There are two different normal forms, namely a single Jordan block of size 4 or two Jordan blocks of sizes 3 and 1, for nilpotent endomorphisms of a 4-dimensional vector space.
Cayley-Hamilton Theorem, states that every matrix satisfies its own characteristic polynomial. However, it is not directly related to the concept of normal forms.
To answer your question, we can use the Jordan Normal Form theorem, which states that every linear operator (or endomorphism) on a finite-dimensional vector space over an algebraically closed field (such as the complex numbers) is similar to a matrix in Jordan normal form.
For a nilpotent endomorphism on a 4-dimensional vector space, there are two possible Jordan normal forms: either a single Jordan block of size 4 with eigenvalue 0, or two Jordan blocks of sizes 3 and 1, also with eigenvalue 0.
Therefore, there are two different normal forms for nilpotent endomorphisms of a 4-dimensional vector space.
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18. Find the area of the triangle.
Answer:
Area = 30
Step-by-step explanation:
Okay, to find the area of this triangle, you have to use the formula [tex]\frac{bh}{2}=A[/tex]. In this case, we are given the height (if we were given the slant height, we could not solve this problem very quickly, so you HAVE to use the regular size.)
Okay, now we substitute in values.
[tex]\frac{bh}{2}=A\\\\\frac{(6)(10)}{2}=A\\\\\frac{60}{2}=A\\\\30=A[/tex]
So, A = 30 is our final answer.
The detailed reason we cannot use slant height is that if you have any line and then put it on a slant, the size would have to be different. For example, if you have support beams on a building going up and down, if you wanted to make one of them slanted, the length of it would have to increase for it to touch the ground appropriately.
Therefore, we cannot use the slant height because it would be longer than the actual height of the triangle.
if the hypothesis test yields a t statistic 5.42 and a p-value of 0.0001, will you reject the null hypothesis or fail to reject the null hypothesis?
We reject the null hypothesis since the p-value of 0.0001 is less than the significance level of 0.05, indicating a significant difference between the sample mean and the hypothesized population mean.
If the hypothesis test yields a t-statistic of 5.42 and a p-value of 0.0001, this indicates that the probability of observing a test statistic as extreme or more extreme than 5.42, assuming the null hypothesis is true, is 0.0001.
This p-value is very small, and if we use a typical significance level of 0.05, we would reject the null hypothesis because the p-value is less than the significance level.
Therefore, we can conclude that we reject the null hypothesis and accept the alternative hypothesis, which suggests that there is a significant difference between the sample mean and the hypothesized population mean.
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What is the area of sector GPH in square yards
The area of sector GPH in square yards is equal to 157 yd².
How to calculate the area of a sector?In Mathematics and Geometry, the area of a sector can be calculated by using the following formula:
Area of sector = θπr²/360
Where:
r represents the radius of a circle.θ represents the central angle.By substituting the given parameters into the area of a sector formula, we have the following;
Area of sector = θπr²/360
Area of sector = 80(3.14/360) × (15)²
Area of sector = 0.6978 × 225
Area of sector = 157 yd²
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The circle graph describes the distribution of preferred transportation methods from a sample of 300 randomly selected San Francisco residents.
circle graph titled San Francisco Residents' Transportation with five sections labeled walk 40 percent, bicycle 8 percent, streetcar 15 percent, bus 10 percent, and cable car 27 percent
Which of the following conclusions can we draw from the circle graph?
Bus is the preferred transportation for 25 residents.
Bicycle is the preferred transportation for 48 residents.
Together, Streetcar and Cable Car are the preferred transportation for 42 residents.
Together, Walk and Streetcar are the preferred transportation for 165 residents.
The correct conclusion that can be drawn from the circle graph is given as follows:
Together, Walk and Streetcar are the preferred transportation for 165 residents.
What is shown by a circle graph?A circle graph, also known as a pie chart, is used to represent data as a circle divided into sectors, where each sector represents a portion of the whole. The size of each sector is proportional to the percentage of the whole that it represents.
Out of 300 residents, the percentages and amounts are given as follows:
Walk: 40% -> 0.4 x 300 = 120 residents.Bicycle: 8% -> 0.08 x 300 = 24 residents.Streetcar: 15% -> 0.15 x 300 = 45 residents.Bus: 10% -> 0.1 x 300 = 30 residents.Cable car: 27% -> 0.27 x 300 = 81 residents.Hence the last option gives the correct option in the context of the problem.
