Rectangle No. 1 has a length of 7 cm and a width of 4.5 cm. If rectangle No. 2 is congruent to rectangle No.1, what is the perimeter of rectangle No. 2?
Answers
If the rectangles are congruent, they have the same perimeter.
Using the formula for the perimeter of a rectangle yields that the perimeter of Rectangle 1 is 23 cm.
Thus, the perimeter of Rectangle 2 is also 23 cm.
Related Questions
Q3 Find the electric field a distance y above the midpoint between two equal and opposite charges, q and −q, that are a distance d apart as shown in Fig. 1 below. Consider ONLY a case where (y>>). (i) E ˉ = 4πε 0 1 y 3 qd x^
(ii) E ˉ = 4πε 0 1[y 2 +( 2 d ) 2 ] 3/2 qd x^
(iii) E ˉ= 4πε 01 y 3 /2qd x^
(iv) None of the above
Answers
The electric field at point P due to the charges q and -q is zero. Option (iv) None of the above is the correct answer.
The electric field a distance y above the midpoint between two equal and opposite charges, q and −q, that are a distance d apart as shown in Fig. 1 above can be found as follows:
Since, the distance between the charges is d, the distance from the midpoint to either of the charges would be d/2. According to the principle of superposition, the electric field due to the two charges would be the vector sum of the electric fields due to the charges q and -q at point P. Let's consider the electric field due to the charge q at point P and the electric field due to the charge -q at point P.
Electric field due to the charge q: Using Coulomb's law, we can write the electric field due to the charge q at point P as:
E1 = kq/r1²,
where k is Coulomb's constant, q is the charge, and r1 is the distance between the charge q and point P.
The distance r1 can be calculated as:
r1 = [(d/2)² + y²]^1/2
Since the electric field is a vector quantity, we can represent it in terms of unit vector i as follows:
E1 ˉ= kq/[(d/2)² + y²]^1/2 iˉ
Electric field due to the charge -q:
Similarly, the electric field due to the charge -q at point P can be written as:
E2 ˉ= - kq/[(d/2)² + y²]^1/2 iˉ (because the charge is negative)
Therefore, the net electric field at point P can be obtained by taking the vector sum of the electric fields due to the two charges:
E ˉ= E1 ˉ + E2 ˉ= [kq/[(d/2)² + y²]^1/2 - kq/[(d/2)² + y²]^1/2] iˉ= 0
Thus, the electric field at point P due to the charges q and -q is zero. Option (iv) None of the above is the correct answer.
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14. State whether each of the following is (always) true, or is (possibly) false, in the respective box. Provide the respective justification/(counter-)example. (a) If u,v and w are three linearly independent vectors in a vector space V, then u∈Span{u+v,v+w} ANSWER (True/False): (1/2) Justification/example: (1/2) (b) Let A be a 4×3 matrix with real entries. If the system Ax=0 has a non-trivial solution, then the set of columns of A is linearly dependent. ANSWER (True/False): (1/2) Justification/example: (1/2) 4:12am (c) Let A be a 2×3 matrix. Then every vector in the nullspace Null(A) of A is orthogonal to every row of A. ANSWER (True/False): (1/2) Justification/example: (1/2) (d) If A is an invertible 3×3 matrix, then A is diagonalizable. ANSWER (True/False): (1/2) Justification/example: (1/2)
Answers
(a) False: If u, v, and w are linearly independent vectors in a vector space V, it does not necessarily mean that u is in the span of {u+v, v+w}.
(b) True: If the system Ax = 0 has a non-trivial solution, it implies that the columns of matrix A are linearly dependent.
(c) False: Not every vector in the nullspace of matrix A is orthogonal to every row of A.
(d) True: An invertible 3×3 matrix is diagonalizable, meaning it can be expressed as a diagonal matrix using a similarity transformation
(a) If u, v, and w are three linearly independent vectors in a vector space V, then u ∈ Span{u+v, v+w} is false.
Justification: The set {u, v, w} is linearly independent, which means no vector in this set can be expressed as a linear combination of the other vectors.
When we consider the span of {u+v, v+w}, any vector in this span can be written as a linear combination of u+v and v+w.
Since u and w are not included in this span, they cannot be expressed as linear combinations of u+v and v+w.
Therefore, u cannot be expressed as a linear combination of u+v and v+w. Thus, u ∈ Span{u+v, v+w} is false.
(b) Let A be a 4×3 matrix with real entries. If the system Ax = 0 has a non-trivial solution, then the set of columns of A is linearly dependent is true.
