Answers
The height of lighthouse is 72.54
Given,
In the question:
To see the figure:
To find the height of lighthouse.
Now, According to the question:
In Triangle ABD
tan 20° = [tex]\frac{h}{20 + x}[/tex]
0.36 = [tex]\frac{h}{20 + x}[/tex]
=> (20 + x)0.36 = h
=> 0.72 + 0.36x = h
=> x = [tex]\frac{h - 72}{0.36}[/tex] .....(1)
In Triangle ABC
tan 34° = h/x
=> 0.67 = [tex]\frac{h}{\frac{h-72}{0.36} }[/tex]
=> 0.67 = 0.36/h - 72
=> 0.67 (h - 72) = 0.36
=> h - 72 = 0.54
=> h = 0.54 + 72
=> h = 72.54
Hence, The height of lighthouse is 72.54
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Related Questions
Maya is playing a trivia game with multiple choice questions. Each question has 222 correct answers among 555 answer choices. Maya has no idea what the answers to a certain question are, so she needs to choose two different answers at random. What is the probability that maya's first guess is correct and her second guess is incorrect?.
Answers
Maya is playing a trivia game with multiple choice questions. Each question has 222 correct answers among 555 answer choices. Maya has no idea what the answers to a certain question are, so she needs to choose two different answers at random.
The probability that maya's first guess is correct and her second guess is incorrect is 0.24.
From the question given above, the following data were obtained:
Correct answer (C) = 222
Total answer = 555
Incorrect answer (I) = 555 – 222 = 333
Next, we shall determine the probability that her 1st guess is correct.
Correct answer, nC = 222
Total answer, nS= 555
Probability of correct answer, P(C) =?
P(C) = nC / nS
P(C) = 222 / 555
Next, we shall determine the probability that her 2nd guess is incorrect
Incorrect answer, nI = 333
Total answer, nS = 554
Probability of incorrect answer, P(I) =?
P(I) = nI / nS
P(I) = 333 / 554
Finally, we shall determine the probability that her first guess is correct and her second guess is incorrect.
Probability of correct answer, P(C) = 222 / 555
Probability of incorrect answer, P(I) = 333 / 554
Probability of 1st correct and 2nd incorrect, P(C n I) =?
P(C n I) = P(C) × P(I)
P(C n I) = (222 / 555) × (333 / 554)
P(C n I) = 0.24
Hence the answer is, The probability that maya's first guess is correct and her second guess is incorrect is 0.24.
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Answer:
0.3
Step-by-step explanation:
Khan Academy ;)
If a = 7 and b equals 13 what is the value of C round your answer to the nearest hundredth
Answers
Answer:
c ≈ 14.76
Step-by-step explanation:
In right triangle ABC, you have short sides a=7 and b=13. You want the length of the hypotenuse, 'c'.
Pythagorean theoremThe Pythagorean theorem tells you the relationship between the sides of a right triangle is ...
c² = a² +b²
ApplicationFilling in the given values, we have ...
c² = 7² +13² = 49 +169 = 218
c = √218 ≈ 14.7648
Rounding to hundredths, we have ...
c ≈ 14.76
__
Additional comment
Your posted question asks for the value of C (capitalized). That refers to the right angle, so its value is C = 90°. It is always helpful if you ask for what you really want to know.
A regular polygon has 16 sides. If one of its angles measures (5h − 29)°, what is the value of h?
h=56.5
h=37.3
h=33.6
h=9
PLEASE HELP
Answers
The value of h in a regular polygon of 16 sides is 37.3.
According to the question,
We have the following information:
A regular polygon has 16 sides. And one of its angles measures (5h − 29)°.
We know that following formula is used to find the sum of interior angles of a polygon:
(n-2)*180 where n is the number of sides of a polygon
(16-2)180
14*180
2520°
Now, in this polygon, there are 16 sides. So, there will be 16 angles.
Now, to find the measurement of one angle, we will divide total sum by number of angles.
One angle = 2520/16
One angle = 157.5°
Now, we have the following expression:
5h-29 = 157.5
5h = 157.5+29
5h = 186.5
h = 186.5/5
h = 37.3
Hence, the correct option is B (the second one).