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What is the interquartile range of the data 10 12 28 59 61 67 89 93
The interquartile range (IQR) is found by subtracting Q1 from Q3.
First, find the median.
10, 12, 28, 59, 61, 67, 89, 93
12, 28, 59, 61, 67, 89
28, 59, 61, 67
59, 61
median = 60
Second, separate the data set at the median and find the median of each of those sections (do not include the median number we just found).
data set one = 10, 12, 28, 59
median of data set one = 20 (a.k.a. Q1)
data set two = 61, 67, 89, 93
median of data set two = 78 (a.k.a. Q3)
Third, subtract Q1 from Q3 to get the IQR.
Q3 - Q1 = IQR
78 - 20 = 58
Answer: 58
Hope this helps!
Answer:
Interquartile Range: 58
Step-by-step explanation:
25th Percentile: 20
50th Percentile: 60
75th Percentile: 78
Interquartile Range: 58
Cassidy's bicycle wheel is 15 inches in diameter. How much ground is covered on one rotation of the wheel?
Answer:
47.1239 inches
Step-by-step explanation:
The ground covered in one rotation of a circular wheel is the same as the circumference of the wheel
Circumference C = π · d
where d is the diameter
Given d = 15 inches
C = π · 15
= 47.1239 inches
Use a graphing or scientific calculator and the law of cosines to find the missing angle to
the nearest degree or length to the nearest whole number.
b=8, c = 10, ZA = 37°, a = ?
A. 9
B. 8
C. 7
D. 6
The length of segment a will is
D. 6
How to find the side using cosine lawsApplying the Law of Cosines with the formula given below
a² = b² + a² - 2bc cos(A)
where
a, b, and c are sides of the triangle and
A, b, ad C are the angles of the triangle
a² = 8² + 10² - 2 x 8 x10 cos (37°).
a² = 64 + 100 - 160 kos(37°).
a² = 164 - 123.2
taking the square root of both sides
a = √40.8
a ≈ 6.39
Therefore, the length of segment a will be 6.39 units.
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13 A number sequence starts 1 2 4
Emma says that the next term is 7
(a) Explain why Emma may be correct.
Emma may be correct because the addition of 1, 2 and 4 gives 7
Explaining why Emma may be correct.From the question, we have the following parameters that can be used in our computation:
Sequence: 1 2 4
Emma says that the next term is 7
This statement may be true because the addition of 1, 2 and 4 gives 7
i.e. next term = 1 + 2 + 4
Evaluate
next term = 7
Hence, Emma is right
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When converting 8 fluid ounces to pints, will the number of pints be greater than
or less than 8?
After converting 8 fluid ounces to pints, the number of pints will be greater than 8.
To convert fluid ounces to pints, we need to use the conversion factor of 1 pint equals 16 fluid ounces. So, to convert 8 fluid ounces to pints, we can divide 8 by 16.
8 fluid ounces / 16 fluid ounces per pint = 0.5 pints
Therefore, 8 fluid ounces is equal to 0.5 pints.
We can see that the number of pints is less than 8. This is because 8 fluid ounces is only half of a pint, since there are 16 fluid ounces in one pint. When we divide 8 by 16, we get 0.5, which means that 8 fluid ounces is equivalent to half of a pint.
The conversion factors when making conversions between units. In this case, we used the conversion factor of 16 fluid ounces per pint to convert from fluid ounces to pints. By using this conversion factor, we were able to determine that 8 fluid ounces is equivalent to 0.5 pints.
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if a given graph that shows one of the x-intercepts is (-3 0) and the vertext is (0,-9) what is the quadratic equation in standard form?
The quadratic equation can be written as y = x² - 9.
To find the quadratic equation in standard form, we need to use the vertex form of the quadratic equation, which is given by:
y = a(x - h)² + k
where (h, k) is the vertex and a is a constant that determines the shape of the parabola.
We know that the vertex is (0, -9), so we can substitute these values into the equation:
y = a(x - 0)² - 9
Simplifying this equation, we get:
y = ax² - 9
Now, we need to find the value of a. We know that one of the x-intercepts is (-3, 0), which means that the parabola intersects the x-axis at x = -3. This tells us that (-3, 0) is a solution of the equation, so we can substitute these values into the equation and solve for a:
0 = a(-3)² - 9
0 = 9a - 9
9 = 9a
a = 1
Therefore, the quadratic equation in standard form is:
y = x² - 9
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I NEED HELP ON THIS ASAP!!!!
