Based on the given conditions, formulate: 9÷(6+10+9)
Calculate the sum or difference: 9/16+9
Calculate the sum or difference:9/25
Multiply a number to both the numerator and the denominator:9 x 4/25 x 4
Calculate the product or quotient: 36/100
Rewrite a fraction with denominator equals 100 to a percentage is 36%
therefore the percentage of the students preferred netball is 36%.
In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100.One percent is one hundredth of a whole. It can therefore be written as both a decimal and a fraction. To write a percentage as a decimal, simply divide it by 100. For example, 50% becomes 0.5, 20% becomes 0.2, 1% becomes 0.01 and so on.Percentages are used widely and in many different areas. For example, discounts in shops, bank interest rates, rates of inflation and many statistics in the media are expressed as percentages. Percentages are important for understanding the financial aspects of everyday life.to know more about percentage ;
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F=9/5(k-273.15)+32 solve the formula for h
The value of k is 5/9(F-32) + 273.15.
What is equation?An equation is a mathematical expression that contains an equals symbol. Equations often contain algebra.
For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
There are different parts of an equation which include coefficients, variables, operators, constants, terms, expressions, and an equal to sign. When we write an equation, it is mandatory to have an "=" sign, and terms on both sides. Both sides should be equal to each other.
Given:
F=9/5(k-273.15)+32
On solving for k
F-32 = 9/5 (k-273.15)
(F-32)*5/9 = (k-273.15)
5/9(F-32) + 273.15 = k
k=5/9F - 290.927
Hence, the value of k is 5/9F - 290.927.
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What is the solution of the system? Use elimination. Check your answer in all three original equations.
x-y+z = -1
x+y+3z= -3
2x-y+2z = 0
By elimination, the solution of the system of equations, x - y + z = -1, x + y + 3z = -3 and 2x - y + 2z = 0, is (4 , 2 , -3).
Given:
x - y + z = -1 (equation 1)
x + y + 3z = -3 (equation 2)
2x - y + 2z = 0 (equation 3)
Using the elimination method, given the equations in x, y, and z, a variable should be eliminated by adding/subtracting the equations.
Subtracting equations 1 and 3 will eliminate the variable y.
2x - y + 2z = 0 (equation 3)
x - y + z = -1 (equation 1)
x + z = 1 (equation 4)
Adding equations 2 and 3 will eliminate the variable y.
x + y + 3z = -3 (equation 2)
2x - y + 2z = 0 (equation 3)
3x + 5z = -3 (equation 5)
Multiply equation 4 by -5 and add with equation 5.
x + z = 1 (equation 4)
⇒ -5x - 5z = -5
+ 3x + 5z = -3 (equation 5)
-2x = -8
x = 4
Substitute the value of x to either equation 4 or 5 and solve for z.
x + z = 1 (equation 4)
4 + z = 1
z = 1 - 4
z = -3
Finally, substitute the value of x and z to any of the first three equations, and solve for y.
x - y + z = -1 (equation 1)
4 - y + (-3) = -1
-y = -1 - 4 + 3
-y = -2
y = 2
Checking if the values x = 4, y = 2, and z = -3 satisfies all the three equation.
x - y + z = -1 (equation 1)
4 - 2 + (-3) = -1
-1 = -1
x + y + 3z = -3 (equation 2)
4 + 2 + 3(-3) = -3
-3 = -3
2x - y + 2z = 0 (equation 3)
2(4) - 2 + 2(-3) = 0
0 = 0
Hence, the solution of the system of equations is (4 , 2 , -3).
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show work, please!!!
Since angle ABC (m∠ABC) is bisected by line BD, the measure of m∠DBC is equal to 44°.
What is a line segment?A line segment can be defined as the part of a line in a geometric figure such as a triangle, quadrilateral, rhombus, parallelogram, circle, etc., that is bounded by two (2) distinct points and it typically has a fixed length.
