Sine of a right-angled triangle is 1 i.e., sin 90°=1
One of the three fundamental functions in trigonometry, along with cosine and tan functions, is the sine function. The ratio of the opposite side of a right triangle to its hypotenuse is known as the sine x or sine theta.
Let the base of the triangle be ‘x’ and the perpendicular be ‘y’ and θ be the angle
Sine acts as the ratio of the lengths of the opposing side and the hypotenuse side for any right-angled triangle measured from any angle.
sin θ =y/1
When the angle measurement hits the positive y-axis, it will have reached 90°, starting with the first quadrant. Since it now contacts the circle's rim, the value of y changes to 1. Consequently, y's value is changed to 1.
sin θ =y/1=1/1
Therefore, sin 90°=1/1
or, sin 90°=1
Hence, proved.
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what is 2 and 2/13 of 52
Answer:
the answer 112
Step-by-step explanation:
hope this helps
If Ellen is X years old.in thirteen years she will be twenty-four years old why’s the answer to that
How much is a domestic letter stamp?.
The First Class Mail (1 oz.) letter rate for postage purchased at the Post Office will increase two cents to $0.60 from $0.58.
Domestic shipping refers to shipping a package via a carrier within a country's borders.
Now, According to the question:
Media Mail rates will increase by 9%. Rates will start at $3.49 (previously $3.19).NEW: Priority Mail will now include $100 of insurance for free (previously $50 of insurance was provided for free).NEW: Cubic pricing is being introduced for Parcel Select Ground.Parcel Select Ground will see a rate decrease of 12.1% for Commercial Base (online postage) in 2022, with rates starting at $7.22 (previously $7.01).The “Metered Mail” rate for First Class Mail (1 oz.) letters which includes online postage and postage meters, will increase 4 cents to $0.57 from $0.53.
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How to determine if a differential equation is linear?
It is linear if and only if the coefficients of y (the dependent variable) and all order derivatives of y are functions of t or constant terms.
What is equation?An equation is a formula in mathematics that expresses the equality of two expressions by connecting them with the equals sign =. In its most basic form, an equation is a mathematical statement that shows that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical equation that depicts the relationship between two expressions on opposite sides of the sign. It mostly consists of one variable and one equal to symbol. 2x - 4 = 2 is an example.
Here,
It is linear if and only if all order derivatives of y (the dependent variable) are functions of t or constant terms.
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For each rhombus, find each angle measure or segment length.
Answer:34xt25
Step-by-step explanation:
Geometry
A jar contains 5 red balls and 3 white balls. A ball is selected and its color is noted, then the ball is replaced. A second ball is selected and its color is noted. Find the probability of each of the following.
a. What is the probability of selecting 2 red balls?
b. What is the probability of selecting 1 red ball and then 1 white ball?
Answer:awnsers below
Step-by-step explanation:
a. The probability of selecting 2 red balls is (5/8) * (5/8) = 25/64. This is because the probability of selecting a red ball on the first draw is 5/8, and the probability of selecting a red ball on the second draw is also 5/8, since the ball is replaced after each draw.
b. The probability of selecting 1 red ball and then 1 white ball is (5/8) * (3/8) = 15/64. This is because the probability of selecting a red ball on the first draw is 5/8, and the probability of selecting a white ball on the second draw is 3/8, since the ball is replaced after each draw.
Answer:
Step-by-step explanation:
a)
P(Red)=5/8
(5/8)^2=25/64
b)
P(Red)=5/8 P(White)=3/8
5/8*3/8=15/64
What is a 1 in 3 angle?.
1 in 3 angle of slope in degree is 18.435°.
In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.
An angle is a shape created by two rays that share a terminus and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located.
The inverse tangent function is called arctangent, often known as arctan or tan-1. Tangent only has a limited domain for its inverse function.
So to find the 1 in 3 angle we have to put the value 1/3 in arctan function
∴ arctan (1/3) = 18.43494882° ≈ 18.435.
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Which value of x is the solution to this equation 5x^2 -3x+45
This means that the solution to the equation x is 6.