Answer:
Step-by-step explanation:
the answers is Ax + By + C = 0 y = mx + c y − y1= m(x − x1) m = Δy/Δx = (y2 − y1)/(x2 − x1)
Question 1(Multiple Choice Worth 2 points)
(Scale Factor MC)
A triangle with a perimeter of 24 meters was created from a triangle with a perimeter of 3 meters using a scale factor. What is the scale factor?
8:1
28:1
32:1
72:1
The scale factor of the triangle is 4:1.
We have,
The ratio of the perimeters of two similar triangles is equal to the ratio of their corresponding sides.
Let's call the scale factor "k", and the length of one side of the original triangle "x".
Then, the length of the corresponding side in the new triangle is kx.
The problem tells us that the perimeters of the two triangles are in the ratio 24:3, or 8:1.
Therefore, we have:
24/3 = (kx + kx + x)/(x + x + x)
Simplifying the left side of the equation, we get:
8 = 2k
Dividing both sides by 2, we get:
k = 4
Therefore,
The scale factor is 4:1.
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Identify the transformations of the graph of f(x) = x³ that produce the graph of the given function g(x). Then graph g(x) on the same coordinate plane as the graph of f(x) by applying the transformations to the reference points (-1,-1),(0,0), and (1,1).
g(x) = x³ + 2
Reference
Points
(-1,-1)
(0,0)
(1,1)
First Transformation Second Transformations?
Step-by-step explanation:
The graph is shifted UP 2 units:
Find the surface area of the prism.
Therefore, the surface area of the prism is 453.5 square meters.
What is surface area?Surface area is the total area that the surface of a three-dimensional object occupies. It is the sum of the areas of all the faces, surfaces, or sides of the object. Surface area is measured in square units, such as square inches, square feet, or square meters, depending on the units used to measure the object's dimensions. Surface area is an important concept in geometry and is used in many real-world applications, such as calculating the amount of paint needed to cover a surface or the amount of material required to build a structure.
Here,
To find the surface area of the prism, we need to find the area of all six faces and then add them together. The prism has two congruent rectangular faces (front and back) and four trapezoidal faces (top, bottom, left, and right).
The area of the rectangular faces is:
20 m × 4 m = 80 m² (each face)
The area of the trapezoidal faces can be found using the formula for the area of a trapezoid:
Area = (a + b) × h / 2
where a and b are the lengths of the parallel sides, h is the height, and the slanting height is used to calculate the height.
For the top and bottom faces, the parallel sides are 5 m and 20 m, and the height is 4.47 m. So, the area of each face is:
(5 m + 20 m) × 4.47 m / 2 = 56.75 m² (each face)
For the left and right faces, the parallel sides are 4 m and 5 m, and the height is 20 m. So, the area of each face is:
(4 m + 5 m) × 20 m / 2 = 90 m² (each face)
Now, we can add up the areas of all six faces to get the total surface area:
Total surface area = 2 × 80 m² + 2 × 56.75 m² + 2 × 90 m²
Total surface area = 160 m² + 113.5 m² + 180 m²
Total surface area = 453.5 m²
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For the past three years, Derek has grown 1 inches each year. How many total inches has he grown in the past three years?
5/12, inch
3 3/4 inches
3, 1/4 inches
1 3/4 inches
The total inches Derek has grown in the past three years is 3 inches.
None of the given options is correct.
Given information:
For the previous three years, Derek has become an inch taller every year.
This means that we can add up those three inches to find his total growth over the three-year period.
Thus, 1 + 1 + 1 equals 3 inches.
Derek has therefore gained 3 inches in total over the last three years.
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in each of the following scenarios, researchers plan to conduct either a hypothesis test for a population mean or for the difference in two population means. are the conditions for use of a t-model met?
In each of the following scenarios, researchers plan to conduct either a hypothesis test for a population mean or for the difference between two population means conditions not met for Scenario 1, and conditions met for Scenarios 2 and 3.
a. Conditions not met; do not proceed with the hypothesis test. Since the distribution is strongly skewed to the right, the sample size should be much larger (i.e., n > 100) for the t-model to be valid.
b. Conditions not met; do not proceed with the hypothesis test. Since the distribution is strongly skewed for females, the sample size of 37 is too small for the t-model to be valid.
c. Conditions met; proceed with the hypothesis test. Since both distributions are fairly normal and the sample sizes for males and females are each 100, the t-model can be used.
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The question is -
In each of the following scenarios, researchers plan to conduct either a hypothesis test for a population mean or for the difference between two population means. Are the conditions for use of a T-model met?
