M is also 2 units.
Therefore, RM = 2.
By the properties of a translation, corresponding sides of the two quadrilaterals are congruent. Hence, side YG of quadrilateral YFGT is congruent to side MK of quadrilateral MKNR, and side GT is congruent to NR. However, the given information does not provide any additional details or measurements to determine the lengths of these sides.
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PLEASE HELP MEEE, I'M FALLING IN MY CLASS
Answers
The average rate of change of the function graphed is -4.
What is average rate of change?
The average rate at which one item is changing in relation to another is known as the average rate of change.
The function y = f(x) is graphed.
We have to find the average rate of change of the function on the interval
2 ≤ x ≤ 4.
The average rate of change is defined as,
Average rate of change = \(\frac{f(b)-f(a)}{b-a} = \frac{f(4)-f(2)}{4-2}\)
From graph,
f(4) = -4, f(2) = 4
So,
Average rate of change = \(\frac{-4-4}{4-2} = \frac{-8}{2} = -4\).
Therefore, for the given graphed function, the average rate of change is, -4.
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what are the 6 steps to designing a statistical study
Answers
Answer:
Step 1: Write your hypotheses and plan your research design
Step 2: Collect data from a sample
Step 3: Summarize your data with descriptive statistics
Step 4: Test hypotheses or make estimates with inferential statistics
Step 5: Interpret your results
Step-by-step explanation:
A store is having a sale on jelly beans and almonds. For 3 pounds of jelly beans and 5 pounds of almonds, the total cost is $27. For 9 pounds of jelly beans and
7 pounds of almonds, the total cost is $51. Find the cost for each pound of jelly beans and each pound of almonds.
Cost for each pound of jelly beans:
Cost for each pound of almonds:
Answers
Answer:
Cost for each pound of jelly beans: $2.75
Cost for each pound of almonds: $3.75
Step-by-step explanation:
Let J be the cost of one pound of jelly beans.
Let A be the cost of one pound of almonds.
Using the given information, we can create a system of equations.
Given 3 pounds of jelly beans and 5 pounds of almonds cost $27:
\(\implies 3J + 5A = 27\)
Given 9 pounds of jelly beans and 7 pounds of almonds cost $51:
\(\implies 9J + 7A = 51\)
Therefore, the system of equations is:
\(\begin{cases}3J+5A=27\\9J+7A=51\end{cases}\)
To solve the system of equations, multiply the first equation by 3 to create a third equation:
\(3J \cdot 3+5A \cdot 3=27 \cdot 3\)
\(9J+15A=81\)
Subtract the second equation from the third equation to eliminate the J term.
\(\begin{array}{crcrcl}&9J & + & 15A & = & 81\\\vphantom{\dfrac12}- & (9J & + & 7A & = & 51)\\\cline{2-6}\vphantom{\dfrac12} &&&8A&=&30\end{array}\)
Solve the equation for A by dividing both sides by 8:
\(\dfrac{8A}{8}=\dfrac{30}{8}\)
\(A=3.75\)
Therefore, the cost of one pound of almonds is $3.75.
Now that we know the cost of one pound of almonds, we can substitute this value into one of the original equations to solve for J.
Using the first equation:
\(3J+5(3.75)=27\)
\(3J+18.75=27\)
\(3J+18.75-18/75=27-18.75\)
\(3J=8.25\)
\(\dfrac{3J}{3}=\dfrac{8.25}{3}\)
\(J=2.75\)
Therefore, the cost of one pound of jelly beans is $2.75.
Find the surface area of this triangular prism. Be sure to include the correct unit in your answer.
Answers
Work Shown:
A = area of bottom rectangular face = 10*5 = 50
B = area of back rectangular face = 12*10 = 120
C = area of slanted front rectangular face = 13*10 = 130
D = area of left triangle = 0.5*base*height = 0.5*5*12 = 30
E = area of triangle on right = 0.5*base*height = 0.5*5*12 = 30
S = total surface area
S = A+B+C+D+E
S = 50+120+130+30+30
S = 360
Calculate the product
20 (-15)
Answers
Answer:
Step-by-step explanation:
Product means multiply.
-300
In which quadrant or on which axis do each of the points (-2,4), (3,-1), (-1,0), (1,2), (-3,-5) and (0,-8) lie?