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Determine the distance between the points (−4, −5) and (8, 0). 13 units 12 units 8 units 29 units
Answers
The distance between the points (-4, -5) and (8, 0) is 13 units
The coordinates of the first point = (-4, -5)
The coordinates of the second point = (8, 0)
The distance between the two points d = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Where d is the distance between two points
[tex](x_1,y_1)[/tex] is the coordinates of the first point
[tex](x_2,y_2)[/tex] is the coordinates of the second point
Substitute the values in the equation
The distance between the two points = [tex]\sqrt{(8--4)^2+(0--5)^2}[/tex]
= [tex]\sqrt{12^2+5^2}[/tex]
Find the square of each term
= [tex]\sqrt{144+25}[/tex]
Add the terms together
= [tex]\sqrt{169}[/tex]
Find the square root of the number
= 13 units
Hence, the distance between the points (-4, -5) and (8, 0) is 13 units
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In a direct variation, y=80 when x=5. Write a direct variation equation that shows the relationship between x and y.
Answers
As per the concept of direct variation, y = 80 when x = 5, then the direct variation equation shows the relationship between x and y will be y = 16x
Equation
Basically, the equation is a statement that two expressions, which include variables and/or numbers, are equal. And in essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.
Given,
In a direct variation, y=80 when x=5.
Here we have to write a direct variation equation that shows the relationship between x and y.
Here we have given that,
The value of y = 80 when x = 5
Therefore, there are often two different sorts of variables in analytics.
And we have obtained that independent variables will have an impact on dependent variables.
Now, what occurs as a result of the independent variable is referred to as a dependent variable.
Here we have given equation x is the independent variable while y is the dependent variable.
So, it can be written as,
=> 80 = 16(5)
Therefore, the resulting equation is y = 16x
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A cyclist rode 5.83 miles in 0.4 hours.
How fast was she going in miles per hour?
At that rate, how long will it take her to go 5.5 miles?
Answers
Answer:
Its 12.5 miles per hour.
Step-by-step explanation:
Distance covered by cyclist=3.75 miles. Time =0.3 hours. Speed =3.75÷0.3=12.5
hope this helps
Answer:
0.4 miles per hour
Step-by-step explanation:
Distance covered= 5.83 miles
Time taken to cover the distance =0.4 hours
[tex] speed \: = \frac{distance}{time} [/tex]
[tex] = \frac{5.83}{0.4} [/tex]
=14.575 ~=14.5 miles per hour
If the rate (speed) = 14.575 miles per hour
Distance = 5.5 miles
[tex]time = \frac{distance}{speed} [/tex]
[tex] = \frac{5.5}{14.575} [/tex]
=0.337 ~= 0.4 hours
help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
By evaluating the exponential equation, we will see that the amount owed after 6 years is $8551.56
How to find the amount owed after 6 years?The formula we need to use is the exponential equation:
A = P*(1 + r/n)^(n*t)
Where:
P is the initial amount, here we know that it is $5,300
r is the rate, in this case is 8%, but it needs to be written as a decimal, so we have r = 0.08
t is the variable, this time is the time in years, we want to find the amount owed after 6 years, so t = 6
n is how many the the rate applies on one unit of t, in this case the rate is monthly, and there are 12 months on a year, so n = 12.
Replacing all that in the given formula we will get:
A = $5,300*(1 + 0.08/12)^(12*6) = $8551.56
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Can someone please help me on this, I don't understand :)
Answers
The values of x and y are 23.3 and 106 as per given diagram.
What is Alternate Interior Angles?
The word "alternate" refers to the transversal's "alternating sides." The "location" of these angles is expressly described by this designation.The alternate interior angles are equal in size when the lines are parallel.The sides of the transversal are "alternated" by alternate interior angles, which are "internal" (between the parallel lines). They are not neighbouring angles, as you can see (next to one another sharing a vertex).The alternate interior angles are equivalent when a transversal cuts two parallel lines.Hence, (3x + 4)° = 74°
3x = 74° - 4°°
x = 70° / 3
x = 23.3
What is Interior Angles on the Same Side of the Transversal?
The name of these angles describes their "location."The measures are supplemental when the lines are parallel.These angles are situated precisely where their names suggests. They are on the same side of the transversal and are "interior" (between the parallel lines).Hence, (3x+4)° + y° = 180°
74° + y° = 180°
y = 106°
Hence, the values of x and y are 23.3 and 106 as per given diagram.
