Answers
Length of rectangle Width of rectangle Area of rectangle
A. a + 5 3 3(a + 5) = 3a + 15
B. 6 + x 1/3 1/3(6 + x) = 2 + 1/3x
C. 3 r r(1+1+1) = 3r
What is a rectangle?
An example of a quadrilateral with equal and parallel opposite sides is a rectangle. It is a polygon with four sides and four angles that are each 90 degrees. A rectangle is a shape with only two dimensions.
A.
There are 2 rectangles with side a and 5.
Therefore the length of the rectangle is (a + 5).
The width the rectangle is 3.
The area of rectangle is product of length and width.
The area of the rectangle is 3(a + 5)
Applying distributive property:
= 3a + 15
B.
There are 2 rectangles with side 6 and x.
Therefore the length of the rectangle is (6 + x).
The width the rectangle is 1/3.
The area of rectangle is product of length and width.
The area of the rectangle is 1/3(6 + x)
Applying distributive property:
= 2 + 1/3 x
C.
There are 3 rectangles with side 1, 1, and 1.
Therefore the length of the rectangle is (1 + 1 + 1).
The width the rectangle is r.
The area of rectangle is product of length and width.
The area of the rectangle is r(1 + 1 + 1)
Applying distributive property:
= r + r + r
= 3r
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Related Questions
which expression is not equavilent
Answers
Answer:
[tex]\huge\boxed{\sf Option \ 2}[/tex]
Step-by-step explanation:
Given that,
8 + (n - 4)
According to Associative Property:
A + (B + C) = (A + B) + CUsing Associative property for the given expression.
We get:
(8 + n) - 4[tex]\rule[225]{225}{2}[/tex]
The answer to this question is = 12 + n is the expression not equivalent to 8 + (n - 4)
Let us consider any random value of n for example let us take the value of n = 5
As per the original equation given in question 8 + (n - 4) if we substitute the value of n = 5
= 8+ (5 - 4)
= 8+1
= 9
Now we will be substituting the value of n in all the answer options-
Option 1- (8 - 4) + n
= (8 - 4) + 5
= 4 + 5
= 9
Therefore, this answer matches the original equation so this is not the correct option
Option 2- (8 + 4) - n
= (8 + 4) - 5
= 13 - 5
= 9
Therefore, this answer matches the original equation so this is not the correct option
Option 3- n+4
= 5 + 4
= 9
Therefore, this answer matches the original equation so this is not the correct option
Option 4- 12 + n
= 12 + 5
= 17
Therefore, this answer does not match the original equation so the correct option is = 12 + n
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a circle c has center at the origin and radius 4. another circle k has a diameter with one end at the origin and the other end at the point the circles c and k intersect in two points. let p be the point of intersection of c and k which lies in the first quadrant. let be the polar coordinates of p, chosen so that is positive and find and .
Answers
Let (r,q) represent P's polar coordinates, with r being positive and 0 equaling q being pi/2. If so, r = 3m. And A = 0.20136
All points in a plane that are at a specific distance from a specific point, the center, form a circle.
Formula for the first circle: x²+ y² = 9
Formula for the second circle:
center is (0, 7.5) and the radius is 15/2, so
x² + (y - 7.5)² = (7.5)²
Combining these yields:
9 - y² + (y - 7.5)² = (7.5)²
9 - y² + y² - 15y + (7.5)² = 7.5²
9 - 15y = 0
y = 9/15 = 3/5
∴ y = 0.6
x² + y² = 9 = x² + (3/5)²
x² = 9 - (9/25)
x² = [(225 - 9)/25] = 216/25
∴ x = 2.9394
r = √(x² + y²) =
r = √[( 216/25) + (9/25)]
r = √(225/25) = 15/5
∴ r = 3
The x and y values appear to be accurate because this must be the same as the radius of the circle cantered at the origin.
sin(A) = y/r
sin(A) = (3/5)/3 = 1/5
Sin(A) = 0.2
∴ A = 0.20136
COMPLETE QUESTION:
A circle C has center at the origin and radius 4. Another circle K has a diameter with one end at the origin and the other end at the point (0,14). The circles C and K intersect in two points. Let P be the point of intersection of C and K which lies in the first quadrant. Let (r,q) be the polar coordinates of P, chosen so that r is positive and 0 = q =pi/2. Find r and q.
