To prove that point d is equidistant from the jungle gym and monkey bars, we need to show that the distances from d to both points are equal.
Let's call the distance from d to the jungle gym "x" and the distance from d to the monkey bars "y". We need to show that x = y.
Since angle acd is a right angle, we can use the Pythagorean theorem to relate the distances:
ad^2 + cd^2 = ac^2
We know that ad = bd (since the jungle gym and monkey bars are the same distance from d), so we can write:
bd^2 + cd^2 = ac^2
We also know that c lies on ab, so we can write:
ac = ab - bc
Substituting this into our equation, we get:
bd^2 + cd^2 = ab^2 - 2abbc + bc^2
Since d is on cd, we can write cd = y, and since c is on ab, we can write ab = x + y. Substituting these into our equation, we get:
bd^2 + y^2 = (x + y)^2 - 2xy + x^2
Simplifying, we get:
bd^2 - x^2 = 2xy - y^2
Now, if we can show that bd = x, then we will have proven that y = x and therefore that point d is equidistant from the jungle gym and monkey bars.
To do this, we can use the fact that triangle adb is isosceles (since ad = bd). This means that angle adb is equal to angle bad. We also know that angle acd is a right angle. Therefore, angle adb + angle acd = 90 degrees.
Since angle adb = angle bad, we can write:
2 angle adb + angle acd = 180 degrees
Substituting in the values of our angles, we get:
2 angle adb + 90 degrees = 180 degrees
Solving for angle adb, we get:
angle adb = 45 degrees
Now, we can use the fact that triangle adb is isosceles to write:
angle bad = (180 - 45)/2 = 67.5 degrees
Finally, we can use the law of sines to relate bd and x:
bd/sin(67.5) = x/sin(45)
Simplifying, we get:
bd = x
Therefore, we have shown that point d is equidistant from the jungle gym and monkey bars.
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Help with these questions Pls?
Answer:12
Step-by-step explanation:30-6=24
24 divided by 2 =12
Find the length of CD.
E
2
D
A1 B
The length of CD is
5
C
unit(s).
The length of CD can be found to be 7. 21 units .
How to find CD ?The length of CD can be found by using the distance formula which is :
= √ [ ( x ₂ - x ₁ ) ² + ( y ₂ - y ₁ ) ² ]
Given the points, ( 3, - 2 ) and ( 7, - 8 ).
The length of CD is :
= √ [ ( 7 - 3 ) ² + ( - 8 - (- 2 ) ) ² ]
= 7. 21
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PLS HELP <33
Which of the numbers listed below are solutions to the equation? Check all
that apply.
|x = -25
A. 25
B. 0
C. 5
D. -5
E.-25
F. None of these
Answer:
There is no value of x that makes the equation be true since an absolute value can never be negative.
No solution
Step-by-step explanation:
Jason wants to dine at five different restaurants during a summer getaway. If three of nine available restaurants serve seafood, find the number of ways that at least one
of the selected restaurants will serve seafood given the following conditions.
(a) The order of selection is important.
(b) The order of selection is not important.
(a) If the order is important, then the number of ways that at least one of the selected restaurants will serve seafood is
answer
C(9, 5) - C(6, 5) + C(3, 1) = 126 - 6 + 3 = 123
explanation
The first term, C(9, 5), represents the number of ways to select 5 restaurants out of 9, regardless of type. The second term, C(6, 5), represents the number of ways to select 5 non-seafood restaurants out of 6. To find the number of ways that at least one of the selected restaurants will serve seafood, we subtract the number of ways to select 5 non-seafood restaurants and add the number of ways to select exactly 1 seafood restaurant, represented by C(3, 1).
The result, 123, represents the number of ways that at least one of the selected restaurants will serve seafood.
Final question no more lives
who ever gives me correct answer will get brainliest
The time take to fill the pool will be 494 hours.
How to calculate the TimeInlet pipe fills in 38 hours = 1 pool
Inlet pipe fills in 1 hours = 1/38
Drain pipe empty in 39 hours = 1 pool
Drain pipe empty in 1 hour = 1/39
If both pipes are opened together then in pool fills in 1 hour = 1/38 - 1/39
= 1/1482
Therefore, 1/1482 fills in 1 hour.
