Answer: The transformed function is y = -0.4√(x - 2).
Step-by-step explanation:
From the given equation, we can identify the following transformations:
Reflected over the x-axis: The negative sign in front of the function (-0.4) indicates a reflection over the x-axis.
Translated 2 units left: The "-2" inside the square root indicates a translation of 2 units to the right.
Compressed by a factor of 0.4: The coefficient "0.4" in front of the square root indicates a vertical compression by a factor of 0.4.
Translated 2 units down: There is no direct indication of a vertical translation in the equation, so this transformation is not applicable.
Therefore, the correct descriptions of the graph of the transformed function compared with the parent function are:
Reflected over the x-axis
Translated 2 units right
Compressed by a factor of 0.4
Explanantion needed with this problem confused on dropping dowen 4 to 8 on the x value
The function value for f(g(4)) include the following: f(g(4)) = 6.
What is a function?In Mathematics and Geometry, a function is a mathematical equation which defines and represents the relationship that exists between two or more variables such as an ordered pair in tables or relations.
By critically observing the table of values of the function f and g shown in the image attached above, we can reasonably infer and logically deduce the following function values:
g(4) = 1
f(g(4)) = f(1)
f(1) = 6.
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A certain retailer increases wholesale prices by 54%. If this retailer offers a 25% discount off the ticket price, what percent profit will the retailer realize?
The realized profit is the amount of money remaining after paying off the wholesale prices. In this case, it should be expressed as a percent of the wholesale price.
The following questions are to help you better understand the final solution. Let's assume the wholesale price for our item is $600.
(1) What is the ticket price (the price including the mark-up)?
$
(2) How much will you save (what is the discount removed from the ticket price)?
$
(3) How much do you have to pay for the item?
$
(4) How much profit does the retailer make (in $)?
$
(5) What is the percent profit?
%
The percent profit will be 15.5%.The formula used to calculate the percentage profit is:Percentage Profit = (Profit / Cost Price) x 100%.
Let's assume that the retailer has an item with a wholesale price of $100. After a 54% increase in the wholesale price, the new wholesale price is $154.Now, when the retailer provides a 25% discount off the ticket price, the new price of the item becomes: $154 x 75% = $115.5.
The cost of producing the item is $100, but the retailer sells it for $115.5. Hence, the profit made by the retailer is:$115.5 - $100 = $15.5 or 15.5% profit.The percent profit that the retailer will realize is 15.5%. Therefore, the percent profit will be 15.5%.The formula used to calculate the percentage profit is:Percentage Profit = (Profit / Cost Price) x 100%.
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Given A matrix with 2 rows and 2 columns where row 1 is 4 and 4 and row 2 is 2 and 1., what is A–1? A matrix with 2 rows and 2 columns, where row 1 is negative 0.25 and 1 and row 2 is 0.5 and negative 1. A matrix with 2 rows and 2 columns where row 1 is negative 1 and negative 1 and row two is negative 0.5 and negative 0.25. A matrix with 2 rows and 2 columns where row 1 is 0.25 and negative 1 and row 2 is negative 0.5 and 1. A matrix with 2 rows and 2 columns where row 1 is 1 and negative 2 and row 2 is negative 4 and 4.
The matrix[tex]A^(-1) is a matrix with 2 rows and 2 columns, where row 1 is -0.25 and 1, and row 2 is 0.5 and -1.[/tex]
To find the inverse of a matrix, we can use the formula:[tex]A^(-1) = (1/det(A)) * adj(A)[/tex]
Where A^(-1) represents the inverse of matrix A, det(A) is the determinant of A, and adj(A) denotes the adjugate of A.
Given the matrix A with 2 rows and 2 columns:
A = | 4 4 |
| 2 1 |
To find A^(-1), we need to calculate the determinant of A and the adjugate of A.
The determinant of A (det(A)) is calculated as:
det(A) = 4 * 1 - 2 * 4 = -4
The adjugate of A (adj(A)) is obtained by swapping the diagonal elements and changing the sign of the off-diagonal elements:
adj(A) = | 1 -4 |
| -2 4 |
Finally, we can find A^(-1) using the formula mentioned earlier:[tex]A^(-1) = (1/det(A)) * adj(A)A^(-1) = (1/-4) * | 1 -4 |[/tex]
| -2 4 |
Simplifying the expression:
A^(-1) = | -0.25 1 |
| 0.5 -1 |
Therefore, the matrix A^(-1) is a matrix with 2 rows and 2 columns, where row 1 is -0.25 and 1, and row 2 is 0.5 and -1.