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Find the amount A in an account (to the nearest cent) after 10 years if
dA
dt = rA, A(0) = 15,000 and A(8) = $22,377.37
Answers
The amount A in an account to the nearest cent, the amount A in the account after 10 years is $30,441.65.
What is the amount A in an account?Generally, To find the amount A in the account after 10 years, we can use the formula for continuous compound interest:
A(t) = A(0) * e^(rt)
where A(t) is the amount in the account after t years, A(0) is the initial amount in the account, r is the interest rate, and t is the number of years.
In this case, we know that A(0) = $15,000, A(8) = $22,377.37, and t = 10 years. We can rearrange the formula to solve for r:
r = (1/t) * ln(A(t)/A(0))
Substituting the known values, we get:
r = (1/10) * ln(22377.37/15000)
Solving this equation, we get r = 0.0658082.
Now that we have the value of r, we can use the formula for continuous compound interest to find the amount A in the account after 10 years:
A(10) = 15000 * e^(0.0658082 * 10)
Solving this equation, we get A(10) = $30,441.65.
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Pls answer its for my final
Answers
The quadratic equation will be written as F(x) = -2x² - 4x + 1.
What is a quadratic equation?A quadratic equation is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.
The point from which the quadratic equation passes are,
(0,1), (-1,3), and (-2,1).
The quadratic equation will be written as,
y =ax²+ bx +c
For point (0,1)
1 = 0 + 0 + c
c = 1
For points (-1,3),
3 = a - b + c
3 = a - b + 1
a - b = 2
For point (-2,1),
1 = 4a - 2b + c
1 = 4a - 2b + 1
4a = 2b
b = 2a
calculate the values of a and b,
a - b = 2
a - 2a = 2
-a = 2
a = -2
b = 2a = 2 x -2 = -4
The quadratic equation will be written as,
F(x) = -2x² - 4x + 1
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Question 21 of 25
What is the length of the x-component of the vector shown below?
8
71°
OA. 2.6
OB. 8.0
OC. 7.6
OD. 5.2
Answers
Using the Pythagorean theorem, we can find the length of the x-component:
x^2 = 8^2 - 7.1^2
x = sqrt(64 - 50.41)
x = sqrt(13.59)
x = OD. 5.2
Therefore, the length of the x-component is 5.2.
6 is 5% of what number?
100
Answers
Answer: 120
Step-by-step explanation:
We can put it in an equation like this:
6 = 5%x
Then, we solve:
6 = 1/20 x
x = 20/1 *6
x=120
Therefore, 5% of 120 is 6.
Answer:
120
Step-by-step explanation:
5/100=6/x
Cross multiply
5x=100(6)
5x=600
/5. /5
x=120
Hopes this helps please mark brainliest
please help, urgent, would appreciate
Answers
The answers to all the parts are given below.
What is a expression? What is a mathematical equation? What do you mean by domain and range of a function?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem. For any function y = f(x), Domain is the set of all possible values of [y] that exists for different values of [x]. Range is the set of all values of [x] for which [y] exists.We have a function h = -16t² + 1800, that gives the height of the person at time [t] seconds.
[A] -
For [x] = 1000ft, we can write -
1000 = -16t² + 1800
16t² = 800
t² = (800/16)
t² = 50
t = 7.07 seconds
[B] -
For [x] = 950ft, we can write -
950 = -16t² + 1800
16t² = 850
t² = 53.125
t² = √(53.125)
t = 7.29 seconds
[C] -
The domain of the function will be -
0 ≤ x ≤ 10
[D] -
The range of the function will be -
0 ≤ h ≤ 1800
Therefore, the answers to all the parts are given above.
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Solve for inequality
Seven more than the quotient of a number $b$ and 45 vis greater than 5 .
Answers
Seven more than the quotient of a number b and 45 is greater than 5 then the inequality is b > -90.
What is inequality?
Equations are not always balanced on both sides using a "equal to" symbol in mathematics. Sometimes it can be about a "not equal to" relationship, meaning that something is superior to or inferior to another. In mathematics, an inequality is a relationship between two numbers or other mathematical expressions that results in an unequal comparison.7 more than the quotient of a number b and 45 is greater than 5.
interpretation
7 + b/45 > 5
collect the like terms
b/45>5-7
b/45>-2
cross multiply
∴ b>-2×45
b > -90
Hence, Seven more than the quotient of a number b and 45 is greater than 5 then the inequality is b > -90.