What is a perpendicular bisector?A perpendicular bisector can be defined as a type of line that bisects (divides) a line segment exactly into two (2) halves and forms an angle of 90 degrees at the point of intersection.
Since angle ABC is bisected by line BD, we have:
m∠ABD = m∠DBC = m∠ABC/2
m∠ABC/2 = 8x/2 = 4x
Substituting the given parameters into the expression, we have;
m∠ABD = m∠DBC = 4x
2x + 22 = 4x
4x - 2x = 22
2x = 22
x = 22/2
x = 11
Now, we can find m∠DBC as follows:
m∠DBC = 4x
m∠DBC = 4 × 11
m∠DBC = 44°.
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A red string of holiday lights blinks every 3 seconds. a blue string of holiday lights blinks every 4 seconds. how many times will they blink in one minute?
If a red string of holiday lights blinks every 3 seconds. a blue string of holiday lights blinks every 4 seconds, then the number of times the red and blue string of holiday lights will blink in one minute is equal to 20 and 15 respectively.
The number of times each string of holiday lights will blink can be determined by using division.
As we have to calculate the number of times they blink in one minute, we can convert one minute into seconds.
One minute = 60 seconds
Now, the number of times each string of light blinks can be calculated by dividing the total seconds by the seconds after which the light blinks
For the red string of holiday lights :
The number of times the light will blink in one minute = 60 ÷ 3 = 20
For the blue string of holiday lights :
The number of times the light will blink in one minute = 60 ÷ 4 = 15
Hence the red string of holiday lights will blink 20 times and the blue string of holiday lights will blink 15 times in one minute.
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Find the value of each variable and the measure of each labeled angle.
Answer:
see explanation
Step-by-step explanation:
(8x - 75) and (5x) are vertically opposite angles and are congruent , then
8x - 75 = 5x ( subtract 5x from both sides )
3x - 75 = 0 ( add 75 to both sides )
3x = 75 ( divide both sides by 3 )
x = 25
Then
5x = 5(25) = 125°
8x - 75 = 8(25) - 75 = 200 - 75 = 125°
Answer: (5x)°=(8x-75)°=125°
Step-by-step explanation:
Property of vertical angles: vertical angles are equal
Hence,
[tex](8x-75)^0=(5x)^0\\(8x)^0-75^0=(5x)^0\\(8x)^0-75^0-(5x)^0=(5x)^0-(5x)^0\\(3x)^0-75^0=0\\(3x)^0-75^0+75^0=0+75^0\\(3x)^0=75^0\\[/tex]
Divide both parts of the equation by 3 :
[tex]x^0=25^0\\(5x)^0=(5*25)^0\\(5x)^0=125^0[/tex]
Find the surface of a cylinder with a height of 11 feet and a base radius of 3 feet! DO NOT ROUND YOUR ANSWER!
The surface area of the concerned cylinder is 263.76 sq. ft..
As per the question statement, we are provided with a reference picture of a cylinder, attached hereby, having a height of 11 feet and a base radius of 3 feet and also, the formula to calculate the surface area, along with the value of Pi to be considered for calculations and instructions about not rounding off our final answer.
We are required to calculate the surface area of the above mentioned cylinder.
The formula to calculate the surface area of the cylinder is provided in the reference picture itself which goes as [SA = (2πr² + 2πrh)], where, "r" is the base radius of the cylinder, and "h" is the height of the cylinder.
Here, (r = 3) and (h = 11), and using these values in the above mentioned formula to calculate the surface area of the cylinder, we get,
Surface Area of our concerned cylinder
[tex]= [(2*3.14*3^{2})+(2*3.14*3*11)]\\= [(2*3.14*9)+(66*3.14)]\\=(56.52+207.24)\\=263.76[/tex]
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In a coordinate plane, points A and B have coordinates (-2,4) and (3,3), respectively. What is the value of A B ?
A. √50
B. (1,7)
C. (5,-1)
D. 1,-1)
E. √26
The correct option is E. √26.