. Therefore, 1/3 will be:
= 1/3 × 1482
= 494 hours.
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70°
160
What is the size in degrees of the missing angle
Answer:
40°
Step-by-step explanation:
The sum of interior angles in a quadrilateral is 360°, from the picture we have a 90°, 160° and 70°.
so
take off from 360° the know angles and we will find the angle "?"
360 - 90 - 160 - 70 =
40° (your answer)
I need help on my homework! Answer number 15, please :)
15) Evaluating the mathematical expression -10 -144/(-12) shows that 144 is being divided by 12 before subtracting 10, following the application of PEMDAS.
16) The value of the algebraic expression is 2.
What is the evaluation of an expression?The evaluation of an expression is finding its value by substituting variables and applying the PEMDAS rule.
PEMDAS means the order of algebraic operations that applies parentheses, exponents, multiplication, division, addition, and subtraction.
-10 -144/(-12)
-10 + (144/12)
-10 + 12
= 2
Thus, we have evaluated the expression to have a value of 2.
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what is the perimeter of the following shapes
(a) 1.4 cm 0.7 cm 0.7 cm
The perimeter of each shape is obtained adding all of their outer side lengths.
How to obtain the perimeter of the polygon?The perimeter of a polygon is composed by the sum of the lengths of the outer edges of the figure.
Hence, for each polygon, you must identify the outer side lengths, and then add them.
Missing InformationThe problem is incomplete, hence the standard procedure to find the polygon of a shape was presented.
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Skylar has 12 pieces of candy left in her Halloween bag. There are 8 pieces of chocolate and 4 pieces of non-chocolate. She
chooses a piece of candy at random and then chooses another piece of candy, without replacement. Draw a tree diagram to
represent this situation and use it to calculate the probabilities that she picks:
Two pieces of non-chocolate
Chocolate only
At least one piece of chocolate
One piece of each type
The others operate in a similar manner. The following must be done, however, in order to determine the probability of anything NOT occurring, such as drawing a sweet that is NOT a kit-kat: 1 - P(kit-kat)
What is probability?Probability is the ability to happen. The subject of this area of mathematics is the occurrence of random events. The value is expressed as a number between 0 and 1.To forecast how likely occurrences are to occur, probability has been introduced in mathematics. The words "probable" and "probability," as well as its cognates in various modern languages, come from the medieval Latin word "probabilis," which Cicero borrowed and used to denote "plausible" or "commonly accepted" in expressing opinions.You only need to multiply the quantity of the selected candy by the total number of candies if you choose to put each piece of candy back after choosing it.
In this case, the desired confectionery is P(snickers). 12 in number.
In total, the bag contains 20 sweets.
P(snickers) = 12/20 = 3/5
The others function in the same way. The following must be done, however, in order to determine the likelihood of anything NOT occurring, such as drawing a sweet that is NOT a kit-kat:
1 - P(kit-kat)
The complete question is:
Suppose a bag of candy contains 12 Snickers, 5 Kit-Kats, and 3 Three Musketeers. Find each probability if you choose one piece of candy at random.
a) P(Snickers) b) P(Kit-Kat) c)P(Three Musketeers) d) P(not Kit-Kat)
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Enter the letter of the graphed function(image)
answer c)
cross x at x = -2, x = 3, and x = 1
the square root tells us that it bounces off that location rather than intercepting
help me, please!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The value of x in the proportion equals 50.
What is Proportion?Proportion is referred to as a part, share, or number considered in comparative relation to a whole. Proportion can be defined as when two ratios are equivalent, they are in proportion. It is an equation or statement used to show that two ratios or fractions are equal.
In proportion, if two sets of numbers are increasing or decreasing in the same ratio, then the ratios are said to be directly proportional to each other. Proportions are denoted using the symbol ":" or "=".