What is equation?An equation is a mathematical statement that expresses the relationship between two values. It typically consists of an equal sign (=) and two expressions that are related to each other. Equations are used to describe how one value depends on another, or how two values are related to each other.
To solve this equation, use the Quadratic Formula,
which states that for an equation of the form ax2 + bx + c = 0,
the solution is x = [-b ± √(b2 - 4ac)] / 2a.
Plugging in the given equation,
we have a = 5, b = -3, and c = 45.
This means that the solution to the equation is x = [-(-3) ± √((-3)2 - 4*5*45)] / 2*5, or x = 6.
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What is the product of 7x 6 2?.
The product of (7x - 6)² is 49x² - 84x + 36.
Equation is (7x - 6)²,
⇒ We will solve the given problem using the algebraic identity
(a - b)² = a² + b² - 2ab
Here a = 7x and b = 6
⇒ (7x - 6)² = (7x)² + 6² - 2(7x)(6)
⇒ (7x - 6)² = 49x² + 36 - 84x
⇒ 49x² - 84x + 36
The equation for a linear equation in one variable is written as ax+b = 0, where a and b are two integers, and x is a variable. This equation has only one solution. For instance, the linear equation 2x+3=8 only has one variable.
A product is the outcome of multiplication in mathematics, or an expression that specifies the factors (numbers or variables) to be multiplied.
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Plssss help!!!! I need to finish this and it is really difficult:
The result of addition and subtraction is
5 (2/3) - 1 (1/4) = 58 (5/12) + 31 (1/6) = 393 (1/4) + 3 (3/5) = 79 (1/10) - 6 (7/10) = 27 (5/8) + 2 (1/7) = 1020 (9/11) - 18 (3/10) = 310 (3/7) + 22 (2/9) = 321 (5/6) + 5 (1/6) = 7113 (1/13) + 86 (9/11) = 20065 (17/20) + 19 (3/25) = 8571 (41/50) + 25 (5/24) = 9712 (13/15) + 18 (2/5) = 31The directions to solve these problems are to round each fraction to the nearest whole number and then add or subtract. We have to round each fraction into the nearest whole number.
If the fraction is more than 1/2 we round it up to 1.If the fraction is less than 1/2 we round it down to 0.1. 5 (2/3) - 1 (1/4) = (5 + 1) - 1 = 6 - 1 = 5
2/3 = 4/62. 8 (5/12) + 31 (1/6) = 8 + 31 = 39
5/123. 3 (1/4) + 3 (3/5) = 3 + (3 + 1) = 3 + 4 = 7
1/44. 9 (1/10) - 6 (7/10) = 9 - (6 + 1) = 9 - 7 = 2
1/105. 7 (5/8) + 2 (1/7) = (7 + 1) + 2 = 8 + 2 = 10
5/86. 20 (9/11) - 18 (3/10) = (20 + 1) - 18 = 21 - 18 = 3
9/11 = 18/227. 10 (3/7) + 22 (2/9) = 10 + 22 = 32
3/7 = 6/148. 1 (5/6) + 5 (1/6) = (1 + 1) + 5 = 2 + 5 = 7
5/69. 113 (1/13) + 86 (9/11) = 113 + (86 + 1) = 113 + 87 = 200
1/13 = 2/2610. 65 (17/20) + 19 (3/25) = (65 + 1) + 19 = 66 + 19 = 85
17/2011. 71 (41/50) + 25 (5/24) = (71 + 1) + 25 = 72 + 25 = 97
41/5012. 12 (13/15) + 18 (2/5) = (12 + 1) + 18 = 13 + 18 = 31
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An artist makes pottery. The artist earns the same amount for each piece of pottery sold
but must pay a fee to rent a booth at a local fair. After analyzing data from recent sales,
the artist finds the equation y=42x-200 models the profit, y, earned for selling x
pieces of pottery after the expense of renting the booth. Which statement is true?
a)
The slope of the equation is -200, and it represents the $200 the artist earns, on
average, for every piece of pottery sold.
b)
The slope of the equation is -200, and it represents the cost of renting the
booth.
c) The slope of the equation is 42, and it represents the $42 the artist earns, on
average, for every piece of pottery sold.
d) The slope of the equation is 42, and it represents the cost of renting the booth.