The distance between the points A and B is √26.
What is defined as distance formula?Algebraic representation that gives the distances between two points based on of those coordinates (see coordinate system). The distance formulas for points throughout rectangular coordinates in two- and three-dimensional Euclidean space are based on the Pythagorean theorem.
Now, as per the given question;
The coordinates of the points A and B are (-2,4) and (3,3).
The formula of distance formula is written as for the points A and B ia-
AB² = (x₂ - x₁)² + (y₂ - y₁)²
AB = √[(x₂ - x₁)² + (y₂ - y₁)²]
The coordinates of A and B are-
(x₁,y₁) = (-2,4) and (x₂,y₂) = (3,3).
Substituting the values in the formula;
AB = √[(3 + 2)² + (3 - 4)²]
AB = √[(5)² + (-1)²]
AB = √[25 + 1]
AB = √26
Therefore, the distance between the coordinates A and B is found to be √26.
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Carol used the expression below to calculate the amount of money she would earn in one year at her part time job
12(
100+20)
The amount that she would earn in one year at her part time job is 1440
How to determine the amountNote that a function is an expression, rule or law that shows the relationship between a dependent and an independent variable.
Given the expression as;
12(100+20)
To determine the amount, we need to use the BODMAS rule by solving the bracket, we have
Amount = 12(100+20)
Amount = 12(120)
Expand the bracket
Amount = 1440
Thus, the amount that she would earn in one year at her part time job is 1440
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what is -188.7 in scientific notation with the correct number of significant digits
Answer:
See below
Step-by-step explanation:
-1.887 x10^2 would be one answer
- 18.87 x 10^1 could be another
Answer:
Step-by-step explanation: Wowee! That's pretty hard.
Scientific Notation:
-1.887 × 102
E-Notation:
-1.887e2
Engineering Notation:
-188.7 × 100
Real Number:
-188.7
Hope this helps!
Jenni wrote a conditional statement and its converse.
Conditional: If each angle of a triangle measures 60°, then the sum of the measures of all the angles is 180°.
Converse: If the sum of all the angles inside of a triangle is 180°, then each angle measures 60°.
Did Jenni write the converse statement properly? Give a counterexample to dispute the validity of the converse statement.
O No; an isosceles triangle
O No; a scalene triangle
OYes; an equilateral triangle
O Yes; a scalene triangle
Yes; The jenni write the converse statement properly. it is an equilateral triangle.
What is a statement?A statement is a declarative sentence that is either true or false but not both. It is sometimes called a proposition. The key is that there must be no ambiguity. To be a statement, a sentence must be true or false, and it cannot be both.
We have been Given that each angle of a triangle measures 60°, then the sum of the measures of all the angles is 180°.
And the converse is that the sum of all the angles inside of a triangle is 180°, then each angle measures 60°.
However, we know that the sum of all angles of an equilateral triangle is 180. each having 60 degrees.
The jenni write the converse statement properly.
Therefore, the correct statement is Yes; an equilateral triangle.
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Answer:
d. Yes; a scalene triangle
Step-by-step explanation:
Simplify each expression.
(-3)(-9)
An expression can be used in algebra to represent a value, and that value may rely on the values given to the variables that appear in the expression.
If the expression be (-3)(-9) then the value of (-3)(-9) is 27.
What is an expression?A mathematical expression is a finite combination of symbols that is well-formed in accordance with context-specific norms.In order to help establish the order of operations and other elements of logical syntax, mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping.An expression can be used in algebra to represent a value, and that value may rely on the values given to the variables that appear in the expression.Let (-3)(-9) be the given expression
We know the rule , (-) × (-) = (+)
(-3) × (-9) = +27
Therefore, the value of (-3)(-9) is 27.
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Which is a terminating decimal?