Answers
Answer:
The point (-2,4) lies in the II Quadrant
The point (3,-1) lies in the IV Quadrant
The point (-1,0) lies on the X-Axis
The point (1,2) lies in the I Quadrant
The point (-3,-5) lies in the III Quadrant
The point (0,-8) lies on the Y-Axis
Desperate Need Of Help
Answers
The domain and range of the graph above in interval notation include the following:
Domain = [-6, 3]
Range = [-3, 3]
What is a domain?In Mathematics and Geometry, a domain refers to the set of all real numbers (x-values) for which a particular function (equation) is defined.
In Mathematics and Geometry, the horizontal portion of any graph is used to represent all domain values and they are both read and written from smaller to larger numerical values, which simply means from the left of any graph to the right.
By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:
Domain = [-6, 3] or -6 ≤ x < 3.
Range = [-3, 3] or -3 < y < 3
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A right prism has a triangle base. The length of the base is 12 yards and the height of the base is 3 yards. The height of the prism is 3.5 yards. What is the volume of the prism?
Answers
Answer:
c
Step-by-step explanation:
What is the median of 2,1,2,5,3
Answers
Answer:
2
Step-by-step explanation:
Rearrange the data set in numerical order: 1, 2, 2, 3, 5 and take the number in the middle.
Aaliyah has x nickels and y pennies. She has a minimum of 20 coins worth no more than $0.40 combined. Solve this system of inequalities graphically and determine one possible solution.
Answers
Answer:
\((x,y) = (5,15)\)
Step-by-step explanation:
Given
\(Nickels = x\)
\(Pennies = y\)
Minimum of 20 coins means:
\(x + y \ge 20\)
A nickel worth $0.05
A penny worth $0.01
So, the worth can be represented as:
\(0.05x + 0.01y \le 0.40\)
See attachment for graph
From the attachment, the solution is:
\((x,y) = (5,15)\)
Use the vertex (h, k) and a point on the graph (x, y) to find the general form of the equation of the quadratic function.(h, k) = (−3, −1), (x, y) = (−5, 3)
Answers
ANSWER:
y = x² + 6x +8
STEP-BY-STEP EXPLANATION:
The equation in its vertex form has the following form:
\(\begin{gathered} y=a(x-h)^2+k \\ \\ \text{ where \lparen h, k\rparen is the vertex } \end{gathered}\)We solve for a which is the coefficient of the principal of the equation as follows:
\(a=\frac{y-k}{(x-h)^2}\)We substitute each value to be able to determine the value of a, like this:
\(a=\frac{3-(-1)}{(-5-(-3))^2}=\frac{3+1}{(-5+3)^2}=\frac{4}{2^2}=1\)Now we calculate education in its vertex form:
\(\begin{gathered} y=1\cdot(x-(-3))^2-1 \\ \\ y=(x+3)^2-1 \\ \\ \text{ We solve to obtain it in its general form, like this:} \\ \\ y=x^2+6x+9-1 \\ \\ y=x^2+6x+8 \end{gathered}\)The general form of the equation of the quadratic function is y = x² + 6x +8
Which function represents the graph ? :)
Answers
Answer:
The function is:
y = -f(x - 4)
3.) There are 1,000 marbles in a large box. Johnny took a scoop of marbles from the box. He
counted 15 red marbles, 20 green marbles, and 5 blue marbles. If the scoop was a good
sample of the marbles in the large box, how many red marbles would you expect to find in
the large box?*
O A) 150 reds
O B) 375 reds
O C) 600 reds
OD) 800 reds
Answers
Answer: B) 375 reds
Step-by-step explanation:
Every 40 marbles 15 are red.
1000/40=25
25 x 15= 375
answer please.. need asap. algebra
Answers
(xy)^3
3x^2y^3
Both are correct it’s just a different way of writing it
Suppose a distant galaxy has a recessional velocity of 8254 km/s. What is its distance given that the hubble constant is 70 km/s/mpc? input your answer as a number only, in units of mpc.
Answers
Galaxy distance is 118 mpc.
Given:
Suppose a distant galaxy has a recessional velocity of 8254 km/s. What is its distance given that the hubble constant is 70 km/s/mpc.