1. In a random sample of 100 university students, the distribution of time spent at university recreational facilities is strongly skewed to the right.
2. In a random sample of 50 university students (37 females and 13 males), the distribution of time spent at university recreational facilities is strongly skewed to the right for females but not strongly skewed for males.
3. In a study of 100 brother-sister sibling pairs at the university, the distribution of time spent at university recreational facilities for the 100 males is compared to the 100 females; both distributions are fairly normal.
A prism has a perimeter of 9 a Height of 6 and a base of 7.8 what is the lateral and surface area
The lateral and total surface area of the prism for the given dimensions is equal to 54 square units and 69.6 square units respectively.
Perimeter of the prism = 9 units
Height of the prism = 6 units
Base area of the prism = 7.8 units
The lateral area of a prism is the sum of the areas of all its lateral faces,
And the surface area is the sum of the areas of all its faces.
Lateral area of the prism = perimeter × height
Substitute the values we have,
⇒ Lateral area of the prism = 9 × 6
⇒ Lateral area of the prism = 54 square units.
Total surface area of the prism
= perimeter × height + 2 × Base area
Substitute the values we have,
⇒Total surface area of the prism
= 9 × 6 + 2 × 7.8
= 54 + 15.6
= 69.6 square units.
Therefore, the lateral surface area and total surface area of the prism are 54 square units and 69.6 square units respectively.
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The above question is incomplete, the complete question is:
A prism has a perimeter of 9 ,a Height of 6 and a base area of 7.8 what is the lateral and total surface area of the prism.
The probability is 0.45 that a traffic fatality involves an intoxicated or alcohol-impaired driver or nonoccupant. In eight traffic fatalities, fine the probability that the number, Y, which involve an intoxicated or alcohol-impaired driver or nonoccupant is a.exactly three; =________ at least three; =_______ at most three =__________ b. between two and four, inclusive c. find and interpet the mean of the random variable Y d. obtain the stand deviation of y
Regarding resolving the given issue, we have P(Y<=3) = 0.3909 (rounded to four decimal places)
What is probability?The likelihood that an event will occur or that a proposition is true is determined by a field of mathematics known as probability theory. An event's probability is expressed as a number between 0 and 1, where 1 indicates certainty and roughly 0 indicates how likely it is that the event will occur. A probability is a numerical expression of the likelihood or potentiality of a given event. Probabilities can alternatively be stated as integers between 0 and 1, percentages between 0% and 100%, or as percentages between 0% and 100%. the fraction of times that all equally probable alternatives occur compared to all potential outcomes.
This issue has the parameters n=8 (the number of trials) and p=0.45 (the chance of success in each trial). It is a binomial distribution problem.
The likelihood that Y=3 is:
[tex]P(Y=3) = (8 choose 3) * 0.45^3 * (1-0.45)^(8-3) = 0.3113[/tex]
The probability that Y is at least 3 is:
[tex]P(Y > =3) = P(Y=3) + P(Y=4) + P(Y=5) + P(Y=6) + P(Y=7) + P(Y=8)[/tex]
[tex]P(Y > =3) = (8 choose 3) * 0.45^3 * (1-0.45)^(8-3) + (8 choose 4) * 0.45^4 * (1-0.45)^(8-4) + (8 choose 5) * 0.45^5 * (1-0.45)^(8-5) + (8 choose 6) * 0.45^6 * (1-0.45)^(8-6) + (8 choose 7) * 0.45^7 * (1-0.45)^(8-7) + (8 choose 8) * 0.45^8 * (1-0.45)^(8-8)[/tex]
P(Y>=3) = 0.5626 (rounded to four decimal places)
The probability that Y is at most 3 is:
[tex]P(Y < =3) = P(Y=0) + P(Y=1) + P(Y=2) + P(Y=3)\\P(Y < =3) = (8 choose 0) * 0.45^0 * (1-0.45)^(8-0) + (8 choose 1) * 0.45^1 * (1-0.45)^(8-1) + (8 choose 2) * 0.45^2 * (1-0.45)^(8-2) + (8 choose 3) * 0.45^3 * (1-0.45)^(8-3)[/tex]
P(Y<=3) = 0.3909 (rounded to four decimal places)
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Select the correct answer. Kathy distributes jelly beans among her friends. Alia gets 4^2 fewer jelly beans than Kelly, who gets 3^3 jelly beans. How many jelly beans does Alia get? A. 4^2 − 3^3 B. 3^3 + 4^2 C. 4 − 3^3 D. 3^3 − 4^2 E. 3^2 − 4^3
Out of the given options, the total quantity of jelly beans that Alia got is D. 3³ − 4²
Jelly beans received by Alia = 4²
Jelly beans received by Kelly = 3³
Quantity refers to the amount or number of something. In the given question, the quantity can be described by the total number of jelly beans received by both the girls.
