Answer: the answer is two :)
Step-by-step explanation:
4x=5+3
4x=8
x= 8/4
x=2
π ≈ 3.14 and round your ansere to the nearest hundredth 7ft
Answer:
SE π ≈ 3.14 and round your answer to the nearest hundredth
Thus, for 3.14, the number in the hundredth place is 4. To round it, we will look at the third digit after the decimal, which is 0. We know any number lower than 5 is rounded down to zero, so we will round down and the rounded number will be 3.14. Conclusion: 3.14 rounded to the nearest hundredth is 3.14 itself.
Answer: 3.14
Step-by-step explanation: It’s not possible to round the answer so it would just be 3.14
When graphed, an exponential decay function shows that as x increases, f(x) approaches O; and. as x decreases. f(x) increases. True or false?
the statement that "as x decreases, f(x) increases" is not true for an exponential decay function.
Define exponentAn exponent, also known as a power or index, is a mathematical operation that indicates how many times a number (the base) is multiplied by itself.
When graphed, an exponential decay function shows that
as x increases
f(x) approaches 0
but as x decreases
f(x) also approaches 0.
The function decreases from left to right, meaning that as x increases, f(x) decreases towards 0. However, it does not increase as x decreases.
In general, an exponential decay function can be represented as f(x) = a ×e⁻ᵇˣ, where a and b are constants. As x gets larger and larger, the exponential term e⁻ᵇˣ approaches 0, which causes the overall function value f(x) to approach 0 as well. As x gets smaller and smaller, the exponential term e⁻ᵇˣ becomes larger, but the function value f(x) still approaches 0.
Therefore, the statement that "as x decreases, f(x) increases" is not true for an exponential decay function.
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if a particle moves along the curve y=x^(2/3), such that dx/dt=3 for all x, find: a.) dy/dt when x=-1 and c.) lim dy/dt as x goes to infinity
Answer:
Step-by-step explanation:
y=x23 so the dt is moved to perticlulate the dy
Every day Jin reads for 0.75
hours in the morning and 1.25
hours in the evening. He uses the expression 0.75d+1.25d
to keep track of the number of hours he has read for any number of days, d
. If Jin reads for 20
days, how many hours has he read?
Answer:
Step-by-step explanation:The number of hours Jin reads in 20 days is 39.8 hours.
The expression for the given situation is 0.75d + 1.24d.
What is an expression?
An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
In the given expression 0.75d + 1.24d, d is number of days.
Substitute d=20 in 0.75d + 1.24d, we get
0.75(20) + 1.24(20)
15+24.8
=39.8 hours
Hence, the number of hours Jin reads in 20 days is 39.8 hours
What is the meaning of "we number the vertices counterclockwise 0, 1, ..., n − 1, and number the axes of symmetry counterclockwise, 0, 1, ..., n − 1 "?
The statement "we number the vertices counterclockwise 0, 1, ..., n − 1, and number the axes of symmetry counterclockwise, 0, 1, ..., n − 1" is likely referring to a specific mathematical context, such as a polygon or a regular solid.
What is the meaning of "we number the vertices counterclockwise 0, 1, ..., n − 1?In this context, "numbering the vertices counterclockwise" means that the vertices (or corners) of the shape are given labels or numbers in a particular order, moving counterclockwise around the shape. For example, in a triangle, the vertices might be labeled as 0, 1, and 2, in counterclockwise order around the triangle.
Similarly, "numbering the axes of symmetry counterclockwise" means that the axes of symmetry (or lines of reflection) in the shape are also given labels or numbers in a particular order, moving counterclockwise around the shape. For example, in a regular pentagon, there are 5 axes of symmetry that can be labeled as 0, 1, 2, 3, and 4 in counterclockwise order around the pentagon.
By establishing this numbering convention, mathematicians and scientists can more easily communicate about the properties and characteristics of the shape or object, and can refer to specific vertices or axes of symmetry in a standardized way.
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PLEASE HURRY WILL GIVE BRAINLIEST AND 5 STARS!!!!!!
To add (or subtract) in Scientific Notation, you must have the same Response area. Then you can Response area the co-efficients and Response area the power of 10.
To multiply in Scientific Notation, you must multiply the Response area and Response area the powers of 10.
To divide in Scientific Notation, you must Response area the co-efficients and Response area the powers of 10.
According to the given information, divide in Scientific Notation, you must divide the co-efficients and subtract the powers of 10.
What is Scientific Notation?