The slope of the equation is 42, and it represents the $42 the artist earns, on is true after analyzing data from recent sales.
What is sales?Sales in mathematics is the process of exchanging goods or services for money. It is a vital part of the economy and involves the transfer of ownership from the seller to the buyer. In mathematical terms, sales can be expressed as a function where the input is the amount of money paid for goods or services and the output is the goods or services received. Sales can also be expressed as an equation in which the variables are the cost of goods or services, the number of goods or services sold, and the total sale amount.
The slope of the equation is 42, and it represents the $42 the artist earns, on average, for every piece of pottery sold.
The constant -200 represents the cost of renting the booth.
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what does x^2 + 12 -35 equal
Answer:
x^2-23
Step-by-step explanation:
Is linear equations in two variables easy class 10?.
Linear equations in two variables can be relatively easy to understand and work with, as they represent straight lines in the xy-plane. The slope-intercept form of a linear equation, y = mx + b, is a simple way to represent a line with a specific slope and y-intercept.
Graphing linear equations is also straightforward, as you can find the x-intercept and y-intercept and plot the line using these points.
However, solving linear equations in two variables can become more challenging when the equations involve multiple terms or are presented in a different form. Also, understanding the concept of slope, y-intercept, and how to graph the line can be challenging for some students.
Overall, linear equations in two variables can be considered as a fundamental concept in algebra and mathematics and it requires practice to gain mastery over it.
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Kim went to the store and bought 4 items: $32.45, $46.78, $12.91, and $52.38. How much did Kim spend if the sales tax is 8%?
To find out how much Kim spent in total with the 8% sales tax included, we first need to add up the cost of all 4 items: $32.45 + $46.78 + $12.91 + $52.38 = $144.52
Next, we'll multiply that total cost by the sales tax rate as a decimal (8% expressed as 0.08) to find out how much tax Kim had to pay: $144.52 x 0.08 = $11.56
Finally, we'll add the total cost of the items and the tax to find out how much Kim spent in total: $144.52 + $11.56 = $156.08
What is the value of x in the triangle?
For each graph, determine the y-intercept using the slope formula. Write the y-intercept in coordinate form.
y = 8/3x + 100 exists the equation of the line in slope-intercept form.
What is meant by Slope of Line?The increase divided by the run, or the ratio of the rise to the run, is known as the line's slope. In the coordinate plane, it describes the slope of the line.
A line's slope and y intercept are represented in the slope intercept form as y = mx + b.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) contains
m = y₂-y₁/x₂-x₁
At two of the points the line passes through in the accompanying graph.
Let the two points be (0, 100) and (42, 148)
Let the equation be m = y₂-y₁/x₂-x₁
substitute the values in the above equation, we get
Slope = 148-100/42
= 48/42 = 8/3
To find y intercept, we get
100 = 8/3(0) + b
b = 100
So slope intercept form exists y = 8/3x + 100
Therefore, y = 8/3x + 100 exists the equation of the line in slope-intercept form.
The complete question is:
Examine the linear graph. Determine the y-intercept and write the y-intercept in coordinate form. Then write the equation of the line in slope-intercept form.
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help pls mathematics
Therefore , the solution of the given problem of inequality comes out to be 13 and 17 is the number of hikers.
What does inequality really mean?In mathematics, an inequality is a linear connection or a collection of numbers even when there is no equal sign. Equity always comes after equilibrium. When two numbers are not equal, inequality exists. Between equality and inequality, there exist differences. The most common symbol was chosen because when parameters aren't the same or comparable (). Values can be compared using a variety of disparities, no matter how few or numerous they are.