Answer:
0.125
Step-by-step explanation:
It has not been bar notated unlike all of the other ones. Bar notation is used for repeating decimals. So therefore if it has not been bar notated it is not a repeating decimal, it is a terminating decimal. Meaning it ends at the last digit and does not go any further.
Hope this helps!
Newton's second law in physics states that F=ma, where F is the force of an object (measured in Newtons), m is the mass of the object (in kilograms) and a is the acceleration of that object (measured in m/s^2).
Calculate the force created from an object with a mass of 310 grams and an acceleration of 5 m/s^2.
F=______ newtons
Answer:
1.55N
Step-by-step explanation:
F=ma
m=310g=0.31kg
a=5m/s^-2.
F=0.31×5
F=1.55N
Carter wants to ride his bicycle 28.7 miles this week. He has already ridden 17 miles.
If he rides for 3 more days, write and solve an equation which can be used to
determine m, the average number of miles he would have to ride each day to meet his
goal. What is the equation?
The equation that we need to solve and the solution is:
A = 11.7mi/3 = 3.9 mi
We conclude that he needs to ride an average of 3.9 miles per day.
What is the equation?
Here we know that Carter wants to ride his bicycle 28.7 miles this week, and he has already ridden 17 miles, so the distance left is:
D = 28.7 mi - 17mi = 11.7mi
Now, if he has 3 days to complete that distance, then the average distance that he needs to travel each day is given by the quotient:
A = 11.7mi/3 = 3.9 mi
So that is the equation that we need to solve and the solution, we conclude that he needs to ride an average of 3.9 miles per day.
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Segment AB intersects the circle with center C . What statement correctly describes the relationship shown in the image?
Answer: Since the radius of the circle is perpendicular to AB, AB is tangent to the circle.
Step-by-step explanation:
Answer:
perpendicular and tangent
Step-by-step explanation:
Given the function g of x is equal to the quantity 3 x squared plus 5 x plus 6 end quantity over the quantity x plus 3 end quantity determine the equation for the slant asymptote.
The equation for the slant asymptote of g(x) = [tex]\frac{3x^2+5x+6}{x+3}[/tex] is 3x-4
The function, g(x) = [tex]\frac{3x^2+5x+6}{x+3}[/tex]
We need to find its slant asymptote. The slant asymptote is determined by checking [tex]\lim_{x \to \infty}( g(x)-(ax+b)) = 0[/tex] .
So we first divide the polynomial [tex]3x^2+5x+6[/tex] by x+3 to find such an (ax+b).
3x - 4
x+3 | [tex]3x^2+5x+6[/tex]
- [tex]3x^2+9x[/tex]
---------------------------
-4x + 6
-4x - 12 -
--------------------------
18
Therefore, [tex]\frac{3x^2+5x+6}{x+3}[/tex] = 3x - 4 + [tex]\frac{18}{x+3}[/tex]
⇒ [tex]\frac{3x^2+5x+6}{x+3}[/tex] - 3x - 4 = [tex]\frac{18}{x+3}[/tex]
⇒ [tex]\lim_{x \to \infty}(\frac{3x^2+5x+6}{x+3}-(3x-4)) = 0[/tex] , since [tex]\frac{18}{x+3}[/tex] [tex]\rightarrow \infty[/tex] as [tex]x \rightarrow \infty[/tex].
So the equation for the slant asymptote of g(x) = [tex]\frac{3x^2+5x+6}{x+3}[/tex] is 3x-4
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Yossi used to have a square garage with 216ft of floor space. recently built an addition to it. The garage is still a square, but now it has 50% more floor space. What was the length of one side of the garage originally? What is the length of one side of the garage now? What was the percent increase in the length of one side?
One side of the garage length is 16.69ft
the length of one side of the garage now has 18 ft
increase in the one side's length is 70 %
According to the given data,
Floor of square garage given in the question is 216 ft
then, we get length of one side of the garage is √216
= 16.69 ft
after built an addition to it garage has 50% more floor space
216 × (1 + 0.5) = 324
√324 = 18 ft
The garage's one side is 18 feet long.