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Convert the equation y = 3x - 5 from slope-intercept form to standard form.
Answers
Find the x- and y-intercepts of the graph of -2x + y = 22. State each answer as an
integer or an improper fraction in simplest form
Answers
The x- and y- intercepts of then graph of; -2x + y = 22 as required in the task content are; -11 and 22 respectively.
What are the x- and y-intercepts of the graph of the given equation?It follows from the task content that the x- and y-intercepts of the graph of the equation; -2x + y = 22 are to be determined.
Recall that the y-intercept of a graph refers to the value of y when x = 0.
Therefore; we have;
-2(0) + y = 22;
y = 22.
Recall that the x-intercept of a graph refers to the value of x when y = 0;
-2x + 0 = 22
x = 22/-2
x = -11.
On this note, it follows that the x-intercept of the graph is at x = -11 while the y-intercept is at; y = 22.
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Gabriel is designing a rectangular planter box for their garden. It needs to cover an area of
15 1/2 m
Gabriel wants it to be 7- m long.
4
How wide does the planter box need to be?
Answers
Answer:
2m Wide
Step-by-step explanation:
A triangle has side lengths of (7x-4)(7x−4) centimeters, (x+3)(x+3) centimeters, and (3y+2)(3y+2) centimeters. Which expression represents the perimeter, in centimeters, of the triangle?
Answers
The perimeter of the triangle is, 8x + 3y +1.
What is perimeter?
A perimeter is a closed path that encloses, surrounds, or delimits a one-dimensional length, a two-dimensional shape, or both. The circumference of a circle or an ellipse is its perimeter. There are numerous practical uses for calculating the perimeter.
Let, the side lengths of the triangle are (7x - 4), (x + 3) and (3y + 2).
Since the perimeter is the sum of all side lengths.
So,
Perimeter = (7x - 4) + (x + 3) + (3y + 2)
= 7x - 4 + x + 3 + 3y + 2
Perimeter = 8x + 3y + 1
Hence, the perimeter of the triangle is, 8x + 3y + 1.
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Given that x is a nonnegative number, a student conjectured that x+4
Answers
The value of x is a counter example to the student's conjecture (x = 2).
What is an expression?
The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that x is a non-negative number, a student conjectured that x + 4 < x².
Since x is a non-negative number, A and B are eliminated.
This leaves C and D at the value of x = 2,
2 + 4 < 2²
6 < 4 is false.
Therefore, the value of x is a counterexample to the student's conjecture (x = 2).
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If someone uses 400 liters of orange juice, how much strawberry juice would they need?
Answers
Answer:
you need to post the rest of the problem for us to figure it out. if someone walked up to you and asked you this you'd think they're out of their mind
34.7 divided by 0.7
round answer to 2 decimal places
Answers
Answer:
49.57
Step-by-step explanation:
0.7 can go into 34.7 49 times. 0.7*49=37.3
34.7-34.3=0.4 and 0.4/0.7 is 4/7 or 0.57...
So 49+.57=49.57
Suppose T: ℝ3→ℝ2 is a linear transformation. Let U, V and W be the vectors given below, and suppose that T(U) and T(V) are as given. Find T(W).
U = 1, -3, 3 V = −1,3,−2 W = −3,9,−7 T(U) = 2,2 T(V) = 0,1
T(W) = ???
Answers
By using the concept of Linear Transformation, the value of T(W) obtained is T(W) = (2, 6)
What is Linear Transformation?
A function through one vector space to the next that respects this same underlying (linear) structure of the each vector space is called a linear transformation. A linear operator, or map, is another name for a linear transformation. The transformation is known as just an endomorphism as well as, if invertible, an automorphism when the range of a transformation matches the domain. The underlying field of the two vector spaces must be identical.