Here,
Given :
a) The minimum number of hikers
who walks between 8 miles and 19 miles :
=> 8 < x < 19
=> 7 +6
=> 13
b) The maximum number of hikers
who walks between 8 miles and 19 miles :
=> 8 < x < 19
=> 7+6+4
=> 17
Therefore , the solution of the given problem of inequality comes out to be 13 and 17 is the number of hikers.
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The American with Diabilitie Act tate that ramp mut have an angle le than or equal to 4. 8 degree. Remember, a 4. 8 degree angle in a right American with Diabilitie Act requirement
The designs that meet the condition have leg lengths that are in the ratio of 1: 12.
Two ramps that meet the Americans Disabilities Act are;
A ramp has leg lengths of 3 feet by 36 feet.A ramp with leg lengths of 5 inches by 60 inches.The needed measure of the angle of a ramp according to the Americans with Disability Act is θ ≤ 4.8°.
The ratio of the legs of a right triangle having a 4.8° angle is 1: 12Given, the ratio of the leg lengths is 1: 12, we have;
Expressed as a fraction, we have;
The required ratio of leg lengths = [tex]\frac{1}{12}[/tex]
Probable leg lengths are seen by multiplying the numerator and denominator of the above fraction by a constant as follows;
Possible leg length for the ramp = [tex]\frac{1 * 3}{12 * 3} = \frac{3}{36}[/tex]
That gives a ramp with having leg length of 3 feet and 36 feet.A second possible combination of leg length for the ramp = [tex]\frac{1 * 5}{12 * 5} = \frac{5}{60}[/tex]
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The complete question is:
The Americans with Disabilities Act states that ramps must have an angle less than or equal to 4.8 degrees. Remember, a 4.8-degree angle in a right triangle has a 1: 12 ratio for the legs. Design 2 ramps that meet the Americans with Disabilities Act requirements.
How do you find the opposite side of a triangle?.
Multiply the hypotenuse of triangle by sinθ to determine the length of the side opposite the angle (θ). Alternatively, to obtain the side next to the angle, multiply the hypotenuse by cos(θ).
Scalene triangles are typically described as triangles with no two sides that are equal. Isosceles triangles are those triangles whose two sides are equal. An equilateral triangle is one with equal lengths on each of its three sides. Clearly, all equilateral triangles are isosceles, but not the opposite.
The side across from the right angle is always the hypotenuse of a right triangle. The opposite and neighboring sides are the other two sides.
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What is 7 8 equivalent to in fractions?.
Equivalent 7/8 is equals to 56/64 in fractions.
In mathematics, equivalent fractions are those with the same denominator but different numerators. For instance, since they both equal 1, 2/4 and 3/6 are comparable fractions. An element of the whole is a fraction. To represent identical components of the total, equivalent fractions are utilized.
The numerator and denominator of each fraction can be multiplied by the same integer to determine the equivalent fraction. Equivalent fractions are those that, despite visible differences, signify the same value. For instance, if you take a piece of cake, divide it into two equal pieces, and then eat one of them, you will have consumed half of the cake.
= 7/8 is equivalent to:
= 7/8 * 8/8
= 56/64
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Correct Question:
What is 7/8 equivalent to in fractions?.
Alyson deposits $500 in the bank for 12 years. The bank offers her a 4% interest rate compounded monthly. How much money will be in her account at the end
of the 12 years? (Remember to round your answer to the nearest cent.)
A-$ type your answer.....
Answer:$917.58.
Step-by-step explanation:
The formula for compound interest is A = P(1 + r/n)^(nt) where A is the final amount, P is the principal (initial deposit), r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.
In this case, the initial deposit is $500, the annual interest rate is 4%, the number of times compounded per year is 12 (monthly), and the number of years is 12.
So, we can plug in the values into the formula:
A = $500(1 + 0.04/12)^(12*12) = $500(1.003333333)^(144) = $500(1.835170816) = $917.585
The final amount in her account after 12 years is $917.58
To round to the nearest cent, we can use the following method:
If the digit in the thousandths place is less than 5, we keep the hundredths digit as is.
If the digit in the thousandths place is greater than 5, we round up the hundredths digit.