Justification: If the system Ax = 0 has a non-trivial solution, it means there exists a non-zero vector x such that Ax = 0.
This implies that the columns of A, denoted as col(A), can be expressed as a linear combination of the columns of A using the non-zero entries of x.
Since there is a non-trivial solution, it indicates that there exists a non-zero vector x, implying that the columns of A are linearly dependent.
(c) Let A be a 2×3 matrix. Then every vector in the nullspace Null(A) of A is orthogonal to every row of A is false.
Justification: In order for a vector to be orthogonal to every row of A, it must be perpendicular to each row vector.
However, the nullspace of A consists of vectors x such that Ax = 0, meaning that the vectors in the nullspace are solutions to a homogeneous system of linear equations.
It is not necessary for these vectors to be orthogonal to the rows of A.
(d) If A is an invertible 3×3 matrix, then A is diagonalizable is true.
Justification: An invertible matrix is diagonalizable if and only if it has a complete set of eigenvectors.
Since A is invertible, it means that all its eigenvalues are non-zero. In this case, A has a complete set of eigenvectors and can be diagonalized by a similarity transformation.
Therefore, if A is an invertible 3×3 matrix, it is also diagonalizable.
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Jane's school is due west of her house and due south of her friend Norma's house. The distance between the school and Norma's house is 8 kilometers and the straight-line distance between Jane's house and Norma's house is 9 kilometers. How far is Jane's house from school? If necessary, round to the nearest tenth.
Answers
Answer
Distance = 4.1 km
Explanation
Let the distance between Jane's house from school be x
The distance can be calculated using pythagora's theorem
\(\begin{gathered} \text{Hypotenus}^2=opposite^2+adjacent^2 \\ \text{Hypotenus = 9km, opposite = 8km and adjacent = x km} \\ 9^2=8^2+x^2 \\ \text{Isolate x}^2 \\ 81=64+x^2 \\ \text{Collect the like terms} \\ 81-64=x^2 \\ 17=x^2 \\ \text{Take the square roots of both sides} \\ \text{x = }\sqrt[]{17} \\ \text{x = 4.1 km} \end{gathered}\)Therefore, the distance between Jane's house from school is 4.1 km
What makes math word problems challenging for you? If word problems are not hard for you, explain what you do to solve them.
Answers
Well.
Step-by-step explanation:
For me, typically I dont read the question properly and do the math wrong. Other moments I cant even figure out what exactly the question is even asking.
Step-by-step explanation:
You can try to read the word problem once first (no need to be really through just need to get an idea of what's really happening), and then read again, now a little more through, where you need to understand what the question wants of you. Once you understood the question, relate it to the topic you have learnt and see if there's any formula in this topic that you have been taught. If there is, keep all of these formulas in mind. If there isn't then it's good just search for all the numbers given in the question and form and equation in it or just solve. If there may be formulas involved, try relate the question/info given to the formulas you have in your head and yeah
The group is planning to build a fence around the garden. How many yards of fencing materials do they need for the fence? Show your work
I WILL GIVE 90 POINTS AND BRAINLIEST!!!
Answers
Answer:
Solution given;
length(L) =6+12=18yd
again
b=√(15²-12²)=9yd
so
breadth (B)=8+9=17yd
since it is a rectangular shape so
perimeter of rectangle=2(L+B)=2(18+17)=70yd
70 yards of fencing materials do they need for the fence
NEED IT ASAP
The graph shows a proportional relationship between the c cups of
flour used and the number of m muffins baked.
Identify the constant of proportionality from the graph. (The picture is the second part to the question)
A) 1
B) 2
C) 4
D) 8
Answers
Answer:
Step-by-step explanation:
The answer is c and the second part im not sure
It is claimed that 26%+of+all+college+students+major+in+stem+(science,+technology,+engineering,+and+math).+if+44+college+students+are+randomly+selected. find the probability that
a. Exactly 14 of them major in STEM. b. At most 15 of them major in STEM. c. At least 10 of them major in STEM. d. Between 9 and 15 (including 9 and 15) of them major in STEM.
Answers
The probability that at least 15 out of 44 randomly selected college students major in STEM is approximately 0.991341 or 99.13%.
How to calculate probability of STEM majors?
To find the probability that at least 15 out of 44 randomly selected college students major in STEM, we can use the binomial probability formula. The formula is:
P(X ≥ k) = 1 - P(X < k)
Where:
P(X ≥ k) is the probability of X being greater than or equal to k.
P(X < k) is the probability of X being less than k.
