Consider the system of equations.
2x+y=1−3x+4y=15
How can the system of equations be solved using Cramer's rule?
Drag a value or determinant expression into each box to correctly solve the system using Cramer's rule.
Answers
The solutions are x = -1 and y = 3 of the given system of equations 2x+y=1, −3x+4y=15 which is determined by Cramer's rule.
We put the tiles in the right order and entered the final result for each x and y.
The main principle is to split determinants as shown by the vertical bars (these are not absolute value bars).
The determinant of the matrix [tex]\begin{bmatrix}2 & 1 \\-3 & 4 \\\end{bmatrix}[/tex], which are the coefficients of the left-hand side of each original equation supplied to you, is in each denominator.
This matrix's numerators are somewhat different. The x determinant requires you to replace the first column with 1 and 15 to produce [tex]\begin{bmatrix}1 & 1 \\15 & 4 \\\end{bmatrix}[/tex], which aids in determining the x solution. The y solution is similar, except we replace the y column rather than the x column. This explains the [tex]\begin{bmatrix}2 & 1 \\-3 & 15 \\\end{bmatrix}[/tex].
You just evaluate each determinant using the formula once you have the right determinants in place and then simplify the outcomes.
Thus, the solutions are x = -1 and y = 3 of the given system of equations 2x+y=1, −3x+4y=15 which is determined by Cramer's rule.
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Related Questions
Graph the line y 3 on the axes shown below. Type of line: Choose one
Answers
We need to graph the line:
[tex]y=3[/tex]Notice that there is no restriction on the values of x. So, all the points with y-coordinate 3 belong to that line.
When we graph that line, we obtain:
Thus, this line is a horizontal line (parallel to the x-axis).
Jeff constructed a square inscribed in a circle:EFFDWhich provides enough justification to prove that CDEF is a square?All four angles of the quadrilateral are 90°.All four sides of the quadrilateral are congruent.O Opposite sides of the quadrilateral are parallel.The diagonals of the quadrilateral are perpendicular and congruent.
Answers
A square is a quadrilateral with four equal straight sides and four right angles.
In this sense since the diagonals of a square bisect each other and meet at 90° and are congruent, we can conclude it is enough justification to prove that CDEF is a square
Solve e–5x = 7.4 for x correct to four decimal places. –0.40030.40030.8692–0.8692
Answers
Question:
[tex]e^{-5x}=7.4[/tex]Step 1: Apply the exponent rule but taking ln of both sides
[tex]\begin{gathered} e^{-5x}=7.4 \\ -5x=\ln 7.4 \end{gathered}[/tex]Step 2:Divide both sides by -5
[tex]\begin{gathered} -5x=\ln 7.4 \\ \frac{-5x}{-5}=\frac{\ln 7.4}{-5} \\ x=\frac{\ln7.4}{-5} \end{gathered}[/tex]Hence,
The value of x is
[tex]\begin{gathered} x=\frac{\ln7.4}{-5} \\ x=-4.003 \end{gathered}[/tex]Hence,
The final answer is = -0.4003
write the ratio that represents the number of cars to total numbers of vehicles.A) 3/2B) 2/3C) 1/2D) 2/1
Answers
This is a simple question to be solved.
First we need to know the number of vehicles (there are 6 vehicles), and second we need to know the number of cars (there are 4 cars). So the relation between the number of cars and vehicles is ----> 4/6
But we can simplify this relation as follows and represent it in a simple way:
So the final answer is the letter B) 2/3
A client is ordered 30 mg of Lovenox by subcutaneous injection.150 mg in 1 ml of liquid for SQ Injection available. How many ml will you administer?
Answers
For this question we just need to use a simple rule of three as follows:
As we can see above, the rule of three solves the question "if we have 150mg for 1ml so how much do we have for 30 mg". So the final answer is 0.2 ml.
5 1 point The following table shows the relationship between the federal taxes owed and the adjusted gross income. Adjusted Gross income Federal tax 16,500 2,475 19,500 2,925 24,000 3,600 Find the tax rate and calculate the amount of federal taxes owed for 31,000. Type your answer... Prbvious
Answers
The answer is very simple
The federal tax rate is the relation between federal tax and the adjusted grooss income
[tex]\text{federal tax rate = }\frac{2475}{16500}=0.15[/tex]and the federal tax for 31000 is
[tex]\text{federal tax = 31000}\cdot0.15=4650[/tex]That is the solution.