Calculating the jelly beans Kelly gets -
= 3³ = 3 x 3 x 3
= 27 jelly beans.
Calculating the jelly beans Alia gets -
= 4² = 4 x 4
= 16
Thus, these are fewer beans than Kelly.
Calculating the number of jelly beans that Alia gets is:
= Total jelly beans with Kelly - Total jelly beans with Alia
= 27 - 16
= 11
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Please do this asap, last question on the packet!!
Answer: c
Step-by-step explanation:
Write the Equation
= 5.5x + 6.2y + 4.3x + 8.3z + 1.6z - 5.1y
Re-arrange them
= 5.5x + 4.3x + 6.2y - 5.1y + 8.3z + 1.6z
Add them
= 9.8x + 0.1y + 9.9z
Can someone help me, please!!!
The length of the base, x is b) 2.90.
Let's call the length of the hypotenuse "h" and the length of the base "x". We can use trigonometry to set up an equation relating these three lengths.
Since we know that the triangle is right-angled, we can use the trigonometric function "sine" to relate the angle between the perpendicular and the hypotenuse to the sides of the triangle:
sin(71) = 4/h
Multiplying both sides by h, we get:
h * sin(71) = 4
Next, we can use the Pythagorean theorem to relate the length of the hypotenuse to the length of the base:
[tex]h^{2}[/tex] = [tex]x^{2}[/tex] + [tex]4^{2}[/tex]
Substituting the first equation into the second equation, we get:
[tex](hsin(71))^{2}[/tex] = [tex]x^{2}[/tex] + [tex]4^{2}[/tex]
Simplifying and solving for x, we get:
x = [tex]\sqrt{(hsin(71))^{2}-4^{2} }[/tex]
Using a calculator, we can evaluate this expression and find that x is approximately equal to 2.90.
Therefore, the answer is (b) 2.90.
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what is m∠S?
I cant figure it out at all
The measure of the angle S of the cyclic quadrilateral QRST is 96 degrees.
We know that the sum of opposite angles of a cyclic quadrilateral is equal to 2 right angles that is 180 degrees.
Here QRST is a cyclic quadrilateral and angle Q and angle S are the opposite angles of this cyclic quadrilateral.
Given that angle Q = x + 51
angle S = x + 63
According to condition then the sum of the angle Q and angle S must be 180 degrees.
x + 51 + x + 63 = 180
2x + 114 = 180
2x = 180 - 114 = 66
x = 66/2 = 33
So the value of angle S = x + 63 = 33 + 63 = 96 degrees.
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Yames had $43. On his birthday, he received $25. Write and solve an equation to find how much money Yames has now. Show work
Step-by-step explanation:
43+25 which is the addition of the two numbers which is 68
Three functions are shown in the table. x f(x) g(x) h(x) 1 512 18 65 2 128 16 33 3 32 14 17 4 8 12 9 5 2 10 5 Part A: Which of the functions represents an exponential function? What is the common ratio of that function? Explain. Part B: What is the average rate of change for the function h(x) over the interval 2 ≤ x ≤ 4? Show your work or explain how you found your answer.
The solution is:
(a)f(x), Common Ratio = 1/4
(b) -12
Explanation:
Part A
From the functions on the table, the function that represents an exponential function is f(x).
The common ratio of f(x) is derived below:
512 × 1/4 = 128
128 × 1/4 = 32
32× 1/4 = 8
8 × 1/4 = 2
The common ratio is 1/4.
Part B
We want to find the average rate of change for the function h(x) over the interval 2 ≤ x ≤ 4.
From the table:
• When x=4, h(x)=9: h(4) = 9
• When x=2, h(x)=33: h(2) = 33
The average rate of change = 9 - 33 /2
= -12
The average rate of change for h(x) over the interval 2 ≤ x ≤ 4 is -12.
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Based on the table, which statement is true?
A. About 40% of the students prefer Chocolate.
B. About 30% of the students prefer Mint.
C. About 20% of the students prefer Orange.
D. About 50% of the students prefer Orange.
The Ratio of student that prefer mint was 30%
What is an equation?An equation is an expression that shows the relationship between numbers and variables using mathematical operators.