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Jori has 7 boxes of books, with each box holding the same number of books. He has 126 books in all. How many books are there per box?
Answer: There will be a total of 18 books per box.
Step-by-step explanation:
Here,
Total number of boxes = 7
Total number of books = 126
Let n be the total number of books per boxes.
Now,
n = 126 / 7 = 18
Therefore, the total number of books per boxes is 18.
If the sum of the zeroes of the polynomial 5x2-px+7 is 9, the find the value of 'p'.
Find the slope-Intercept form of the equation of the line that passes through (-2,-1) and is perpendicular to y + 15 = (x + 10).
The slope-intercept form of the equation of the line that passes through (-2, -1) and is perpendicular to y + 15 = x + 10 is y = -x - 3.
To find the slope-intercept form of the equation of a line that is perpendicular to a given line, we need to determine the slope of the given line and then find the negative reciprocal of that slope.
The given line equation is y + 15 = x + 10. To rewrite it in slope-intercept form (y = mx + b), we isolate y:
y = x + 10 - 15
y = x - 5.
From this equation, we can see that the slope of the given line is 1.
To find the slope of the line perpendicular to this, we take the negative reciprocal of 1, which is -1.
Now that we have the slope (-1) and a point (-2, -1) that the line passes through, we can use the point-slope form of a line to find the equation.
The point-slope form of a line is given by: y - y1 = m(x - x1), where (x1, y1) is a point on the line.
Plugging in the values (-2, -1) and -1 for x1, y1, and m respectively, we get:
y - (-1) = -1(x - (-2))
y + 1 = -1(x + 2)
y + 1 = -x - 2.
To rewrite this equation in slope-intercept form (y = mx + b), we isolate y:
y = -x - 2 - 1
y = -x - 3.
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f(x)=-9x+9 and g(x)=√x+1
Answer:
-5
Step-by-step explanation:
Select all that apply. Which of the following is included in the table for each unit? A brief quiz A list of all questions from the lessons Description of what you need to know or apply Concepts tested Reference column
The options that apply are:
A. A list of all questions from the lessons
B. Description of what you need to know or apply
C. Concepts tested
D. Reference column.
The options that are typically included in a table for each unit are:
- A list of all questions from the lessons: This helps in organizing and categorizing the questions based on the specific unit or topic.
- Description of what you need to know or apply: This provides an overview or summary of the key concepts, knowledge, or skills that are covered in the unit.
- Concepts tested: This section highlights the specific concepts or skills that will be tested or assessed in relation to the unit. It helps students understand the focus areas and what they need to prioritize in their learning.
- Reference column: This column may include additional information such as page numbers, section titles, or references to specific resources or materials that are relevant to the unit. It serves as a guide for further exploration or reference.
A brief quiz, on the other hand, is not typically included in a table for each unit. Quizzes are usually separate assessments that are administered to evaluate understanding and mastery of the unit's content.
So, the options that apply are:
- A list of all questions from the lessons
- Description of what you need to know or apply
- Concepts tested
- Reference column
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A project has a net present value of Rs. "6172" when discount rate is 9%. What will be the Net present value if discount rate is increased by 12%?
The discount rate is increased by 12%, the new net present value will be approximately Rs. 5514.29.
To determine the net present value (NPV) when the discount rate is increased by 12%, we need to recalculate the NPV using the new discount rate.
Given:
Current NPV = Rs. 6172
Current discount rate = 9%
Increase in discount rate = 12%
To find the new NPV, we can use the formula:
New NPV = Current NPV / (1 + Increase in discount rate)
Calculating the new NPV:
New NPV = 6172 / (1 + 0.12)
New NPV = 6172 / 1.12
New NPV ≈ Rs. 5514.29
Therefore, if the discount rate is increased by 12%, the new net present value will be approximately Rs. 5514.29.