Scientific notation, also known as standard form or exponential notation, is a way of expressing numbers that are either very large or very small, using powers of 10. In scientific notation, a number is expressed in the form:
a x 10ⁿ
where "a" is a number between 1 and 10 (usually a decimal), and "n" is an integer (positive or negative) that represents the power of 10 by which the number is multiplied.
To add (or subtract) in Scientific Notation, you must have the same power of 10. Then you can add (or subtract) the co-efficients and keep the power of 10.
To multiply in Scientific Notation, you must multiply the co-efficients and add the powers of 10.
To divide in Scientific Notation, you must divide the co-efficients and subtract the powers of 10.
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23 cats and 27 dogs were entered into a cat and dog show. What percentage of the entries were dogs?
Which best describes the relationship between the line that passes through the points (9, –5) and (5, –2) and the line that passes through the points (–4, –2) and (–8, 1)?
A. same line
B. parallel
C. neither perpendicular nor parallel
D. perpendicular
Answer:
B. Parallel
Step-by-step explanation:
Let S1 be the slope of the line passing through the points
(9, - 5) and (5, - 2).
S1 = (- 2 -(- 5))/(5 - 9)
= (- 2 + 5)/(- 4)
= 3/(- 4)
S1 = - 3/4
Let S2 be the slope of the line passing through the points
(- 4, - 2) and (- 8, 1).
S2 = (1 -(- 2))/(-8 -(- 4))
= (1 + 2)/(- 8 + 4)
= 3/(-4)
S2 = - 3/4
Since,
the slope of two lines are same.
They are parallel.
What are the roots of 2x2-6x+18=0
Answer:
What are the roots of 2x2-6x+18=0
Step-by-step explanation:
Scott has a flat screen TV with an area of A
square inches. The width of the TV is 36 inches. Which equation represents x the length of the TV in inches?
A. X = 36/A
B. X= A + 36
C. X = A - 2(36)
D. X= A/36
Explain here:
Answer:
D
Step-by-step explanation:
A=LW
A=L(36)
Divide by 36
L=A/36
(L=X)
:)
Find the resolved part of the vector p = (6i-3j+9k) in the direction of a = (2i+2j-k)
The calculated resolved part of vector p (6i-3j+9k) in the direction of a is 2i + 2j - k.
Calculating the resolved part of the vectorGiven that
p = (6i-3j+9k)
a = (2i+2j-k)
To find the resolved part of the vector p in the direction of a, we can use the following formula:
r = (p · a) / |a|
where · denotes the dot product and |a| denotes the magnitude of vector a.
First, we need to calculate the magnitude of vector a:
|a| = √(2² + 2² + (-1)²)
|a| = √(4 + 4 + 1)
|a| = √9
|a| = 3
Next, we need to calculate the dot product p · a:
p · a = (6i - 3j + 9k) · (2i + 2j - k)
= 12i + 12j - 6k - 6i - 6j + 3k
= 6i + 6j - 3k
Finally, we can calculate the resolved part of p in the direction of a:
r = (p · a) / |a|
= (6i + 6j - 3k) / 3
= 2i + 2j - k
Therefore, the resolved part of vector p in the direction of a is 2i + 2j - k.
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Four tomatoes cost $3.40. What is the uint raet? pleease help
Answer: $0.85 per tomato
Step-by-step explanation:
To find the unit rate, we need to determine the cost of one tomato. We can do this by dividing the total cost of the four tomatoes by the number of tomatoes:
$3.40 ÷ 4 = $0.85
Therefore, the cost of one tomato is $0.85. The unit rate can also be expressed as a fraction, which is:
$0.85 per tomato, or 85 cents per tomato
Answer:
The Unit rate is 0.85
Step-by-step explanation:
You divide it by 4
1) Find fraction numerator d y over denominator d x end fraction for y equals x squared ln open parentheses fraction numerator x over denominator x plus 3 end fraction close parentheses
Halle dy/dx para y = x^2In(x/x+3)
The result is, [tex]\dfrac{dy}{dx} = x \times ln\dfrac{x}{(x+3)} + 2x\times ln\dfrac{x}{(x+3)} - \dfrac{(3x^2)}{(x+3)^2}[/tex].
The derivative of a function is a measure of how much the function changes as its input (often time or space) changes. More specifically, the derivative is the instantaneous rate of change of the function at a particular point.