The length of one side = [tex]\frac{18}{16.69}[/tex]
= 1.07
The percentage increase in one side's length is 1.07-1 = 0.07 = 70 percent.
Area of square : The area is the space covered by square object. It is the approximately occupied by any shape. While estimating the area of a square, we consider only the length of the square because all the sides of a square are equal.
Similarly, we get the area of the other shapes such as rectangle, triangle or any polygon shape, based on its sides. Area of the surface is compute based on the radius or the distance of its outer line from the axis for curved surface objects.
Area of a Square Formula
area of square formula used for calculating the area occupied, let us we find area. You are required to calculate the area of a side 5 cm. Using this dimension, a square having 1 cm × 1 cm squares. The square covers 36 complete squares.
Thus, the area of the square is 36 square cm, which can be written as 6cm × 6 cm, that is, side × side.
We know the area of a square is:
Area of a Square = Side × Side
and the perimeter of any square = 4 × side units
Here given, Some conversions of units:
1 m = 100 cm
1 sq. m = 10,000 sq. cm
1 km = 1000 m
1 sq. km = 1,000,000 sq. m
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PLS HELP ASAP!
Masha bought red, green, and yellow balloons for a party. She bought 40 red balloons. The number of green balloons Masha bought is 3/5 of the number of red balloons. The number of green balloons is also 2/3 of the number of yellow balloons. while being inflated, 1/20 of the red balloons, 1/12 of the green balloons, and 1/36 of the yellows balloons popped. The remaining balloons were used as decoration. What part of all the balloons Masha purchased to decorate the party?
There was a question like this before. And the Answer to that question was: 95% or 95/100
solve x/5+2=2
i dont understand the question
Answer:
x = 0
Step-by-step explanation:
You are solving for x
[tex]\frac{x}{5}[/tex] + 2 = 2 Subtract 2 from both sides of the equation
[tex]\frac{x}{5}[/tex] = 0 Multiply both sides by
[tex]\frac{x}{5}[/tex] [tex](\frac{5}{1})[/tex] = 0 [tex]\frac{5}{1}[/tex]
x = 0
SOMEBODY, PLEASE HELP ASAP PLEASE PLEASE PLEASE
Jack earns 2 cents per second. Jack works 40 hours a week. Determine how many dollars per year jack earns.
Answer:
1 hour has 3600 seconds
to get how many dollars Jack earns we have to do this
3600 sec x $0.02 = $72
40 weeks x $72 = $2880
Answer:
$149,760
Step-by-step explanation:
As:
1 minute = 60 seconds1 hour = 60 minutes⇒ 1 hour = 60 × 60 seconds = 3600 seconds
As:
1 year = 52 weeksJack works 40 hours per week.⇒ 52 × 40 = 2080 hours per year
Therefore, the number of seconds Jack works per year is:
⇒ 2080 × 3600 = 7,488,000 seconds
If Jack earns $0.02 per second, then the number of dollars per year he earns is:
⇒ $0.02 × 7,488,000 = $149,760
Refer to ®F .
Identify a chord that is not a diameter.
A chord is any circle segment that connects two points. A circle chord is always used as the diameter. The chords AE and DE do not intersect in the center. As a result, they are not diameters.
What is the difference between the diameter and chord of a circle?In geometry, a circle's diameter is any straight line segment that passes through the center of the circle and has endpoints on the circle. It is also referred to as the circle's longest chord. Both definitions apply to a sphere's diameter.
The chord of a circle is defined as the line segment connecting any two points on its circumference. It should be noted that the diameter of a circle is the longest chord passing through its center.
A circle chord is a straight line with both ends on a circular arc. A secant line, or simply secant, is the infinite line extension of a chord. A chord is a segment of a line that connects two points on a curve, such as an ellipse.