Donna and her husband are each starting a saving plan. Donna will initially set aside S50 and then add $20.55 every week to the savings. The amount A (in
dollars) saved this way is given by the function = 50+20.55N, where N is the number of weeks she has been saving.
Her husband will not set an initial amount aside but will add $80.55 to the savings every week. The amount B (in dollars) saved using this plan is given by the
function B=80.55 N.
Let T be total amount (in dollars) saved using both plans combined. Write an equation relating T to N. Simplify your answer as much as possible.
Answers
The total amount (in dollars) saved using both plans combined is T = 50 + 101.1N.
How to illustrate the equation?Based on the information, the function = 50+20.55N.
where N is the number of weeks she has been saving.
For the second function, this is illustrated as:
function B = 80.55 N.
Therefore, the total of the plans combined will be:
T = 50 + 20.55N + 80.55N
T = 50 + 101.1N
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Complete the function for this graph.
Enter the correct
symbol,+ or -.
y = [?] |x|
Answers
Answer:
Step-by-step explanation:
y = -|x|
The graph is facing downwards, meaning it is negative.
If x = 3, y = 6, then cos e equal to:
Answers
The cosine of an angle theta in a right triangle is given by its adjacent side divided by the hypotenuse:
[tex]\cos \theta=\frac{x}{r}[/tex]We don't know the value of r but with x, y and the Pythagorean Theorem we can find it:
[tex]\begin{gathered} r=\sqrt[]{x^2+y^2}=\sqrt[]{3^2+6^2}=\sqrt[]{9+36}=\sqrt[]{45} \\ r=6.71 \end{gathered}[/tex]Then the cosine we are looking for is:
[tex]\cos \theta=\frac{x}{r}=\frac{3}{6.71}=0.45[/tex]Then the correct option is the second one since:
[tex]\frac{\sqrt[]{5}}{5}=0.45[/tex]Write the relation as a set of ordered pairs.
A relation. An arrow goes from negative 2 to 4, 0 to 6, 2 to 8.
a.
ordered pairs: {(4, –2), (0, 6), (2, 8)}
b.
ordered pairs: {(–2, 4), (0, 6), (2, 8)}
c.
ordered pairs: {(4, –2), (0, 6), (8, 2)}
d.
ordered pairs: {(–2, 4), (6, 0), (8, 2)}
Its not c.
Answers
The set of coordinate pairs that represents the relation is the one in option b.
{(–2, 4), (0, 6), (2, 8)}
How to write the relation as a set?
A relation maps elements "x" into elements "y", such that the notation used is:
An arrow that goes from x to y.A ordered pair fo the form (x, y)Here we know that:
An arrow goes from negative 2 to 4, 0 to 6, 2 to 8.
Then we have the coordinate pairs:
(-2, 4)
(0, 6)
(2, 8)
Then the correct option is B: {(–2, 4), (0, 6), (2, 8)}
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Answer:
b
Step-by-step explanation:
PLEASE HELP!!
A fair die is rolled 4 times. What is the probability of having no 1 and no 3 among the rolls? Round your answer to three decimal places.
Answers
Answer:
66.667%
Step-by-step explanation:
In a fair die, there are 6 possible rolls. Out of the 6, 1 number is chosen each time. Since orde does not matter in this problem, we will be applying combination, so this would be written as 6C1 x 4. In order to exclude 3 and 4, from 6, the choices must be narrowed down to 4. Written out as an equation, this would be 4C1 x 4. To get the percentage, simply divide the two equations.
(4C1 x 4)/(6C1 x 4) = 0.66667 = 66.667%
hope it will be helpful
The scores of 12th-grade students on the National Assessment of Educational Progress year 2000 mathematics test have a distribution that is approximately Normal with mean μ = 300 and standard deviation σ = 35. (a) Choose one 12th-grader at random. What is the probability that his or her score is higher than 300? Higher than 335? Explain and show your work. (b) Now choose an SRS of four 12th-graders and calculate their mean score x. If you did this many times, what would be the mean and standard deviation of all the x-values? Explain and show your work. (c) What is the probability that the mean score for your SRS is higher than 300? Higher than 335? Explain and show your work.