Let u, v be two element of a vector space V and let c be a scalar
T is said to be a Linear Transformation if
i) T(u + v) = T(u) + T(v)
ii) T(cu) = cT(u)
T: [tex]\mathbb{R}^{3} \rightarrow \mathbb{R}^2[/tex] is a linear transformation
U = (1, -3, 3), V = (−1,3,−2)
W = [tex]c_1[/tex] U + [tex]c_2[/tex] V
(-3, 9, -7) = [tex]c_1[/tex](1, -3, 3) + [tex]c_2[/tex](-1, 3, -2)
[tex]c_1 - c_2 = -3[/tex] ...... (1)
[tex]3c_1 - 2c_2 = -7[/tex] ..... (2)
Multiplying (1) by 2
[tex]2c_1 - 2c_2 = -6[/tex] .... (3)
Subtracting (2) from (3),
[tex]c_1 = 1[/tex]
Putting the value of [tex]c_1[/tex] in (1)
1 - [tex]c_2[/tex] = -3
[tex]c_2 = 3 + 1\\c_2 = 4[/tex]
T(W) = T(U) + 4T(V)
T(W) = (2, 2) + 4(0, 1)
T(W) = (2, 6)
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Find the equation of the linear function represented
by the table below in slope-intercept form.
X
1
2
3
4
y
0
-5
-10
-15
Answers
The equation of the linear function in slope-intercept form is [tex]y=-5x+5[/tex]
What is slope-intercept form of linear function?When you know the slope of the line to be investigated and the given point is also the y intercept, you can utilize the slope-intercept formula, y = mx + b. (0, b). The y value of the y intercept point is denoted by the symbol b in the formula.
Different values of x and y are given.
Find the slope using any two points from the given points.
[tex]m=\frac{-5-0}{2-1}\\ =-5[/tex]
Use the point-slope form of line to obtain the equation.
[tex]y-0=-5(x-1)\\[/tex]
Arrange the equation in slope- intercept form.
[tex]y=-5x+5[/tex]
So, the equation of the linear function in slope-intercept form is [tex]y=-5x+5[/tex].
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four cards are selected at random without replacement from a well-shuffled deck of 52 playing cards. find the probability of the given event. (round your answer to four decimal places.) four cards of the same suit are drawn.
Answers
The probability of selecting four cards of the same suit is 0.0106.
What is probability?A probability is a number that reflects the chance or likelihood that a particular event will occur.
Given that, four cards are selected at random without replacement from a well-shuffled deck of 52 playing cards
No. of cards for each suit = 13
Total types of four suits = 4(hearts, spades, diamond, clubs)
Probability = (conditional case)/(total case)
So, total number of conditional case = No. of case of selecting all 4 cards of hearts suit + no. of case of selecting all 4 cards of spades suit + no. of case of selecting all 4 cards of clubs suit + no. of case of selecting all 4 cards of diamonds suit
= 13C4 + 13C4 + 13C4 + 13C4
= 4*13C4 = 4*13!/9!4! = 4*13*12*11*10*9!/9!*4*3*2*1 = 2860
Total number of cases = 52C4 = 52!/48!4! = 270725
So, probability of getting all 4 cards of the same suit =
2860/270725
= 0.0106.
Hence, The probability of selecting four cards of the same suit is 0.0106.
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Can you locate the school where sir isaac newton was once the lucasian professor of mathematics?.
Answers
Answer:
The second period from 1669 to 1687 was the highly productive period in which he was Lucasian professor at Cambridge. The third period (nearly as long as the other two combined) saw Newton as a highly paid government official in London with little further interest in mathematical research.
Step-by-step explanation:
42 km of 120 km help pls
Answers
Answer: 42 km of 120km is 35%
Step-by-step explanation: 42 ÷ 120 is 0.35 then you move decimal 2 places right to get percent.
A number reduced by two, then multiplied by 9
Answers
(x-2)9
9x-18
good luck <33
Factorise the following 2x + 10
Answers
Answer:
2(x+5) I believe
Step-by-step explanation:
how to solve peggy is preparing a colored frosting for a cure. for the right shade of purple, she needs 25 milliliters of a 44% concentration food coloring. the store has a 25% red and a 50% blue concentration of food coloring. how many milliliters each of blue food coloring and red food coloring should be mixed to make the necessary amount of purple food coloring?
Answers
Answer:
25% red and 28% blue.
Step-by-step explanation:
Bella manages a cafe.She bought 15.625 pounds of oranges . She mutiplies the weigh of the oranges by 0.4 to find the weight of the oranges she will use in fruit salads
Answers
The weight of an object is the amount of gravitational force applied on the object by the earth. The weight of the oranges to be used is 6.25 pounds.