To find the derivative of y = x^2ln(x/(x+3)), we use the product rule and the chain rule.
y = x^2 * ln(x/(x+3))
[tex]y' = 2x \times ln\dfrac{x}{(x+3)} + x^2 \times \dfrac{d}{dx}ln\dfrac{x}{(x+3)}[/tex]
To find the derivative of ln(x/(x+3)), we use the quotient rule:
[tex]\dfrac{d}{dx} ln\dfrac{x}{(x+3)} = \dfrac{1}{\dfrac{x}{(x+3)}} \times \dfrac{d}{dx}\dfrac{x}{(x+3)} - \dfrac{1}{\dfrac{x+3}{x}} \times \dfrac{d}{dx}\dfrac{(x+3)}{x}[/tex]
= [(x+3)/(x^2)] - [x/(x+3)^2]
= (x^2 + 3x - x^2)/(x^2(x+3)^2)
= 3(x+1)/(x^2(x+3)^2)
Substituting this back into the original equation, we get:
y' = 2x * ln(x/(x+3)) + x^2 * [3(x+1)/(x^2(x+3)^2)]
= 2x * ln(x/(x+3)) + 3(x+1)/(x+3)^2
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Question 6 (4 marks available)
.
A group of students were given a spelling test.
The table shows their marks.
a) Work out the range of the marks.
b) How many students are in the group?
c) Work out the mean mark of the group.
Represent and Analyse C
Mark
6
7
8
9
10
Frequency
5
4
7
10
4
Answer:
A) Range = 2
B) 30 Students
C) 8 Marks
Step-by-step explanation:
A) Range = Biggest - Smallest
Frequency = How many students achieved that many marks
Range = 9-7 = 2
C) Mean = Times the Marks by the Frequencies, add them together, then divide by total frequency (No. of students)
6x5=30
7x4=28
8x7=56
9x10=90
10x4=40
30+28+56+90+40=244
Total Frequency = 30
244/30=8.13
Round to nearest mark = 8
Hope this helped
Find the vertex and the
�
x- and
�
y-intercepts of the equation
�
=
�
2
−
2
�
−
8
y=x
2
−2x−8
Then, use the points to graph the parabola.
a) What is the vertex of the parabola? Enter your answer as an ordered pair.
Vertex
Preview
b) Identify the
�
x-intercept(s) of the parabola. Enter your answers as ordered pairs. Use a comma to separate answers as needed. If there are none, enter
None
None.
�
x-intercept
Preview
c) Identify the
�
y-intercept of the parabola. Enter your answer as an ordered pair.
�
y-intercept
Preview
d) Use the points you found to graph the parabola.
The vertex of the parabola is at (1, -9). The x-intercepts are (-2, 0) and (4, 0), which are the points where the parabola crosses the x-axis. The y-intercept is (0, -8), which is the point where the parabola crosses the y-axis.
What is vertex ?
To find the vertex and the x- and y-intercepts of the equation y = x² - 2x - 8, we can start by completing the square to put the equation in vertex form:
y = x² - 2x - 8
y + 8 = x² - 2x
y + 8 + 1 = x² - 2x + 1
y + 9 = (x - 1)²
So, the vertex of the parabola is at (1, -9). The x-coordinate of the vertex is found by taking the opposite of the coefficient of x in the equation (which is -2) and dividing by two times the coefficient of x (which is 1), giving x = -(-2) / (2*1) = 1. The y-coordinate is found by substituting x = 1 into the equation.
What are the intercepts?
To find the x-intercepts, we set y = 0 and solve for x:
0 = x² - 2x - 8
0 = (x - 4)(x + 2)
So, the x-intercepts are at (-2, 0) and (4, 0).
To find the y-intercept, we set x = 0 and solve for y:
y = 0² - 2(0) - 8
y = -8
So, the y-intercept is at (0, -8).
To graph the parabola, we can use the vertex and intercepts we found.
The vertex is (1, -9), which is the lowest point on the parabola. The x-intercepts are (-2, 0) and (4, 0), which are the points where the parabola crosses the x-axis. The y-intercept is (0, -8), which is the point where the parabola crosses the y-axis.
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Anna borrowed N$20 000 at 5% for three and half years. She wants to pay N$8000 on maturity. To achieve
this, she is planning to pay 2000 in 10 months, 5000 in 16 months from now. How much should she pay in two
and half years from now to meet her obligation?
Anna should pay N$289,711.85 in two and a half years from now to meet her obligation.
What is interest rate?An interest rate is the rate at which a borrower pays to a lender for the use of borrowed money. It is expressed as a percentage of the principal amount borrowed and is typically calculated on an annual basis.