Answers
a) To find the probability that the score is higher than 300 you have to find the Z-score for 300, by using the formula:
[tex]\begin{gathered} Z=\frac{x-\mu}{\sigma} \\ Z=\frac{300-300}{35}=\frac{0}{35}=0 \end{gathered}[/tex]The probability of x>300 P(z>0)=1-P(z<=0)
Using the Standard Normal Cumulative Probability Table, P(z<=0)=0.5
Then,
[tex]P(Z>0)=1-0.5=0.5[/tex]Now, you can do the same to find the probability that the score is higher than 335, let' see:
[tex]Z=\frac{335-300}{35}=\frac{35}{35}=1[/tex]The probability of x>335 is P(Z>1), then
[tex]P(Z>1)=1-P(Z\leq1)=1-0.8413=0.1587[/tex]These results mean that it is a 50% of probability that the score of the student chosen is greater than 300, and a 15.87% of probability that the score is greater than 335.
b) SRS=4, their mean score will be the same as the mean of the population = 300, the standard deviation of the sample is the standard deviation of the population divided by √n (n is the size of the sample=4).
[tex]\mu=300\text{ and }\sigma=\frac{35}{\sqrt[]{4}}=17.5[/tex]c) The probability that the mean score for the SRS is higher than 300 is:
[tex]\begin{gathered} Z=\frac{x-\mu}{\sigma} \\ Z=\frac{300-300}{17.5}=\frac{0}{17.5}=0 \end{gathered}[/tex][tex]P(Z>0)=1-P(Z\leq0)=1-0.5=0.5[/tex]The probability that the mean score for the SRS is higher than 335 is:
[tex]Z=\frac{335-300}{17.5}=2[/tex][tex]P(Z>2)=1-P(Z\leq2)=1-0.9772=0.0228[/tex]These results mean that it is a 50% of probability that the mean score of the SRS is greater than 300, and a 2.28% of probability that the mean score is greater than 335.
riya won a LCD TV in amall raffle draw , the tv screen measures 16 inches in height and 12 inches in width. find the hypotenuse of the TV
Answers
Step by step
Pythagorean theorem states
a^2 + b^2 = c^2
Solve for hypotenuse by substituting h & w for a and b and solve for c
16^2 + 12^2 = c^2
256 + 144 = c^2
400 = c^2
Take square root of both sides
20 = c
The tv screen diagonal = 20”
The length of the base of an isosceles triangle is 49.96 meters. Each base angle is 31.43°. Find the length of each of the two equal sides of the triangle. Round to the hundredths place.
Answers
Given that:
- The triangle is isosceles.
- Its base is 49.96 meters.
- Each base angle is 31.43°.
You can draw the triangle. See the picture shown below (it is not drawn the scale):
Notice that the Isosceles Triangle can be divided into two equal Right Triangles. Then, you know that:
[tex]CD=BD=\frac{49.96m}{2}=24.98m[/tex]Since it is isosceles, the sides AB and AC have equal length.
Then, you can choose one of the equal Right Triangles and use the following Trigonometric Function in order to find the length of each equal side:
[tex]\cos \beta=\frac{adjacent}{hypotenuse}[/tex]In this case, you can set up that:
[tex]\begin{gathered} \beta=31.43\degree \\ adjacent=24.98 \\ hypotenuse=AC \end{gathered}[/tex]Therefore, substituting values and solving for AC, you get:
[tex]\begin{gathered} \cos (31.43\degree)=\frac{24.98}{AC} \\ \\ AC\cdot\cos (31.43\degree)=24.98 \end{gathered}[/tex][tex]\begin{gathered} AC=\frac{24.98}{\cos (31.43\degree)} \\ \\ AC\approx29.28 \end{gathered}[/tex]Hence, the answer is:
The length of the two equal sides of the triangle is:
[tex]length\approx29.28m[/tex]in July Leia sold 32 fruit bars what was her profit
Answers
A bag contains 6 red marbles and 7 white marbles. Two marbles are drawn in succession without replacement. Find the probabilities of the following events:
1. The first marble drawn is red and the second is white.
2. Both marbles drawn are red.
Answers
Using it's concept, the probabilities are given as follows:
1. Red then white: 7/26.
2. Both red: 5/26.
What is a probability?The probability of an event in an experiment is calculated as the number of desired outcomes of the experiment divided by the number of total outcomes of the experiment.
For item 1, we have that:
For the first marble, the probability of it being red is of 6/13, as of the 13 marbles, 6 are red.Supposing that the first marble is red, the probability of the second being white is of 7/12, as of the 12 remaining marbles, 7 are white.Hence the probability is:
6/13 x 7/12 = 7/26.