A chord is any circle segment that connects two points. A circle chord is always used as the diameter. The chords AE and DE do not intersect in the center. As a result, they are not diameters.
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find the equation of the line shown
[tex]format \: \: y = mx + c[/tex]
[tex]m = \frac{5 - 0}{10 - 0} = \frac{5}{10} = \frac{1}{2} [/tex]
[tex]c = 0 \: since \: the \: line \: passes \: through \: the \: origin \\ [/tex]
[tex](d) \: \: \: y = \frac{x}{2} [/tex]
R = x²/y.
x = 3.8 × 105
y = 5.9 × 104
Work out the value of R.
Give your answer in standard form to an appropriate degree of accuracy.
The value of the expression R = x^2/y when y = 3.8 x 10^5 and x = 5.9 x 10^4 is 9.2 x 10^3
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to evaluate the expression?The expression is given as
R = x^2/y
Where
y = 3.8 x 10^5
x = 5.9 x 10^4
Substitute y = 3.8 x 10^5 and x = 5.9 x 10^4 in the equation R = x^2/y
So, we have
R = (5.9 x 10^4)^2/3.8 x 10^5
Evaluate the exponent in the above equation
So, we have
R = 34.81 x 10^8/3.8 x 10^5
Evaluate the quotient in the above equation
So, we have
R = 9.16052631579 x 10^3
Approximate the above expression
So, we have
R = 9.2 x 10^3
Hence, the value of the expression R = x^2/y when y = 3.8 x 10^5 and x = 5.9 x 10^4 is 9.2 x 10^3
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Which of the following represents the series?
-13 + (-7) + (-1) + 5 + 11
Answer:
Adding +6 in turn
Step-by-step explanation:
-13 + 6 = (-7)
(-7) + 6 = (-1)
(-1) + 6 = 5
5 + 6 = 11
11 + 6 = 17
17 + 6 = 23
23 + 6 = 29
29 + 6 = 35
...........And so on
Brianliest if answer I really need help
Step-by-step explanation:
out of the 3 values, there is for every line one missing. so, we need to use the formula that calculates the missing value out of the other 2.
and based on the density value (in most cases already given in the table) we mark float or sink (as your paper says, if it is smaller than 1g/cm³, it will float, if it is larger, it will sink).
1.
density is missing
D = M/V = 12/0.5 = 12/0.5 × 2/2 = 24/1 = 24 g/cm³
sinks
2.
volume is missing.
V = M/D = 16/0.2 = 80 cm³
floats
3.
mass is missing.
M = D×V = 5×20 = 100 g
sinks
4.
volume is missing.
V = M/D = 0.9/0.3 = 3 cm³
floats
5.
density is missing
D = M/V = 6/4 = 3/2 × 0.5/0.5 = 1.5/1 = 1.5 g/cm³
sinks
6.
density is missing
D = M/V = 8/1.8 = 4.444444444... g/cm³
sinks
7.
mass is missing.
M = D×V = 9×13 = 117 g
sinks
8.
density is missing
D = M/V = 14.7/15 = 0.98 g/cm³
floats
9.
mass is missing.
M = D×V = 2×1.1 = 2.2 g
sinks
10.
volume is missing.
V = M/D = 17/3 = 5.66666666... cm³
sinks
find the reciprocal of 2/7
Probability and statistics question any help is appreciated!
Answer:
75.92
Step-by-step explanation:
add 186+59=245
186 is in state so 186/245=75.92
here you gooooooo :))) hope you get it right
Find the distance between each pair of parallel lines with the given equations.)
y=-0.75 x-1
3 x+4 y=20
The distance between the given parallel lines is 4 units
In the given statement is :
The equations of the pair of each parallel lines is:
y=-0.75 x-1
3 x+4 y=20
To find the distance between each pair of parallel lines.
Two lines a₁x +b₁y + c₁=0 and a₂x+b₂y+c₂=0 are said to be parallel if a₁=a₂ , b₁=b₂.