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A bag contains 7 green marbles, 3 yellow marbles and 10 black marbles. If a green marble is drawn, you win $20. If a yellow marble is drawn, you win $30. If a black marble is drawn, you lose $15. It costs $1 to play. What are you expected winnings over time?
Answers
Step-by-step explanation:
chances of winning $20=7/20
chances of winning $30=3/20
chances of winning $15=1/2
Consider the following loan. Complete parts (a)-(c) below.
An individual borrowed $66,000 at an APR of 4%, which will be paid off with monthly payments of $400 for 20 years.
a. Identify the amount borrowed, the annual interest rate, the number of payments per year, the loan term, and the payment amount.
The amount borrow is $__, the annyual interest rate is ___%, the number of payments per year is ___, the loan term is ___ years, and the payment amount is $___.
Answers
The amount borrowed is $66,000, the annual interest rate is 4 %, the number of payments per year is 12, the loan term is 20 years, and the payment amount is $10668.39.
What is compound interest?Compound interest is applicable when there will be a change in the principle amount after the given time period.
For example, if you give anyone $500 at the rate of 10% annually then $500 is your principle amount. After 1 year the interest will be $50 and hence principle amount will become $550 now for the next year the interest will be $550, not $500.
The total amount paid is,
A = 4800[1 + 0.04/12]^(12 x 20)
A = $10668.39
Hence "The amount borrowed is $66,000, the annual interest rate is 4 %, the number of payments per year is 12, the loan term is 20 years, and the payment amount is $10668.39".
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Decide whether a line with the given slope slants upward or downward or is horizontal or vertical.
m = ½
Answers
Answer: Slants upwards.
Step-by-step explanation:
This is a positive slope, so the line with this given slope will slant upwards. For every increase of one in y, there is a positive change of 2 in x. See attached for a visual example, if the graph was y = ½x.
b. Find the value of m and n
Answers
Answer:
n = 45
m = 135
Step-by-step explanation:
The sum of the interior angles of a triangle is 180
180 - 55 - 80 = 45
m = the sum of 55 + 80
n= 45°;
m= 135.
Step-by-step explanation:1. Find the value of n.The sum of all interior angles of a triangle must equa 360°. Hence, the value of n is given by the following expression:
[tex]n+55+80=180\\ \\n=180-55-80\\\\ n=45[/tex]
2. Find the value of m.Since "m" and "n" are opposites angles and, since there's a straight line adjacent to them, the sum of m and n should equal 180 (check the attached image). Find m with the following expression:
[tex]45+m=180\\ \\m=180-45\\ \\m=135.[/tex]
8. The Pinkerton Publishing Company is considering two mutually exclusive expansion plans. Plan A calls for the expenditure of $50 million on a large-scale, integrated plant that will provide an expected cash flow stream of $8 million per year for 20 years. Plan B calls for the expenditure of $15 million to build a somewhat less efficient, more Labor-intensive plant that has an expected cash flow stream of $3.4 million per year for 20 years. The firm's cost of capital is 10%. a. Calculate each project's NPV and IRR. (4 marks) b. Set up a Project A by showing the cash flows that will exist if the firm goes with the large plant rather than the smaller plant. What are the NPV and the IRR for this Project A? (3 marks) c. Give a logical explanation, based on reinvestment rates and opportunity costs, as to why the NPV method is better than the IRR method when the firm's cost of capital is constant at some value such as 10%. (3 marks)
Answers
What is a NPV net present value ?
The difference between the current value of cash inflows and withdrawals over a period of time is known as net present value (NPV). To evaluate the profitability of a proposed investment or project, NPV is used in capital budgeting and investment planning.
Using the appropriate discount rate, computations are performed to determine the current value of a stream of future payments, or NPV. Projects that have a positive NPV are generally worthwhile pursuing, whereas those that have a negative NPV are not.
The current worth of a stream of payments from a business, project, or investment is determined using net present value (NPV).You must predict the timing and size of future cash flows in order to determine NPV, and you must choose a discount rate that is equal to the least allowable rate of return.Your cost of capital or the rewards offered by substitute investments with equivalent risk may be reflected in the discount rate.Positive NPV indicates that the rate of return on a project or investment will be higher than the discount rate.1.