According to question:To solve this problem, we can use the formula for the future value of an annuity:
FV = [tex]P * [(1 + r)^n - 1]/r[/tex]
Where FV is the future value of the annuity, P is the periodic payment, r is the interest rate per period, and n is the total number of periods.
We know that Anna borrowed N$20,000 at 5% for three and a half years, which is equivalent to 42 months. The periodic payment, P, is the sum of N$2,000 and N$5,000, which is N$7,000.
First, we can calculate the future value of the annuity after 42 months:
FV = 7,000 * [(1 + 0.05/12)[tex]^42[/tex] - 1]/(0.05/12)
FV = 7,000 * 56.3743
FV = N$394,120.10
Since Anna wants to pay N$8,000 on maturity, she will need to pay N$386,120.10 at the end of the 42 months to meet her obligation.
Now we can calculate how much Anna should pay in two and a half years from now, which is equivalent to 30 months:
[tex]PV = FV / (1 + r)^n[/tex]
PV = 386,120.10 / (1 + 0.05/12)[tex]^30[/tex]
PV = N$289,711.85
Therefore, Anna should pay N$289,711.85 in two and a half years from now to meet her obligation.
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a) The temperature the day after Hurricane Katrina in August 2005 was 91°F. It then fell three degrees, rose 5 degrees and fell another 2°F. What was the final temperature?
Margo borrows $1300, agreeing to pay it back with 3% annual interest after 14 months. How much interest will she pay?
Round your answer to the nearest cent, if necessary.
Margo will pay approximately $45.50 in interest on the loan.
What is interest?
Borrowers must pay lenders simple interest as a fee in exchange for a loan.
First, we need to calculate the interest that Margo will pay on the loan.
Interest = Principal x Rate x Time
where:
Principal = $1300
Rate = 3% per year (or 0.03)
Time = 14/12 years (since there are 12 months in a year)
Plugging in the values, we get:
Interest = $1300 x 0.03 x (14/12)
Interest ≈ $45.50
Therefore, Margo will pay approximately $45.50 in interest on the loan.
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Which of the following relations is a function? A. (7, 1), (-2, 4), (4, 1), (7, 2) B. (4, 0), (-2, 3), (7, 1), (-2, 5) C. (4, 4), (-2, 2), (7, 1), (-7, 2) D. (4, 4), (-2, 6), (4, 3), (-7, 2)
C. (4, 4), (-2, 2), (7, 1), (-7, 2)
In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y.[1] The set X is called the domain of the function[2] and the set Y is called the codomain of the function
The equation A equals P quantity 1 plus 0.06 over 4 end quantity all raised to the power of 4 times t represents the amount of money earned on a compound interest savings account with an annual interest rate of 6% compounded quarterly. If after 15 years the amount in the account is $16,497.06, what is the value of the principal investment? Round the answer to the nearest hundredths place.
The value of the principal investment (rounded to the nearest hundredth) is $9,000.39.
What is interest rate?Interest rate refers to the percentage amount charged or paid on a loan or investment, usually expressed as an annual percentage rate (APR). It represents the cost of borrowing or the return earned on an investment.
According to question:The equation you provided represents the compound interest formula:
A = P[tex](1 + r/n)^(n*t)[/tex]
Given that the annual interest rate is 6% and is compounded quarterly (i.e., n = 4), and the amount in the account after 15 years is $16,497.06, These values can be plugged into the equation to find P.
A = $16,497.06
r = 0.06 (6% expressed as a decimal)
n = 4
t = 15
$16,497.06 = P[tex](1 + 0.06/4)^(4*15)[/tex]
Dividing both sides by [tex](1 + 0.06/4)^(4*15)[/tex] to isolate P, we get:
P = $16,497.06 / [tex](1 + 0.06/4)^(4*15)[/tex]
Plugging in the values and solving for P using a calculator, we get:
P ≈ $9,000.39
So, the value of the principal investment (rounded to the nearest hundredth) is $9,000.39.
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The circumference of a circle is 6.3mm.
Find the length of the diameter.
Give your answer rounded to 3 SF.
The diameter of the circle is equal to 2.00 mm rounded to 3 significant figures.
What is the diameter of a circleThe diameter of a circle is a straight line that passes through the center of the circle and whose endpoints are on the circumference of the circle. We can use the formula for the circumference of a circle to calculate for the diameter.
circumference of is derived using πD or 2πr, where D is the diameter, π is 22/7, and r the radius.