16/50 = x/156.25
x = 156.25 x 16 / 50
x = 2500 / 50
x = 50
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Faith needs 300 milliliters of a 57% acid solution for a chemistry experiment. She has two acid solutions, A and B, that can be mixed together to form the solution. Solution A is 50% acid, and Solution B is 60% acid. How much of each solution should she use to create the mixture?
She should use milliliters of Solution A.
She should use milliliters of Solution B.
The needed amount of each solution is given as follows:
90 milliliters of Solution B.210 milliliters of Solution B.How to obtain the amounts?The amounts are obtained using a system of equations, for which the variables are given as follows:
Variable x: amount of Solution A.Variable y: amount of Solution B.Faith needs 300 milliliters of the solution, hence:
x + y = 300.
x = 300 - y.
The percentage is of 57%, hence:
0.5x + 0.6y = 0.57 x 300
0.5x + 0.6y = 171.
Replacing the first equation into the second, the value of y is obtained as follows:
0.5(300 - y) + 0.6y = 171
0.1y = 21
y = 21/0.1
y = 210.
The value of x is then given as follows:
x = 300 - 210
x = 90.
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If Lisa works part-time, she will make 35% less than she does now.
How much will her monthly net income be?
What will their new total net income be?
Answer:
Lisa: $3302Family: $11372Step-by-step explanation:
Given a family net income of $13150, Lisa's current annual gross of $76200, deductions of 20% of Lisa's gross salary, you want to know Lisa's monthly net income and the new family net income if Lisa makes 35% less by working part-time.
Lisa's incomeLisa's current annual income is $76200, and her annual net income is 80% of that, or $60960. On a monthly basis, her net income is ...
$60960/12 = $5080 . . . . . . Lisa's current net monthly income
If her income is reduced by 35%, the reduction is ...
0.35 × $5080 = $1778
Then Lisa's part-time monthly net income will be ...
$5080 -1778 = $3302 . . . . . Lisa's part-time monthly net income
Family incomeThe family net income will be reduced by the same amount:
$13150 -1778 = $11372 . . . . . new family monthly net income
__
Additional comment
It appears the total of budgeted items is $10343, so those items can be paid even if Lisa works part-time. The family's current surplus income of $2807 would be reduced to $1029, about a 63% reduction. That gives a lot less cushion to pay for off-budget expenses that may come up.
A worker earned a 3% increase in her annual salary for each of 5 years. They plan to continue working in
their position for an additional n years. If they continue to earn a 3% increase in their annual salary, which
statement describes the expression that can be used to calculate the total percent increase in their annual
salary from the first year to the last year?
A. The expression 1.035 can be used because (1.035)" = 1.035.
OB. The expression 1.035 ca
can be used because 1.035 x 1.03 = 1.035.
O C. The expression 1.035+ can be used because 1.035 x 1.03 = 1.035+
O D. The expression 1.035+ can be used because 1.035 +1.03n = 1.035+n.
Using an exponential function, it is found that the expression that can be used to calculate the total percent increase in their annual salary from the first year to the last year is given by:
P= 100%[([tex]1.03^{t}[/tex]) - 1]
What is an exponential function?An exponent refers to the number of times a number is multiplied by itself. For example, 2 to the 3rd (written like this: 23) means: 2 x 2 x 2 = 8. 23 is not the same as 2 x 3 = 6. Remember that a number raised to the power of 1 is itself.
here, we have,
An increasing exponential function is modeled by:
A(t)= A(0)[tex](1+r)^{t}[/tex]
In which:
A(0) is the initial value.
r is the decay rate, as a decimal.
As a percentage, the increase is modeled by:
P= 100%[[tex](1+r)^{t}[/tex] - 1]
In this problem, the growth rate is of r = 0.03, hence:
P= 100%[ [tex](1+0.03)^{t}[/tex]- 1]
P= 100%[[tex](1.03)^{t}[/tex]- 1]
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A function is given.
f(x) = x3 − 7x2; x = 0, x = 10
(a) Determine the net change between the given values of the variable.
(b) Determine the average rate of change between the given values of the variable.