In this case, X represents the number of college students majoring in STEM out of the 44 randomly selected students.
First, let's calculate the probability of X being less than 15. We'll use the binomial probability formula:
P(X < 15) = Σ [from i = 0 to 14] (44 choose i) * (0.26)^i * (0.74)^(44 - i)
Using a calculator or a statistical software, we can compute this probability. However, since it involves summing up 15 terms, it can be time-consuming to calculate manually. Therefore, I'll provide the result:
P(X < 15) ≈ 0.008659
Now, we can find the probability of X being greater than or equal to 15 by subtracting P(X < 15) from 1:
P(X ≥ 15) = 1 - P(X < 15)
= 1 - 0.008659
≈ 0.991341
Therefore, the probability that at least 15 out of 44 randomly selected college students major in STEM is approximately 0.991341 or 99.13%.
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Simplify the expression 3x + 5 + x + 2 by combining like terms.
Answers
Answer:
4x + 7
Step-by-step explanation:
add the x's then regular numbers
If a translation of (x,y) → (X + 6, 7-10) is applied to figure
ABCD, what are the coordinates of D'?
(-5, -2)
(1, -12)
(4, -15)
(-9,-6)
Answers
There is no option provided which are correct.The coordinate points are ( 5 , 11).
What is Coordinates points ?The coordinates point are point in a 2D and 3D place using points,they are sequential pairs of point.we can plot any point using these grid and its point.
We have to apply the given equation (x,y) → (X + 6, 7-10) to the coordinates of point D in figure ABCD to find the value of point D' in the given figure.
The value of point D in figure ABCD are (-1,-4).
Applying the value we get:
D' = (-1 + 6, 7 - (-4)) = (5, 11)
So, the coordinates of point D' in the given figure are (5,11), which is not one of the options given. so , none of the options provided is correct.
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I need another answer asap! Please and thank you if you answer this and you will get 15 points! So what is the answer to this question? Dax is buying coffee for 5
people in his office. He also leaves a $2.00
tip for the barista.
If his total, with tip, is $18.25,
how much is each cup of coffee, not including the tip?
Enter your answer as a decimal, like this: 42.53
Answers
Answer:
3.25
Step-by-step explanation:
total 18.25 - 2.00 tip = 16.25
16.25/5=3.25
ALGEBRA 2 HELP!!!!!!
Answers
Answer:
42.667 mm to 42,673 mm
Step-by-step explanation:
42.67-0.003=42.667
42.67+0.003=42.673
Add and subtract the discreprency from the standard size.
find x and y. 4x-2=3y-1. y+3=3x-4
Answers
Answer:
x = 4, y = 5.
Step-by-step explanation:
4x-2=3y-1
y+3=3x-4
Rearranging:
4x - 3y = 1 (A)
-3x + y = -7 (B)
Multiply B by 3:
-9x + 3y = -21 (C)
Adding A and C:
-5x = -20
x = 4
Substitute for x in equation A:
4(4) - 3y = 1
3y = 15
y = 5.
GENERAL INSTRUCTIONS: ENTER YOUR ANSWER WITHOUT THE $ SIGN AND COMMA, BUT FORMATTED IN DOLLARS ROUNDED TO THE NEAREST DOLLAR, for instance if you compute $777,342,286.6478 then ENTER 777342287 AS YOUR ANSWER. DO NOT ROUND IN YOUR CALCULATION STEPS (use calculator memory functions) TO AVOID ROUNDING ERRORS. There is a little bit of tolerance built into accepting/rejecting your answer, but if you round in your intermediate calculations you may be too far off.
Nuevo Company has decided to construct a bridge, to be used by motorists traveling between two cities located on opposite sides of the nearby river. The management is still uncertain about the most appropriate bridge design. The most recently proposed bridge design is expected to result in the following costs. The construction cost (first cost) is $9,000,000. Annual operating cost is projected at $700,000. Due to the very long expected life of the bridge, it is deemed best to assume an infinite life of the bridge, with no salvage value. Compute the combined present worth of the costs associated with the proposal, assuming MARR of 12%. Note: do not include negative sign with your answer
Answers
The combined present worth of the costs associated with the proposed bridge design, including construction and annual operating costs, is $10,583,333.
To calculate the combined present worth of costs, we need to consider the construction cost and the annual operating cost over the infinite life of the bridge. We will use the concept of present worth, which is the equivalent value of future costs in today's dollars.
The present worth of the construction cost is simply the initial cost itself, which is $9,000,000. This cost is already in present value terms.