The given circle have 6.3 mm circumference, so;
6.3 mm = 22/7 × D
D = (6.3 mm × 7)22 {cross multiplication}
D = 44.1 mm/22
D = 2.0045
Therefore, the diameter of the circle is equal to 2.00 mm rounded to 3 significant figures.
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Write down all of the statements below that are correct.
7.2 cm³ > 720 mm³
0.087 m³ <8700 cm³
300 mm³ = 0.03 cm³
8 m³=8,000,000 cm³
The correct statements for inequality are:
0.087 m³ < 8700 cm³
8 m³ = 8,000,000 cm³
What is inequality?An inequality is a mathematical statement that compares two expressions or values and indicates that one is greater than, less than, or not equal to the other. Inequalities use symbols such as "<" (less than), ">" (greater than), "≤" (less than or equal to), "≥" (greater than or equal to), and "≠" (not equal to) to show the relationship between the two expressions.
Here,
The statement "300 mm³ = 0.03 cm³" is incorrect because 300 mm³ is equal to 0.3 cm³ (since 1 cm = 10 mm).
The statement "7.2 cm³ > 720 mm³" is incorrect because 1 cm³ is equal to 1000 mm³, so 7.2 cm³ is equal to 7200 mm³. Therefore, 7.2 cm³ is less than 720 mm³.
Note: When comparing volumes, it is important to make sure that the units are consistent (e.g. converting all volumes to the same unit of measurement) before making any comparisons.
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A number, c, rounded to 1 d.p. is 47.3
Another number, d, rounded to 1 d.p. is 4.6
What are the lower and upper bounds of c - d?
The lower bound of c - d is 42.66 and the upper bound of c - d is 42.7.
Calculating the lower and upper bounds of c - d?Given that
c, rounded to 1 d.p. is 47.3d, rounded to 1 d.p. is 4.6To find the upper and lower bounds of c - d, we first need to find the maximum and minimum possible values of c and d.
For c rounded to 1 decimal place, the actual value of c could be between 47.25 and 47.34.
This is because when we round to 1 decimal place, we take the first decimal place and round up or down depending on the second decimal place.
Similarly, we have
d = 4.59 to 4.64
So, we have
c - d = 47.25 - 4.59 to 47.34 - 4.64
Evaluate
c - d = 42.66 to 42.7
Therefore, the lower bound of c - d is 42.66 and the upper bound of c - d is 42.7.
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vEvaluate this table.
X 5 10 15 25 40
Y 1 2 3 5 8
The table represents a(n)
multiplicative
relationship
Answer:
y = 1/2 x
Step-by-step explanation:
y = mx + b
We need to find the m (slope) and the b (y-intercept)
The slope is the change in y over the change in x. Use to points on the line to find the slope.
(4,2) and (6,3)
[tex]\frac{3-2}{6-4}[/tex] = [tex]\frac{1}{2}[/tex]
The slope (m) is 1/2.
Use the slope and one of the points to calculate b
I will use the point (4,2)
y = mx + b
2 = 1/2(4) +b
2 = 2 +b Subtract 2 from both sides
0 = b
The y-intercept (b) is 0
y = _m + _
y = 1/2x + 0
y = 1/2 x
Helping in the name of Jesus.
What is the radian value for 2/3 pi?
Answer:120 degrees
Step-by-step explanation:
2pi = 360 degrees
pi = 180 degrees
2pi/3 = 120 degrees
the breaking strength of a rivet has a mean value of 9,950 psi and a standard deviation of 502 psi. (a) what is the probability that the sample mean breaking strength for a random sample of 40 rivets is between 9,850 and 10,150? (round your answer to four decimal places.) (b) if the sample size had been 15 rather than 40, could the probability requested in part (a) be calculated from the given information? explain your reasoning. - yes, the probability in part (a) can still be calculated from the given information.
- no, n should be greater than 30 in order to apply the central limit theorem. - no, n should be greater than 20 in order to apply the central limit theorem. - no, n should be greater than 50 in order to apply the central limit theorem.
a) The probability that the sample mean breaking strength for a random sample of 40 rivets is between 9,850 and 10,150 is equal to 0.8903.
b) No, because n should be greater than 30 in order to apply the central limit theorem. So, right choice for answer is option (b).