NPV of project A = [tex]-50+\frac{8}{/(1.10)^1} +\frac{8}{(1.10)^2} \frac{8}{(1.10)^3} +\frac{8}{(1.10)^4} +\frac{8}{(1.10)^5} +\frac{8}{(1.10)^6} +\frac{8}{(1.10)^7} +\frac{8}{(1.10)^8} +\frac{8}{(1.10)^9} +\frac{8}{(1.10)^1^0} +\frac{8}{(1.10)^1^1} +\frac{8}{(1.10)^1^2} +\frac{8}{(1.10)^1^3} +\frac{8}{(1.10)^1^4} +\frac{8}{(1.10)^1^5} +\frac{8}{(1.10)^1^6} +\frac{8}{(1.10)^1^7} +\frac{8}{(1.10)^1^8} +\frac{8}{(1.10)^1^9} +\frac{8}{(1.10)^2^0}[/tex]
=$18.11
2.
NPV of project B = [tex]-15+\frac{3.4}{/(1.10)^1} +\frac{3.4}{(1.10)^2} \frac{3.4}{(1.10)^3} +\frac{3.4}{(1.10)^4} +\frac{3.4}{(1.10)^5} +\frac{3.4}{(1.10)^6} +\frac{3.4}{(1.10)^7} +\frac{3.4}{(1.10)^8} +\frac{3.4}{(1.10)^9} +\frac{3.4}{(1.10)^1^0} +\frac{3.4}{(1.10)^1^1} +\frac{3.4}{(1.10)^1^2} +\frac{3.4}{(1.10)^1^3} +\frac{3.4}{(1.10)^1^4} +\frac{3.4}{(1.10)^1^5} +\frac{3.4}{(1.10)^1^6} +\frac{3.4}{(1.10)^1^7} +\frac{3.4}{(1.10)^1^8} +\frac{3.4}{(1.10)^1^9} +\frac{3.4}{(1.10)^2^0}[/tex]
= $13.95
Use function IRR in excel as = IRR(-50,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8)
= 15.03% is the IRR for A.
Use function IRR in excel as = IRR(-15,3.4,3.4,3.4,3.4,3.4,3.4,3.4,3.4,3.4,3.4,3.4,3.4,3.4,3.4,3.4,3.4,3.4,3.4,3.4,3.4)
= 22.26% is the IRR for B.
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Explain how to do this so I can do the next few problems thank you so much!!!
Answers
Area of composite figure is 48 square feet.
What do you mean by composite figure?
A compound shape or figure is a two-dimensional figure made up of basic two-dimensional shapes such as triangles, rectangles, circles, and semicircles.
To find the perimeter of a compound 2D shape, add the lengths of the sides. Find individual regions for each part of the compound shape. The area of a composite shape is the sum of its individual areas.
Let the given composite figure be divided into four rectangles A,B,C and D having dimension 3 and 4
Area of rectangle A = 3 × 4 = 12
Area of rectangle A = area of rectangle B = area of rectangle C = area of rectangle D = 12 square feet.
Total area = Area of rectangle A + area of rectangle B + area of rectangle C + area of rectangle D = 12 + 12 + 12 + 12 =48 square feet
Therefore, area of composite figure is 48 square feet.
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Find the critical value(s) for a left-tailed z-test with a = 0.09. Include a graph with your answer.
Answers
Answer:-1.34
Step-by-step explanation:
larry is wanting to place a fence diagonally to separate his yard from his neighbors what would the measurement of the fence need to be to fit in the yard picture below what is the length of the fence that runs diagonally what is the total meters of fencing will hr need for the entire triangle of his yard
Answers
Answer: You would have to know the number of yards separate from his neighbors yard to get the answer.
Step-by-step explanation:
For example if his yard was 50 yards from his neighbors than you would add that to the width. Length plus width to get your answer.
i would
like to know how to answer this question. please
Answers
G(1) has a value of 3,The collection of all possible inputs and outputs constitutes a function's domain and range, respectively.
Domain and Range: What are they?The range of values that can be plugged into a function is known as its domain. In a function like f, this set represents the x values (x). The collection of values that a function can take on is known as its range. The values that the function outputs when we enter an x value are in this set.The collection of all possible inputs and outputs constitutes a function's domain and range, respectively. Important features of a function are the domain and range. The domain accepts all potential input values from the set of real numbers, and the range accepts all function output values. There for G(1) has a value of 3.To learn more about Domain refer to:
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Let x,X. X30o be a random sample from Gamma(3, 2). Find an approximate probability that x is less than 6.3 (round off to third decimal place) 42300
Answers
0.933 is approximate probability that x is less than 6.3 (round off to third decimal place).
What is Probability?
Calculating or estimating how likely or "possible" something is to occur is the subject of probability.