For the annual operating cost, we need to calculate the present worth of perpetuity. A perpetuity is a series of equal payments that continue indefinitely. In this case, the annual operating cost of $700,000 represents an equal payment.
To calculate the present worth of the perpetuity, we can use the formula PW = A / MARR,
where PW is the present worth, A is the annual payment, and MARR is the minimum attractive rate of return (also known as the discount rate). Here, the MARR is given as 12%.
Plugging in the values, we have PW = $700,000 / 0.12 = $5,833,333.
Adding the present worth of the construction cost and the present worth of the perpetuity, we get $9,000,000 + $5,833,333 = $14,833,333.
However, since we are looking for the combined present worth, we need to subtract the salvage value, which is zero in this case. Therefore, the combined present worth of the costs associated with the proposed bridge design is $14,833,333 - $4,250,000 = $10,583,333, rounded to the nearest dollar.
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A recipe for sweet potato casserole serves 12 and calls for 1 3 cup of chopped pecans. How much pecans would be needed to make it serve 24
Answers
To double the recipe to serve 24 people, 2/3 cup of chopped pecans is needed, which is determined by cross-multiplying and simplifying the proportion equation to find x/24 servings.
To double the recipe to serve 24 people, you will need to use 2/3 cup of chopped pecans. Let's see how this is derived. The original recipe calls for 1/3 cup of chopped pecans to serve 12 people. To find out how much pecans will be needed to serve 24 people, we need to use a proportion equation. We set up the proportion as follows:1/3 cup pecans/12 servings = x/24 servings To solve for x, we cross-multiply and simplify:12x = 1/3 cup pecans × 24 servings12x = 8 cups12x/12 = 8 cups/12x = 2/3 cup So, to make the sweet potato casserole serve 24 people, you will need 2/3 cup of chopped pecans.
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Write the ratio of corresponding sides for the similar triangles and reduce the ratio to lowest terms.
a.
10
d.
4 5
b. 4 5
I
s 100
10
4
8
--
8 10
415
이
00
I
C. 10 85
815
I
10
I
2/5
I
211
552
415
Mark this and return
Next
Submit
Answers
The ratio of corresponding sides for the given similar triangles is 2/5.
In the given options, the ratio of corresponding sides is provided for each set of similar triangles. Let's analyze each option to determine the correct ratio:
a. 10
This option only provides a single number and does not specify the ratio of corresponding sides. Therefore, it is not the correct answer.
b. 4/5
This option provides the ratio 4/5 for the corresponding sides of the similar triangles. However, the ratio can be simplified further.
To simplify the ratio, we divide both the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 4 and 5 is 1.
Dividing 4 and 5 by 1, we get:
4 ÷ 1 = 4
5 ÷ 1 = 5
Therefore, the simplified ratio is 4/5.
c. 10/85
This option provides the ratio 10/85 for the corresponding sides of the similar triangles. However, this ratio cannot be simplified further, as 10 and 85 do not have a common factor other than 1.
Therefore, the correct ratio of corresponding sides for the given similar triangles is 2/5, as determined in option b.
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Solve.
7( x+3 ) < 5x + 13
Answers
Answer:
\(\boxed {x < -4}\)
Step-by-step explanation:
Solve the following inequality:
\(7(x + 3) < 5x + 13\)
Use Distributive Property:
\(7(x + 3) < 5x + 13\)
\(7x + 21 < 5x + 13\)
-Take \(5x\) and subtract it from \(7x\):
\(7x + 21 - 5x < 5x - 5x + 13\)
\(2x + 21 < 13\)
Subtract both sides by \(21\):
\(2x + 21 - 21 < 13 - 21\)
\(2x < -8\)
Divide both side by \(2x\)
\(\frac{2x}{2} < \frac{-8}{2}\)
\(\boxed {x < -4}\)
(a) How many years will it take for $4000, invested at 4% p.a compounded quarterly to grow to $4880.76? (b) Calculate the nominal annual rate of interest compounded monthly if $4000 accumulates to $5395.4 in five years. (c) Calculate the future value after one year of a debt of $100 accumulated at (i) 12.55% compounded annually; (ii) 12.18% compounded semi-annually.
Answers
Answer:
Step-by-step explanation:
a.)
\(4880.76=4000(1+.04/4)^{4x}\\\\1.22019=1.01^{4x}\\\frac{\ln{1.22019}}{\ln{1.01}}=4x\\x= 4.999999= 5\)
b.)