For item 2, we have that:
For the first marble, the probability of it being red is of 6/13, as of the 13 marbles, 6 are red.Supposing that the first marble is red, the probability of the second being red is of 5/12, as of the 12 remaining marbles, 5 are red.Hence the probability is:
6/13 x 5/12 = 5/26.
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* I didn’t mean to choose 1 * I really need help because I don’t know how to solve this …
Answers
Okay, here we have this;
Considering the provided graph, we are going to calculate the requested height, so we obtain the following:
So to calculate the height of the trapezoid, we will replace in the area formula with the given information, so we have:
A=(b1+b2)h/2
10 ft²=(7ft+3ft)h/2
10 ft²*2=(10 ft)h
20 ft²=(10 ft)h
h=20 ft²/10 ft
h=2 ft
Finally we obtain that the height of the ramp is 2ft, then the correct answer is the second option.
If Sally has 5 apples, 4 oranges, 3 bananas, 2 grapes, and a plum, how many people does it take to screw in a lightbulb?
Answers
Some responses are incorrect. They overlooked the fact that we must eventually add up the cost of one banana.
1 Apple = 7
5 + 7 Equals 12 grapes in a bunch.
After substituting the preceding variables, we arrive to the result that 1 banana equals 2 (7 = 1 + 3 bananas). 21 is incorrect
The second equation has 12 grapes, therefore after solving it, we obtain 1 grape = 1.
However, the final equation has 11 grapes, so we end up with (7+11+2)=20.
Eric, counting the grapes was difficult
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complete question:
If Sally has 5 apples, 4 oranges, 3 bananas, 2 grapes, and a plum, how many people does it take to screw in a lightbulb?
2x+2y = 4 2x + 2y = 3 One Solution No Solutions Infinitely Many Solutions
Answers
The system has no solutions
Here, we want to solve the system of linear equations
As we can see, the exact expression is what we have on the left side of both equations
The only different thing is what we have on the right hand side
What this mean is that no values of x and y can satisfy both equations
With that in mind, we have it that the system of equations has no solutions
4% of a number is what fraction of that number?
Answers
First, let's remember how we calculate a percentage:
If we call the number "x", 4% is calculated by dividing x by 100 and then multiplying by 4:
[tex]\frac{x}{100}\times4[/tex]This can also be represented as follows:
[tex]\frac{4}{100}\times x[/tex]Thus, 4% of a number is 4/100 of that number. We can still simplify this result as follows:
[tex]\frac{4}{100}=\frac{1}{25}[/tex]We divide 4 by 4 and get 1, and also divide 100 by 4 and get 25.
Answer: 4% of a number is 1/25 of that number.
Sketch a graph representing f(x), indicating all intercepts and min or max points.
Answers
Given the function below;
[tex]f(x)=4-\frac{x^2}{8}[/tex]The x-intercept is the point where f(x) = 0 as shown:
[tex]\begin{gathered} 0=4-\frac{x^2}{8} \\ 0=32-x^2 \\ x^2=32 \\ x=\pm\sqrt{32} \\ x=\pm5.66 \end{gathered}[/tex]The x-intercept of the graph will be at (5.66, 0) and (-5.66, 0)
The y-intercept occurs at the. point where x = 0 to have:
[tex]\begin{gathered} f(0)=4-\frac{0^2}{8} \\ f(0)=4 \end{gathered}[/tex]The y-intercept is (0, 4)
The equivalent graphis as shown below
The graph shows that the function has a maxmum point at (0, 4) with no minimum point.
So far, Benny has run 3/2 miles, but that is only 2/5 of his total running distance. What is his total running
distance?
Answers
Step-by-step explanation:
this is 2/5 of his total.
that means we have to divide it by 2 (that delivers 1/5) and multiply by 5 (that delivers 5/5 or 1 = the whole).
in short : multiply by 5/2
3/2 × 5/2 = 15/4 miles = 3 3/4 miles
write the place value of 8 in 15.0008
Answers
Three partners A, B, C start a business. B's Capital is four times C's capital
and twice A's capital is equal to thrice B's capital. If the total profit is Tk. 16500
at the end of a year, Find out B's share in it.
Answers
Suppose C's capital = x then
B's capital = 4x (Since B's Capital is four times C's capital)
A's capital = 6x ( Since twice A's capital is equal to thrice B's capital)
A : B : C =6x : 4x : x
= 6 : 4 : 1
B's share = 16500×411
= 1500 × 4 = 6000.