The level of influence of the earth's gravitational pull on an object determines its weight. This depends also on the size of the mass of the object.
Given that Bella bought 15.625 pounds of oranges.
Let the weight of the oranges required to prepare fruit salad be represented by W. Then the weight of the oranges required is 0.4 of the weight of oranges bought, so that;
W = 0.4 * 15.625
= 6.25
W = 6.25
Thus, the weight of the oranges required to be used for fruit salad is 6.25 pounds.
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PLEASE HELP THIS IS OVERDO
What is the product of 2p + q and –3q – 6p + 1?
–12p2 – 6pq – 4p – 3q + 1
–12p2– 12pq + 2p – 3q2 + q
–9p2q2 + 12pq – 2p + q
12p2 + 12pq +2p + 3q2 + q
Answers
The product of the algebraic expression as the product of (2p + q) and (-3q - 6p + 1) is; - 12p² - 12pq + 2p - 3q²+ q
How to multiply algebraic expressions?
We want to find the product of (2p + q) and (-3q - 6p + 1) and this gives;
(2p + q) * (-3q - 6p + 1)
Now, this can be broken down further using distributive property of algebra into;
2p(-3q - 6p + 1) + q(-3q - 6p + 1)
= -6pq - 12p² + 2p - 3q² - 6pq + q
= - 12p² - 3q² - 12pq + 2p + q
Rearranging gives us;
- 12p² - 12pq + 2p - 3q²+ q
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Paul has to put shingles on a roof. A brand new construction worker takes 12 hours to do it alone. When Paul asks the new worker to help him, they can do the job in 2 hours less than it takes Paul to do it alone. How many hours does it take Paul to do the job alone? Workingtogetherformula1a+1b=1T
Answers
The number of hours that it takes for Paul to do the job alone is of:
6 hours.
How to obtain the time it takes for Paul do to the job alone?The time that it takes for Paul to do the job alone is given by the together rate, which is obtained as the sum of the separate rates.
The rates in the context of this problem are given as follows:
Construction worker: 1/12.Paul: 1/x.Together rate: 1/(x - 2) -> 2 hours less than Paul's alone.Hence the value of x is obtained applying the together rate, and it gives the number of hours that it takes for Paul to do the job alone.
Hence:
1/(x - 2) = 1/x + 1/12
1/(x - 2) = (12 + x)/(12x)
Applying cross multiplication, we have that:
(12 + x)(x - 2) = 12x
x² + 10x - 24 = 12x
x² - 2x - 24 = 0
(x + 4)(x - 6).
Applying the Factor Theorem, the solutions are given as follows:
x + 4 = 0 -> x = -4 -> extraneous solution, as the number of hours cannot be negative.x - 6 = 0 -> x = 6 -> actual solution.More can be learned about the together rate at https://brainly.com/question/27859524
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also confused about this
Answers
Graph (B) represents the base function f (x)=√x and the stretched function [tex]g (x) = \frac{-3}{2} \sqrt{x}[/tex].
What is graph?Graphs are used to map functions of two variables on a Cartesian coordinate system, which is composed of a horizontal x-axis, vertical y-axis.
The graph of this function can be obtained by putting different values of x.
x = 0 gives f (x) = 0
x = 1 gives f (x) = 1
x = 2 gives f (x) = 1.414
x = 3 gives f (x) = 1.732
Drawing these points in the graph and connecting we get a curve(black) which can be seen in all given diagram (A), (B), (C), (D).
Now, we have stretched function [tex]g (x) = \frac{-3}{2} \sqrt{x}[/tex]
The graph of this function can be obtained by putting different values of x.
x = 0 gives g (x) = 0
x = 1 gives g (x) = -1.5
x = 2 gives g (x) = -2.121
x = 3 gives g (x) = -2.598
Drawing these points in the graph and connecting we get a curve(red) which can be seen in diagram (D).
By combining these two graphs we get the graph of diagram (D).
Therefore, the base function f (x) and the stretched function g (x) together represents the diagram (D).
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Challenge Andy and Emily each go to a hardware store to buy wire. The table shows the cost y in dollars for x inches of the
wire they need. Andy needs 25 feet of the wire. Emily needs 15 yards of the wire. How much will each of them spend for wire?