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Calculate the surface area of a triangular prism 10.8cm long and having a triangle bar face of dimensions 8.8cm by 5.7cm by 6.8cm
Answer:
268.8
Step-by-step explanation:
Let the sides of the base triangle be:
a = 8.8 cm
b = 5.7 cm
c = 6.8 cm
Let h be the length
h = 10.8 cm
The surface area is given by:
[tex]SA = (a + b + c)*l + 2\sqrt{ s(s - a)(s - b)(s - c)}[/tex]
Where
[tex]s = \frac{a + b + c}{2} \\\\= \frac{8.8 + 5.7 + 6.8}{2} \\\\=\frac{21.3}{2} \\\\= 10.65[/tex]
[tex]SA = (a + b + c)*l + 2\sqrt{ s(s - a)(s - b)(s - c)}\\\\= (8.8 + 5.7 + 6.8)*10.8 + 2\sqrt{ 10.65(10.65 - 8.8)(10.65 - 5.7)(10.65 - 6.8)}\\\\= 21.3*10.8 +2\sqrt{ 10.65(10.65 - 8.8)(10.65 - 5.7)(10.65 - 6.8)}\\\\=230.04 + 2\sqrt{ 10.65(1.85)(4.95)(3.85)}\\\\=230.04 + 2\sqrt{ 375.48}\\\\= 230.04 + 2*19.38\\\\=230.04 +38.76\\\\=268.8[/tex]
The midpoint of segment AB is M(-2,2). If A is located at (-5,7) find the coordinates of the endpoint B
Answer:
B (1, -3)
Step-by-step explanation:
Step 1: Use the midpoint formula to find the coordinates of the endpoint:
Normally, we find the midpoint of a segment using the midpoint formula, which is given by:
M = (x1 + x2) / 2, (y1 + y2) / 2, where
M is the midpoint,(x1, y1) are one endpoint on the segment,and (x2, y2) are the other endpoint of the segment.Since we're solving for the coordinates of an endpoint, we can allow (-5, 7) to be our (x1, y1) point and plug in (-2, 2) for M to find (x2, y2), the coordinates of the endpoint B:
x-coordinate of B:
x-coordinate of midpoint = (x1 + x2) / 2
(-2 = (-5 + x2) / 2) * 2
(-4 = -5 + x2) + 5
1 = x2
Thus, the x-coordinate of the endpoint B is 1.
y-coordinate of B:
y-coordinate of midpoint = (y1 + y2) / 2
(2 = (7 + x2) / 2) * 2
(4 = 7 + x2) -7
-3 = y2
Thus, the y-coordinate of the endpoint B is -3.
Thus, the coordinates of the endpoint B are (1, -3).
the dice was thrown 35 times and following numbers were obtained prepare frequency table51423266142545361526254132141626333
This table shows the frequency of each number obtained after throwing the die 35 times
How to prepare frequency tableTo prepare a frequency table based on the numbers obtained from throwing a die 35 times, we can list the numbers from 1 to 6 and count the frequency of each number.
Numbers: 1, 2, 3, 4, 5, 6
Frequency: 5, 14, 6, 4, 5, 1
Based on the given numbers, the frequency table would look like this:
Number | Frequency
1 5
2 14
3 6
4 4
5 5
6 1
This table shows the frequency of each number obtained after throwing the die 35 times.
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Given the equation, y=2x+6, what is its slope? Select one: a. 6 b. 3 c. 1 d. 2
Answer:
D. 2
Step-by-step explanation:
y=mx+b
m is the slope in this case, and by your equation, we can easily see that the answer should be D, with a slope of 2.
Answer:
d.2
Step-by-step explanation:
y=mx+b
m=slope
b=y-intercept
y=2x+6
m=2
b=6
slope=2
Find the area of the triangle.
3 9
A
5
B
?] units²
The area of the triangle is 47.91 units²
How to find the area of the triangle?When all three sides of the triangle are known we can use Heron's formula. Consider the triangle ABC with sides a, b, and c has shown in the image.
Heron’s formula is:
Area =√s(s−a)(s−b)(s−c)
where,
a, b, c are the side length of the triangle
s is the semi-perimeter. s = (a+b+c)/2
In this case:
Using the knowledge of the radius of a circle. We can say:
a = BC = 3 + 9 = 12 units
b = AC = 5 + 3 = 8 units
c = AB = 5 + 9 = 14 units
s = (a+b+c)/2
s = (12+8+14)/2
s = 34/2
s = 17 units
Area = √s(s−a)(s−b)(s−c)
Area = √17(17−12)(17−8)(17−14)
Area = √17(5)(9)(3)
Area = √2295
Area = 47.91 units²
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Find the value of an investment of $10,000 for 13 years at an annual interest rate of 3.15% compounded continuously.
Answer:
Step-by-step explanation:
To find the value of an investment compounded continuously, we can use the formula:
A = P * e^(rt)
Where:
A is the final amount
P is the principal amount (initial investment)
e is the mathematical constant approximately equal to 2.71828
r is the annual interest rate (as a decimal)
t is the time period in years
In this case, P = $10,000, r = 0.0315 (3.15% expressed as a decimal), and t = 13.