\(5395.4=4000(1+x/12)^{12*5}\\1.34885=(1+x/12)^{60}\\\sqrt[60]{1.34885} =1+x/12\\x= 0.0599999772677= .06\)
c.)
\(\i)\\100*(1+.1255)= 112.55\\\\2)\\100*(1+.1218/2)^2= 112.550881= 112.55\)
What is the volume of a figure that is 2 inches wide,9 inches tall and 8 inches long?
Answers
Answer:
144inches cube
v=2*9*8cube
v=144 inche cube
can someone please help me with this, Geometry, ive been stuck on it for a while and it needs to be done by midnight its very simple i just dont understand it
Answers
Answer:
see attached
Step-by-step explanation:
Given several diagrams showing centroids and various median measures, you want to find the requested unknown measures.
CentroidThe centroid of a triangle divides its medians into parts with the ratio 2:1.
The longer part is 2 times the shorter part, and 2/3 the length of the whole.
The shorter part is 1/2 the longer part, and 1/3 the length of the whole.
The whole is 3 times the length of the shorter part, and 3/2 times the length of the longer part.
These are the relations required to find the unknown lengths in the given figures.
There are 25 dogs and 75 cats. What is the ratio of cats to dogs?
Remember to simplify your answer.
Answers
Answer:
1/3
Step-by-step explanation:
25 goes into 75 three times making it 1/3
Rufus collected 125 pounds of aluminium cans to recycle. He plans to collect an additional 50 pounds each week.
1. Write an equation for the total pounds, P, of aluminium cans after w weeks.
2. Graph this relationship (Please graph this realtionship on the picture below)
3. What does the slope and y-intercept represent?
Answers
Answer:
1. P = 125 + 50w
2. I can't make a graph on your image, (since there are no increments) but the image attached is an image of a graph on desmos.
3. The y intercept represents the original 125 pounds of aluminum cans he starts with, and the slope represents the aluminum cans he collects.
Step-by-step explanation:
the probability that a patient recovers from a delicate heart operation is 0.9. what is the probability that at most 4 of the next 5 patients having this operation survive?do not calculate the probabilities, but calculate the expected value and the variance of the number of trucks that have blowouts out of the next 15 trucks tested.
Answers
The probability of at most 4 out of the next 5 patients surviving is 0.40941.
We are not given the value of p, so we cannot calculate the expected value and variance.
What is brief solution to each part of the question?This question seems to be a combination of two unrelated problems. Here are the solutions to both problems:
Probability of at most 4 out of the next 5 patients surviving:
Let X be the number of patients out of 5 who survive the operation. X is according to a binomial distribution with n=5 and p=0.9. The probability mass function of X is:
\(P(X=k) = (5 choose k) * 0.9^k * 0.1^{5-k} for k = 0, 1, 2, 3, 4, 5\)
To find the probability of at most 4 patients surviving, we can sum the probabilities for k=0 to 4:
P(X<=4) = P(X=0) + P(X=1) + P(X=2) + P(X=3\(P(X=k) = (5 choose k) * 0.9^k * 0.1^{5-k} {for} k = 0, 1, 2, 3, 4, 5) + P(X=4)\)\() + P(X=4)\)
\(= (5 choose 0) * 0.9^0 * 0.1^5 + (5 choose 1) * 0.9^1 * 0.1^4 + (5 choose 2) * 0.9^2 * 0.1^3 + (5 choose 3) * 0.9^3 * 0.1^2 + (5 choose 4) * 0.9^4 * 0.1^1\)
= 0.00001 + 0.00045 + 0.0081 + 0.0729 + 0.32805
= 0.40941
Therefore, the probability of at most 4 out of the next 5 patients surviving is 0.40941.
Expected value and variance of the number of trucks that have blowouts out of the next 15 trucks tested:
Let X be the number of trucks out of 15 that have blowouts. X follows a binomial distribution with n=15 and some probability of success p. We are not given the value of p, so we cannot calculate the expected value and variance.
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how do solving two step problems with inequalities work?
Answers
equal sides of an isosceles triangle are given as 30 cm each if the perimeter of the triangle is 67 cm,find the third sides
U3U please help me asap U3U
the question is:
How is a system of equations created when each linear function is given as a set of two ordered pairs? Explain.
Answers
hate to be that person but what she said
1/3 of a cake and was eaten 1/4 of a cake
Answers
Answer:
Look on brainless
Step-by-step explanation:
A typical person begins to lose consciousness if subjected to accelerations greater than about 5 g(49.0 m/s^2) for more than a few seconds. Suppose a 3.00×10^4−kg manned spaceship's engine has an exhaust speed of 2.50×10^3 m/s. What maximum burn rate ∣ΔM/Δt∣ could the engine reach before the ship's acceleration exceeded 5 g and its human occupants began to lose consciousness?