What is meant by Capital?
A factory and its equipment, intellectual property like patents, or the financial assets of a company or a person are all examples of things that provide value or benefit to their owners and fall within the wide definition of capital.
While money in and of itself might be considered capital, the term is most frequently used to refer to money that is being used for investments or productive purposes. In general, capital is an essential part of managing firm day-to-day and funding its expansion in the future.
Business capital may be generated via activities or obtained through debt or equity finance. Typical sources of funding are as follows:
individual savings
relatives and friends
Angel backers
financiers for startups (VC)
Corporations
State, municipal, or federal governments
Personal loans
Working or conducting business
getting an IPO to go public
Working capital, equity capital, and debt capital are the three types of capital that firms of all sizes commonly concentrate on when creating budgets. A company in the financial sector names trading capital as the fourth element.
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The students in Cassie's class got to choose between pizza and burgers for the celebration on the last day of school. 8 students picked the pizza. If there are 10 students in all in Cassie's class, what percentage of the students picked the pizza? Write your answer using a percent sign (%).
Answers
There is a total of 10 students in Cassie's class.
8 students choose Pizza
So, the percentage of the students who picked the pizza is 80%.
[tex]Percentage\%= \frac{Students who picked Pizza}{Total number of students in class} *100[/tex]
[tex]Percentage\%= \frac{8}{10}*100\%[/tex]
[tex]=\frac{800}{10}\%[/tex]
[tex]=80\%[/tex]
And 20% of students picked Burgers.
About Percentage
The Latin adverb "percent" means "by the hundred." The 16th century saw its invention. The abbreviation was later changed to %. Later, the period was eliminated, and the two words were merged to form the term "percent." Brief explanations employ the annotation sign %. Calculate your percentage of marks by comparing your final score to your overall score.
The percentage is a fraction or a ratio in which the value of the whole is always 100. For example, if Sam scored 30% marks in his math test, it means that he scored 30 marks out of 100. It is written as 30/100 in the fraction form and 30:100 in terms of ratio.
Percentage Definition:
The percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
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C lies at (1,5) and is the midpoint of AB. If A is at (3,2), find the coordinate for point B.(-1.8)(8.-1)(5.-1)(60)
Answers
Given:
The coordinates of C, the midpoint of AB, (X, Y)=(1, 5).
The coordinates of A, (x1, y1)=(3, 2).
Let the coordinates of B be (x2, y2).
The midpoint formula is given by,
[tex](X,\text{ Y)=(}\frac{x1+x2}{2},\text{ }\frac{y1+y2}{2})[/tex]Hence,
[tex]\begin{gathered} X\text{=}\frac{x1+x2}{2}\text{ ---(1)} \\ Y=\frac{y1+y2}{2}\text{ ---(2)} \end{gathered}[/tex]Substitute the known values in equation (1) and solve for x2.
[tex]\begin{gathered} 1=\frac{3+x2}{2} \\ 2=3+x2 \\ x2=2-3 \\ x2=-1 \end{gathered}[/tex]Hence, x2=-1.
Substitute the known values in equation (2) and solve for y2.
[tex]\begin{gathered} 5=\frac{2+y2}{2} \\ 5\times2=2+y2 \\ 10=2+y2 \\ y2=10-2 \\ y2=8 \end{gathered}[/tex]Therefore, the coordinates of point B is (x2,y2)=(-1, 8).
Solve by graphing. If the population of a town is growing at a rate of 2.5% each year and the current population is 50,000. After how many years will the population reach 100,000 people. Round to the NEAREST whole number. Be sure to label your answer.
Answers
The situation describes an exponential growth, which can be expressed using the general formula:
[tex]y=a(1+r)^x[/tex]Where
a is the initial value
r is the growth rate, expressed as a decimal value
x is the number of times intervals
y is the final value after x time intervals
For the studied population, the growth rate is 2.5%, to express this number as a decimal value you have to divide it by 100:
[tex]\begin{gathered} r=\frac{2.5}{100} \\ r=0.025 \end{gathered}[/tex]The initial value is the current population of the town: a=50000
You can express the equation of exponential growth for this population as follows:
[tex]\begin{gathered} y=50000(1+0.025)^x \\ y=50000(1.025)^x \end{gathered}[/tex]We know that after x years the population will be y=100000, to determine how many years it will take to reach this value you have to equal the equation to 100000 and solve for x:
[tex]100000=50000(1.025)^x[/tex]-Divide both sides of the expression by 50000
[tex]\begin{gathered} \frac{100000}{50000}=\frac{50000(1.025)^x}{50000} \\ 2=(1.025)^x \end{gathered}[/tex]-Apply logarithm to both sides of the equal sign:
[tex]\begin{gathered} \log (2)=\log (1.025^x) \\ \log (2)=x\cdot\log (1.025) \end{gathered}[/tex]-Divide both sides by the logarithm of 1.025
[tex]\begin{gathered} \frac{\log(2)}{\log(1.025)}=\frac{x\cdot\log (1.025)}{\log (1.025)} \\ x\approx28.07\approx28 \end{gathered}[/tex]After approximately 28 years the population of the town will be 100,000.