On solving the provided question, we can say that the function is
[tex]f(z) = 3 - 4z^2[/tex] and f(-2) = -13 and f(0) = 3.
what is function?The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.
the function is
[tex]f(z) = 3 - 4z^2[/tex]
[tex]f(-2) = 3 - 4(-2)^2[/tex]
= 3 - 4(4)
= 3 - 16
=-13
[tex]f(0) = 3 - 4(0)^2[/tex]
= 3 - 4(0)
= 3 - 0
= 3
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8) A certain rubber ball, when dropped from a height of 2 meters onto a
hard floor, bounces back up to 75% of the height from which it was
dropped.
What is the height of the ball after the 5th bounce?
The height of the ball after the 5th bounce is approximately 0.4746 meters or 47.46 centimeters.
What is called height?
Height, altitude, and elevation mean the vertical distance either between the top and bottom of something or between a base and something above it. height refers to something measured vertically whether high or low.
Each time the ball bounces, it reaches a height of 75% of its previous height.
Since the ball was dropped from a height of 2 meters, its height after the first bounce will be:
2 meters x 0.75 = 1.5 meters
After the second bounce, the height of the ball will be:
1.5 meters x 0.75 = 1.125 meters
After the third bounce, the height of the ball will be:
1.125 meters x 0.75 = 0.84375 meters
After the fourth bounce, the height of the ball will be:
0.84375 meters x 0.75 = 0.6328125 meters
After the fifth bounce, the height of the ball will be:
0.6328125 meters x 0.75 = 0.474609375 meters
Therefore, the height of the ball after the 5th bounce is approximately 0.4746 meters or 47.46 centimeters.
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Solve the system by graphing.
a)
y = x
y = 2x+2
By the given graph we can conclude that the solution of the equation (i.e point of intersection of lines) is (-2, -2).
Solving the system of equations:To solve the system of equations, graph the given two lines' first equation. Now determine whether the lines are parallel, intersect, or are the same line.
In the next step, we need to Identify the solution to the system.
If the lines are intersected, the point of intersection is the solution.
If the lines are parallel, the system will have no solution.
If the lines are the same or coincident, then the system will have an infinite number of solutions.
Here we have
y = x ----- (1)
y = 2x+2 ---- (2)
From (1) and (2)
=> y = 2y + 2
=> 2y - y = -2
=> y = - 2
Hence, the solution of the given system of the equation is (-2, -2)
We can check it by graphing the lines as shown figure.
Therefore,
By the given graph we can conclude that the solution of the equation (i.e point of intersection of lines) is (-2, -2).
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Find the values of x and y.
The value of x is 5, while the value of y is 24
How to solve for x and yIn order to get the value of x we would first have to find the value of y
The sum of angles on a straight line = 180
hence we would have:
5y + 2y + 12 = 180
7y = 180 - 12
7y = 168
y = 24 degrees
The angle that is made at R is 90 degrees
we would have
2y + 12 + 5x = 90
y = 24
2 * 24 + 12 + 5x = 90
60 + 5x = 90
5x = 90 - 60
5x = 30
x = 30 / 6
x = 5
Hence the value of x is 5
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Triangle XYZ is rotated 90° clockwise about the origin to form triangle x'Y'Z'.
Which statement is true?
The true statement is (d) The area of triangle XYZ is equal to the area of triangle X'Y′Z
How to determine the true statementFrom the question, we have the following parameters that can be used in our computation:
Triangle XYZ is rotated 90° clockwise about the origin to form triangle X'Y'Z'.
The rotation is a rigid transformation
This means that it does not change the side length and angles of a shape when applies
Using the above as a guide, we have the following:
The image and the preiamage have the same area
Hence, the true statement is (d)
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Complete question
Triangle XYZ is rotated 90° clockwise about the origin to form triangle X'Y′Z'.
y. z. y. x. x.
Which statement is true?
The sum of the angle measures of triangle XYZ is 90° less than the sum of the angle measures of triangle X'Y′Z'.
The angle measures of triangle XYZ are less than the corresponding angle measures of triangle X'Y′Z'.
Triangle XYZ is not congruent to triangle X'Y′Z'.