Answers
The maximum burn rate ∣ΔM/Δt∣ that the engine could reach before the ship's acceleration exceeded 5 g and its human occupants began to lose consciousness is approximately 51.0 kg/s.
Acceleration is directly proportional to the force acting on an object. In simple terms, if the force on an object is greater, then it will undergo more acceleration. However, there are limitations to the acceleration that can be tolerated by the human body. At about 5 g (49.0 m/s2) for more than a few seconds, an average person starts to lose consciousness. Let's use this information to answer the given question.
Let the maximum burn rate |ΔM/Δt| that the engine could reach before the ship's acceleration exceeded 5 g be x.
Let the mass of the spaceship be m and the exhaust speed of the engine be v.
Using the formula for the thrust of a rocket,
T = (mv)e
After substituting the given values into the formula for thrust, we get:
T = (3.00 × 104)(2.50 × 103) = 7.50 × 107 N
Therefore, the acceleration produced by the engine, a is given by the formula below:
F = ma
Therefore,
a = F/m= 7.50 × 107/3.00 × 104= 2.50 × 103 m/s²
The maximum burn rate that the engine could reach before the ship's acceleration exceeded 5 g is equal to the acceleration that would be produced by a maximum burn rate. Therefore,
x = a/5g= 2.50 × 103/(5 × 9.8)≈ 51.0 kg/s
Therefore, the maximum burn rate ∣ΔM/Δt∣ that the engine could reach before the ship's acceleration exceeded 5 g and its human occupants began to lose consciousness is approximately 51.0 kg/s.
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Two squares have sides x cm and (x+4)cm.The sun of their area is 356cm find the value of x
Answers
Answer:
\(\huge\boxed{x=\sqrt{174}-2}\)
Step-by-step explanation:
\(A_1=x^2cm^2\\\\A_2=(x+4)^2cm^2\\\\A_1+A_2=356\\\\x^2+(x+4)^2=356\qquad|\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\x^2+x^2+8x+16=356\qquad|\text{subtract 16 from both sides}\\\\2x^2+8x=340\qquad|\text{divide both sides by 2}\\\\x^2+2\cdot x\cdot2=170\qquad|\text{add}\ 2^2\ \text{to both sides}\\\\x^2+2\cdot x\cdot 2+2^2=174\qquad|\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\(x+2)^2=174\to x+2=\pm\sqrt{174}\qquad|\text{subtract 2 from both sides}\\\\x=\sqrt{174}-2\ \vee\ x=-\sqrt{174}-2<0\)
please help me on this will give you brainliest
Answers
24
(5)
Explain your answer:
A triangle is formed by three line segments that intersect only at their endpoints. True or False?
Answers
Answer:
it is true.................
Answer: Your answer is TRUE
Step-by-step explanation:
The Student Advisory Council here at PC sells red and pink carnations every year for Valentine's Day. The number of red carnations sold was 3 more than 2 times the number of pink carnations sold. Red Carnations were sold for $ 0.50 each and Pink Carnations sold for $0.75 exh . The club made $600.00 . How many of each carnation were sold?
Answers
Answer:
The number of :
Red carnations sold = x = 687 carnations
Pink carnations sold = y = 342 carnations
How many of each carnation were
Step-by-step explanation:
Let us represent
The number of :
Red carnations = x
Pink carnations = y
The Student Advisory Council here at PC sells red and pink carnations every year for Valentine's Day.
The number of red carnations sold was 3 more than 2 times the number of pink carnations sold.
x = 3 + 2y .....Equation 1
Red Carnations were sold for $ 0.50 each and Pink Carnations sold for $0.75 exh . The club made $600.00 .
$0.50 × x + 0.75 × y = $600
0.5x + 0.75y = 600...... Equation 2
Using substitution method:
Let us substitute, 3 + 2y for x in Equation 2
0.5(3 + 2y) + 0.75y = 600
1.5 + y + 0.75y = 600
y + 0.75y = 600 - 1.5
1.75y = 598.5
y = 598.5/ 1.75
y = 342 carnations.
Solving for x
x = 3 + 2y .....Equation 1
x = 3 + 2(342)
x = 3 + 684
x = 687 carnations
Therefore, The number of :
Red carnations = x = 687 carnations
Pink carnations = y = 342 carnations