In this case the digit in the thousandths is 5 so, we have to round up the hundredths digit of $917.58.
So, the final amount in her account after 12 years is $917.59.
Answer: $800.516
Step-by-step explanation:
We use the equation
A = P(1 + )^nt
P = principal
r = rate of interest
t = times
Now let's solve
P = $500
r = 4% = 0.04
t = 12 years
A = $500(1 +[tex]\frac{0.04}{12}[/tex] ) ^12 = $800.516
find the solution set x^2 -8x+ 7=0
Step-by-step explanation:
x²-8x+7=0
x²-7x-x+7=0
x(x-7) -1(x-7)=0
(x-7) (x-1)=0
Either, x-7=0 i.e x=7
or, x-1=0 i.e x=1
Is 999 a cube number?.
=> 999 is not a perfect cube.
Because cube root of 999 is 3 [tex]\sqrt[3]{37}[/tex] .
Now, According to the question:
A cube number is the result when a number has been multiplied by itself twice. The symbol for cubed is 3. For example, 8 is a cube number because it's 2 x 2 x 2 (2 multiplied by itself twice); this is also written as [tex]2^3[/tex] (“two cubed”).
It is the real solution of the equation [tex]x^3[/tex] = 999.
The cube root of 999 is expressed as [tex]\sqrt[3]{999}[/tex] or 3 [tex]\sqrt[3]{37}[/tex] in the radical form and as[tex](999)^\frac{1}{3}[/tex] or [tex](999)^0^.^3^3[/tex] in the exponent form.
The prime factorization of 999 is 3 × 3 × 3 × 37, hence, the cube root of 999 in its lowest radical form is expressed as 3 [tex]\sqrt[3]{37}[/tex].
Cube root of 999: 9.996665555Cube root of 999 in Exponential Form: [tex](999)^\frac{1}{3}[/tex]Cube root of 999 in Radical Form: [tex]\sqrt[3]{999}[/tex] or 3 [tex]\sqrt[3]{37}[/tex] .Learn more about Cube Number at:
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A family ha two car. During one particular week, the firt car conumed 30 gallon of ga and the econd conumed 40 gallon of ga. The two car drove a combined total of 1850 mile, and the um of their fuel efficiencie wa 55 mile per gallon. What were the fuel efficiencie of each of the car that week?
The fuel efficiency of the first car was 40.72 miles per gallon and the fuel efficiency of the second car was 14.28 miles per gallon.
The problem can be solved by using a system of equations.
We can call the fuel efficiency of the first car x and the fuel efficiency of the second car y.
From the problem, we know:
x + y = 55 (the combined fuel efficiency of the two cars is 55 miles per gallon)
We can also use the information about the amount of gas consumed and the distance has driven to set up another equation:
(30 gallons) * (x miles per gallon) + (40 gallons) * (y miles per gallon) = 1850 miles
Now we have a system of two equations with two variables (x and y):
x + y = 55
(30)x + (40)y = 1850
We can solve this system of equations using any method of solving such as substitution or elimination.
x = 55 - y
and substitute it in the second equation
(30)(55-y) + (40)y = 1850
1650 - 30y + 40y = 1850
-14y = -200
y = 14.28
x = 55 - 14.28 = 40.72
So the fuel efficiency of the first car was 40.72 miles per gallon and the fuel efficiency of the second car was 14.28 miles per gallon.
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What are the two types of indirect proof in geometry?.
There are two methods of indirect proof:
Proof of the contrapositive and proof by contradiction.
Now, According to the question:
Let's know:
An indirect proof, also called a proof by contradiction, is a roundabout way of proving that a theory is true. When we use the indirect proof method, we assume the opposite of our theory to be true. In other words, we assume our theory is false.
Hence, There are two methods of indirect proof:
Proof of the contrapositive and proof by contradiction.