The area of triangle XYZ is equal to the area of triangle X'Y′Z
I will give brainliest and ratings if you get this correct
The first order derivative of the given function is f'(x) = [tex](1+\frac{1}{2(x+x^{\frac{1}{2} })}(1+\frac{1}{2x^{\frac{1}{2} }} )) \frac{1}{2(x+(x+x^{\frac{1}{2} })^{\frac{1}{2} })^{\frac{1}{2} }}[/tex].
What is the differentiation?The process of finding derivatives of a function is called differentiation in calculus. A derivative is the rate of change of a function with respect to another quantity.
The given function is [tex]f(x)=\sqrt{x+\sqrt{x+\sqrt{x} } }[/tex].
The derivative using the chain and power rules is
f'(x) = [tex](1+\frac{1}{2(x+x^{\frac{1}{2} })}(1+\frac{1}{2x^{\frac{1}{2} }} )) \frac{1}{2(x+(x+x^{\frac{1}{2} })^{\frac{1}{2} })^{\frac{1}{2} }}[/tex]
Therefore, the first order derivative is f'(x) = [tex](1+\frac{1}{2(x+x^{\frac{1}{2} })}(1+\frac{1}{2x^{\frac{1}{2} }} )) \frac{1}{2(x+(x+x^{\frac{1}{2} })^{\frac{1}{2} })^{\frac{1}{2} }}[/tex].
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here is a probability that a randomly selected 30-year-old male lives through the year. A life insurance company charges $154 for insuring that the male will live through the year. If the male does not survive the year, the policy pays out $ as a death benefit. Complete parts (a) through (c) below. Question content area bottom Part 1 a. From the perspective of the -year-old male, what are the monetary values corresponding to the two events of surviving the year and not surviving? The value corresponding to surviving the year is $ negative 195. The value corresponding to not surviving the year is $ 99,805. (Type integers or decimals. Do not round.) Part 2 b. If the -year-old male purchases the policy, what is his expected value? The expected value is $ enter your response here.
Answer: a. From the perspective of the 30-year-old male, the monetary value corresponding to surviving the year is -$154 (the cost of the insurance policy). The monetary value corresponding to not surviving the year is $99,805 (the death benefit payout).
b. If the 30-year-old male purchases the policy, his expected value can be calculated using the formula:
Expected Value = (Probability of Event A) * (Value of Event A) + (Probability of Event B) * (Value of Event B)
In this case, the probability of surviving the year and not surviving the year can be assumed to be the same, as we don't have any specific information on the individual's health or life expectancy. Therefore, the probabilities can be assumed to be 0.5 each.
Plugging in the values, we get:
Expected Value = (0.5) * (-$154) + (0.5) * ($99,805) = ($50,326)
So, the expected value for the 30-year-old male purchasing the policy is $50,326.
Step-by-step explanation:
A bank developed a model for predicting the average checking and savings account balance as balance= −17,732 + 367×age + 1,300×years education + 0.116×household wealth
The interpret the numbers in this model is -17,732 is a constant amount credited from the savings account, 367 is the amount saved per year of age, 1300 is the amount saved per year of education.
What is a linear equation?A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0. In mathematics, a linear equation is an equation that may be put in the form [tex]{\displaystyle a_{1}x_{1}+\ldots +a_{n}x_{n}+b=0, } where x_{1}, \ldots, x_{n} are the variables, and {\displaystyle b, a_{1}, \ldots, a_{n}}[/tex] are the coefficients, which are often real numbers.
Given that;
The equation of savings account balance as balance= −17,732 + 367×age + 1,300×years education + 0.116×household wealth.
Now,
-17,732 is a constant amount credited from the savings acount
367 is the amount saved per year of age
1300 is the amount saved per year of education
0.116 is the amount save per household wealth
Therefore, the following are the interpretations of the equation.
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please help me with math i’ll give you brainlist!!
Answer: A) Dashed line with shading below
Step-by-step explanation:
because, as you can see the < sign is only less than not 'less than and equal to' so it will be dashed...
Answer:
A
Step-by-step explanation:
A dashed line is used if < or > is used to indicate that the boundary is not part of the solution. Then shade the appropriate region.