According to hubble's law:
v = \(H_0\\\) * D
where
v = velocity = 8254
\(H_0\\\) = hubble constant = 70
D = v/\(H_0\\\)
= 8254/70
= 4127/35
= 117.91
≈ 118 mpc.
Therefore Galaxy distance is 118 mpc.
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A college student plans to use a credit card to cover the cost of purchasing a $3,200 campus meal plan. If the credit card has annual interest rate of 12.99% compounded continuously and the student plans to pay off the loan in 16 months, how much interest will be owed?
A: $739.25
B: $733.73
C: $605.13
D: $600.69
Answers
The student has to pay the interest of $733.73.
Option (B) is correct.
What is compound interest?
Compound interest is the interest that is calculated not only on the principal amount of a loan or investment, but also on any interest that has accumulated on the principal in previous periods. It is a way for lenders or investors to earn interest on their money over time, and it can lead to significant growth in the value of an investment or loan balance.
To calculate the interest owed on the credit card in this scenario, we can use the formula for compound interest:
A =\(P(1 + r/n)^{(nt)\)
where:
A = the total amount owed (principal plus interest)
P = the initial principal amount ($3,200 in this case)
r = the annual interest rate as a decimal (0.1299 in this case)
n = the number of times the interest is compounded per year (continuous compounding in this case)
t = the time period in years (16/12 = 4/3 years in this case)
Substituting in these values, we get:
A =\(3200(1 + 0.1299/1)^{(1/3*4)\)
Simplifying this expression gives:
A = 3200(1.0363)¹'³³³
A = $3,933.73
So the total amount owed after 16 months is $3,933.73. To find the amount of interest owed, we subtract the initial principal amount of $3,200:
Interest = $3,933.73 - $3,200
Interest = $733.73
Therefore, the student has to pay the interest of $733.73.
Option (B) is correct.
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You can use the equation A =(HW/3600)^1/2
to approximate a person's body surface area A (in square meters), where H
is height (in centimeters) and W is weight (in kilograms). Approximate the body surface area of a person with a height
of 160 centimeters and a weight of 64 kilograms.
Body surface area:______
m²
Answers
The body surface area is given by the equation A = 1.6865 m²
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the body surface area be represented as A
Now , the equation will be
A = ( HW / 3600 )^1/2
A = √( HW / 3600 ) be equation (1)
where H is the height in centimeters and W is the weight in kilograms
Now , the value of H = 160 cm
The value of W = 64 kg
Substituting the values in the equation , we get
A = √ [ ( 160 x 64 ) / 3600 ]
On simplifying the equation , we get
A = √ ( 10240/3600 )
A = √ ( 2.8444 )
A = 1.6865 m²
Therefore , the body surface area is 1.6865 m²
Hence , the equation is A = 1.6865 m²
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Last year, Parr Co. had sales of $900,000, based on a unit selling price of $200. The variable cost per unit was $125, and fixed costs were $225,000. The maximum sales within Parr Cos relevant range are 7,500 units. Parr Co. is considering a proposal to spend an additional $112,500 on billboard advertising during the current year in an attempt to increase sales and utilize unused capacity.
Instructions
1. Construct a cost-volume-profit chart indicating the break-even sales for last year. Verify your answer, using the break-even equation.
2. Using the cost-volume-profit chart prepared in part (1), determine (a) the operating income for last year and (b) the maximum operating income that could have been realized during the year. Verify your answers using the mathematical approach to cost-volume-profit analysis.
Answers
(1)The break - even sales for last year is $600000.
(2)(a) The operating income for last year is $300000.
(b) The maximum operating income that could have been realized during the year is $337500.
What is range?In mathematics, a range refers to the set of all possible values or outputs that a function or relation can produce. It is the collection or set of all values that a function can take on as its output when given various inputs from its domain.
Define volume?The term "volume" typically refers to the measure of the amount of space occupied by a three-dimensional object. It is a quantitative measure of the capacity or size of a solid shape in three-dimensional space. Volume is often used to describe the amount of space enclosed by an object or the amount of material it can hold.
Cost-Volume-Profit (CVP) Chart for Last Year:
To construct a CVP chart, we need to plot the sales, variable costs, fixed costs, and profit (or operating income) on the y-axis and the number of units sold on the x-axis.