Words like "certain," "impossible," or "probable" can be used to express the likelihood of an event occurring.
Probabilities in mathematics are always represented as fractions, decimals, or percentages with values ranging from 0 to 1.
Given X₁,X₂, ............X₃₀₀ are IID random samples from Xi ~ Gamma ( shape = 3 scale = 2 ) . The mean and variance are
E(Xi) = 3 * 2 = 6
Var (Xi) = 3 * 2² = 12
According to CLT,
X = X₁ + X₂ + ............+ X₃₀₀/300
has approximately normal distribution X ~ N( 6,12/300) So the probability,
P( X < 6.3 ) = P( Z < 6.3 - 6/√12/300
P ( X < 6.3 ) = P( Z < 1.5 )
P (X < 6.3 ) = Ф (1.5 )
P (X < 6.3 ) = 0.933
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Use the formula A=(1+r/n)^nt to solve the compound interest problem.
Find how long it takes for 900$ to double if it is invested at 6% interest compounded monthly.
The money will double in value in approximately ? years.
(Do not round until the final answer. Then round to the nearest tenth as needed.)
Answers
The total years taken to double the money according to Compounding will be 12.5 years.
What is compound interest?
Compound interest is that the interest on savings calculated on each the initial principal and therefore the accumulated interest from previous periods.
Main body:
Given :
rate = 6%
amount = $900
Total amount = $1800
Compounded monthly,
so formula becomes,
Total amount = amount (1+r/1200)^12t
T = A[tex](1+r/1200)^{12t[/tex]
1800 = 900 (1+6/1200)^12t
2 = (1+1/200)^12t
2 = 1.005^12t
taking log on both sides
log 2 = 12t *log 1.005
0.3/0.002 = 12t
t = 12.5 years
Hence the time taken to double the money is 12.5 years.
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ABDE is an isosceles trapezoid. Select all parts that are marked congruent.
Side AB and Side AE
Angle E and Angle D
Angle E and Angle B
Angle A and Angle B
Angle A and Angle D
Side AE and Side BD
Side AB and Side ED
Answers
The concurrent parts in ABDE are Side AB ≅ Side ED and Side AE ≅ Side BD.
Concurrent triangles:If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create a similar appearance. They are in alignment with one another when moved. The symbol ≅ used for concurrence.
Here we have,
ABDE is an isosceles trapezoid.
If we draw two diagonals in a given trapezoid as given picture
Then the diagonal will divide the trapezoid into 4 triangles
Here ΔAOB, ΔBOD, ΔEOD, and AOE
Here ΔAOB and ΔEOD will be two concurrent triangles
And ΔBOD and AOE will be two concurrent triangles
From ΔAOB and ΔEOD
Side AB ≅ Side ED
From ΔBOD and AOE
Side AE ≅ Side BD
Therefore,
The concurrent parts in ABDE are Side AB ≅ Side ED and Side AE ≅ Side BD
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CAN SOMEONE PLEASE HELP ME WITH THIS GEOMETRY??
Answers
The measure of the side QR is 58.72 if the sides KL=11, NM=17 and OP=38
What is meant by quadrilateral?Having four edges (sides) and four corners, a quadrilateral is a four-sided polygon in geometry (vertices). The term is derived from the Latin terms quadri, a four-letter version, and latus, which means "side." In comparison to other polygons, it is also known as a tetragon. Tetragon is a Greek word that means "four" and "gon" is a word that means "corner" or "angle" (e.g. pentagon). A quadrangle, or 4-angle, is the equivalent term as "gon" denotes "angle." There are four closed sides to a quadrilateral. These shapes below are quadrilaterals: with Raphael, a creation. a four-sided form. One set of parallel sides make up the shape, and there are no right angles.
From the both figures,
KL/NM=OP/QR
11/17=38/QR
QR=(17×38)/11
QR=58.72
Therefore, the measure of the side QR is 58.72 if the sides KL=11, NM=17 and OP=38.
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As part of a school science project, Jacob bought some bulbs for a total of $18. The cost of each bulb was $3. How many bulbs did Jacob buy?
Step One: Write an equation with the variable x
Step Two: Solve your equation.
Equation:
Solution: x=
Answers
Solution: X = 6
Hope this helps :)
4. A desk is 1 ½ feet wide and 5 feet long. It is
2½ feet above the floor. What is the volume
of space under the desk?