Plugging in the values into the formula, we get:
A = $10,000 * e^(0.0315 * 13)
Calculating the exponential part:
A = $10,000 * e^(0.4095)
Using a calculator or a math software, we can evaluate e^(0.4095) to get approximately 1.506.
A = $10,000 * 1.506
A ≈ $15,060.
Noa was walking in the forest and measured the circumference of two trees that he found. The first tree measured 37 and StartFraction 5 over 8 EndFraction inches around, and the second tree measured 45 and one-third inches around. Noa wanted to find the difference of the circumferences of the two trees. He recorded his steps in the table.
Steps
Noa’s work
Step 1
45 and one-third minus 37 and StartFraction 5 over 8 EndFraction
Step 2
45 and StartFraction 8 over 24 EndFraction minus 37 and StartFraction 15 over 24 EndFraction
Step 3
44 and StartFraction 32 over 24 EndFraction minus 37 and StartFraction 15 over 24 EndFraction
Step 4
44 and StartFraction 32 over 24 EndFraction minus 37 and StartFraction 15 over 24 EndFraction = 8 and StartFraction 17 over 24 EndFraction
In which step did Noa first make an error?
Step 1
Step 2
Step 3
Step 4
Answer:step 4
Step-by-step explanation: I just took the test pookies
10.) Find the surface area of this cone shaped megaphone. Use 3.14 for
pi. (Assume it is a solid)
2.25 ft slant hight
1.2 ft diameter
Image in the solid 6 in by 6 in
Options for answers are
5.3 ft
5.4 ft
53 ft
54ft
Answer:
5.4 ft²
Step-by-step explanation:
To find the surface area of the cone-shaped megaphone, use the surface area of a cone formula.
[tex]\boxed{\begin{minipage}{7cm}\underline{Surface area of a cone}\\\\$S.A.=\pi r^2+\pi rl$\\\\where:\\\phantom{ww}$\bullet$ $r$ is the radius of the circular base.\\ \phantom{ww}$\bullet$ $l$ is the slant height of the cone.\\\end{minipage}}[/tex]
The radius of a circle is half its diameter.
Therefore, if the diameter of the cone's circular base is 1.2 ft, then its radius is r = 0.6 ft.
Given values:
r = 0.6 ftl = 2.25 ftπ ≈ 3.14Substitute the values into the formula and solve:
[tex]\begin{aligned}\textsf{Surface area}&=3.14 \cdot0.6^2+3.14 \cdot 0.6 \cdot 2.25\\&=3.14 \cdot 0.36+3.14 \cdot 0.6 \cdot 2.25\\&=1.1304+1.884 \cdot 2.25\\&=1.1304+4.239\\&=5.3694\\&=5.4\; \sf ft^2\;(nearest\;tenth)\end{aligned}[/tex]
Therefore, the surface area of the cone-shaped megaphone is 5.4 ft² (rounded to the nearest tenth).
Please help!!!! I literally don’t know what I’m doing
Answer:
5 + m^3 n^2
----------------------
m^2 n^2
Step-by-step explanation:
To add fractions, we need to get a common denominator:
The common denominator is m^2 n^2.
Multiply the second term by m^2n/ m^2n
m/n * m^2n / m^2 n = m^3n / m^2n^2
Now we can add the two terms
5 m^3 n^2
------ + ---------------------------
m^2 n^2 m^2 n^2
5 + m^3 n^2
----------------------
m^2 n^2
The most obese countries in the world have obesity rates that range from 11.4% to 74.6%. This data is summarized in the following table.
Percent of Population Obese Number of Countries
11.4–20.45 29
20.45–29.45 12
29.45–38.45 4
38.45–47.45 0
47.45–56.45 3
56.45–65.45 2
65.45–74.45 1
74.45–83.45 1
(a) What is the best estimate of the average obesity percentage for these countries? (Round your answer to two decimal places.)
(b) The United States has an average obesity rate of 33.9%. Is this rate above average or below? (Round your answers to two decimal places.)
Since the average for the United Sates is 33.9%, compared to the average obesity rate of
%, the United States has an obesity rate
% higher than average.
(c) How does the United States compare to other countries? (Assume that the United States is included in the data. Assume the other countries in the range 29.45–38.45 have higher obesity than the United States.)
The United States has an obesity rate higher than about 81% of the other countries listed.
The United States has an obesity rate equal to about 81% of the other countries listed.
The United States has an obesity rate lower than about 50% of the other countries listed.