Based on the given information:
Sales = $900,000
Unit selling price = $200
Variable cost per unit = $125
Fixed costs = $225,000
Maximum sales within relevant range = 7,500 units
Using the formula for calculating the break-even point:
Break-even point (in units) = Fixed Costs / (Unit Selling Price - Variable Cost per Unit)
Break-even point (in units) = $225,000 / ($200 - $125) = 3,000 units
Now we can construct the CVP chart:
Sales:
The sales line will start from the origin (0,0) and have a slope of $200 per unit, as the unit selling price is $200.
Variable Costs:
The variable costs line will also start from the origin (0,0) and have a slope of $125 per unit, as the variable cost per unit is $125.
Fixed Costs:
The fixed costs line will be a horizontal line parallel to the x-axis, at a height of $225,000, as the fixed costs are constant and do not change with the number of units sold.
Profit (Operating Income):
The profit line can be calculated by subtracting the total variable costs and fixed costs from the total sales. So, the profit line will start from the origin (0,0) and have a slope of ($200 - $125) per unit, which is the difference between the unit selling price and variable cost per unit.
The break-even point will be the point where the profit line intersects the x-axis, which is at 3,000 units. So, the break-even sales for last year is 3,000 units x $200 per unit = $600,000.
Verification using the break-even equation:
Break-even point (in units) = Fixed Costs / (Unit Selling Price - Variable Cost per Unit)
Break-even point (in units) = $225,000 / ($200 - $125) = 3,000 units
Operating Income for Last Year and Maximum Operating Income:
Operating Income for Last Year:
Operating Income = Sales - Variable Costs - Fixed Costs
Operating Income = $900,000 - ($125 x Number of Units Sold) - $225,000
Substituting the break-even point of 3,000 units, we get:
Operating Income = $900,000 - ($125 x 3,000) - $225,000
Operating Income = $900,000 - $375,000 - $225,000
Operating Income = $300,000
Maximum Operating Income:
The maximum operating income can be achieved at the maximum sales within the relevant range, which is 7,500 units.
Operating Income = Sales - Variable Costs - Fixed Costs
Operating Income = ($200 x 7,500) - ($125 x 7,500) - $225,000
Operating Income = $1,500,000 - $937,500 - $225,000
Operating Income = $337,500
Verification using the mathematical approach to CVP analysis:
Plugging in the values for last year's sales of 7,500 units:
Let's calculate the maximum operating income using the mathematical approach to CVP analysis:
Operating Income = (Unit Selling Price x Number of Units Sold) - (Variable Cost per Unit x Number of Units Sold) - Fixed Costs
Given:
Unit Selling Price = $200
Variable Cost per Unit = $125
Fixed Costs = $225,000
Number of Units Sold = 7,500
Putting the values:
Operating Income = ($200 x 7,500) - ($125 x 7,500) - $225,000
Operating Income = $1,500,000 - $937,500 - $225,000
Operating Income = $337,500
So, the maximum operating income that could have been realized during the year is $337,500.
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2x-5y=9
3x+4y=2
Simultaneous equation find x and y
Answers
Answer:
x = 2
y = -1
Step-by-step explanation:
2x - 5y = 9
3x + 4y = 2
find x in terms of y using the first equation
2x - 5y = 9
2x = 9 + 5y
x = 4.5 + 2.5y
substitute x for 4.5 + 2.5y in the second equation
3x + 4y = 2
3(4.5 + 2.5y) + 4y = 2
13.5 + 7.5y + 4y = 2
13.5 + 11.5y = 2
11.5y = 2 - 13.5
11.5y = -11.5
y = -1
now substitute y for -1 in the first equation
2x - 5y = 9
2x + 5 = 9
2x = 9 - 5
2x = 4
x = 2
Pls help step by step, loves <3 (special right triangles)
Answers
Answer:
x ≈ 30,37
y ≈ 29,00
Step-by-step explanation:
Use trigonometry:
\( \sin(38°) = \frac{9}{x} \)
Now, use the property of the proportion to find x:
\(x = \frac{9}{ \sin(38°) } ≈30.37\)
Do the same thing to find y:
\( \tan(38°) = \frac{9}{y} \)
\(y = \frac{9}{ \tan(38°) } ≈29.00\)