From the table:
Total number of students = 34 + 38 + 35 + 27 + 36 + 35 = 205 students
Students that prefer chocolate = 34 + 38 = 72 students
Ratio of student that prefer chocolate = 72/205 * 100% = 35%
Students that prefer mint = 35 + 27 = 62 students
Ratio of student that prefer mint = 62/205 * 100% = 30%
Students that prefer orange = 36+ 35 = 71 students
Ratio of student that prefer orange = 71/205 * 100% = 35%
The Ratio of student that prefer mint was 30%
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a) Work out the bearing of A from B.
b) Work out the bearing of B from A.
(Hint: bearings are written with three digits.)
N
A
293°
67°
113°
Z+
N
B
247°
Not drawn accurately
Answer:
247° and 067°
Step-by-step explanation:
the bearing of one point to another is the measure of the angle from the north point N at one point in a clockwise direction to the other point.
(a)
bearing of B from A = 247° ( from N at B clockwise to A )
(b)
bearing of B from A = 067° ( from N at A clockwise to B )
I'm stuck on a geometry problem where one angle is 43, the equation to find one is (3x), and the 3rd angle says (5x-5).
Answer:
Step-by-step explanation:
To solve for the angles, you can use the fact that the sum of the angles in a triangle is 180 degrees.
So, you can set up an equation:
43 + 3x + (5x-5) = 180
Simplifying, you get:
8x + 38 = 180
Subtracting 38 from both sides:
8x = 142
Dividing both sides by 8:
x = 17.75
Now that you know x, you can plug it into the expressions for the other two angles to find their measures:
First angle = 3x = 3(17.75) = 53.25
Third angle = 5x - 5 = 5(17.75) - 5 = 83.75
Therefore, the three angles are 43 degrees, 53.25 degrees, and 83.75 degrees.
If a 12-year-old boy is 1/3 as old as his father, how old will the father be when his son is 24?
If a boy having age as 12 years is "1/3" as old as his father, then his father will be 72 years when his son is 24.
We know that, the 12-year-old boy is 1/3 as old as his father,
So, we write an equation to express this relationship:
⇒ 12 = (1/3)F, where F = age of father.
On simplifying,
We get,
⇒ 36 = F,
So, the father's current-age is = 36 years old.
We have to find how the age of father when his son is 24.
So, 24 = (1/3)F,
On simplifying,
We get,
⇒ 72 = F
Therefore, father will be 72 years old when his son is 24.
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Jacque is using a soup can for a school project and wants to paint it. If the can is 11 cm tall and has a diameter of 9 cm, at least how many square centimeters of paint is needed? Approximate using π = 3.14.
374.45 cm2
139.50 cm2
699.44 cm2
438.03 cm2
The approximate amount of paint needed = 438.03 cm²
The correct answer is an option (D)
We know that the formula for the surface area of the cylinder is :
A = (2 × π × r × h) + (2 × π × r²)
Here, the diameter of the can is 9 sm
So, the radius of the can would be,
r = d/2
r = 9/2
r = 4.5 cm
And the height of the can is h = 11 cm
Since the can is cylindrical, we use above formula of surface area of the cylinder to find the amount of paint needed.
Using above formula,
A = (2 × π × r × h) + (2 × π × r²)
A = (2 × π × (4.5) × (11)) + (2 × π × (4.5)²)
A = 311.02 + 127.01
A = 438.03 cm²
Therefore, the correct answer is an option (D)
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Find the price of apples and pears in pence
The price of the apple and the pears at the shop in pence would be = 0.5 and 0.73 pence respectively.
How to calculate tye cost of both the apple and pears?Let's represent the apple as = X
Let's represent the pear as = y
That is ;
4x + 3 y = 4.10. ---> equation 1
5x +8y = 6.40 ----> equation 2
Make X the subject of formula in equation 1
4x = 4.1-3y
X = (4.1-3y)/4
substitute X = (4.1-3y)/4 into equation 2.
5[(4.1-3y)/4] + 8y = 6.40
20.5-15y+8y = 6.40×4
20.5 - 7y = 25.6
-7y = 5.1
y = 5.1/7
y = 0.73
Substitute y = 0.73 into equation 1;
4x + 3(0.73) = 4.10.
4x + 2.19 = 4.10
4x = 4.20-2.19
4x = 2.01
X = 2.01/4
X = 0.5
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