Owen, Caden, and Luke played basketball. Owen scored 26 more points than Caden, who scored 68 points. Luke scored half of the total of Owen and Caden's score. How many points did Luke score?
Please give an explanation! Whoever answers first and correctly gets brainlist!!
Answers
Answer:
81
Step-by-step explanation:
68+26=94+68=162/2=81
Solve 4|x + 7| = 24.
O A. x= -13 and x = -1
OB. x = 13 and x = -1
O C. x= 13 and x = -13
OD. x= -13 and x = 1
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Blank 1 - 2850342043504625 Blank 2. - 20253035Blank 3 4350462550755225 Blank 4 20253035
Answers
The determinant of the matrix for the pineapple cake is 4350
The price of a pineapple cake is $30
The determinant of the matrix for the chocolate cake is 5075
The price of a chocolate cake is $35
Basically, what we want to do in this question is to form a set of linear equations then use matrix determinant method to solve for the unknowns in the linear equation.
Before we set up these equations,we need to use variables to represent the fruit prices;
Let p represent the price a of pineapple
Let c represent the price of a chocolate;
So let us proceed to form the linear equations;
The equation for the weekdays sales will be;
[tex]45p\text{ + 62c = 3520}[/tex]The equation for the weekend sales will be;
[tex]55p\text{ + 79c = }4415[/tex]Now, we have two equations that we need to use the matrix determinant method to solve;
[tex]\begin{bmatrix}{45} & {62} \\ {55} & {79} \\ {} & {}\end{bmatrix}\text{ }\begin{bmatrix}{p} & \\ {c} & {} \\ {} & \end{bmatrix}\text{ = }\begin{bmatrix}{3520} & {} & \\ {4415} & {} & \\ {} & {} & \end{bmatrix}[/tex]The above is the matrix set up we wil use;
Now, we start by calculating the determinant of 2 * 2 matrix; that would be;
[tex]\begin{gathered} \Delta\text{ = (45 }\times\text{ 79) - (62 }\times\text{ 55)} \\ \Delta\text{ = 3555-3410 = 145} \end{gathered}[/tex]Next is to find the determinant of the pineapple cake matrix;
To find this, what we will do is to substitute the coefficient of p with the total sales value to get a new matrix set;
The matrix for the pineapple cake will be;
[tex]\begin{gathered} \begin{bmatrix}{3520} & {62} \\ {4415} & {79} \\ {} & {}\end{bmatrix}\text{ } \\ \\ \text{The }\det er\min ant\text{ here will be ;} \\ \Delta_{p\text{ = }}(3520\text{ }\times\text{ 79) - (62 }\times\text{ 4415)} \\ =\text{ 4350} \end{gathered}[/tex]Next is to find the determinant of the chocolate cake matrix;
To find this, what we will do is to substitute the coefficient of c with the total sales value to get a new matrix set;
The matrix for the chocolate cake will be;
[tex]\begin{gathered} \begin{bmatrix}{45} & {3520} \\ {55} & {4415} \\ {} & {}\end{bmatrix} \\ \\ \Delta_c\text{ = (45 }\times\text{ 4415) - (55 }\times\text{ 3520)} \\ =\text{ 5075} \end{gathered}[/tex]Finally, we proceed to get the prices for the pineapple and the cake;
To get this, we simply divide the matrix of each by the initial matrix value;
[tex]\begin{gathered} p\text{ = }\frac{\Delta_p}{\Delta}=\frac{4350}{145}=30_{} \\ \\ c\text{ = }\frac{\Delta_c}{\Delta}\text{ = }\frac{5075}{145}\text{ = 35} \end{gathered}[/tex]