The normal distribution forms a bell shaped curve. The parameter of normal distribution is [tex]\mu[/tex] and [tex]\sigma ^2 [/tex]. It is a continuous distribution. Now, Mean value of breaking strength of a rivet = 9,950
Standard deviations = 502
Let's X be variable denotes breaking strength of a rivet.
a) Now, a random sample is choosen from X such that, Sample size, n = 40. By using central limit theorem, sample mean follows approximately normal distribution with mean 9950 and standard deviations = 502/√40 = 79.3732 that is [tex]\bar X \: \tilde \: \: N( 9950, ( 79.3732)²)[/tex]
[tex]P( 9,850 < \bar X < 10,150 ) = P( \bar X < 10,150) -
P( \bar X < 9,850) \\ [/tex]
= [tex] P(\frac{\bar X - \mu }{\sigma} < \frac{10,150 - 9950}{79.3732} )- P(\frac{\bar X - \mu }{\sigma} < \frac{10,150 - 9850}{79.3732}) \\ [/tex]
= P( Z < 2.52 ) - P( Z < -1.26)
= 0.9941 - 0.1038
= 0.8903
b) If sample size,n is 15 instead of 40, then the probability requested in part (a) will not be calculated from the provide information. Because, for applying central limit theorem we have sample size must be grater than 30. So, option(b) is correct.
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If a coordinate system is set up such that the positive x axis points in a direction 60° above the horizontal, what should be the angle between the x axis and the y axis?
What should be the direction of the positive y axis?
(measured from the horizontal)
The two axes should be perpendicular, so the angle betwen them is 90°, and the y-axis is 150° above the horizontal.
What should be the angle between the x axis and the y axis?If we have a coordinate axis, the two axis should be perpendicular between them, this means that the angle between the positive x-axis and the positive y-axis should always be 90°.
Now, what should be the direction of the positive y axis?
We know that the positive x-axis is 60° above the horizontal, and the angle between the two axes is 90°, then the positive y axis is at:
60° + 90° = 150°
The positive y-axis is at 150° above the horizontal line.
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In the xy-plane, a line crosses the y-axis at the point (0, 3) and passes through the point (4, 5). Which of the following is an equation of the line?
Answer:
y = 1/2 x + 3
Step-by-step explanation:
y = mx + b
You need to find the slope (m) and the y-intercept (b) to write the equation
The slope is the change in y over the change in x.
(0,3) (4,5) The y values are 5 and 3. The x values are 4 and 0. You find the change by subtracting.
[tex]\frac{5-3}{4-0}[/tex] = [tex]\frac{2}{4}[/tex] = [tex]\frac{1}{2}[/tex]
The slope (m) is 1/2.
The y-intercept is the point (0,b). They give us this with the point (0,3) The y-intercept (b) is 3
y = 1/2 x + 3
Helping in the name of Jesus.
Is there a composition of transformations that maps triangle ABC onto triangle XYZ.
Use the drop down options to accurately complete the sentences below about
transformations involving these two triangles.
Triangle ABC can be mapped onto triangle XYZ by a composition of transformations represented by (x,y) → (x+3,y-6) and followed by a dilation with center (0,0) and scale factor 1/3 represented by (x,y) → (x/3,y/3).
Describe Dilation?Dilation is a geometric transformation that involves changing the size of an object while maintaining its shape and proportions. In dilation, every point of the original figure is expanded or contracted away from a fixed point called the center of dilation.
The ratio of the distance between the center of dilation and each point of the original figure is the same for all corresponding points in the dilated figure. This ratio is called the scale factor, and it determines the degree of dilation.
If the scale factor is greater than 1, the figure is enlarged or dilated, while if the scale factor is less than 1, the figure is reduced or contracted. If the scale factor is negative, the figure is reflected across the center of dilation before being dilated.
Triangle ABC can be mapped onto triangle XYZ by a composition of transformations represented by (x,y) → (x+3,y-6) and followed by a dilation with center (0,0) and scale factor 1/3 represented by (x,y) → (x/3,y/3).
Triangle ABC is similar to Triangle XYZ.
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establish the identity
The identity is cos²∅+sin²∅= 1.
What is trignometric ratios?
This is the boundary or contour length of a 2D geometric shape.
Depending on their size, multiple shapes may have the same circumference. For example, imagine a triangle made up of wires of length L.
The same wire can be used to create a square if all sides are the same length.
The length covered by the perimeter of the shape is called the perimeter. Therefore, the units of circumference are the same as the units of length.
As we can say, the surroundings are one-dimensinal. As a result, you can measure in meters, kilometers, millimeters, etc.
Inches, feet, yards, and miles are other globally recognized units of circumference measurement.
According to our question-
cos(90∘−θ)=sinθ
sin(90∘−θ)=cosθ
cos²∅+sin²∅= 1.
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