The United States has an obesity rate higher than about 19% of the other countries listed.
Consider the shape of a circle inside a square: 1.3.1 Calculate the area of the circle. eserved r = 5 cm
The area of the circle with a radius of 5 cm is approximately 78.53975 square centimeters.
To calculate the area of a circle, we need to use the formula A = πr², where A represents the area and r represents the radius of the circle. In this case, the given radius is 5 cm.
Plugging the value of the radius into the formula, we get:
A = π(5 cm)²
Simplifying the equation further, we have:
A = π(25 cm²)
Using the value of π (pi) as approximately 3.14159, we can calculate the area:
A ≈ 3.14159 × 25 cm²
A ≈ 78.53975 cm²
It's important to note that the area of a circle is always expressed in square units, as it represents the amount of space enclosed by the circle.
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The distance between two cities on a map is 25 inches. The actual distance between the two cities is 300 miles. How many miles would 35 inches be on the map?
Answer:
Step-by-step explanation:
Sure, I can help you with that.
The scale of the map is 300 miles / 25 inches = 12 miles / inch.
Therefore, 35 inches on the map would be 35 * 12 = 420 miles.
Here's the calculation:
Code snippet
scale = actual distance / distance on map
12 miles / inch = 300 miles / 25 inches
35 inches * 12 miles / inch = 420 miles
Use code with caution. Learn more
I hope this helps! Let me know if you have other questions.
If f (x) = 4x^3+ 1 then what is the remainder when f (x) is divided by x - 5?
Answer:
[tex]\frac{6}{x-5}[/tex]
Step-by-step explanation:
Helping in the name of Jesus.
Evaluate each expression below
if a = 32 and b = 150
1) 2a - 100
2) b (-12)
3) 4a + b
4) 9b - 2a
1) 2a - 100
Substituting the value of a here,
[tex] \rm 2(32) - 100 [/tex]
[tex] \rm 64 - 100 [/tex]
[tex] \rm -36 [/tex]
2) b (-12)
Substituting the value of b here,
[tex] \rm 150 (-12) [/tex]
[tex] \rm -1800 [/tex]
3) 4a + b
Substituting the values of a and b here,
[tex] \rm 4(32) + 150 [/tex]
[tex] \rm 128 + 150 [/tex]
[tex] \rm 278 [/tex]
4) 9b - 2a
Substituting the values of a and b here,
[tex] \rm 9(150) - 2 (32) [/tex]
[tex] \rm 1350 - 64 [/tex]
[tex] \rm 1286 [/tex]
The answers are:
below in [tex]\bold{bold}[/tex]
Work/explanation:
Plug in 32 for a
[tex]\sf{2(32)-100}[/tex]
[tex]\sf{64-100}[/tex]
[tex]\bf{-36}[/tex]
____________
[tex]\sf{b(-12)}[/tex]
[tex]\sf{150\cdot(-12)}[/tex]
[tex]\bf{1,800}[/tex]
____________
[tex]\sf{4a+b}[/tex]
[tex]\sf{4(32)+150}[/tex]
[tex]\sf{128+150}[/tex]
[tex]\bf{278}[/tex]
____________
[tex]\sf{9b-2a}[/tex]
[tex]\sf{9(150)-2(32)}[/tex]
[tex]\sf{1,350-64}[/tex]
[tex]\bf{1,286}[/tex]
____________
Please help! it would be great thank you
Answer:
a. The cost at 3% is $46.57 b. The cost at 4% is $49.33 c. The cost at 5% is $52.21
Step-by-step explanation:
Enter the number that belongs in the green box
Using the Law of Cosines with angle 103° and adjacent sides 9 and 6, the remaining side is approximately 12.26 units long.
To find the remaining sides of the triangle, we can use the Law of Cosines. Let's assume that the angle of 103 degrees is opposite side c, and the adjacent sides are a = 9 and b = 6.
The Law of Cosines states:
[tex]c^2 = a^2 + b^2[/tex] - 2ab * cos(C)
Plugging in the known values:
[tex]c^2 = 9^2 + 6^2[/tex] - 2 * 9 * 6 * cos(103°)
Simplifying the equation:
[tex]c^2[/tex] = 81 + 36 - 108 * cos(103°)
Now we need to evaluate cos(103°).
Using a scientific calculator or trigonometric table, we find that cos(103°) ≈ -0.3090.