As we know that distance between the parallel lines (d) is given as:-
d = [tex]\frac{c_{2}-c_{1} }{\sqrt{a^{2} +b^{2} } }[/tex]
Parallel lines equation as:
y=-0.75 x-1...(1)
3 x+4 y=20....(2)
Divide by -3 in equation (2)
Now, The equations is
-0.75x -y -1 =0
-0.75x -y +4 =0
Here,
a = -0.75 , b = -1, c1 = -1 , c2 = 4
Therefore, putting the values
[tex]d =\frac{4-(-1)}{\sqrt{(-0.75^{2} )+(-1)^{2} } } \\\\d=\frac{5}{\sqrt{0.5625+1} }\\ \\d = \frac{5}{\sqrt{1.5625} }[/tex]
d = 4 units
Hence, The distance between the given parallel lines is 4 units
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If 4 cosx²+4 sin x = 5, show that sinx = 1/2
Answer:
See proof below
Step-by-step explanation:
[tex]4cos^2(x) +4sin(x) = 5\\\\\sf Divide\; both \; sides\; by\; 4\\== > cos^2(x) + sin(x) = \dfrac{5}{4} .................(1)\\\\cos^2(x) + sin^2(x) = 1\\\\cos^2(x) = 1- sin^2(x) \\\\\textsf {Substituting into equation (1) }\\1-sin^2(x) + sin(x) = \dfrac{5}{4}\\\\\\sf Subtract\; 1\; from\; both \; sides\\\mathsf{-\sin^2(x) + \sin(x) = \dfrac{5}{4} - 1}\\\\ \dfrac{5}{4} - 1 = \dfrac{5}{4} - \dfrac{4}{4} = \dfrac{1}{4}\\[/tex]
[tex]\sf {-\sin^2(x) + \sin(x) = \dfrac{1}{4}\\[/tex]
[tex]\sf Subtract\; \dfrac{1}{4}\;from\;both\;sides\\[/tex]
[tex]{-\sin^2(x) + \sin(x) - \dfrac{1}{4} = 0\\\\[/tex]
Multiply throughout by -1
[tex]\sf \sin^2(x) - \sin(x) + \dfrac{1}{4} = 0\\\\[/tex]
Let u = sin(x). Substituting we get
[tex]\sf u^2 - u + \dfrac{1}{4} = 0[/tex]
This is a quadratic equation which can be solved using sum of squars
Note that
[tex]\sf (u - \dfrac{1}{2})^2 = u^2 -2\cdot \dfrac{1}{4}u + (\dfrac{1}{2})^2 \\= \sf u^2 - u + \dfrac{1}{4} = 0[/tex]
So
[tex]\sf (u - \dfrac{1}{2})^2 = 0\\Solution\; is \;u = \dfrac{1}{2}\\\\Substituting\sin(x) \;for\;u \;gives\\sin(x) = \dfrac{1}{2}[/tex]
PROVED
Find the first five terms of each sequence. an =n² -2 n
The first, second, third, fourth, and fifth term of the sequence are -1, 0, 3, 8, and 15.
According to the given question.
We have a formula or rule for finding the terms of a sequence i.e.
an =n² -2 n.
Therefore,
The first term of the sequence an =n² -2 n is given by
a(1) = 1^2 - 2(1) = 1 - 2 = -1
The second term of the sequence an =n² -2 is given by
a(2) = 2^2 - 2(2) = 4 - 4 = 0
The third term of the sequence an =n² -2 is given by
a(3) = 3^3 - 2(3) = 9 - 6 = 3
The fourth term of the sequence an =n² -2 is given by
a(4) = 4^2 - 2(4) = 16 - 8 = 8
The fifth term of the sequence an =n² -2 is given by
a(5) = 5^2 - 2(5) = 25 - 10 = 15
Hence, the first, second, third, fourth, and fifth term of the sequence are -1, 0, 3, 8, and 15.
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