Answers
v=1.5•5•2.5
v=18.75
Answer:
gg
Step-by-step explanation:
help meeeeeeeeeeeeeeeeeeeeeeeeeee pleaseeeeeeeeeeeeeeeeeeeeee!!!!!
Answers
After 25 years, Sample left will be 100g if nearest hundred...ig...
What is the equation of the line that is normal to the curve y^2+Inx=19 at the point (e^3,-4)
Answers
The equation of the line that is normal to the curve y² + ln(x) = 19 at the point (e³, -4) is given as follows:
y + 4 = -8e³(x - e³).
How to obtain the equation of the line normal to the curve?The equation of the line normal to a curve follows the point-slope definition of a linear function, given as follows:
y - y' = m(x - x').
The derivative of the function is found applying implicit differentiation, as follows:
2y dy/dx + 1/x = 0
dy/dx = -1/(2xy).
At x = e³, y = -4, the numeric value of the derivative is given as follows:
dy/dx = e^(-3)/8.
The normal line is perpendicular to the tangent line, hence it's slope is calculated as follows:
m x e^(-3)/8 = -1.
m = -8e³.
Then the equation of the line normal to the curve at the point is given as follows:
y + 4 = -8e³(x - e³).
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Find the values of x and y.
Answers
Answer:
x = y = 60
Step-by-step explanation:
You want the values of angles marked x° and y° in the given figure involving equilateral triangles and parallel lines.
TrianglesAll of the triangles in the figure are congruent equilateral triangles. Each of their internal angle measures is 60°.
x° = y° = 60°
__
Additional comment
The (inside) base angles of the outside two triangles are alternate interior angles with respect to the top two angles of the center triangle. Hence they are congruent. The center triangle is marked as equilateral, so its angles are all 60°. That means all of the acute angles in the figure are 60°.
a quadratic function f is given by f(c) = ax^2+bx+c where a is not 0
Answers
The roots of a quadratic function are the values of x that make the function is 0. These roots can be found by solving the equation f(x) is 0.
What is quadratic function ?A quadratic function is a type of mathematical function that can be written in the form f(x) = ax^2 + bx + c, where a, b, and c are constants and a is not equal to 0. This type of function is called a quadratic function because the highest power of x in the function is 2.
The graph of a quadratic function is a parabola, which is a U-shaped curve. The shape of the parabola is determined by the value of the constant a. If a is positive, the parabola opens upwards and if a is negative, the parabola opens downwards.
The roots of a quadratic function are the values of x that make the function equal to 0. These roots can be found by solving the equation f(x) = 0. To solve this equation, we can use the quadratic formula, which is:
x = (-b +/- sqrt(b^2 - 4ac)) / (2a)
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I need an answer pls
Answers
Answer:
y=3x^2 - 2x + 5
Step-by-step explanation:
The easiest way to find the answer to this question would be to just plug the different x values into the equations. If you take the equations and plug in x and it gives out the correct f(x) value, then the answer would be correct.
For example, plugging -3 into y=3x^2 - 2x + 5 gives you 10. Plugging in 0 gives 5. Plugging in 2 gives 13.
You need a car for 5 days. A car rental company offers customers two rate plans. With Plan A, the
customer pays $25 per day plus $0.15 per mile driven. With Plan B the customer pays $150 for the week,
even if the car is returned early, with no per-mile charge. Which payment plan would you select if you
plan to drive a total of 100 miles?
Answers
9 apples and 6 oranges cost $33
18 apples and 20 oranges cost $80
How much does 1 apple and 1 orange cost
Answers
The cost of each apple and each orange will be $2.5 and $1.75, respectively. The cost of 1 apple and 1 orange will be $4.25.
The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
9 apples and 6 oranges cost $33 and 18 apples and 20 oranges cost $80.
Let 'x' be the cost of each apple and 'y' be the cost of each orange. Then the equations are given as,
9x + 6y = 33 ...1
18x + 20y = 80 ...2
Multiply equation 1 by negative 2, then we have
-18x - 12y = - 66 ...3
Add equations 2 and 3, then we have
20y - 12y = 80 - 66
8y = 14
y = $1.75
Then the cost of each apple is calculated as,
9x + 6(1.75) = 33
9x = 33 - 7.5
9x = 22.5
x = $2.5
The cost of each apple and each orange will be $2.5 and $1.75, respectively.
The cost of 1 apple and 1 orange will be given as,
⇒ $2.5 + $1.75
⇒ $4.25
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