Substituting the value of cos(103°) back into the equation:
[tex]c^2[/tex] = 81 + 36 - 108 * (-0.3090)
Simplifying further:
[tex]c^2[/tex] = 117 + 33.2724
[tex]c^2[/tex]≈ 150.2724
Taking the square root of both sides:
c ≈ √150.2724
c ≈ 12.26
Therefore, the remaining side (opposite the angle of 103 degrees) is approximately 12.26 units long.
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Which of the following are geometric sequences? Select all correct answers.
Answer:
A, B, E
Step-by-step explanation:
Notice that A, B, and E all maintain their common ratios, while C and D do not.
Use the following table of index numbers based on the price of a pound of coffee. The index numbers use 2012 as the
base year. If you spent $4.48 for a pound of coffee in 2015, what would the price have been in 2009?
Year
Coffee index
2005
75.3
2012 2013 2014 2015
2006 2007 2008 2009 2010 2011
77.6 81.4 87.1 89.8 93.4 96.2 100.0 103.0 107.1 114.6
***
The price of coffee in 2009 would have been approximately $5.15.
How to determine the price of coffee in 2009To find the price of coffee in 2009, we need to use the index number for that year. According to the table, the index number for 2009 is 103.0.
We can set up a proportion to solve for the price in 2009:
Price in 2015 / Index in 2015 = Price in 2009 / Index in 2009
Let's denote the price in 2009 as x:
$4.48 / 89.8 = x / 103.0
Now we can solve for x:
x = ($4.48 / 89.8) * 103.0
x ≈ $5.15
Therefore, the price of coffee in 2009 would have been approximately $5.15.
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6 out of 11 players played well on the baseball team. What percent is it?.
40.45%
45.45%
51.45%
54.55%
Answer:
Ok, Here is your answer
Step-by-step explanation:
To find the percentage of players who played well on the baseball team, we need to divide the number of players who played well by the total number of players and then multiply by 100.
Number of players who played well = 6
Total number of players = 11
Percentage of players who played well = (6/11) x 100%
= 54.55%
Therefore, the answer is 54.55%. Hence, option D, 54.55%, is the correct answer.
MARK ME AAS BRAINLIESTEliminate the parameter in the equations x = t^1/3 and y = t – 4. How can the rectangular equation be described?
This is the rectangular equation described by the parameter equation x = t1/3 and y = t – 4.
Elimination of the parameter means to rewrite the equations in terms of only x and y. To do this, substitute t from one equation into the other equation. Here, the two equations are:x = t1/3 and y = t – 4Substitute t from the first equation into the second equation:y = (x^3) – 4Now the equation is in terms of x and y only.
This is the rectangular equation described by the parameter equation x = t1/3 and y = t – 4.The rectangular equation, y = (x^3) – 4 can be plotted on a graph. It is a cubic equation. The graph will look like a curve that passes through the point (0, -4) and continues to move towards infinity. The graph will be symmetric to the origin because the equation involves an odd power of x.
If the equation involved an even power of x, the graph would be symmetric to the y-axis. The graph will never touch the x-axis or y-axis, it will only approach them.In conclusion, the rectangular equation y = (x^3) – 4 is derived from the two parameter equations, x = t1/3 and y = t – 4. The graph of this equation is a cubic curve that is symmetric to the origin. The curve passes through (0, -4) and approaches the x and y-axes but never touches them.
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− 5 � − 6 � = −5x−6y= − 32 −32 4 � − 6 � = 4x−6y= 4
Answer:
Step-by-step explanation:
x-6y=4
To solve these equations, we can use the elimination method. We want to eliminate one of the variables, either x or y, by multiplying one of the equations by a constant so that the coefficients of one variable will be the same in both equations but with opposite signs. For example, we can multiply the first equation by 4 to get:
-20x - 24y = -128
Then we can add this equation to the second equation to eliminate y:
-20x - 24y + 4x - 6y = -128 + 4
Simplifying this equation gives:
-16x - 30y = -124
Now we can isolate one variable in terms of the other:
-16x - 30y = -124
-16x = 30y - 124
x = (30/(-16))y + (-124/(-16))
x = (-15/8)y + 31/2
We can substitute this expression for x into either of the original equations to solve for y. For example, substituting into the first equation gives:
-5((-15/8)y + 31/2) - 6y = -32
Multiplying by -8 to clear the fractions gives:
75y - 248 - 48y = 256
Simplifying and solving for y gives:
27y = 504
y = 18.67
Then we can substitute this value of y back into our expression for x to find:
x = (-15/8)(18.67) + 31/2
x = -12.25
Therefore, the solution to the system of equations is:
x = -12.25
y = 18.67