Cost of Wire
Length in
Inches (x)
110
125
160
185
Cost in
Dollars (y)
5.50
6.25
8.00
9.25
Answers
Andy will spend $15 for her wire. Emily will spend $27.25 for her wire.
1 = 12 ℎ
1 = 3 = 36 ℎ
=5.50/110 (⁄ℎ)
=6.25/125 (⁄ℎ)
=8.00/160 (⁄ℎ)
=9.25/185 (⁄ℎ)
Andy needs 25 feet of the wire
25(12 inches) = 300 inches
300(5.50 / 110) = 15(Dollars)
Andy will spend $15 for her wire.
Emily needs 15 yards of the wire
15(36 ℎ) = 540 ℎs
110a + 125b + 160c + 185d ≥ 540
6(110) = 660
4(110) + 125 = 565
3(110) + 2(125) = 580
110 + 3(125) = 485
2(125) + 2(160) = 570
110(5.50/110) + 3(145)6.25/125 = 27.25
540 (5.50/110) = 27
Emily will spend $27.25 for her wire.
If she can cut the wire, then Emily will spend $27 for her wire.
∴ Andy will spend $15 for her wire. Emily will spend $27.25 for her wire.
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Barabas received a mark of 50% on a recent test. Barabas answered 13 of the first 20 questions correctly. Barabas also answered 25% of the remaining questions on the test correctly. If each question on the test was worth one mark, how many questions in total were on the test?
Answers
Answer:
32
Step-by-step explanation:
You want the total number of questions on the test if the final score was 50%, and there were 13 correct out of the first 20, and 25% correct among the remainder.
SetupLet q represent the number of questions on the test. Then (q-20) is the number of remaining questions, and the number correct is ...
13 +0.25(q -20) = 0.5(q)
Solution8 +0.25q = 0.5q . . . . . . . simplify
8 = 0.25q . . . . . . . . . . . . subtract 0.25q
32 = q . . . . . . . . . . . . . . multiply by 4
There were 32 questions in total on the test.
A veterinarian has been asked to prepare a diet, x ounces of Brand A and y ounces of Brand B, for a group of dogs to be used in a nutrition study at the School of Animal Science. It has been stipulated that each serving should be no larger than 8 oz and must contain at least 29 units of Nutrient I and 20 units of Nutrient II. The vet has decided that the diet may be prepared from two brands of dog food: Brand A and Brand B. Each ounce of Brand A contains 3 units of Nutrient I and 4 units of Nutrient II. Each ounce of Brand B contains 5 units of Nutrient I and 2 units of Nutrient II. Brand A costs 5 cents/ounce, and Brand B costs 7 cents/ounce. Determine how many ounces of each brand of dog food should be used per serving to meet the given requirements at a minimum cost. (x,y)=... What is the minimum cost? (Round your answer to the nearest cent.) ..... cents per serving
Answers
To meet the given requirements 3 ounces of Brand A and 4 ounces of Brand B should be served , the minimum cost is $43 .
In the question ,
it is given that ,
the each serving should not be larger than 8oz .
let the number of Ounces of Brand A food = x , and
let the number of ounces of brand B = y ,
So , x + y ≤ 8
Brand A has 3 units of Nutrient 1 and 4 units of Nutrient 2 , and
Brand B has 5 units of Nutrient 1 and 2 units of Nutrient 2 ,
So , 3x + 5y ≥ 29 ,
and 4x + 2y ≥ 20,
and x , y ≥ 0 .
given, that
cost of Brand A = 5 cents/ounce
cost of Brand B = 7 cents/ounce
So , the cost equation is c(x) = 5x + 7y ,
drawing the given inequalities on the graph ,
From the graph given below , we find that the vertices of the feasible region are ,
(2,6) , (5.5,2.5) , (3,4)
Substituting the points in the cost equation , we get
For point (2,6) , C = 5(2) + 7(6) = 10 + 42 = 52
For point (3,4), C = 5(3) + 7(4) = 15 + 28 = 43
For point (5.5,2.5) , C = 5(5.5) + 7(2.5) = 45 ,
the minimum cost is at point (3,4) ,
So , 3 ounces of Brand A and 4 ounces of Brand B should be used .
Therefore , To meet the given requirements 3 ounces of Brand A and 4 ounces of Brand B should be served , the minimum cost is $43 .
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