As in the question, y is less than 4/3x + 2 therefore, the region below the line is shaded.
Write as a product.
(5c-3d)²-9d²
Answer:
the answer is 25c²
Step-by-step explanation:
(5c-3d)²-9d²
5²c²+3²d²-9d²
25c²+9d²-9d²
25c²
Answer:
= 25c² - 30cd
Step-by-step explanation:
(5c-3d)²-9d²
[tex](5c - 3d)(5c - 3d) - 9 {d}^{2} \\ 5c(5c - 3d) - 3d(5c - 3d) - 9{d}^{2} \ \\ 25 {c}^{2} - 15cd - 15cd + 9 {d}^{2} - 9 {d}^{2} \\25 {c}^{2} - 30cd[/tex]
Question is in the picture
The relations that represent functions are given as follows:
Table.The square of a number x plus one.y = x/2 + 5.Graph at the bottom.When does a relation represents a function?A relation represents a function when each input value is mapped to a single output value.
Hence the two items that are not functions in this problem are given as follows:
Graph -> second item -> vertically aligned points for x > 0, meaning that the values of x > 0 are mapped to two values of y.The set of ordered pairs, as the input of 4 is mapped to outputs of -2 and 2.More can be learned about relations and functions at brainly.com/question/10283950
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What is the amplitude of the function given? f(x) = -7cos(1x) + -3
On solving the provided question we can say that here, trigonometry, f(x) = -7cos(1x) + -3 => f(1) = -7
What exactly is trigonometry?Trigonometry is a branch of mathematics that studies the relationship between triangle side lengths and angles. From the use of geometry in astronomical study, the area first appeared in the Hellenistic era, around the third century BC. Exact methods is a branch of mathematics that deals with specific trigonometric functions and how they can be used in calculations. In trigonometry, there are six popular trigonometric functions. Their names and acronyms are sine, cosine, tangent, cotangent, secant, and cosecant (csc). Trigonometry is the study of the properties of triangles, particularly right triangles. However, the study of geometry is the characteristics of all geometric figures.
Trigonometry is used here.
f(x) = -7cos(1x) plus -3
f(1) = -7
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Suppose
−5x−15≤f(x)≤x2+3x+1
Use this to compute the following limit.
limx→−4f(x)
The limits lim x→ −4 f(x) is 5
The method is substitution method
How to determine the limitsFrom the question, we have the following parameters that can be used in our computation:
−5x − 15 ≤ f(x) ≤ x² + 3x + 1
The limits is given as
lim x→ −4 f(x)
By direct substitution, we have
−5(-4) − 15 ≤ f(x) ≤ (-4)² + 3(-4) + 1
Evaluate the exponents and the products
20 − 15 ≤ f(x) ≤ 16 - 12 + 1
Evaluate the difference
5 ≤ f(x) ≤ 5
This means that
f(x) = 5
So, we have
lim x→ −4 f(x) = 5
The method used is the direct substitution method
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The angle y° and 49° are complementary,find the value y
Answer:
41°
Step-by-step explanation:
We know that,
y°+49°= 90°
y° = 90°-49°
y=41°
So, the value of y is 41°
Find a positive angle less than 360° that is coterminal with the given angle
-1025°
The positive coterminal angle less than 360° is, 55°
What are coterminal angles ?Angles with the same initial and terminal sides but a multiple of 360° degree difference are known as coterminal angles (or a full rotation). In other words, you can create an angle that is coterminal with the original angle by taking it and adding or subtracting 360 degrees (or any multiple of 360 degrees).
To find a positive angle that is coterminal with -1025°,
we can add or subtract any multiple of 360° until we get an angle between 0° and 360°.
Adding 1080° (which is 3 revolutions of 360°) to -1,025° gives us:
= -1,025° + 1080°
= 55°
Since this angle is less than 360°,
Therefore, a positive angle less than 360° that is coterminal with -1025° is 55°.
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Solve it down guys :)
Refer to the attached images.
**Should be arctan(tanx)=x on the last page**