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Solve this equation for the given domain.
cos(2x + 45°) = 0.8 for 0° ≤ x ≤ 180°
The solution to the equation cos(2x + 45°) = 0.8 in the domain of 0° to 180° is x = 15° and X=139° or X=176 °
How to find the solution?Because Cos (±37° +360k) = 0.8
0≤2X ≤ 360°
0+45°=2x+45° 360°+45° 45°≤ 2x+45°< 405°
50 2x+45° = 360°-37° or 2x+45° = 360° + 37°
{list the equation} 397° -45°=2X = 323-45°
2X = 323-45°. 2x=397° -45°
2x= 278°. 2x= 352°
X = 139°. X=176°
So , x = 139° or x = 176°
To discover the solution set of an equation with a particular domain, first insert each domain value into the equation to obtain the associated range values. Make ordered pairs out of these values and put them down as a set. That set is your solution!
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Dennis and Gail Schultz are looking over the repayment schedule for their $5,500 loan for lake house remodeling at 15% interest for 42 months with a monthly payment of $168.85. They note that the balance after payment 18 is $3,493.39, after 24 is $2,718.43, and after 30 is $1,883.50. How much would they save by paying off the loan earlv at payment (a) 19, (b) 25, or (c) 31?
Answer:
c)31
Step-by-step explanation:
The goal of this exercise is to determine the total savings by paying the debt early at
�
)
a)
19
19th payments
�
)
b)
25
25th payments and
�
)
c)
31
31st payments.
make x the subject of the formula 13x=6y
The formula which represents the solution of the given equations; 13x = 6y for variable, x is; x = 6y / 13.
What is the solution of the given equation for x?It follows from the task content that the solution of the given equation for variable, x is to be determined.
Since the given equation is; 13x = 6y.
It follows that the equation can be solved as follows;
13x = 6y
Divide both sides of the equation by 13 so that we have;
x = 6y / 13.
Ultimately, the formula for x is; x = 6y / 13.
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what is the following product? Assume x>0 3root x^2 times 4 root x ^3
The product is 3x * 4x^(3/2) = 12x^(5/2)
How to do the product of root?
When multiplying two terms with the same base and different exponents, you can add their exponents.
For example, √(a^m) * √(a^n) = √(a^m * a^n) = √(a^(m+n)) = a^((m+n)/2)
The product of 3√(x^2) * 4√(x^3) is equal to:
12x^(5/2)
This is because when you multiply two terms with the same base, you can add their exponents:
3√(x^2) * 4√(x^3) = (3*4)√(x^(2+3/2)) = 12x^(5/2)
This is because
√(x^2) = x^(2/2) = x
√(x^3) = x^(3/2) = x^(3/2)
so we can write 3root x^2 = 3x and 4root x^3 = 4x^(3/2)
Hence, the product is 3x * 4x^(3/2) = 12x^(5/2)
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Divide 1 hour in the ratio 1:5
Answer: ratio of 1: 10mins
ratio of 5: 50mins
Step-by-step explanation:
The ratio of 1:
[tex]\frac{1}{6}[/tex] x 60 (hours should be converted to minutes therefore it is 60 mins and
the denominator seen here is taken by adding the two values in the
given ratio and since we're still finding 1 you should divide 1 by the
added denominator and the same applies when finding the ratio 5)
Answer= 10mins
The ratio of 5:
[tex]\frac{5}{6}[/tex] x 60 (refer to the underlined explanation above)
answer= 50mins
so if you want to verify you add the two values you got to see if you got 60 as 60mins in hours was divided in ratio so when you add it will be 60 which means your answer is correct!
Answer: 12:60
Step-by-step explanation: To find the ratio, we must take 1 h and turn it into minutes. So as we know, it's 60 minutes. So next, we shall change the ratio into fraction form (don't worry it's the same basic format)
[tex]\frac{1}{5} = \frac{?}{60}[/tex]
So with that given information, we know that 60 would be our denominator. So, we need to divide both denominators, and then whatever we get from that, multiply that by the given numerator. So, we would do:
60 / 5
= 12
12 * 1
= 12
Therefore we now know that 1/5 = 12/60 as a ratio. I hope this helped :)
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